method of data analysis in descriptive research

• What is PESTLE Analysis?
• Entrepreneurs
• Permissions
• Privacy Policy

Descriptive Analysis: How-To, Types, Examples

We review the basics of descriptive analysis, including what exactly it is, what benefits it has, how to do it, as well as some types and examples.

From diagnostic to predictive, there are many different types of data analysis . Perhaps the most straightforward of them is descriptive analysis, which seeks to describe or summarize past and present data, helping to create accessible data insights. In this short guide, we'll review the basics of descriptive analysis, including what exactly it is, what benefits it has, how to do it, as well as some types and examples.

What Is Descriptive Analysis?

Descriptive analysis, also known as descriptive analytics or descriptive statistics, is the process of using statistical techniques to describe or summarize a set of data. As one of the major types of data analysis, descriptive analysis is popular for its ability to generate accessible insights from otherwise uninterpreted data.

Unlike other types of data analysis, the descriptive analysis does not attempt to make predictions about the future. Instead, it draws insights solely from past data, by manipulating in ways that make it more meaningful.

Benefits of Descriptive Analysis

Descriptive analysis is all about trying to describe or summarize data. Although it doesn't make predictions about the future, it can still be extremely valuable in business environments . This is chiefly because descriptive analysis makes it easier to consume data, which can make it easier for analysts to act on.

Another benefit of descriptive analysis is that it can help to filter out less meaningful data. This is because the statistical techniques used within this type of analysis usually focus on the patterns in data, and not the outliers.

Types of Descriptive Analysis

According to CampusLabs.com , descriptive analysis can be categorized as one of four types. They are measures of frequency, central tendency, dispersion or variation, and position.

Measures of Frequency

In descriptive analysis, it's essential to know how frequently a certain event or response occurs. This is the purpose of measures of frequency, like a count or percent. For example, consider a survey where 1,000 participants are asked about their favourite ice cream flavor. A list of 1,000 responses would be difficult to consume, but the data can be made much more accessible by measuring how many times a certain flavor was selected.

Measures of Central Tendency

In descriptive analysis, it's also worth knowing the central (or average) event or response. Common measures of central tendency include the three averages — mean, median, and mode. As an example, consider a survey in which the height of 1,000 people is measured. In this case, the mean average would be a very helpful descriptive metric.

Measures of Dispersion

Sometimes, it may be worth knowing how data is distributed across a range. To illustrate this, consider the average height in a sample of two people. If both individuals are six feet tall, the average height is six feet. However, if one individual is five feet tall and the other is seven feet tall, the average height is still six feet. In order to measure this kind of distribution, measures of dispersion like range or standard deviation can be employed.

Measures of Position

Last of all, descriptive analysis can involve identifying the position of one event or response in relation to others. This is where measures like percentiles and quartiles can be used.

How to Do Descriptive Analysis

Like many types of data analysis, descriptive analysis can be quite open-ended. In other words, it's up to you what you want to look for in your analysis. With that said, the process of descriptive analysis usually consists of the same few steps.

• Collect data

The first step in any type of data analysis is to collect the data. This can be done in a variety of ways, but surveys and good old fashioned measurements are often used.

Another important step in descriptive and other types of data analysis is to clean the data. This is because data may be formatted in inaccessible ways, which will make it difficult to manipulate with statistics. Cleaning data may involve changing its textual format, categorizing it, and/or removing outliers.

• Apply methods

Finally, descriptive analysis involves applying the chosen statistical methods so as to draw the desired conclusions. What methods you choose will depend on the data you are dealing with and what you are looking to determine. If in doubt, review the four types of descriptive analysis methods explained above.

When to Do Descriptive Analysis

Descriptive analysis is often used when reviewing any past or present data. This is because raw data is difficult to consume and interpret, while the metrics offered by descriptive analysis are much more focused.

Descriptive analysis can also be conducted as the precursor to diagnostic or predictive analysis , providing insights into what has happened in the past before attempting to explain why it happened or predicting what will happen in the future.

Descriptive Analysis Example

As an example of descriptive analysis, consider an insurance company analyzing its customer base.

The insurance company may know certain traits about its customers, such as their gender, age, and nationality. To gain a better profile of their customers, the insurance company can apply descriptive analysis.

Measures of frequency can be used to identify how many customers are under a certain age; measures of central tendency can be used to identify who most of their customers are; measures of dispersion can be used to identify the variation in, for example, the age of their customers; finally, measures of position can be used to compare segments of customers based on specific traits.

Final Thoughts

Descriptive analysis is a popular type of data analysis. It's often conducted before diagnostic or predictive analysis, as it simply aims to describe and summarize past data.

To do so, descriptive analysis uses a variety of statistical techniques, including measures of frequency, central tendency, dispersion, and position. How exactly you conduct descriptive analysis will depend on what you are looking to find out, but the steps usually involve collecting, cleaning, and finally analyzing data.

In any case, this business analysis process is invaluable when working with data.

SWOT Analysis of Artificial Intelligence

Learn to Convert LinkedIn Cold Messages Using These 14 Proven Prospecting Messages

How cashless payments are transforming retail operations

Educational resources and simple solutions for your research journey

What is Descriptive Research? Definition, Methods, Types and Examples

Descriptive research is a methodological approach that seeks to depict the characteristics of a phenomenon or subject under investigation. In scientific inquiry, it serves as a foundational tool for researchers aiming to observe, record, and analyze the intricate details of a particular topic. This method provides a rich and detailed account that aids in understanding, categorizing, and interpreting the subject matter.

Descriptive research design is widely employed across diverse fields, and its primary objective is to systematically observe and document all variables and conditions influencing the phenomenon.

After this descriptive research definition, let’s look at this example. Consider a researcher working on climate change adaptation, who wants to understand water management trends in an arid village in a specific study area. She must conduct a demographic survey of the region, gather population data, and then conduct descriptive research on this demographic segment. The study will then uncover details on “what are the water management practices and trends in village X.” Note, however, that it will not cover any investigative information about “why” the patterns exist.

Table of Contents

What is descriptive research?

If you’ve been wondering “What is descriptive research,” we’ve got you covered in this post! In a nutshell, descriptive research is an exploratory research method that helps a researcher describe a population, circumstance, or phenomenon. It can help answer what , where , when and how questions, but not why questions. In other words, it does not involve changing the study variables and does not seek to establish cause-and-effect relationships.

Importance of descriptive research

Now, let’s delve into the importance of descriptive research. This research method acts as the cornerstone for various academic and applied disciplines. Its primary significance lies in its ability to provide a comprehensive overview of a phenomenon, enabling researchers to gain a nuanced understanding of the variables at play. This method aids in forming hypotheses, generating insights, and laying the groundwork for further in-depth investigations. The following points further illustrate its importance:

Provides insights into a population or phenomenon: Descriptive research furnishes a comprehensive overview of the characteristics and behaviors of a specific population or phenomenon, thereby guiding and shaping the research project.

Offers baseline data: The data acquired through this type of research acts as a reference for subsequent investigations, laying the groundwork for further studies.

Allows validation of sampling methods: Descriptive research validates sampling methods, aiding in the selection of the most effective approach for the study.

Helps reduce time and costs: It is cost-effective and time-efficient, making this an economical means of gathering information about a specific population or phenomenon.

Ensures replicability: Descriptive research is easily replicable, ensuring a reliable way to collect and compare information from various sources.

When to use descriptive research design?

Determining when to use descriptive research depends on the nature of the research question. Before diving into the reasons behind an occurrence, understanding the how, when, and where aspects is essential. Descriptive research design is a suitable option when the research objective is to discern characteristics, frequencies, trends, and categories without manipulating variables. It is therefore often employed in the initial stages of a study before progressing to more complex research designs. To put it in another way, descriptive research precedes the hypotheses of explanatory research. It is particularly valuable when there is limited existing knowledge about the subject.

Some examples are as follows, highlighting that these questions would arise before a clear outline of the research plan is established:

• In the last two decades, what changes have occurred in patterns of urban gardening in Mumbai?
• What are the differences in climate change perceptions of farmers in coastal versus inland villages in the Philippines?

Characteristics of descriptive research

Coming to the characteristics of descriptive research, this approach is characterized by its focus on observing and documenting the features of a subject. Specific characteristics are as below.

• Quantitative nature: Some descriptive research types involve quantitative research methods to gather quantifiable information for statistical analysis of the population sample.
• Qualitative nature: Some descriptive research examples include those using the qualitative research method to describe or explain the research problem.
• Observational nature: This approach is non-invasive and observational because the study variables remain untouched. Researchers merely observe and report, without introducing interventions that could impact the subject(s).
• Cross-sectional nature: In descriptive research, different sections belonging to the same group are studied, providing a “snapshot” of sorts.
• Springboard for further research: The data collected are further studied and analyzed using different research techniques. This approach helps guide the suitable research methods to be employed.

Types of descriptive research

There are various descriptive research types, each suited to different research objectives. Take a look at the different types below.

• Surveys: This involves collecting data through questionnaires or interviews to gather qualitative and quantitative data.
• Observational studies: This involves observing and collecting data on a particular population or phenomenon without influencing the study variables or manipulating the conditions. These may be further divided into cohort studies, case studies, and cross-sectional studies:
• Cohort studies: Also known as longitudinal studies, these studies involve the collection of data over an extended period, allowing researchers to track changes and trends.
• Case studies: These deal with a single individual, group, or event, which might be rare or unusual.
• Cross-sectional studies : A researcher collects data at a single point in time, in order to obtain a snapshot of a specific moment.
• Focus groups: In this approach, a small group of people are brought together to discuss a topic. The researcher moderates and records the group discussion. This can also be considered a “participatory” observational method.
• Descriptive classification: Relevant to the biological sciences, this type of approach may be used to classify living organisms.

Descriptive research methods

Several descriptive research methods can be employed, and these are more or less similar to the types of approaches mentioned above.

• Surveys: This method involves the collection of data through questionnaires or interviews. Surveys may be done online or offline, and the target subjects might be hyper-local, regional, or global.
• Observational studies: These entail the direct observation of subjects in their natural environment. These include case studies, dealing with a single case or individual, as well as cross-sectional and longitudinal studies, for a glimpse into a population or changes in trends over time, respectively. Participatory observational studies such as focus group discussions may also fall under this method.

Researchers must carefully consider descriptive research methods, types, and examples to harness their full potential in contributing to scientific knowledge.

Examples of descriptive research

Now, let’s consider some descriptive research examples.

• In social sciences, an example could be a study analyzing the demographics of a specific community to understand its socio-economic characteristics.
• In business, a market research survey aiming to describe consumer preferences would be a descriptive study.
• In ecology, a researcher might undertake a survey of all the types of monocots naturally occurring in a region and classify them up to species level.

These examples showcase the versatility of descriptive research across diverse fields.

Advantages of descriptive research

There are several advantages to this approach, which every researcher must be aware of. These are as follows:

• Owing to the numerous descriptive research methods and types, primary data can be obtained in diverse ways and be used for developing a research hypothesis .
• It is a versatile research method and allows flexibility.
• Detailed and comprehensive information can be obtained because the data collected can be qualitative or quantitative.
• It is carried out in the natural environment, which greatly minimizes certain types of bias and ethical concerns.
• It is an inexpensive and efficient approach, even with large sample sizes

Disadvantages of descriptive research

On the other hand, this design has some drawbacks as well:

• It is limited in its scope as it does not determine cause-and-effect relationships.
• The approach does not generate new information and simply depends on existing data.
• Study variables are not manipulated or controlled, and this limits the conclusions to be drawn.
• Descriptive research findings may not be generalizable to other populations.
• Finally, it offers a preliminary understanding rather than an in-depth understanding.

To reiterate, the advantages of descriptive research lie in its ability to provide a comprehensive overview, aid hypothesis generation, and serve as a preliminary step in the research process. However, its limitations include a potential lack of depth, inability to establish cause-and-effect relationships, and susceptibility to bias.

Frequently asked questions

When should researchers conduct descriptive research.

Descriptive research is most appropriate when researchers aim to portray and understand the characteristics of a phenomenon without manipulating variables. It is particularly valuable in the early stages of a study.

What is the difference between descriptive and exploratory research?

Descriptive research focuses on providing a detailed depiction of a phenomenon, while exploratory research aims to explore and generate insights into an issue where little is known.

What is the difference between descriptive and experimental research?

Descriptive research observes and documents without manipulating variables, whereas experimental research involves intentional interventions to establish cause-and-effect relationships.

Is descriptive research only for social sciences?

No, various descriptive research types may be applicable to all fields of study, including social science, humanities, physical science, and biological science.

How important is descriptive research?

The importance of descriptive research lies in its ability to provide a glimpse of the current state of a phenomenon, offering valuable insights and establishing a basic understanding. Further, the advantages of descriptive research include its capacity to offer a straightforward depiction of a situation or phenomenon, facilitate the identification of patterns or trends, and serve as a useful starting point for more in-depth investigations. Additionally, descriptive research can contribute to the development of hypotheses and guide the formulation of research questions for subsequent studies.

Editage All Access is a subscription-based platform that unifies the best AI tools and services designed to speed up, simplify, and streamline every step of a researcher’s journey. The Editage All Access Pack is a one-of-a-kind subscription that unlocks full access to an AI writing assistant, literature recommender, journal finder, scientific illustration tool, and exclusive discounts on professional publication services from Editage.  

Based on 22+ years of experience in academia, Editage All Access empowers researchers to put their best research forward and move closer to success. Explore our top AI Tools pack, AI Tools + Publication Services pack, or Build Your Own Plan. Find everything a researcher needs to succeed, all in one place –  Get All Access now starting at just $14 a month !    

Related Posts

What are the Best Research Funding Sources

Inductive vs. Deductive Research Approach

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Descriptive Statistics | Definitions, Types, Examples

Published on July 9, 2020 by Pritha Bhandari . Revised on June 21, 2023.

Descriptive statistics summarize and organize characteristics of a data set. A data set is a collection of responses or observations from a sample or entire population.

In quantitative research , after collecting data, the first step of statistical analysis is to describe characteristics of the responses, such as the average of one variable (e.g., age), or the relation between two variables (e.g., age and creativity).

The next step is inferential statistics , which help you decide whether your data confirms or refutes your hypothesis and whether it is generalizable to a larger population.

Table of contents

Types of descriptive statistics, frequency distribution, measures of central tendency, measures of variability, univariate descriptive statistics, bivariate descriptive statistics, other interesting articles, frequently asked questions about descriptive statistics.

There are 3 main types of descriptive statistics:

• The distribution concerns the frequency of each value.
• The central tendency concerns the averages of the values.
• The variability or dispersion concerns how spread out the values are.

You can apply these to assess only one variable at a time, in univariate analysis, or to compare two or more, in bivariate and multivariate analysis.

• Go to a library
• Watch a movie at a theater
• Visit a national park

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
• Vague sentences
• Style consistency

See an example

A data set is made up of a distribution of values, or scores. In tables or graphs, you can summarize the frequency of every possible value of a variable in numbers or percentages. This is called a frequency distribution .

• Simple frequency distribution table
• Grouped frequency distribution table

From this table, you can see that more women than men or people with another gender identity took part in the study. In a grouped frequency distribution, you can group numerical response values and add up the number of responses for each group. You can also convert each of these numbers to percentages.

Measures of central tendency estimate the center, or average, of a data set. The mean, median and mode are 3 ways of finding the average.

Here we will demonstrate how to calculate the mean, median, and mode using the first 6 responses of our survey.

The mean , or M , is the most commonly used method for finding the average.

To find the mean, simply add up all response values and divide the sum by the total number of responses. The total number of responses or observations is called N .

The median is the value that’s exactly in the middle of a data set.

To find the median, order each response value from the smallest to the biggest. Then , the median is the number in the middle. If there are two numbers in the middle, find their mean.

The mode is the simply the most popular or most frequent response value. A data set can have no mode, one mode, or more than one mode.

To find the mode, order your data set from lowest to highest and find the response that occurs most frequently.

Measures of variability give you a sense of how spread out the response values are. The range, standard deviation and variance each reflect different aspects of spread.

The range gives you an idea of how far apart the most extreme response scores are. To find the range , simply subtract the lowest value from the highest value.

Standard deviation

The standard deviation ( s or SD ) is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.

There are six steps for finding the standard deviation:

• List each score and find their mean.
• Subtract the mean from each score to get the deviation from the mean.
• Square each of these deviations.
• Add up all of the squared deviations.
• Divide the sum of the squared deviations by N – 1.
• Find the square root of the number you found.

Step 5: 421.5/5 = 84.3

Step 6: √84.3 = 9.18

The variance is the average of squared deviations from the mean. Variance reflects the degree of spread in the data set. The more spread the data, the larger the variance is in relation to the mean.

To find the variance, simply square the standard deviation. The symbol for variance is s 2 .

Prevent plagiarism. Run a free check.

Univariate descriptive statistics focus on only one variable at a time. It’s important to examine data from each variable separately using multiple measures of distribution, central tendency and spread. Programs like SPSS and Excel can be used to easily calculate these.

If you were to only consider the mean as a measure of central tendency, your impression of the “middle” of the data set can be skewed by outliers, unlike the median or mode.

Likewise, while the range is sensitive to outliers , you should also consider the standard deviation and variance to get easily comparable measures of spread.

If you’ve collected data on more than one variable, you can use bivariate or multivariate descriptive statistics to explore whether there are relationships between them.

In bivariate analysis, you simultaneously study the frequency and variability of two variables to see if they vary together. You can also compare the central tendency of the two variables before performing further statistical tests .

Multivariate analysis is the same as bivariate analysis but with more than two variables.

Contingency table

In a contingency table, each cell represents the intersection of two variables. Usually, an independent variable (e.g., gender) appears along the vertical axis and a dependent one appears along the horizontal axis (e.g., activities). You read “across” the table to see how the independent and dependent variables relate to each other.

Interpreting a contingency table is easier when the raw data is converted to percentages. Percentages make each row comparable to the other by making it seem as if each group had only 100 observations or participants. When creating a percentage-based contingency table, you add the N for each independent variable on the end.

From this table, it is more clear that similar proportions of children and adults go to the library over 17 times a year. Additionally, children most commonly went to the library between 5 and 8 times, while for adults, this number was between 13 and 16.

Scatter plots

A scatter plot is a chart that shows you the relationship between two or three variables . It’s a visual representation of the strength of a relationship.

In a scatter plot, you plot one variable along the x-axis and another one along the y-axis. Each data point is represented by a point in the chart.

From your scatter plot, you see that as the number of movies seen at movie theaters increases, the number of visits to the library decreases. Based on your visual assessment of a possible linear relationship, you perform further tests of correlation and regression.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Statistical power
• Pearson correlation
• Degrees of freedom
• Statistical significance

Methodology

• Cluster sampling
• Stratified sampling
• Focus group
• Systematic review
• Ethnography
• Double-Barreled Question

Research bias

• Implicit bias
• Publication bias
• Cognitive bias
• Placebo effect
• Pygmalion effect
• Hindsight bias
• Overconfidence bias

Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.

The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.

• Distribution refers to the frequencies of different responses.
• Measures of central tendency give you the average for each response.
• Measures of variability show you the spread or dispersion of your dataset.
• Univariate statistics summarize only one variable  at a time.
• Bivariate statistics compare two variables .
• Multivariate statistics compare more than two variables .

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Bhandari, P. (2023, June 21). Descriptive Statistics | Definitions, Types, Examples. Scribbr. Retrieved August 21, 2024, from https://www.scribbr.com/statistics/descriptive-statistics/

Is this article helpful?

Pritha Bhandari

Other students also liked, central tendency | understanding the mean, median & mode, variability | calculating range, iqr, variance, standard deviation, inferential statistics | an easy introduction & examples, what is your plagiarism score.

• Privacy Policy

Home » Descriptive Statistics – Types, Methods and Examples

Descriptive Statistics – Types, Methods and Examples

Table of Contents

Descriptive Statistics

Descriptive statistics is a branch of statistics that deals with the summarization and description of collected data. This type of statistics is used to simplify and present data in a manner that is easy to understand, often through visual or numerical methods. Descriptive statistics is primarily concerned with measures of central tendency, variability, and distribution, as well as graphical representations of data.

Here are the main components of descriptive statistics:

• Measures of Central Tendency : These provide a summary statistic that represents the center point or typical value of a dataset. The most common measures of central tendency are the mean (average), median (middle value), and mode (most frequent value).
• Measures of Dispersion or Variability : These provide a summary statistic that represents the spread of values in a dataset. Common measures of dispersion include the range (difference between the highest and lowest values), variance (average of the squared differences from the mean), standard deviation (square root of the variance), and interquartile range (difference between the upper and lower quartiles).
• Measures of Position : These are used to understand the distribution of values within a dataset. They include percentiles and quartiles.
• Graphical Representations : Data can be visually represented using various methods like bar graphs, histograms, pie charts, box plots, and scatter plots. These visuals provide a clear, intuitive way to understand the data.
• Measures of Association : These measures provide insight into the relationships between variables in the dataset, such as correlation and covariance.

Descriptive Statistics Types

Descriptive statistics can be classified into two types:

Measures of Central Tendency

These measures help describe the center point or average of a data set. There are three main types:

• Mean : The average value of the dataset, obtained by adding all the data points and dividing by the number of data points.
• Median : The middle value of the dataset, obtained by ordering all data points and picking out the one in the middle (or the average of the two middle numbers if the dataset has an even number of observations).
• Mode : The most frequently occurring value in the dataset.

Measures of Variability (or Dispersion)

These measures describe the spread or variability of the data points in the dataset. There are four main types:

• Range : The difference between the largest and smallest values in the dataset.
• Variance : The average of the squared differences from the mean.
• Standard Deviation : The square root of the variance, giving a measure of dispersion that is in the same units as the original dataset.
• Interquartile Range (IQR) : The range between the first quartile (25th percentile) and the third quartile (75th percentile), which provides a measure of variability that is resistant to outliers.

Descriptive Statistics Formulas

Sure, here are some of the most commonly used formulas in descriptive statistics:

Mean (μ or x̄) :

The average of all the numbers in the dataset. It is computed by summing all the observations and dividing by the number of observations.

Formula : μ = Σx/n or x̄ = Σx/n (where Σx is the sum of all observations and n is the number of observations)

The middle value in the dataset when the observations are arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers.

The most frequently occurring number in the dataset. There’s no formula for this as it’s determined by observation.

The difference between the highest (max) and lowest (min) values in the dataset.

Formula : Range = max – min

Variance (σ² or s²) :

The average of the squared differences from the mean. Variance is a measure of how spread out the numbers in the dataset are.

Population Variance formula : σ² = Σ(x – μ)² / N Sample Variance formula: s² = Σ(x – x̄)² / (n – 1)

(where x is each individual observation, μ is the population mean, x̄ is the sample mean, N is the size of the population, and n is the size of the sample)

Standard Deviation (σ or s) :

The square root of the variance. It measures the amount of variability or dispersion for a set of data. Population Standard Deviation formula: σ = √σ² Sample Standard Deviation formula: s = √s²

Interquartile Range (IQR) :

The range between the first quartile (Q1, 25th percentile) and the third quartile (Q3, 75th percentile). It measures statistical dispersion, or how far apart the data points are.

Formula : IQR = Q3 – Q1

Descriptive Statistics Methods

Here are some of the key methods used in descriptive statistics:

This method involves arranging data into a table format, making it easier to understand and interpret. Tables often show the frequency distribution of variables.

Graphical Representation

This method involves presenting data visually to help reveal patterns, trends, outliers, or relationships between variables. There are many types of graphs used, such as bar graphs, histograms, pie charts, line graphs, box plots, and scatter plots.

Calculation of Central Tendency Measures

This involves determining the mean, median, and mode of a dataset. These measures indicate where the center of the dataset lies.

Calculation of Dispersion Measures

This involves calculating the range, variance, standard deviation, and interquartile range. These measures indicate how spread out the data is.

Calculation of Position Measures

This involves determining percentiles and quartiles, which tell us about the position of particular data points within the overall data distribution.

Calculation of Association Measures

This involves calculating statistics like correlation and covariance to understand relationships between variables.

Summary Statistics

Often, a collection of several descriptive statistics is presented together in what’s known as a “summary statistics” table. This provides a comprehensive snapshot of the data at a glanc

Descriptive Statistics Examples

Descriptive Statistics Examples are as follows:

Example 1: Student Grades

Let’s say a teacher has the following set of grades for 7 students: 85, 90, 88, 92, 78, 88, and 94. The teacher could use descriptive statistics to summarize this data:

• Mean (average) : (85 + 90 + 88 + 92 + 78 + 88 + 94)/7 = 88
• Median (middle value) : First, rearrange the grades in ascending order (78, 85, 88, 88, 90, 92, 94). The median grade is 88.
• Mode (most frequent value) : The grade 88 appears twice, more frequently than any other grade, so it’s the mode.
• Range (difference between highest and lowest) : 94 (highest) – 78 (lowest) = 16
• Variance and Standard Deviation : These would be calculated using the appropriate formulas, providing a measure of the dispersion of the grades.

Example 2: Survey Data

A researcher conducts a survey on the number of hours of TV watched per day by people in a particular city. They collect data from 1,000 respondents and can use descriptive statistics to summarize this data:

• Mean : Calculate the average hours of TV watched by adding all the responses and dividing by the total number of respondents.
• Median : Sort the data and find the middle value.
• Mode : Identify the most frequently reported number of hours watched.
• Histogram : Create a histogram to visually display the frequency of responses. This could show, for example, that the majority of people watch 2-3 hours of TV per day.
• Standard Deviation : Calculate this to find out how much variation there is from the average.

Importance of Descriptive Statistics

Descriptive statistics are fundamental in the field of data analysis and interpretation, as they provide the first step in understanding a dataset. Here are a few reasons why descriptive statistics are important:

• Data Summarization : Descriptive statistics provide simple summaries about the measures and samples you have collected. With a large dataset, it’s often difficult to identify patterns or tendencies just by looking at the raw data. Descriptive statistics provide numerical and graphical summaries that can highlight important aspects of the data.
• Data Simplification : They simplify large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary, making it easier to understand and interpret the dataset.
• Identification of Patterns and Trends : Descriptive statistics can help identify patterns and trends in the data, providing valuable insights. Measures like the mean and median can tell you about the central tendency of your data, while measures like the range and standard deviation tell you about the dispersion.
• Data Comparison : By summarizing data into measures such as the mean and standard deviation, it’s easier to compare different datasets or different groups within a dataset.
• Data Quality Assessment : Descriptive statistics can help identify errors or outliers in the data, which might indicate issues with data collection or entry.
• Foundation for Further Analysis : Descriptive statistics are typically the first step in data analysis. They help create a foundation for further statistical or inferential analysis. In fact, advanced statistical techniques often assume that one has first examined their data using descriptive methods.

When to use Descriptive Statistics

They can be used in a wide range of situations, including:

• Understanding a New Dataset : When you first encounter a new dataset, using descriptive statistics is a useful first step to understand the main characteristics of the data, such as the central tendency, dispersion, and distribution.
• Data Exploration in Research : In the initial stages of a research project, descriptive statistics can help to explore the data, identify trends and patterns, and generate hypotheses for further testing.
• Presenting Research Findings : Descriptive statistics can be used to present research findings in a clear and understandable way, often using visual aids like graphs or charts.
• Monitoring and Quality Control : In fields like business or manufacturing, descriptive statistics are often used to monitor processes, track performance over time, and identify any deviations from expected standards.
• Comparing Groups : Descriptive statistics can be used to compare different groups or categories within your data. For example, you might want to compare the average scores of two groups of students, or the variance in sales between different regions.
• Reporting Survey Results : If you conduct a survey, you would use descriptive statistics to summarize the responses, such as calculating the percentage of respondents who agree with a certain statement.

Applications of Descriptive Statistics

Descriptive statistics are widely used in a variety of fields to summarize, represent, and analyze data. Here are some applications:

• Business : Businesses use descriptive statistics to summarize and interpret data such as sales figures, customer feedback, or employee performance. For instance, they might calculate the mean sales for each month to understand trends, or use graphical representations like bar charts to present sales data.
• Healthcare : In healthcare, descriptive statistics are used to summarize patient data, such as age, weight, blood pressure, or cholesterol levels. They are also used to describe the incidence and prevalence of diseases in a population.
• Education : Educators use descriptive statistics to summarize student performance, like average test scores or grade distribution. This information can help identify areas where students are struggling and inform instructional decisions.
• Social Sciences : Social scientists use descriptive statistics to summarize data collected from surveys, experiments, and observational studies. This can involve describing demographic characteristics of participants, response frequencies to survey items, and more.
• Psychology : Psychologists use descriptive statistics to describe the characteristics of their study participants and the main findings of their research, such as the average score on a psychological test.
• Sports : Sports analysts use descriptive statistics to summarize athlete and team performance, such as batting averages in baseball or points per game in basketball.
• Government : Government agencies use descriptive statistics to summarize data about the population, such as census data on population size and demographics.
• Finance and Economics : In finance, descriptive statistics can be used to summarize past investment performance or economic data, such as changes in stock prices or GDP growth rates.
• Quality Control : In manufacturing, descriptive statistics can be used to summarize measures of product quality, such as the average dimensions of a product or the frequency of defects.

Limitations of Descriptive Statistics

While descriptive statistics are a crucial part of data analysis and provide valuable insights about a dataset, they do have certain limitations:

• Lack of Depth : Descriptive statistics provide a summary of your data, but they can oversimplify the data, resulting in a loss of detail and potentially significant nuances.
• Vulnerability to Outliers : Some descriptive measures, like the mean, are sensitive to outliers. A single extreme value can significantly skew your mean, making it less representative of your data.
• Inability to Make Predictions : Descriptive statistics describe what has been observed in a dataset. They don’t allow you to make predictions or generalizations about unobserved data or larger populations.
• No Insight into Correlations : While some descriptive statistics can hint at potential relationships between variables, they don’t provide detailed insights into the nature or strength of these relationships.
• No Causality or Hypothesis Testing : Descriptive statistics cannot be used to determine cause and effect relationships or to test hypotheses. For these purposes, inferential statistics are needed.
• Can Mislead : When used improperly, descriptive statistics can be used to present a misleading picture of the data. For instance, choosing to only report the mean without also reporting the standard deviation or range can hide a large amount of variability in the data.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Methodological Framework – Types, Examples and...

Histogram – Types, Examples and Making Guide

Graphical Methods – Types, Examples and Guide

Uniform Histogram – Purpose, Examples and Guide

Discriminant Analysis – Methods, Types and...

Regression Analysis – Methods, Types and Examples

• What is descriptive research?

Last updated

5 February 2023

Reviewed by

Cathy Heath

Short on time? Get an AI generated summary of this article instead

Descriptive research is a common investigatory model used by researchers in various fields, including social sciences, linguistics, and academia.

Read on to understand the characteristics of descriptive research and explore its underlying techniques, processes, and procedures.

Analyze your descriptive research

Dovetail streamlines analysis to help you uncover and share actionable insights

Descriptive research is an exploratory research method. It enables researchers to precisely and methodically describe a population, circumstance, or phenomenon.

As the name suggests, descriptive research describes the characteristics of the group, situation, or phenomenon being studied without manipulating variables or testing hypotheses . This can be reported using surveys , observational studies, and case studies. You can use both quantitative and qualitative methods to compile the data.

Besides making observations and then comparing and analyzing them, descriptive studies often develop knowledge concepts and provide solutions to critical issues. It always aims to answer how the event occurred, when it occurred, where it occurred, and what the problem or phenomenon is.

• Characteristics of descriptive research

The following are some of the characteristics of descriptive research:

Quantitativeness

Descriptive research can be quantitative as it gathers quantifiable data to statistically analyze a population sample. These numbers can show patterns, connections, and trends over time and can be discovered using surveys, polls, and experiments.

Qualitativeness

Descriptive research can also be qualitative. It gives meaning and context to the numbers supplied by quantitative descriptive research .

Researchers can use tools like interviews, focus groups, and ethnographic studies to illustrate why things are what they are and help characterize the research problem. This is because it’s more explanatory than exploratory or experimental research.

Uncontrolled variables

Descriptive research differs from experimental research in that researchers cannot manipulate the variables. They are recognized, scrutinized, and quantified instead. This is one of its most prominent features.

Cross-sectional studies

Descriptive research is a cross-sectional study because it examines several areas of the same group. It involves obtaining data on multiple variables at the personal level during a certain period. It’s helpful when trying to understand a larger community’s habits or preferences.

Carried out in a natural environment

Descriptive studies are usually carried out in the participants’ everyday environment, which allows researchers to avoid influencing responders by collecting data in a natural setting. You can use online surveys or survey questions to collect data or observe.

Basis for further research

You can further dissect descriptive research’s outcomes and use them for different types of investigation. The outcomes also serve as a foundation for subsequent investigations and can guide future studies. For example, you can use the data obtained in descriptive research to help determine future research designs.

• Descriptive research methods

There are three basic approaches for gathering data in descriptive research: observational, case study, and survey.

You can use surveys to gather data in descriptive research. This involves gathering information from many people using a questionnaire and interview .

Surveys remain the dominant research tool for descriptive research design. Researchers can conduct various investigations and collect multiple types of data (quantitative and qualitative) using surveys with diverse designs.

You can conduct surveys over the phone, online, or in person. Your survey might be a brief interview or conversation with a set of prepared questions intended to obtain quick information from the primary source.

Observation

This descriptive research method involves observing and gathering data on a population or phenomena without manipulating variables. It is employed in psychology, market research , and other social science studies to track and understand human behavior.

Observation is an essential component of descriptive research. It entails gathering data and analyzing it to see whether there is a relationship between the two variables in the study. This strategy usually allows for both qualitative and quantitative data analysis.

Case studies

A case study can outline a specific topic’s traits. The topic might be a person, group, event, or organization.

It involves using a subset of a larger group as a sample to characterize the features of that larger group.

You can generalize knowledge gained from studying a case study to benefit a broader audience.

This approach entails carefully examining a particular group, person, or event over time. You can learn something new about the study topic by using a small group to better understand the dynamics of the entire group.

• Types of descriptive research

There are several types of descriptive study. The most well-known include cross-sectional studies, census surveys, sample surveys, case reports, and comparison studies.

Case reports and case series

In the healthcare and medical fields, a case report is used to explain a patient’s circumstances when suffering from an uncommon illness or displaying certain symptoms. Case reports and case series are both collections of related cases. They have aided the advancement of medical knowledge on countless occasions.

The normative component is an addition to the descriptive survey. In the descriptive–normative survey, you compare the study’s results to the norm.

Descriptive survey

This descriptive type of research employs surveys to collect information on various topics. This data aims to determine the degree to which certain conditions may be attained.

You can extrapolate or generalize the information you obtain from sample surveys to the larger group being researched.

Correlative survey

Correlative surveys help establish if there is a positive, negative, or neutral connection between two variables.

Performing census surveys involves gathering relevant data on several aspects of a given population. These units include individuals, families, organizations, objects, characteristics, and properties.

During descriptive research, you gather different degrees of interest over time from a specific population. Cross-sectional studies provide a glimpse of a phenomenon’s prevalence and features in a population. There are no ethical challenges with them and they are quite simple and inexpensive to carry out.

Comparative studies

These surveys compare the two subjects’ conditions or characteristics. The subjects may include research variables, organizations, plans, and people.

Comparison points, assumption of similarities, and criteria of comparison are three important variables that affect how well and accurately comparative studies are conducted.

For instance, descriptive research can help determine how many CEOs hold a bachelor’s degree and what proportion of low-income households receive government help.

• Pros and cons

The primary advantage of descriptive research designs is that researchers can create a reliable and beneficial database for additional study. To conduct any inquiry, you need access to reliable information sources that can give you a firm understanding of a situation.

Quantitative studies are time- and resource-intensive, so knowing the hypotheses viable for testing is crucial. The basic overview of descriptive research provides helpful hints as to which variables are worth quantitatively examining. This is why it’s employed as a precursor to quantitative research designs.

Some experts view this research as untrustworthy and unscientific. However, there is no way to assess the findings because you don’t manipulate any variables statistically.

Cause-and-effect correlations also can’t be established through descriptive investigations. Additionally, observational study findings cannot be replicated, which prevents a review of the findings and their replication.

The absence of statistical and in-depth analysis and the rather superficial character of the investigative procedure are drawbacks of this research approach.

• Descriptive research examples and applications

Several descriptive research examples are emphasized based on their types, purposes, and applications. Research questions often begin with “What is …” These studies help find solutions to practical issues in social science, physical science, and education.

Here are some examples and applications of descriptive research:

Determining consumer perception and behavior

Organizations use descriptive research designs to determine how various demographic groups react to a certain product or service.

For example, a business looking to sell to its target market should research the market’s behavior first. When researching human behavior in response to a cause or event, the researcher pays attention to the traits, actions, and responses before drawing a conclusion.

Scientific classification

Scientific descriptive research enables the classification of organisms and their traits and constituents.

Measuring data trends

A descriptive study design’s statistical capabilities allow researchers to track data trends over time. It’s frequently used to determine the study target’s current circumstances and underlying patterns.

Conduct comparison

Organizations can use a descriptive research approach to learn how various demographics react to a certain product or service. For example, you can study how the target market responds to a competitor’s product and use that information to infer their behavior.

• Bottom line

A descriptive research design is suitable for exploring certain topics and serving as a prelude to larger quantitative investigations. It provides a comprehensive understanding of the “what” of the group or thing you’re investigating.

This research type acts as the cornerstone of other research methodologies . It is distinctive because it can use quantitative and qualitative research approaches at the same time.

What is descriptive research design?

Descriptive research design aims to systematically obtain information to describe a phenomenon, situation, or population. More specifically, it helps answer the what, when, where, and how questions regarding the research problem rather than the why.

How does descriptive research compare to qualitative research?

Despite certain parallels, descriptive research concentrates on describing phenomena, while qualitative research aims to understand people better.

How do you analyze descriptive research data?

Data analysis involves using various methodologies, enabling the researcher to evaluate and provide results regarding validity and reliability.

Should you be using a customer insights hub?

Do you want to discover previous research faster?

Do you share your research findings with others?

Do you analyze research data?

Start for free today, add your research, and get to key insights faster

Editor’s picks

Last updated: 18 April 2023

Last updated: 27 February 2023

Last updated: 22 August 2024

Last updated: 5 February 2023

Last updated: 16 August 2024

Last updated: 9 March 2023

Last updated: 30 April 2024

Last updated: 12 December 2023

Last updated: 11 March 2024

Last updated: 4 July 2024

Last updated: 6 March 2024

Last updated: 5 March 2024

Last updated: 13 May 2024

Latest articles

Related topics, .css-je19u9{-webkit-align-items:flex-end;-webkit-box-align:flex-end;-ms-flex-align:flex-end;align-items:flex-end;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:row;-ms-flex-direction:row;flex-direction:row;-webkit-box-flex-wrap:wrap;-webkit-flex-wrap:wrap;-ms-flex-wrap:wrap;flex-wrap:wrap;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;row-gap:0;text-align:center;max-width:671px;}@media (max-width: 1079px){.css-je19u9{max-width:400px;}.css-je19u9>span{white-space:pre;}}@media (max-width: 799px){.css-je19u9{max-width:400px;}.css-je19u9>span{white-space:pre;}} decide what to .css-1kiodld{max-height:56px;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}@media (max-width: 1079px){.css-1kiodld{display:none;}} build next, decide what to build next, log in or sign up.

Get started for free

What is Descriptive Research and How is it Used?

Introduction

What does descriptive research mean, why would you use a descriptive research design, what are the characteristics of descriptive research, examples of descriptive research, what are the data collection methods in descriptive research, how do you analyze descriptive research data, ensuring validity and reliability in the findings.

Conducting descriptive research offers researchers a way to present phenomena as they naturally occur. Rooted in an open-ended and non-experimental nature, this type of research focuses on portraying the details of specific phenomena or contexts, helping readers gain a clearer understanding of topics of interest.

From businesses gauging customer satisfaction to educators assessing classroom dynamics, the data collected from descriptive research provides invaluable insights across various fields.

This article aims to illuminate the essence, utility, characteristics, and methods associated with descriptive research, guiding those who wish to harness its potential in their respective domains.

At its core, descriptive research refers to a systematic approach used by researchers to collect, analyze, and present data about real-life phenomena to describe it in its natural context. It primarily aims to describe what exists, based on empirical observations .

Unlike experimental research, where variables are manipulated to observe outcomes, descriptive research deals with the "as-is" scenario to facilitate further research by providing a framework or new insights on which continuing studies can build.

Definition of descriptive research

Descriptive research is defined as a research method that observes and describes the characteristics of a particular group, situation, or phenomenon.

The goal is not to establish cause and effect relationships but rather to provide a detailed account of the situation.

The difference between descriptive and exploratory research

While both descriptive and exploratory research seek to provide insights into a topic or phenomenon, they differ in their focus. Exploratory research is more about investigating a topic to develop preliminary insights or to identify potential areas of interest.

In contrast, descriptive research offers detailed accounts and descriptions of the observed phenomenon, seeking to paint a full picture of what's happening.

The evolution of descriptive research in academia

Historically, descriptive research has played a foundational role in numerous academic disciplines. Anthropologists, for instance, used this approach to document cultures and societies. Psychologists have employed it to capture behaviors, emotions, and reactions.

Over time, the method has evolved, incorporating technological advancements and adapting to contemporary needs, yet its essence remains rooted in describing a phenomenon or setting as it is.

Descriptive research serves as a cornerstone in the research landscape for its ability to provide a detailed snapshot of life. Its unique qualities and methods make it an invaluable method for various research purposes. Here's why:

Benefits of obtaining a clear picture

Descriptive research captures the present state of phenomena, offering researchers a detailed reflection of situations. This unaltered representation is crucial for sectors like marketing, where understanding current consumer behavior can shape future strategies.

Facilitating data interpretation

Given its straightforward nature, descriptive research can provide data that's easier to interpret, both for researchers and their audiences. Rather than analyzing complex statistical relationships among variables, researchers present detailed descriptions of their qualitative observations . Researchers can engage in in depth analysis relating to their research question , but audiences can also draw insights from their own interpretations or reflections on potential underlying patterns.

Enhancing the clarity of the research problem

By presenting things as they are, descriptive research can help elucidate ambiguous research questions. A well-executed descriptive study can shine light on overlooked aspects of a problem, paving the way for further investigative research.

Addressing practical problems

In real-world scenarios, it's not always feasible to manipulate variables or set up controlled experiments. For instance, in social sciences, understanding cultural norms without interference is paramount. Descriptive research allows for such non-intrusive insights, ensuring genuine understanding.

Building a foundation for future research

Often, descriptive studies act as stepping stones for more complex research endeavors. By establishing baseline data and highlighting patterns, they create a platform upon which more intricate hypotheses can be built and tested in subsequent studies.

Descriptive research is distinguished by a set of hallmark characteristics that set it apart from other research methodologies . Recognizing these features can help researchers effectively design, implement , and interpret descriptive studies.

Specificity in the research question

As with all research, descriptive research starts with a well-defined research question aiming to detail a particular phenomenon. The specificity ensures that the study remains focused on gathering relevant data without unnecessary deviations.

Focus on the present situation

While some research methods aim to predict future trends or uncover historical truths, descriptive research is predominantly concerned with the present. It seeks to capture the current state of affairs, such as understanding today's consumer habits or documenting a newly observed phenomenon.

Standardized and structured methodology

To ensure credibility and consistency in results, descriptive research often employs standardized methods. Whether it's using a fixed set of survey questions or adhering to specific observation protocols, this structured approach ensures that data is collected uniformly, making it easier to compare and analyze.

Non-manipulative approach in observation

One of the standout features of descriptive research is its non-invasive nature. Researchers observe and document without influencing the research subject or the environment. This passive stance ensures that the data gathered is a genuine reflection of the phenomenon under study.

Replicability and consistency in results

Due to its structured methodology, findings from descriptive research can often be replicated in different settings or with different samples. This consistency adds to the credibility of the results, reinforcing the validity of the insights drawn from the study.

Analyze data quickly and efficiently with ATLAS.ti

Download a free trial to see how you can make sense of complex qualitative data.

Numerous fields and sectors conduct descriptive research for its versatile and detailed nature. Through its focus on presenting things as they naturally occur, it provides insights into a myriad of scenarios. Here are some tangible examples from diverse domains:

Conducting market research

Businesses often turn to data analysis through descriptive research to understand the demographics of their target market. For instance, a company launching a new product might survey potential customers to understand their age, gender, income level, and purchasing habits, offering valuable data for targeted marketing strategies.

Evaluating employee behaviors

Organizations rely on descriptive research designs to assess the behavior and attitudes of their employees. By conducting observations or surveys , companies can gather data on workplace satisfaction, collaboration patterns, or the impact of a new office layout on productivity.

Understanding consumer preferences

Brands aiming to understand their consumers' likes and dislikes often use descriptive research. By observing shopping behaviors or conducting product feedback surveys , they can gauge preferences and adjust their offerings accordingly.

Documenting historical patterns

Historians and anthropologists employ descriptive research to identify patterns through analysis of events or cultural practices. For instance, a historian might detail the daily life in a particular era, while an anthropologist might document rituals and ceremonies of a specific tribe.

Assessing student performance

Educational researchers can utilize descriptive studies to understand the effectiveness of teaching methodologies. By observing classrooms or surveying students, they can measure data trends and gauge the impact of a new teaching technique or curriculum on student engagement and performance.

Descriptive research methods aim to authentically represent situations and phenomena. These techniques ensure the collection of comprehensive and reliable data about the subject of interest.

The most appropriate descriptive research method depends on the research question and resources available for your research study.

Surveys and questionnaires

One of the most familiar tools in the researcher's arsenal, surveys and questionnaires offer a structured means of collecting data from a vast audience. Through carefully designed questions, researchers can obtain standardized responses that lend themselves to straightforward comparison and analysis in quantitative and qualitative research .

Survey research can manifest in various formats, from face-to-face interactions and telephone conversations to digital platforms. While surveys can reach a broad audience and generate quantitative data ripe for statistical analysis, they also come with the challenge of potential biases in design and rely heavily on respondent honesty.

Observations and case studies

Direct or participant observation is a method wherein researchers actively watch and document behaviors or events. A researcher might, for instance, observe the dynamics within a classroom or the behaviors of shoppers in a market setting.

Case studies provide an even deeper dive, focusing on a thorough analysis of a specific individual, group, or event. These methods present the advantage of capturing real-time, detailed data, but they might also be time-intensive and can sometimes introduce observer bias .

Interviews and focus groups

Interviews , whether they follow a structured script or flow more organically, are a powerful means to extract detailed insights directly from participants. On the other hand, focus groups gather multiple participants for discussions, aiming to gather diverse and collective opinions on a particular topic or product.

These methods offer the benefit of deep insights and adaptability in data collection . However, they necessitate skilled interviewers, and focus group settings might see individual opinions being influenced by group dynamics.

Document and content analysis

Here, instead of generating new data, researchers examine existing documents or content . This can range from studying historical records and newspapers to analyzing media content or literature.

Analyzing existing content offers the advantage of accessibility and can provide insights over longer time frames. However, the reliability and relevance of the content are paramount, and researchers must approach this method with a discerning eye.

Descriptive research data, rich in details and insights, necessitates meticulous analysis to derive meaningful conclusions. The analysis process transforms raw data into structured findings that can be communicated and acted upon.

Qualitative content analysis

For data collected through interviews , focus groups , observations , or open-ended survey questions , qualitative content analysis is a popular choice. This involves examining non-numerical data to identify patterns, themes, or categories.

By coding responses or observations , researchers can identify recurring elements, making it easier to comprehend larger data sets and draw insights.

Using descriptive statistics

When dealing with quantitative data from surveys or experiments, descriptive statistics are invaluable. Measures such as mean, median, mode, standard deviation, and frequency distributions help summarize data sets, providing a snapshot of the overall patterns.

Graphical representations like histograms, pie charts, or bar graphs can further help in visualizing these statistics.

Coding and categorizing the data

Both qualitative and quantitative data often require coding. Coding involves assigning labels to specific responses or behaviors to group similar segments of data. This categorization aids in identifying patterns, especially in vast data sets.

For instance, responses to open-ended questions in a survey can be coded based on keywords or sentiments, allowing for a more structured analysis.

Visual representation through graphs and charts

Visual aids like graphs, charts, and plots can simplify complex data, making it more accessible and understandable. Whether it's showcasing frequency distributions through histograms or mapping out relationships with networks, visual representations can elucidate trends and patterns effectively.

In the realm of research , the credibility of findings is paramount. Without trustworthiness in the results, even the most meticulously gathered data can lose its value. Two cornerstones that bolster the credibility of research outcomes are validity and reliability .

Validity: Measuring the right thing

Validity addresses the accuracy of the research. It seeks to answer the question: Is the research genuinely measuring what it aims to measure? In descriptive research, where the objective is to paint an authentic picture of the current state of affairs, ensuring validity is crucial.

For instance, if a study aims to understand consumer preferences for a product category, the questions posed should genuinely reflect those preferences and not veer into unrelated territories. Multiple forms of validity, including content, criterion, and construct validity, can be examined to ensure that the research instruments and processes are aligned with the research goals.

Reliability: Consistency in findings

Reliability, on the other hand, pertains to the consistency of the research findings. When a study demonstrates reliability, this suggests that others could repeat the study and the outcomes would remain consistent across repetitions.

In descriptive research, factors like the clarity of survey questions , the training of observers , and the standardization of interview protocols play a role in enhancing reliability. Techniques such as test-retest and internal consistency measurements can be employed to assess and improve reliability.

Make your research happen with ATLAS.ti

Analyze descriptive research with our powerful data analysis interface. Download a free trial of ATLAS.ti.

• Business Essentials
• Leadership & Management
• Credential of Leadership, Impact, and Management in Business (CLIMB)
• Entrepreneurship & Innovation
• Digital Transformation
• Finance & Accounting
• Business in Society
• For Organizations
• Support Portal
• Media Coverage
• Founding Donors
• Leadership Team

• Harvard Business School →
• HBS Online →
• Business Insights →

Business Insights

Harvard Business School Online's Business Insights Blog provides the career insights you need to achieve your goals and gain confidence in your business skills.

• Career Development
• Communication
• Decision-Making
• Earning Your MBA
• Negotiation
• News & Events
• Productivity
• Staff Spotlight
• Student Profiles
• Work-Life Balance
• AI Essentials for Business
• Alternative Investments
• Business Analytics
• Business Strategy
• Business and Climate Change
• Creating Brand Value
• Design Thinking and Innovation
• Digital Marketing Strategy
• Disruptive Strategy
• Economics for Managers
• Entrepreneurship Essentials
• Financial Accounting
• Global Business
• Launching Tech Ventures
• Leadership Principles
• Leadership, Ethics, and Corporate Accountability
• Leading Change and Organizational Renewal
• Leading with Finance
• Management Essentials
• Negotiation Mastery
• Organizational Leadership
• Power and Influence for Positive Impact
• Strategy Execution
• Sustainable Business Strategy
• Sustainable Investing
• Winning with Digital Platforms

What Is Descriptive Analytics? 5 Examples

• 09 Nov 2021

Data analytics is a valuable tool for businesses aiming to increase revenue, improve products, and retain customers. According to research by global management consulting firm McKinsey & Company, companies that use data analytics are 23 times more likely to outperform competitors in terms of new customer acquisition than non-data-driven companies. They were also nine times more likely to surpass them in measures of customer loyalty and 19 times more likely to achieve above-average profitability.

Data analytics can be broken into four key types :

• Descriptive, which answers the question, “What happened?”
• Diagnostic , which answers the question, “Why did this happen?”
• Predictive , which answers the question, “What might happen in the future?”
• Prescriptive , which answers the question, “What should we do next?”

Each type of data analysis can help you reach specific goals and be used in tandem to create a full picture of data that informs your organization’s strategy formulation and decision-making.

Descriptive analytics can be leveraged on its own or act as a foundation for the other three analytics types. If you’re new to the field of business analytics, descriptive analytics is an accessible and rewarding place to start.

Access your free e-book today.

What Is Descriptive Analytics?

Descriptive analytics is the process of using current and historical data to identify trends and relationships. It’s sometimes called the simplest form of data analysis because it describes trends and relationships but doesn’t dig deeper.

Descriptive analytics is relatively accessible and likely something your organization uses daily. Basic statistical software, such as Microsoft Excel or data visualization tools , such as Google Charts and Tableau, can help parse data, identify trends and relationships between variables, and visually display information.

Descriptive analytics is especially useful for communicating change over time and uses trends as a springboard for further analysis to drive decision-making .

Here are five examples of descriptive analytics in action to apply at your organization.

Related: 5 Business Analytics Skills for Professionals

5 Examples of Descriptive Analytics

1. traffic and engagement reports.

One example of descriptive analytics is reporting. If your organization tracks engagement in the form of social media analytics or web traffic, you’re already using descriptive analytics.

These reports are created by taking raw data—generated when users interact with your website, advertisements, or social media content—and using it to compare current metrics to historical metrics and visualize trends.

For example, you may be responsible for reporting on which media channels drive the most traffic to the product page of your company’s website. Using descriptive analytics, you can analyze the page’s traffic data to determine the number of users from each source. You may decide to take it one step further and compare traffic source data to historical data from the same sources. This can enable you to update your team on movement; for instance, highlighting that traffic from paid advertisements increased 20 percent year over year.

The three other analytics types can then be used to determine why traffic from each source increased or decreased over time, if trends are predicted to continue, and what your team’s best course of action is moving forward.

2. Financial Statement Analysis

Another example of descriptive analytics that may be familiar to you is financial statement analysis. Financial statements are periodic reports that detail financial information about a business and, together, give a holistic view of a company’s financial health.

There are several types of financial statements, including the balance sheet , income statement , cash flow statement , and statement of shareholders’ equity. Each caters to a specific audience and conveys different information about a company’s finances.

Financial statement analysis can be done in three primary ways: vertical, horizontal, and ratio.

Vertical analysis involves reading a statement from top to bottom and comparing each item to those above and below it. This helps determine relationships between variables. For instance, if each line item is a percentage of the total, comparing them can provide insight into which are taking up larger and smaller percentages of the whole.

Horizontal analysis involves reading a statement from left to right and comparing each item to itself from a previous period. This type of analysis determines change over time.

Finally, ratio analysis involves comparing one section of a report to another based on their relationships to the whole. This directly compares items across periods, as well as your company’s ratios to the industry’s to gauge whether yours is over- or underperforming.

Each of these financial statement analysis methods are examples of descriptive analytics, as they provide information about trends and relationships between variables based on current and historical data.

3. Demand Trends

Descriptive analytics can also be used to identify trends in customer preference and behavior and make assumptions about the demand for specific products or services.

Streaming provider Netflix’s trend identification provides an excellent use case for descriptive analytics. Netflix’s team—which has a track record of being heavily data-driven—gathers data on users’ in-platform behavior. They analyze this data to determine which TV series and movies are trending at any given time and list trending titles in a section of the platform’s home screen.

Not only does this data allow Netflix users to see what’s popular—and thus, what they might enjoy watching—but it allows the Netflix team to know which types of media, themes, and actors are especially favored at a certain time. This can drive decision-making about future original content creation, contracts with existing production companies, marketing, and retargeting campaigns.

4. Aggregated Survey Results

Descriptive analytics is also useful in market research. When it comes time to glean insights from survey and focus group data, descriptive analytics can help identify relationships between variables and trends.

For instance, you may conduct a survey and identify that as respondents’ age increases, so does their likelihood to purchase your product. If you’ve conducted this survey multiple times over several years, descriptive analytics can tell you if this age-purchase correlation has always existed or if it was something that only occurred this year.

Insights like this can pave the way for diagnostic analytics to explain why certain factors are correlated. You can then leverage predictive and prescriptive analytics to plan future product improvements or marketing campaigns based on those trends.

Related: What Is Marketing Analytics?

5. Progress to Goals

Finally, descriptive analytics can be applied to track progress to goals. Reporting on progress toward key performance indicators (KPIs) can help your team understand if efforts are on track or if adjustments need to be made.

For example, if your organization aims to reach 500,000 monthly unique page views, you can use traffic data to communicate how you’re tracking toward it. Perhaps halfway through the month, you’re at 200,000 unique page views. This would be underperforming because you’d like to be halfway to your goal at that point—at 250,000 unique page views. This descriptive analysis of your team’s progress can allow further analysis to examine what can be done differently to improve traffic numbers and get back on track to hit your KPI.

Using Data to Identify Relationships and Trends

“Never before has so much data about so many different things been collected and stored every second of every day,” says Harvard Business School Professor Jan Hammond in the online course Business Analytics . “In this world of big data, data literacy —the ability to analyze, interpret, and even question data—is an increasingly valuable skill.”

Leveraging descriptive analytics to communicate change based on current and historical data and as a foundation for diagnostic, predictive, and prescriptive analytics has the potential to take you and your organization far.

Do you want to become a data-driven professional? Explore our eight-week Business Analytics course and our three-course Credential of Readiness (CORe) program to deepen your analytical skills and apply them to real-world business problems.

About the Author

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Springer Nature - PMC COVID-19 Collection

Descriptive Statistics for Summarising Data

Ray w. cooksey.

UNE Business School, University of New England, Armidale, NSW Australia

This chapter discusses and illustrates descriptive statistics . The purpose of the procedures and fundamental concepts reviewed in this chapter is quite straightforward: to facilitate the description and summarisation of data. By ‘describe’ we generally mean either the use of some pictorial or graphical representation of the data (e.g. a histogram, box plot, radar plot, stem-and-leaf display, icon plot or line graph) or the computation of an index or number designed to summarise a specific characteristic of a variable or measurement (e.g., frequency counts, measures of central tendency, variability, standard scores). Along the way, we explore the fundamental concepts of probability and the normal distribution. We seldom interpret individual data points or observations primarily because it is too difficult for the human brain to extract or identify the essential nature, patterns, or trends evident in the data, particularly if the sample is large. Rather we utilise procedures and measures which provide a general depiction of how the data are behaving. These statistical procedures are designed to identify or display specific patterns or trends in the data. What remains after their application is simply for us to interpret and tell the story.

The first broad category of statistics we discuss concerns descriptive statistics . The purpose of the procedures and fundamental concepts in this category is quite straightforward: to facilitate the description and summarisation of data. By ‘describe’ we generally mean either the use of some pictorial or graphical representation of the data or the computation of an index or number designed to summarise a specific characteristic of a variable or measurement.

We seldom interpret individual data points or observations primarily because it is too difficult for the human brain to extract or identify the essential nature, patterns, or trends evident in the data, particularly if the sample is large. Rather we utilise procedures and measures which provide a general depiction of how the data are behaving. These statistical procedures are designed to identify or display specific patterns or trends in the data. What remains after their application is simply for us to interpret and tell the story.

Reflect on the QCI research scenario and the associated data set discussed in Chap. 10.1007/978-981-15-2537-7_4. Consider the following questions that Maree might wish to address with respect to decision accuracy and speed scores:

• What was the typical level of accuracy and decision speed for inspectors in the sample? [see Procedure 5.4 – Assessing central tendency.]
• What was the most common accuracy and speed score amongst the inspectors? [see Procedure 5.4 – Assessing central tendency.]
• What was the range of accuracy and speed scores; the lowest and the highest scores? [see Procedure 5.5 – Assessing variability.]
• How frequently were different levels of inspection accuracy and speed observed? What was the shape of the distribution of inspection accuracy and speed scores? [see Procedure 5.1 – Frequency tabulation, distributions & crosstabulation.]
• What percentage of inspectors would have ‘failed’ to ‘make the cut’ assuming the industry standard for acceptable inspection accuracy and speed combined was set at 95%? [see Procedure 5.7 – Standard ( z ) scores.]
• How variable were the inspectors in their accuracy and speed scores? Were all the accuracy and speed levels relatively close to each other in magnitude or were the scores widely spread out over the range of possible test outcomes? [see Procedure 5.5 – Assessing variability.]
• What patterns might be visually detected when looking at various QCI variables singly and together as a set? [see Procedure 5.2 – Graphical methods for dispaying data, Procedure 5.3 – Multivariate graphs & displays, and Procedure 5.6 – Exploratory data analysis.]

This chapter includes discussions and illustrations of a number of procedures available for answering questions about data like those posed above. In addition, you will find discussions of two fundamental concepts, namely probability and the normal distribution ; concepts that provide building blocks for Chaps. 10.1007/978-981-15-2537-7_6 and 10.1007/978-981-15-2537-7_7.

Procedure 5.1: Frequency Tabulation, Distributions & Crosstabulation

Frequency tabulation and distributions.

Frequency tabulation serves to provide a convenient counting summary for a set of data that facilitates interpretation of various aspects of those data. Basically, frequency tabulation occurs in two stages:

• First, the scores in a set of data are rank ordered from the lowest value to the highest value.
• Second, the number of times each specific score occurs in the sample is counted. This count records the frequency of occurrence for that specific data value.

Consider the overall job satisfaction variable, jobsat , from the QCI data scenario. Performing frequency tabulation across the 112 Quality Control Inspectors on this variable using the SPSS Frequencies procedure (Allen et al. 2019 , ch. 3; George and Mallery 2019 , ch. 6) produces the frequency tabulation shown in Table 5.1 . Note that three of the inspectors in the sample did not provide a rating for jobsat thereby producing three missing values (= 2.7% of the sample of 112) and leaving 109 inspectors with valid data for the analysis.

Frequency tabulation of overall job satisfaction scores

The display of frequency tabulation is often referred to as the frequency distribution for the sample of scores. For each value of a variable, the frequency of its occurrence in the sample of data is reported. It is possible to compute various percentages and percentile values from a frequency distribution.

Table 5.1 shows the ‘Percent’ or relative frequency of each score (the percentage of the 112 inspectors obtaining each score, including those inspectors who were missing scores, which SPSS labels as ‘System’ missing). Table 5.1 also shows the ‘Valid Percent’ which is computed only for those inspectors in the sample who gave a valid or non-missing response.

Finally, it is possible to add up the ‘Valid Percent’ values, starting at the low score end of the distribution, to form the cumulative distribution or ‘Cumulative Percent’ . A cumulative distribution is useful for finding percentiles which reflect what percentage of the sample scored at a specific value or below.

We can see in Table 5.1 that 4 of the 109 valid inspectors (a ‘Valid Percent’ of 3.7%) indicated the lowest possible level of job satisfaction—a value of 1 (Very Low) – whereas 18 of the 109 valid inspectors (a ‘Valid Percent’ of 16.5%) indicated the highest possible level of job satisfaction—a value of 7 (Very High). The ‘Cumulative Percent’ number of 18.3 in the row for the job satisfaction score of 3 can be interpreted as “roughly 18% of the sample of inspectors reported a job satisfaction score of 3 or less”; that is, nearly a fifth of the sample expressed some degree of negative satisfaction with their job as a quality control inspector in their particular company.

If you have a large data set having many different scores for a particular variable, it may be more useful to tabulate frequencies on the basis of intervals of scores.

For the accuracy scores in the QCI database, you could count scores occurring in intervals such as ‘less than 75% accuracy’, ‘between 75% but less than 85% accuracy’, ‘between 85% but less than 95% accuracy’, and ‘95% accuracy or greater’, rather than counting the individual scores themselves. This would yield what is termed a ‘grouped’ frequency distribution since the data have been grouped into intervals or score classes. Producing such an analysis using SPSS would involve extra steps to create the new category or ‘grouping’ system for scores prior to conducting the frequency tabulation.

Crosstabulation

In a frequency crosstabulation , we count frequencies on the basis of two variables simultaneously rather than one; thus we have a bivariate situation.

For example, Maree might be interested in the number of male and female inspectors in the sample of 112 who obtained each jobsat score. Here there are two variables to consider: inspector’s gender and inspector’s j obsat score. Table 5.2 shows such a crosstabulation as compiled by the SPSS Crosstabs procedure (George and Mallery 2019 , ch. 8). Note that inspectors who did not report a score for jobsat and/or gender have been omitted as missing values, leaving 106 valid inspectors for the analysis.

Frequency crosstabulation of jobsat scores by gender category for the QCI data

The crosstabulation shown in Table 5.2 gives a composite picture of the distribution of satisfaction levels for male inspectors and for female inspectors. If frequencies or ‘Counts’ are added across the gender categories, we obtain the numbers in the ‘Total’ column (the percentages or relative frequencies are also shown immediately below each count) for each discrete value of jobsat (note this column of statistics differs from that in Table 5.1 because the gender variable was missing for certain inspectors). By adding down each gender column, we obtain, in the bottom row labelled ‘Total’, the number of males and the number of females that comprised the sample of 106 valid inspectors.

The totals, either across the rows or down the columns of the crosstabulation, are termed the marginal distributions of the table. These marginal distributions are equivalent to frequency tabulations for each of the variables jobsat and gender . As with frequency tabulation, various percentage measures can be computed in a crosstabulation, including the percentage of the sample associated with a specific count within either a row (‘% within jobsat ’) or a column (‘% within gender ’). You can see in Table 5.2 that 18 inspectors indicated a job satisfaction level of 7 (Very High); of these 18 inspectors reported in the ‘Total’ column, 8 (44.4%) were male and 10 (55.6%) were female. The marginal distribution for gender in the ‘Total’ row shows that 57 inspectors (53.8% of the 106 valid inspectors) were male and 49 inspectors (46.2%) were female. Of the 57 male inspectors in the sample, 8 (14.0%) indicated a job satisfaction level of 7 (Very High). Furthermore, we could generate some additional interpretive information of value by adding the ‘% within gender’ values for job satisfaction levels of 5, 6 and 7 (i.e. differing degrees of positive job satisfaction). Here we would find that 68.4% (= 24.6% + 29.8% + 14.0%) of male inspectors indicated some degree of positive job satisfaction compared to 61.2% (= 10.2% + 30.6% + 20.4%) of female inspectors.

This helps to build a picture of the possible relationship between an inspector’s gender and their level of job satisfaction (a relationship that, as we will see later, can be quantified and tested using Procedure 10.1007/978-981-15-2537-7_6#Sec14 and Procedure 10.1007/978-981-15-2537-7_7#Sec17).

It should be noted that a crosstabulation table such as that shown in Table 5.2 is often referred to as a contingency table about which more will be said later (see Procedure 10.1007/978-981-15-2537-7_7#Sec17 and Procedure 10.1007/978-981-15-2537-7_7#Sec115).

Frequency tabulation is useful for providing convenient data summaries which can aid in interpreting trends in a sample, particularly where the number of discrete values for a variable is relatively small. A cumulative percent distribution provides additional interpretive information about the relative positioning of specific scores within the overall distribution for the sample.

Crosstabulation permits the simultaneous examination of the distributions of values for two variables obtained from the same sample of observations. This examination can yield some useful information about the possible relationship between the two variables. More complex crosstabulations can be also done where the values of three or more variables are tracked in a single systematic summary. The use of frequency tabulation or cross-tabulation in conjunction with various other statistical measures, such as measures of central tendency (see Procedure 5.4 ) and measures of variability (see Procedure 5.5 ), can provide a relatively complete descriptive summary of any data set.

Disadvantages

Frequency tabulations can get messy if interval or ratio-level measures are tabulated simply because of the large number of possible data values. Grouped frequency distributions really should be used in such cases. However, certain choices, such as the size of the score interval (group size), must be made, often arbitrarily, and such choices can affect the nature of the final frequency distribution.

Additionally, percentage measures have certain problems associated with them, most notably, the potential for their misinterpretation in small samples. One should be sure to know the sample size on which percentage measures are based in order to obtain an interpretive reference point for the actual percentage values.

For example

In a sample of 10 individuals, 20% represents only two individuals whereas in a sample of 300 individuals, 20% represents 60 individuals. If all that is reported is the 20%, then the mental inference drawn by readers is likely to be that a sizeable number of individuals had a score or scores of a particular value—but what is ‘sizeable’ depends upon the total number of observations on which the percentage is based.

Where Is This Procedure Useful?

Frequency tabulation and crosstabulation are very commonly applied procedures used to summarise information from questionnaires, both in terms of tabulating various demographic characteristics (e.g. gender, age, education level, occupation) and in terms of actual responses to questions (e.g. numbers responding ‘yes’ or ‘no’ to a particular question). They can be particularly useful in helping to build up the data screening and demographic stories discussed in Chap. 10.1007/978-981-15-2537-7_4. Categorical data from observational studies can also be analysed with this technique (e.g. the number of times Suzy talks to Frank, to Billy, and to John in a study of children’s social interactions).

Certain types of experimental research designs may also be amenable to analysis by crosstabulation with a view to drawing inferences about distribution differences across the sets of categories for the two variables being tracked.

You could employ crosstabulation in conjunction with the tests described in Procedure 10.1007/978-981-15-2537-7_7#Sec17 to see if two different styles of advertising campaign differentially affect the product purchasing patterns of male and female consumers.

In the QCI database, Maree could employ crosstabulation to help her answer the question “do different types of electronic manufacturing firms ( company ) differ in terms of their tendency to employ male versus female quality control inspectors ( gender )?”

Software Procedures

Procedure 5.2: Graphical Methods for Displaying Data

Graphical methods for displaying data include bar and pie charts, histograms and frequency polygons, line graphs and scatterplots. It is important to note that what is presented here is a small but representative sampling of the types of simple graphs one can produce to summarise and display trends in data. Generally speaking, SPSS offers the easiest facility for producing and editing graphs, but with a rather limited range of styles and types. SYSTAT, STATGRAPHICS and NCSS offer a much wider range of graphs (including graphs unique to each package), but with the drawback that it takes somewhat more effort to get the graphs in exactly the form you want.

Bar and Pie Charts

These two types of graphs are useful for summarising the frequency of occurrence of various values (or ranges of values) where the data are categorical (nominal or ordinal level of measurement).

• A bar chart uses vertical and horizontal axes to summarise the data. The vertical axis is used to represent frequency (number) of occurrence or the relative frequency (percentage) of occurrence; the horizontal axis is used to indicate the data categories of interest.
• A pie chart gives a simpler visual representation of category frequencies by cutting a circular plot into wedges or slices whose sizes are proportional to the relative frequency (percentage) of occurrence of specific data categories. Some pie charts can have a one or more slices emphasised by ‘exploding’ them out from the rest of the pie.

Consider the company variable from the QCI database. This variable depicts the types of manufacturing firms that the quality control inspectors worked for. Figure 5.1 illustrates a bar chart summarising the percentage of female inspectors in the sample coming from each type of firm. Figure 5.2 shows a pie chart representation of the same data, with an ‘exploded slice’ highlighting the percentage of female inspectors in the sample who worked for large business computer manufacturers – the lowest percentage of the five types of companies. Both graphs were produced using SPSS.

Bar chart: Percentage of female inspectors

Pie chart: Percentage of female inspectors

The pie chart was modified with an option to show the actual percentage along with the label for each category. The bar chart shows that computer manufacturing firms have relatively fewer female inspectors compared to the automotive and electrical appliance (large and small) firms. This trend is less clear from the pie chart which suggests that pie charts may be less visually interpretable when the data categories occur with rather similar frequencies. However, the ‘exploded slice’ option can help interpretation in some circumstances.

Certain software programs, such as SPSS, STATGRAPHICS, NCSS and Microsoft Excel, offer the option of generating 3-dimensional bar charts and pie charts and incorporating other ‘bells and whistles’ that can potentially add visual richness to the graphic representation of the data. However, you should generally be careful with these fancier options as they can produce distortions and create ambiguities in interpretation (e.g. see discussions in Jacoby 1997 ; Smithson 2000 ; Wilkinson 2009 ). Such distortions and ambiguities could ultimately end up providing misinformation to researchers as well as to those who read their research.

Histograms and Frequency Polygons

These two types of graphs are useful for summarising the frequency of occurrence of various values (or ranges of values) where the data are essentially continuous (interval or ratio level of measurement) in nature. Both histograms and frequency polygons use vertical and horizontal axes to summarise the data. The vertical axis is used to represent the frequency (number) of occurrence or the relative frequency (percentage) of occurrences; the horizontal axis is used for the data values or ranges of values of interest. The histogram uses bars of varying heights to depict frequency; the frequency polygon uses lines and points.

There is a visual difference between a histogram and a bar chart: the bar chart uses bars that do not physically touch, signifying the discrete and categorical nature of the data, whereas the bars in a histogram physically touch to signal the potentially continuous nature of the data.

Suppose Maree wanted to graphically summarise the distribution of speed scores for the 112 inspectors in the QCI database. Figure 5.3 (produced using NCSS) illustrates a histogram representation of this variable. Figure 5.3 also illustrates another representational device called the ‘density plot’ (the solid tracing line overlaying the histogram) which gives a smoothed impression of the overall shape of the distribution of speed scores. Figure 5.4 (produced using STATGRAPHICS) illustrates the frequency polygon representation for the same data.

Histogram of the speed variable (with density plot overlaid)

Frequency polygon plot of the speed variable

These graphs employ a grouped format where speed scores which fall within specific intervals are counted as being essentially the same score. The shape of the data distribution is reflected in these plots. Each graph tells us that the inspection speed scores are positively skewed with only a few inspectors taking very long times to make their inspection judgments and the majority of inspectors taking rather shorter amounts of time to make their decisions.

Both representations tell a similar story; the choice between them is largely a matter of personal preference. However, if the number of bars to be plotted in a histogram is potentially very large (and this is usually directly controllable in most statistical software packages), then a frequency polygon would be the preferred representation simply because the amount of visual clutter in the graph will be much reduced.

It is somewhat of an art to choose an appropriate definition for the width of the score grouping intervals (or ‘bins’ as they are often termed) to be used in the plot: choose too many and the plot may look too lumpy and the overall distributional trend may not be obvious; choose too few and the plot will be too coarse to give a useful depiction. Programs like SPSS, SYSTAT, STATGRAPHICS and NCSS are designed to choose an ‘appropriate’ number of bins to be used, but the analyst’s eye is often a better judge than any statistical rule that a software package would use.

There are several interesting variations of the histogram which can highlight key data features or facilitate interpretation of certain trends in the data. One such variation is a graph is called a dual histogram (available in SYSTAT; a variation called a ‘comparative histogram’ can be created in NCSS) – a graph that facilitates visual comparison of the frequency distributions for a specific variable for participants from two distinct groups.

Suppose Maree wanted to graphically compare the distributions of speed scores for inspectors in the two categories of education level ( educlev ) in the QCI database. Figure 5.5 shows a dual histogram (produced using SYSTAT) that accomplishes this goal. This graph still employs the grouped format where speed scores falling within particular intervals are counted as being essentially the same score. The shape of the data distribution within each group is also clearly reflected in this plot. However, the story conveyed by the dual histogram is that, while the inspection speed scores are positively skewed for inspectors in both categories of educlev, the comparison suggests that inspectors with a high school level of education (= 1) tend to take slightly longer to make their inspection decisions than do their colleagues who have a tertiary qualification (= 2).

Dual histogram of speed for the two categories of educlev

Line Graphs

The line graph is similar in style to the frequency polygon but is much more general in its potential for summarising data. In a line graph, we seldom deal with percentage or frequency data. Instead we can summarise other types of information about data such as averages or means (see Procedure 5.4 for a discussion of this measure), often for different groups of participants. Thus, one important use of the line graph is to break down scores on a specific variable according to membership in the categories of a second variable.

In the context of the QCI database, Maree might wish to summarise the average inspection accuracy scores for the inspectors from different types of manufacturing companies. Figure 5.6 was produced using SPSS and shows such a line graph.

Line graph comparison of companies in terms of average inspection accuracy

Note how the trend in performance across the different companies becomes clearer with such a visual representation. It appears that the inspectors from the Large Business Computer and PC manufacturing companies have better average inspection accuracy compared to the inspectors from the remaining three industries.

With many software packages, it is possible to further elaborate a line graph by including error or confidence intervals bars (see Procedure 10.1007/978-981-15-2537-7_8#Sec18). These give some indication of the precision with which the average level for each category in the population has been estimated (narrow bars signal a more precise estimate; wide bars signal a less precise estimate).

Figure 5.7 shows such an elaborated line graph, using 95% confidence interval bars, which can be used to help make more defensible judgments (compared to Fig. 5.6 ) about whether the companies are substantively different from each other in average inspection performance. Companies whose confidence interval bars do not overlap each other can be inferred to be substantively different in performance characteristics.

Line graph using confidence interval bars to compare accuracy across companies

The accuracy confidence interval bars for participants from the Large Business Computer manufacturing firms do not overlap those from the Large or Small Electrical Appliance manufacturers or the Automobile manufacturers.

We might conclude that quality control inspection accuracy is substantially better in the Large Business Computer manufacturing companies than in these other industries but is not substantially better than the PC manufacturing companies. We might also conclude that inspection accuracy in PC manufacturing companies is not substantially different from Small Electrical Appliance manufacturers.

Scatterplots

Scatterplots are useful in displaying the relationship between two interval- or ratio-scaled variables or measures of interest obtained on the same individuals, particularly in correlational research (see Fundamental Concept 10.1007/978-981-15-2537-7_6#Sec1 and Procedure 10.1007/978-981-15-2537-7_6#Sec4).

In a scatterplot, one variable is chosen to be represented on the horizontal axis; the second variable is represented on the vertical axis. In this type of plot, all data point pairs in the sample are graphed. The shape and tilt of the cloud of points in a scatterplot provide visual information about the strength and direction of the relationship between the two variables. A very compact elliptical cloud of points signals a strong relationship; a very loose or nearly circular cloud signals a weak or non-existent relationship. A cloud of points generally tilted upward toward the right side of the graph signals a positive relationship (higher scores on one variable associated with higher scores on the other and vice-versa). A cloud of points generally tilted downward toward the right side of the graph signals a negative relationship (higher scores on one variable associated with lower scores on the other and vice-versa).

Maree might be interested in displaying the relationship between inspection accuracy and inspection speed in the QCI database. Figure 5.8 , produced using SPSS, shows what such a scatterplot might look like. Several characteristics of the data for these two variables can be noted in Fig. 5.8 . The shape of the distribution of data points is evident. The plot has a fan-shaped characteristic to it which indicates that accuracy scores are highly variable (exhibit a very wide range of possible scores) at very fast inspection speeds but get much less variable and tend to be somewhat higher as inspection speed increases (where inspectors take longer to make their quality control decisions). Thus, there does appear to be some relationship between inspection accuracy and inspection speed (a weak positive relationship since the cloud of points tends to be very loose but tilted generally upward toward the right side of the graph – slower speeds tend to be slightly associated with higher accuracy.

Scatterplot relating inspection accuracy to inspection speed

However, it is not the case that the inspection decisions which take longest to make are necessarily the most accurate (see the labelled points for inspectors 7 and 62 in Fig. 5.8 ). Thus, Fig. 5.8 does not show a simple relationship that can be unambiguously summarised by a statement like “the longer an inspector takes to make a quality control decision, the more accurate that decision is likely to be”. The story is more complicated.

Some software packages, such as SPSS, STATGRAPHICS and SYSTAT, offer the option of using different plotting symbols or markers to represent the members of different groups so that the relationship between the two focal variables (the ones anchoring the X and Y axes) can be clarified with reference to a third categorical measure.

Maree might want to see if the relationship depicted in Fig. 5.8 changes depending upon whether the inspector was tertiary-qualified or not (this information is represented in the educlev variable of the QCI database).

Figure 5.9 shows what such a modified scatterplot might look like; the legend in the upper corner of the figure defines the marker symbols for each category of the educlev variable. Note that for both High School only-educated inspectors and Tertiary-qualified inspectors, the general fan-shaped relationship between accuracy and speed is the same. However, it appears that the distribution of points for the High School only-educated inspectors is shifted somewhat upward and toward the right of the plot suggesting that these inspectors tend to be somewhat more accurate as well as slower in their decision processes.

Scatterplot displaying accuracy vs speed conditional on educlev group

There are many other styles of graphs available, often dependent upon the specific statistical package you are using. Interestingly, NCSS and, particularly, SYSTAT and STATGRAPHICS, appear to offer the most variety in terms of types of graphs available for visually representing data. A reading of the user’s manuals for these programs (see the Useful additional readings) would expose you to the great diversity of plotting techniques available to researchers. Many of these techniques go by rather interesting names such as: Chernoff’s faces, radar plots, sunflower plots, violin plots, star plots, Fourier blobs, and dot plots.

These graphical methods provide summary techniques for visually presenting certain characteristics of a set of data. Visual representations are generally easier to understand than a tabular representation and when these plots are combined with available numerical statistics, they can give a very complete picture of a sample of data. Newer methods have become available which permit more complex representations to be depicted, opening possibilities for creatively visually representing more aspects and features of the data (leading to a style of visual data storytelling called infographics ; see, for example, McCandless 2014 ; Toseland and Toseland 2012 ). Many of these newer methods can display data patterns from multiple variables in the same graph (several of these newer graphical methods are illustrated and discussed in Procedure 5.3 ).

Graphs tend to be cumbersome and space consuming if a great many variables need to be summarised. In such cases, using numerical summary statistics (such as means or correlations) in tabular form alone will provide a more economical and efficient summary. Also, it can be very easy to give a misleading picture of data trends using graphical methods by simply choosing the ‘correct’ scaling for maximum effect or choosing a display option (such as a 3-D effect) that ‘looks’ presentable but which actually obscures a clear interpretation (see Smithson 2000 ; Wilkinson 2009 ).

Thus, you must be careful in creating and interpreting visual representations so that the influence of aesthetic choices for sake of appearance do not become more important than obtaining a faithful and valid representation of the data—a very real danger with many of today’s statistical packages where ‘default’ drawing options have been pre-programmed in. No single plot can completely summarise all possible characteristics of a sample of data. Thus, choosing a specific method of graphical display may, of necessity, force a behavioural researcher to represent certain data characteristics (such as frequency) at the expense of others (such as averages).

Virtually any research design which produces quantitative data and statistics (even to the extent of just counting the number of occurrences of several events) provides opportunities for graphical data display which may help to clarify or illustrate important data characteristics or relationships. Remember, graphical displays are communication tools just like numbers—which tool to choose depends upon the message to be conveyed. Visual representations of data are generally more useful in communicating to lay persons who are unfamiliar with statistics. Care must be taken though as these same lay people are precisely the people most likely to misinterpret a graph if it has been incorrectly drawn or scaled.

Procedure 5.3: Multivariate Graphs & Displays

Graphical methods for displaying multivariate data (i.e. many variables at once) include scatterplot matrices, radar (or spider) plots, multiplots, parallel coordinate displays, and icon plots. Multivariate graphs are useful for visualising broad trends and patterns across many variables (Cleveland 1995 ; Jacoby 1998 ). Such graphs typically sacrifice precision in representation in favour of a snapshot pictorial summary that can help you form general impressions of data patterns.

It is important to note that what is presented here is a small but reasonably representative sampling of the types of graphs one can produce to summarise and display trends in multivariate data. Generally speaking, SYSTAT offers the best facilities for producing multivariate graphs, followed by STATGRAPHICS, but with the drawback that it is somewhat tricky to get the graphs in exactly the form you want. SYSTAT also has excellent facilities for creating new forms and combinations of graphs – essentially allowing graphs to be tailor-made for a specific communication purpose. Both SPSS and NCSS offer a more limited range of multivariate graphs, generally restricted to scatterplot matrices and variations of multiplots. Microsoft Excel or STATGRAPHICS are the packages to use if radar or spider plots are desired.

Scatterplot Matrices

A scatterplot matrix is a useful multivariate graph designed to show relationships between pairs of many variables in the same display.

Figure 5.10 illustrates a scatterplot matrix, produced using SYSTAT, for the mentabil , accuracy , speed , jobsat and workcond variables in the QCI database. It is easy to see that all the scatterplot matrix does is stack all pairs of scatterplots into a format where it is easy to pick out the graph for any ‘row’ variable that intersects a column ‘variable’.

Scatterplot matrix relating mentabil , accuracy , speed , jobsat & workcond

In those plots where a ‘row’ variable intersects itself in a column of the matrix (along the so-called ‘diagonal’), SYSTAT permits a range of univariate displays to be shown. Figure 5.10 shows univariate histograms for each variable (recall Procedure 5.2 ). One obvious drawback of the scatterplot matrix is that, if many variables are to be displayed (say ten or more); the graph gets very crowded and becomes very hard to visually appreciate.

Looking at the first column of graphs in Fig. 5.10 , we can see the scatterplot relationships between mentabil and each of the other variables. We can get a visual impression that mentabil seems to be slightly negatively related to accuracy (the cloud of scatter points tends to angle downward to the right, suggesting, very slightly, that higher mentabil scores are associated with lower levels of accuracy ).

Conversely, the visual impression of the relationship between mentabil and speed is that the relationship is slightly positive (higher mentabil scores tend to be associated with higher speed scores = longer inspection times). Similar types of visual impressions can be formed for other parts of Fig. 5.10 . Notice that the histogram plots along the diagonal give a clear impression of the shape of the distribution for each variable.

Radar Plots

The radar plot (also known as a spider graph for obvious reasons) is a simple and effective device for displaying scores on many variables. Microsoft Excel offers a range of options and capabilities for producing radar plots, such as the plot shown in Fig. 5.11 . Radar plots are generally easy to interpret and provide a good visual basis for comparing plots from different individuals or groups, even if a fairly large number of variables (say, up to about 25) are being displayed. Like a clock face, variables are evenly spaced around the centre of the plot in clockwise order starting at the 12 o’clock position. Visual interpretation of a radar plot primarily relies on shape comparisons, i.e. the rise and fall of peaks and valleys along the spokes around the plot. Valleys near the centre display low scores on specific variables, peaks near the outside of the plot display high scores on specific variables. [Note that, technically, radar plots employ polar coordinates.] SYSTAT can draw graphs using polar coordinates but not as easily as Excel can, from the user’s perspective. Radar plots work best if all the variables represented are measured on the same scale (e.g. a 1 to 7 Likert-type scale or 0% to 100% scale). Individuals who are missing any scores on the variables being plotted are typically omitted.

Radar plot comparing attitude ratings for inspectors 66 and 104

The radar plot in Fig. 5.11 , produced using Excel, compares two specific inspectors, 66 and 104, on the nine attitude rating scales. Inspector 66 gave the highest rating (= 7) on the cultqual variable and inspector 104 gave the lowest rating (= 1). The plot shows that inspector 104 tended to provide very low ratings on all nine attitude variables, whereas inspector 66 tended to give very high ratings on all variables except acctrain and trainapp , where the scores were similar to those for inspector 104. Thus, in general, inspector 66 tended to show much more positive attitudes toward their workplace compared to inspector 104.

While Fig. 5.11 was generated to compare the scores for two individuals in the QCI database, it would be just as easy to produce a radar plot that compared the five types of companies in terms of their average ratings on the nine variables, as shown in Fig. 5.12 .

Radar plot comparing average attitude ratings for five types of company

Here we can form the visual impression that the five types of companies differ most in their average ratings of mgmtcomm and least in the average ratings of polsatis . Overall, the average ratings from inspectors from PC manufacturers (black diamonds with solid lines) seem to be generally the most positive as their scores lie on or near the outer ring of scores and those from Automobile manufacturers tend to be least positive on many variables (except the training-related variables).

Extrapolating from Fig. 5.12 , you may rightly conclude that including too many groups and/or too many variables in a radar plot comparison can lead to so much clutter that any visual comparison would be severely degraded. You may have to experiment with using colour-coded lines to represent different groups versus line and marker shape variations (as used in Fig. 5.12 ), because choice of coding method for groups can influence the interpretability of a radar plot.

A multiplot is simply a hybrid style of graph that can display group comparisons across a number of variables. There are a wide variety of possible multiplots one could potentially design (SYSTAT offers great capabilities with respect to multiplots). Figure 5.13 shows a multiplot comprising a side-by-side series of profile-based line graphs – one graph for each type of company in the QCI database.

Multiplot comparing profiles of average attitude ratings for five company types

The multiplot in Fig. 5.13 , produced using SYSTAT, graphs the profile of average attitude ratings for all inspectors within a specific type of company. This multiplot shows the same story as the radar plot in Fig. 5.12 , but in a different graphical format. It is still fairly clear that the average ratings from inspectors from PC manufacturers tend to be higher than for the other types of companies and the profile for inspectors from automobile manufacturers tends to be lower than for the other types of companies.

The profile for inspectors from large electrical appliance manufacturers is the flattest, meaning that their average attitude ratings were less variable than for other types of companies. Comparing the ease with which you can glean the visual impressions from Figs. 5.12 and 5.13 may lead you to prefer one style of graph over another. If you have such preferences, chances are others will also, which may mean you need to carefully consider your options when deciding how best to display data for effect.

Frequently, choice of graph is less a matter of which style is right or wrong, but more a matter of which style will suit specific purposes or convey a specific story, i.e. the choice is often strategic.

Parallel Coordinate Displays

A parallel coordinate display is useful for displaying individual scores on a range of variables, all measured using the same scale. Furthermore, such graphs can be combined side-by-side to facilitate very broad visual comparisons among groups, while retaining individual profile variability in scores. Each line in a parallel coordinate display represents one individual, e.g. an inspector.

The interpretation of a parallel coordinate display, such as the two shown in Fig. 5.14 , depends on visual impressions of the peaks and valleys (highs and lows) in the profiles as well as on the density of similar profile lines. The graph is called ‘parallel coordinate’ simply because it assumes that all variables are measured on the same scale and that scores for each variable can therefore be located along vertical axes that are parallel to each other (imagine vertical lines on Fig. 5.14 running from bottom to top for each variable on the X-axis). The main drawback of this method of data display is that only those individuals in the sample who provided legitimate scores on all of the variables being plotted (i.e. who have no missing scores) can be displayed.

Parallel coordinate displays comparing profiles of average attitude ratings for five company types

The parallel coordinate display in Fig. 5.14 , produced using SYSTAT, graphs the profile of average attitude ratings for all inspectors within two specific types of company: the left graph for inspectors from PC manufacturers and the right graph for automobile manufacturers.

There are fewer lines in each display than the number of inspectors from each type of company simply because several inspectors from each type of company were missing a rating on at least one of the nine attitude variables. The graphs show great variability in scores amongst inspectors within a company type, but there are some overall patterns evident.

For example, inspectors from automobile companies clearly and fairly uniformly rated mgmtcomm toward the low end of the scale, whereas the reverse was generally true for that variable for inspectors from PC manufacturers. Conversely, inspectors from automobile companies tend to rate acctrain and trainapp more toward the middle to high end of the scale, whereas the reverse is generally true for those variables for inspectors from PC manufacturers.

Perhaps the most creative types of multivariate displays are the so-called icon plots . SYSTAT and STATGRAPHICS offer an impressive array of different types of icon plots, including, amongst others, Chernoff’s faces, profile plots, histogram plots, star glyphs and sunray plots (Jacoby 1998 provides a detailed discussion of icon plots).

Icon plots generally use a specific visual construction to represent variables scores obtained by each individual within a sample or group. All icon plots are thus methods for displaying the response patterns for individual members of a sample, as long as those individuals are not missing any scores on the variables to be displayed (note that this is the same limitation as for radar plots and parallel coordinate displays). To illustrate icon plots, without generating too many icons to focus on, Figs. 5.15 , 5.16 , 5.17 and 5.18 present four different icon plots for QCI inspectors classified, using a new variable called BEST_WORST , as either the worst performers (= 1 where their accuracy scores were less than 70%) or the best performers (= 2 where their accuracy scores were 90% or greater).

Chernoff’s faces icon plot comparing individual attitude ratings for best and worst performing inspectors

Profile plot comparing individual attitude ratings for best and worst performing inspectors

Histogram plot comparing individual attitude ratings for best and worst performing inspectors

Sunray plot comparing individual attitude ratings for best and worst performing inspectors

The Chernoff’s faces plot gets its name from the visual icon used to represent variable scores – a cartoon-type face. This icon tries to capitalise on our natural human ability to recognise and differentiate faces. Each feature of the face is controlled by the scores on a single variable. In SYSTAT, up to 20 facial features are controllable; the first five being curvature of mouth, angle of brow, width of nose, length of nose and length of mouth (SYSTAT Software Inc., 2009 , p. 259). The theory behind Chernoff’s faces is that similar patterns of variable scores will produce similar looking faces, thereby making similarities and differences between individuals more apparent.

The profile plot and histogram plot are actually two variants of the same type of icon plot. A profile plot represents individuals’ scores for a set of variables using simplified line graphs, one per individual. The profile is scaled so that the vertical height of the peaks and valleys correspond to actual values for variables where the variables anchor the X-axis in a fashion similar to the parallel coordinate display. So, as you examine a profile from left to right across the X-axis of each graph, you are looking across the set of variables. A histogram plot represents the same information in the same way as for the profile plot but using histogram bars instead.

Figure 5.15 , produced using SYSTAT, shows a Chernoff’s faces plot for the best and worst performing inspectors using their ratings of job satisfaction, working conditions and the nine general attitude statements.

Each face is labelled with the inspector number it represents. The gaps indicate where an inspector had missing data on at least one of the variables, meaning a face could not be generated for them. The worst performers are drawn using red lines; the best using blue lines. The first variable is jobsat and this variable controls mouth curvature; the second variable is workcond and this controls angle of brow, and so on. It seems clear that there are differences in the faces between the best and worst performers with, for example, best performers tending to be more satisfied (smiling) and with higher ratings for working conditions (brow angle).

Beyond a broad visual impression, there is little in terms of precise inferences you can draw from a Chernoff’s faces plot. It really provides a visual sketch, nothing more. The fact that there is no obvious link between facial features, variables and score levels means that the Chernoff’s faces icon plot is difficult to interpret at the level of individual variables – a holistic impression of similarity and difference is what this type of plot facilitates.

Figure 5.16 produced using SYSTAT, shows a profile plot for the best and worst performing inspectors using their ratings of job satisfaction, working conditions and the nine attitude variables.

Like the Chernoff’s faces plot (Fig. 5.15 ), as you read across the rows of the plot from left to right, each plot corresponds respectively to a inspector in the sample who was either in the worst performer (red) or best performer (blue) category. The first attitude variable is jobsat and anchors the left end of each line graph; the last variable is polsatis and anchors the right end of the line graph. The remaining variables are represented in order from left to right across the X-axis of each graph. Figure 5.16 shows that these inspectors are rather different in their attitude profiles, with best performers tending to show taller profiles on the first two variables, for example.

Figure 5.17 produced using SYSTAT, shows a histogram plot for the best and worst performing inspectors based on their ratings of job satisfaction, working conditions and the nine attitude variables. This plot tells the same story as the profile plot, only using histogram bars. Some people would prefer the histogram icon plot to the profile plot because each histogram bar corresponds to one variable, making the visual linking of a specific bar to a specific variable much easier than visually linking a specific position along the profile line to a specific variable.

The sunray plot is actually a simplified adaptation of the radar plot (called a “star glyph”) used to represent scores on a set of variables for each individual within a sample or group. Remember that a radar plot basically arranges the variables around a central point like a clock face; the first variable is represented at the 12 o’clock position and the remaining variables follow around the plot in a clockwise direction.

Unlike a radar plot, while the spokes (the actual ‘star’ of the glyph’s name) of the plot are visible, no interpretive scale is evident. A variable’s score is visually represented by its distance from the central point. Thus, the star glyphs in a sunray plot are designed, like Chernoff’s faces, to provide a general visual impression, based on icon shape. A wide diameter well-rounded plot indicates an individual with high scores on all variables and a small diameter well-rounded plot vice-versa. Jagged plots represent individuals with highly variable scores across the variables. ‘Stars’ of similar size, shape and orientation represent similar individuals.

Figure 5.18 , produced using STATGRAPHICS, shows a sunray plot for the best and worst performing inspectors. An interpretation glyph is also shown in the lower right corner of Fig. 5.18 , where variables are aligned with the spokes of a star (e.g. jobsat is at the 12 o’clock position). This sunray plot could lead you to form the visual impression that the worst performing inspectors (group 1) have rather less rounded rating profiles than do the best performing inspectors (group 2) and that the jobsat and workcond spokes are generally lower for the worst performing inspectors.

Comparatively speaking, the sunray plot makes identifying similar individuals a bit easier (perhaps even easier than Chernoff’s faces) and, when ordered as STATGRAPHICS showed in Fig. 5.18 , permits easier visual comparisons between groups of individuals, but at the expense of precise knowledge about variable scores. Remember, a holistic impression is the goal pursued using a sunray plot.

Multivariate graphical methods provide summary techniques for visually presenting certain characteristics of a complex array of data on variables. Such visual representations are generally better at helping us to form holistic impressions of multivariate data rather than any sort of tabular representation or numerical index. They also allow us to compress many numerical measures into a finite representation that is generally easy to understand. Multivariate graphical displays can add interest to an otherwise dry statistical reporting of numerical data. They are designed to appeal to our pattern recognition skills, focusing our attention on features of the data such as shape, level, variability and orientation. Some multivariate graphs (e.g. radar plots, sunray plots and multiplots) are useful not only for representing score patterns for individuals but also providing summaries of score patterns across groups of individuals.

Multivariate graphs tend to get very busy-looking and are hard to interpret if a great many variables or a large number of individuals need to be displayed (imagine any of the icon plots, for a sample of 200 questionnaire participants, displayed on a A4 page – each icon would be so small that its features could not be easily distinguished, thereby defeating the purpose of the display). In such cases, using numerical summary statistics (such as averages or correlations) in tabular form alone will provide a more economical and efficient summary. Also, some multivariate displays will work better for conveying certain types of information than others.

Information about variable relationships may be better displayed using a scatterplot matrix. Information about individual similarities and difference on a set of variables may be better conveyed using a histogram or sunray plot. Multiplots may be better suited to displaying information about group differences across a set of variables. Information about the overall similarity of individual entities in a sample might best be displayed using Chernoff’s faces.

Because people differ greatly in their visual capacities and preferences, certain types of multivariate displays will work for some people and not others. Sometimes, people will not see what you see in the plots. Some plots, such as Chernoff’s faces, may not strike a reader as a serious statistical procedure and this could adversely influence how convinced they will be by the story the plot conveys. None of the multivariate displays described here provide sufficiently precise information for solid inferences or interpretations; all are designed to simply facilitate the formation of holistic visual impressions. In fact, you may have noticed that some displays (scatterplot matrices and the icon plots, for example) provide no numerical scaling information that would help make precise interpretations. If precision in summary information is desired, the types of multivariate displays discussed here would not be the best strategic choices.

Virtually any research design which produces quantitative data/statistics for multiple variables provides opportunities for multivariate graphical data display which may help to clarify or illustrate important data characteristics or relationships. Thus, for survey research involving many identically-scaled attitudinal questions, a multivariate display may be just the device needed to communicate something about patterns in the data. Multivariate graphical displays are simply specialised communication tools designed to compress a lot of information into a meaningful and efficient format for interpretation—which tool to choose depends upon the message to be conveyed.

Generally speaking, visual representations of multivariate data could prove more useful in communicating to lay persons who are unfamiliar with statistics or who prefer visual as opposed to numerical information. However, these displays would probably require some interpretive discussion so that the reader clearly understands their intent.

Procedure 5.4: Assessing Central Tendency

The three most commonly reported measures of central tendency are the mean, median and mode. Each measure reflects a specific way of defining central tendency in a distribution of scores on a variable and each has its own advantages and disadvantages.

The mean is the most widely used measure of central tendency (also called the arithmetic average). Very simply, a mean is the sum of all the scores for a specific variable in a sample divided by the number of scores used in obtaining the sum. The resulting number reflects the average score for the sample of individuals on which the scores were obtained. If one were asked to predict the score that any single individual in the sample would obtain, the best prediction, in the absence of any other relevant information, would be the sample mean. Many parametric statistical methods (such as Procedures 10.1007/978-981-15-2537-7_7#Sec22 , 10.1007/978-981-15-2537-7_7#Sec32 , 10.1007/978-981-15-2537-7_7#Sec42 and 10.1007/978-981-15-2537-7_7#Sec68) deal with sample means in one way or another. For any sample of data, there is one and only one possible value for the mean in a specific distribution. For most purposes, the mean is the preferred measure of central tendency because it utilises all the available information in a sample.

In the context of the QCI database, Maree could quite reasonably ask what inspectors scored on the average in terms of mental ability ( mentabil ), inspection accuracy ( accuracy ), inspection speed ( speed ), overall job satisfaction ( jobsat ), and perceived quality of their working conditions ( workcond ). Table 5.3 shows the mean scores for the sample of 112 quality control inspectors on each of these variables. The statistics shown in Table 5.3 were computed using the SPSS Frequencies ... procedure. Notice that the table indicates how many of the 112 inspectors had a valid score for each variable and how many were missing a score (e.g. 109 inspectors provided a valid rating for jobsat; 3 inspectors did not).

Measures of central tendency for specific QCI variables

Each mean needs to be interpreted in terms of the original units of measurement for each variable. Thus, the inspectors in the sample showed an average mental ability score of 109.84 (higher than the general population mean of 100 for the test), an average inspection accuracy of 82.14%, and an average speed for making quality control decisions of 4.48 s. Furthermore, in terms of their work context, inspectors reported an average overall job satisfaction of 4.96 (on the 7-point scale, or a level of satisfaction nearly one full scale point above the Neutral point of 4—indicating a generally positive but not strong level of job satisfaction, and an average perceived quality of work conditions of 4.21 (on the 7-point scale which is just about at the level of Stressful but Tolerable.

The mean is sensitive to the presence of extreme values, which can distort its value, giving a biased indication of central tendency. As we will see below, the median is an alternative statistic to use in such circumstances. However, it is also possible to compute what is called a trimmed mean where the mean is calculated after a certain percentage (say, 5% or 10%) of the lowest and highest scores in a distribution have been ignored (a process called ‘trimming’; see, for example, the discussion in Field 2018 , pp. 262–264). This yields a statistic less influenced by extreme scores. The drawbacks are that the decision as to what percentage to trim can be somewhat subjective and trimming necessarily sacrifices information (i.e. the extreme scores) in order to achieve a less biased measure. Some software packages, such as SPSS, SYSTAT or NCSS, can report a specific percentage trimmed mean, if that option is selected for descriptive statistics or exploratory data analysis (see Procedure 5.6 ) procedures. Comparing the original mean with a trimmed mean can provide an indication of the degree to which the original mean has been biased by extreme values.

Very simply, the median is the centre or middle score of a set of scores. By ‘centre’ or ‘middle’ is meant that 50% of the data values are smaller than or equal to the median and 50% of the data values are larger when the entire distribution of scores is rank ordered from the lowest to highest value. Thus, we can say that the median is that score in the sample which occurs at the 50th percentile. [Note that a ‘percentile’ is attached to a specific score that a specific percentage of the sample scored at or below. Thus, a score at the 25th percentile means that 25% of the sample achieved this score or a lower score.] Table 5.3 shows the 25th, 50th and 75th percentile scores for each variable – note how the 50th percentile score is exactly equal to the median in each case .

The median is reported somewhat less frequently than the mean but does have some advantages over the mean in certain circumstances. One such circumstance is when the sample of data has a few extreme values in one direction (either very large or very small relative to all other scores). In this case, the mean would be influenced (biased) to a much greater degree than would the median since all of the data are used to calculate the mean (including the extreme scores) whereas only the single centre score is needed for the median. For this reason, many nonparametric statistical procedures (such as Procedures 10.1007/978-981-15-2537-7_7#Sec27 , 10.1007/978-981-15-2537-7_7#Sec37 and 10.1007/978-981-15-2537-7_7#Sec63) focus on the median as the comparison statistic rather than on the mean.

A discrepancy between the values for the mean and median of a variable provides some insight to the degree to which the mean is being influenced by the presence of extreme data values. In a distribution where there are no extreme values on either side of the distribution (or where extreme values balance each other out on either side of the distribution, as happens in a normal distribution – see Fundamental Concept II ), the mean and the median will coincide at the same value and the mean will not be biased.

For highly skewed distributions, however, the value of the mean will be pulled toward the long tail of the distribution because that is where the extreme values lie. However, in such skewed distributions, the median will be insensitive (statisticians call this property ‘robustness’) to extreme values in the long tail. For this reason, the direction of the discrepancy between the mean and median can give a very rough indication of the direction of skew in a distribution (‘mean larger than median’ signals possible positive skewness; ‘mean smaller than median’ signals possible negative skewness). Like the mean, there is one and only one possible value for the median in a specific distribution.

In Fig. 5.19 , the left graph shows the distribution of speed scores and the right-hand graph shows the distribution of accuracy scores. The speed distribution clearly shows the mean being pulled toward the right tail of the distribution whereas the accuracy distribution shows the mean being just slightly pulled toward the left tail. The effect on the mean is stronger in the speed distribution indicating a greater biasing effect due to some very long inspection decision times.

Effects of skewness in a distribution on the values for the mean and median

If we refer to Table 5.3 , we can see that the median score for each of the five variables has also been computed. Like the mean, the median must be interpreted in the original units of measurement for the variable. We can see that for mentabil , accuracy , and workcond , the value of the median is very close to the value of the mean, suggesting that these distributions are not strongly influenced by extreme data values in either the high or low direction. However, note that the median speed was 3.89 s compared to the mean of 4.48 s, suggesting that the distribution of speed scores is positively skewed (the mean is larger than the median—refer to Fig. 5.19 ). Conversely, the median jobsat score was 5.00 whereas the mean score was 4.96 suggesting very little substantive skewness in the distribution (mean and median are nearly equal).

The mode is the simplest measure of central tendency. It is defined as the most frequently occurring score in a distribution. Put another way, it is the score that more individuals in the sample obtain than any other score. An interesting problem associated with the mode is that there may be more than one in a specific distribution. In the case where multiple modes exist, the issue becomes which value do you report? The answer is that you must report all of them. In a ‘normal’ bell-shaped distribution, there is only one mode and it is indeed at the centre of the distribution, coinciding with both the mean and the median.

Table 5.3 also shows the mode for each of the five variables. For example, more inspectors achieved a mentabil score of 111 more often than any other score and inspectors reported a jobsat rating of 6 more often than any other rating. SPSS only ever reports one mode even if several are present, so one must be careful and look at a histogram plot for each variable to make a final determination of the mode(s) for that variable.

All three measures of central tendency yield information about what is going on in the centre of a distribution of scores. The mean and median provide a single number which can summarise the central tendency in the entire distribution. The mode can yield one or multiple indices. With many measurements on individuals in a sample, it is advantageous to have single number indices which can describe the distributions in summary fashion. In a normal or near-normal distribution of sample data, the mean, the median, and the mode will all generally coincide at the one point. In this instance, all three statistics will provide approximately the same indication of central tendency. Note however that it is seldom the case that all three statistics would yield exactly the same number for any particular distribution. The mean is the most useful statistic, unless the data distribution is skewed by extreme scores, in which case the median should be reported.

While measures of central tendency are useful descriptors of distributions, summarising data using a single numerical index necessarily reduces the amount of information available about the sample. Not only do we need to know what is going on in the centre of a distribution, we also need to know what is going on around the centre of the distribution. For this reason, most social and behavioural researchers report not only measures of central tendency, but also measures of variability (see Procedure 5.5 ). The mode is the least informative of the three statistics because of its potential for producing multiple values.

Measures of central tendency are useful in almost any type of experimental design, survey or interview study, and in any observational studies where quantitative data are available and must be summarised. The decision as to whether the mean or median should be reported depends upon the nature of the data which should ideally be ascertained by visual inspection of the data distribution. Some researchers opt to report both measures routinely. Computation of means is a prelude to many parametric statistical methods (see, for example, Procedure 10.1007/978-981-15-2537-7_7#Sec22 , 10.1007/978-981-15-2537-7_7#Sec32 , 10.1007/978-981-15-2537-7_7#Sec42 , 10.1007/978-981-15-2537-7_7#Sec52 , 10.1007/978-981-15-2537-7_7#Sec68 , 10.1007/978-981-15-2537-7_7#Sec76 and 10.1007/978-981-15-2537-7_7#Sec105); comparison of medians is associated with many nonparametric statistical methods (see, for example, Procedure 10.1007/978-981-15-2537-7_7#Sec27 , 10.1007/978-981-15-2537-7_7#Sec37 , 10.1007/978-981-15-2537-7_7#Sec63 and 10.1007/978-981-15-2537-7_7#Sec81).

Procedure 5.5: Assessing Variability

There are a variety of measures of variability to choose from including the range, interquartile range, variance and standard deviation. Each measure reflects a specific way of defining variability in a distribution of scores on a variable and each has its own advantages and disadvantages. Most measures of variability are associated with a specific measure of central tendency so that researchers are now commonly expected to report both a measure of central tendency and its associated measure of variability whenever they display numerical descriptive statistics on continuous or ranked-ordered variables.

This is the simplest measure of variability for a sample of data scores. The range is merely the largest score in the sample minus the smallest score in the sample. The range is the one measure of variability not explicitly associated with any measure of central tendency. It gives a very rough indication as to the extent of spread in the scores. However, since the range uses only two of the total available scores in the sample, the rest of the scores are ignored, which means that a lot of potentially useful information is being sacrificed. There are also problems if either the highest or lowest (or both) scores are atypical or too extreme in their value (as in highly skewed distributions). When this happens, the range gives a very inflated picture of the typical variability in the scores. Thus, the range tends not be a frequently reported measure of variability.

Table 5.4 shows a set of descriptive statistics, produced by the SPSS Frequencies procedure, for the mentabil, accuracy, speed, jobsat and workcond measures in the QCI database. In the table, you will find three rows labelled ‘Range’, ‘Minimum’ and ‘Maximum’.

Measures of central tendency and variability for specific QCI variables

Using the data from these three rows, we can draw the following descriptive picture. Mentabil scores spanned a range of 50 (from a minimum score of 85 to a maximum score of 135). Speed scores had a range of 16.05 s (from 1.05 s – the fastest quality decision to 17.10 – the slowest quality decision). Accuracy scores had a range of 43 (from 57% – the least accurate inspector to 100% – the most accurate inspector). Both work context measures ( jobsat and workcond ) exhibited a range of 6 – the largest possible range given the 1 to 7 scale of measurement for these two variables.

Interquartile Range

The Interquartile Range ( IQR ) is a measure of variability that is specifically designed to be used in conjunction with the median. The IQR also takes care of the extreme data problem which typically plagues the range measure. The IQR is defined as the range that is covered by the middle 50% of scores in a distribution once the scores have been ranked in order from lowest value to highest value. It is found by locating the value in the distribution at or below which 25% of the sample scored and subtracting this number from the value in the distribution at or below which 75% of the sample scored. The IQR can also be thought of as the range one would compute after the bottom 25% of scores and the top 25% of scores in the distribution have been ‘chopped off’ (or ‘trimmed’ as statisticians call it).

The IQR gives a much more stable picture of the variability of scores and, like the median, is relatively insensitive to the biasing effects of extreme data values. Some behavioural researchers prefer to divide the IQR in half which gives a measure called the Semi-Interquartile Range ( S-IQR ) . The S-IQR can be interpreted as the distance one must travel away from the median, in either direction, to reach the value which separates the top (or bottom) 25% of scores in the distribution from the remaining 75%.

The IQR or S-IQR is typically not produced by descriptive statistics procedures by default in many computer software packages; however, it can usually be requested as an optional statistic to report or it can easily be computed by hand using percentile scores. Both the median and the IQR figure prominently in Exploratory Data Analysis, particularly in the production of boxplots (see Procedure 5.6 ).

Figure 5.20 illustrates the conceptual nature of the IQR and S-IQR compared to that of the range. Assume that 100% of data values are covered by the distribution curve in the figure. It is clear that these three measures would provide very different values for a measure of variability. Your choice would depend on your purpose. If you simply want to signal the overall span of scores between the minimum and maximum, the range is the measure of choice. But if you want to signal the variability around the median, the IQR or S-IQR would be the measure of choice.

How the range, IQR and S-IQR measures of variability conceptually differ

Note: Some behavioural researchers refer to the IQR as the hinge-spread (or H-spread ) because of its use in the production of boxplots:

• the 25th percentile data value is referred to as the ‘lower hinge’;
• the 75th percentile data value is referred to as the ‘upper hinge’; and
• their difference gives the H-spread.

Midspread is another term you may see used as a synonym for interquartile range.

Referring back to Table 5.4 , we can find statistics reported for the median and for the ‘quartiles’ (25th, 50th and 75th percentile scores) for each of the five variables of interest. The ‘quartile’ values are useful for finding the IQR or S-IQR because SPSS does not report these measures directly. The median clearly equals the 50th percentile data value in the table.

If we focus, for example, on the speed variable, we could find its IQR by subtracting the 25th percentile score of 2.19 s from the 75th percentile score of 5.71 s to give a value for the IQR of 3.52 s (the S-IQR would simply be 3.52 divided by 2 or 1.76 s). Thus, we could report that the median decision speed for inspectors was 3.89 s and that the middle 50% of inspectors showed scores spanning a range of 3.52 s. Alternatively, we could report that the median decision speed for inspectors was 3.89 s and that the middle 50% of inspectors showed scores which ranged 1.76 s either side of the median value.

Note: We could compare the ‘Minimum’ or ‘Maximum’ scores to the 25th percentile score and 75th percentile score respectively to get a feeling for whether the minimum or maximum might be considered extreme or uncharacteristic data values.

The variance uses information from every individual in the sample to assess the variability of scores relative to the sample mean. Variance assesses the average squared deviation of each score from the mean of the sample. Deviation refers to the difference between an observed score value and the mean of the sample—they are squared simply because adding them up in their naturally occurring unsquared form (where some differences are positive and others are negative) always gives a total of zero, which is useless for an index purporting to measure something.

If many scores are quite different from the mean, we would expect the variance to be large. If all the scores lie fairly close to the sample mean, we would expect a small variance. If all scores exactly equal the mean (i.e. all the scores in the sample have the same value), then we would expect the variance to be zero.

Figure 5.21 illustrates some possibilities regarding variance of a distribution of scores having a mean of 100. The very tall curve illustrates a distribution with small variance. The distribution of medium height illustrates a distribution with medium variance and the flattest distribution ia a distribution with large variance.

The concept of variance

If we had a distribution with no variance, the curve would simply be a vertical line at a score of 100 (meaning that all scores were equal to the mean). You can see that as variance increases, the tails of the distribution extend further outward and the concentration of scores around the mean decreases. You may have noticed that variance and range (as well as the IQR) will be related, since the range focuses on the difference between the ends of the two tails in the distribution and larger variances extend the tails. So, a larger variance will generally be associated with a larger range and IQR compared to a smaller variance.

It is generally difficult to descriptively interpret the variance measure in a meaningful fashion since it involves squared deviations around the sample mean. [Note: If you look back at Table 5.4 , you will see the variance listed for each of the variables (e.g. the variance of accuracy scores is 84.118), but the numbers themselves make little sense and do not relate to the original measurement scale for the variables (which, for the accuracy variable, went from 0% to 100% accuracy).] Instead, we use the variance as a steppingstone for obtaining a measure of variability that we can clearly interpret, namely the standard deviation . However, you should know that variance is an important concept in its own right simply because it provides the statistical foundation for many of the correlational procedures and statistical inference procedures described in Chaps. 10.1007/978-981-15-2537-7_6 , 10.1007/978-981-15-2537-7_7 and 10.1007/978-981-15-2537-7_8.

When considering either correlations or tests of statistical hypotheses, we frequently speak of one variable explaining or sharing variance with another (see Procedure 10.1007/978-981-15-2537-7_6#Sec27 and 10.1007/978-981-15-2537-7_7#Sec47 ). In doing so, we are invoking the concept of variance as set out here—what we are saying is that variability in the behaviour of scores on one particular variable may be associated with or predictive of variability in scores on another variable of interest (e.g. it could explain why those scores have a non-zero variance).

Standard Deviation

The standard deviation (often abbreviated as SD, sd or Std. Dev.) is the most commonly reported measure of variability because it has a meaningful interpretation and is used in conjunction with reports of sample means. Variance and standard deviation are closely related measures in that the standard deviation is found by taking the square root of the variance. The standard deviation, very simply, is a summary number that reflects the ‘average distance of each score from the mean of the sample’. In many parametric statistical methods, both the sample mean and sample standard deviation are employed in some form. Thus, the standard deviation is a very important measure, not only for data description, but also for hypothesis testing and the establishment of relationships as well.

Referring again back to Table 5.4 , we’ll focus on the results for the speed variable for discussion purposes. Table 5.4 shows that the mean inspection speed for the QCI sample was 4.48 s. We can also see that the standard deviation (in the row labelled ‘Std Deviation’) for speed was 2.89 s.

This standard deviation has a straightforward interpretation: we would say that ‘on the average, an inspector’s quality inspection decision speed differed from the mean of the sample by about 2.89 s in either direction’. In a normal distribution of scores (see Fundamental Concept II ), we would expect to see about 68% of all inspectors having decision speeds between 1.59 s (the mean minus one amount of the standard deviation) and 7.37 s (the mean plus one amount of the standard deviation).

We noted earlier that the range of the speed scores was 16.05 s. However, the fact that the maximum speed score was 17.1 s compared to the 75th percentile score of just 5.71 s seems to suggest that this maximum speed might be rather atypically large compared to the bulk of speed scores. This means that the range is likely to be giving us a false impression of the overall variability of the inspectors’ decision speeds.

Furthermore, given that the mean speed score was higher than the median speed score, suggesting that speed scores were positively skewed (this was confirmed by the histogram for speed shown in Fig. 5.19 in Procedure 5.4 ), we might consider emphasising the median and its associated IQR or S-IQR rather than the mean and standard deviation. Of course, similar diagnostic and interpretive work could be done for each of the other four variables in Table 5.4 .

Measures of variability (particularly the standard deviation) provide a summary measure that gives an indication of how variable (spread out) a particular sample of scores is. When used in conjunction with a relevant measure of central tendency (particularly the mean), a reasonable yet economical description of a set of data emerges. When there are extreme data values or severe skewness is present in the data, the IQR (or S-IQR) becomes the preferred measure of variability to be reported in conjunction with the sample median (or 50th percentile value). These latter measures are much more resistant (‘robust’) to influence by data anomalies than are the mean and standard deviation.

As mentioned above, the range is a very cursory index of variability, thus, it is not as useful as variance or standard deviation. Variance has little meaningful interpretation as a descriptive index; hence, standard deviation is most often reported. However, the standard deviation (or IQR) has little meaning if the sample mean (or median) is not reported along with it.

Knowing that the standard deviation for accuracy is 9.17 tells you little unless you know the mean accuracy (82.14) that it is the standard deviation from.

Like the sample mean, the standard deviation can be strongly biased by the presence of extreme data values or severe skewness in a distribution in which case the median and IQR (or S-IQR) become the preferred measures. The biasing effect will be most noticeable in samples which are small in size (say, less than 30 individuals) and far less noticeable in large samples (say, in excess of 200 or 300 individuals). [Note that, in a manner similar to a trimmed mean, it is possible to compute a trimmed standard deviation to reduce the biasing effect of extreme data values, see Field 2018 , p. 263.]

It is important to realise that the resistance of the median and IQR (or S-IQR) to extreme values is only gained by deliberately sacrificing a good deal of the information available in the sample (nothing is obtained without a cost in statistics). What is sacrificed is information from all other members of the sample other than those members who scored at the median and 25th and 75th percentile points on a variable of interest; information from all members of the sample would automatically be incorporated in mean and standard deviation for that variable.

Any investigation where you might report on or read about measures of central tendency on certain variables should also report measures of variability. This is particularly true for data from experiments, quasi-experiments, observational studies and questionnaires. It is important to consider measures of central tendency and measures of variability to be inextricably linked—one should never report one without the other if an adequate descriptive summary of a variable is to be communicated.

Other descriptive measures, such as those for skewness and kurtosis 1 may also be of interest if a more complete description of any variable is desired. Most good statistical packages can be instructed to report these additional descriptive measures as well.

Of all the statistics you are likely to encounter in the business, behavioural and social science research literature, means and standard deviations will dominate as measures for describing data. Additionally, these statistics will usually be reported when any parametric tests of statistical hypotheses are presented as the mean and standard deviation provide an appropriate basis for summarising and evaluating group differences.

Fundamental Concept I: Basic Concepts in Probability

The concept of simple probability.

In Procedures 5.1 and 5.2 , you encountered the idea of the frequency of occurrence of specific events such as particular scores within a sample distribution. Furthermore, it is a simple operation to convert the frequency of occurrence of a specific event into a number representing the relative frequency of that event. The relative frequency of an observed event is merely the number of times the event is observed divided by the total number of times one makes an observation. The resulting number ranges between 0 and 1 but we typically re-express this number as a percentage by multiplying it by 100%.

In the QCI database, Maree Lakota observed data from 112 quality control inspectors of which 58 were male and 51 were female (gender indications were missing for three inspectors). The statistics 58 and 51 are thus the frequencies of occurrence for two specific types of research participant, a male inspector or a female inspector.

If she divided each frequency by the total number of observations (i.e. 112), whe would obtain .52 for males and .46 for females (leaving .02 of observations with unknown gender). These statistics are relative frequencies which indicate the proportion of times that Maree obtained data from a male or female inspector. Multiplying each relative frequency by 100% would yield 52% and 46% which she could interpret as indicating that 52% of her sample was male and 46% was female (leaving 2% of the sample with unknown gender).

It does not take much of a leap in logic to move from the concept of ‘relative frequency’ to the concept of ‘probability’. In our discussion above, we focused on relative frequency as indicating the proportion or percentage of times a specific category of participant was obtained in a sample. The emphasis here is on data from a sample.

Imagine now that Maree had infinite resources and research time and was able to obtain ever larger samples of quality control inspectors for her study. She could still compute the relative frequencies for obtaining data from males and females in her sample but as her sample size grew larger and larger, she would notice these relative frequencies converging toward some fixed values.

If, by some miracle, Maree could observe all of the quality control inspectors on the planet today, she would have measured the entire population and her computations of relative frequency for males and females would yield two precise numbers, each indicating the proportion of the population of inspectors that was male and the proportion that was female.

If Maree were then to list all of these inspectors and randomly choose one from the list, the chances that she would choose a male inspector would be equal to the proportion of the population of inspectors that was male and this logic extends to choosing a female inspector. The number used to quantify this notion of ‘chances’ is called a probability. Maree would therefore have established the probability of randomly observing a male or a female inspector in the population on any specific occasion.

Probability is expressed on a 0.0 (the observation or event will certainly not be seen) to 1.0 (the observation or event will certainly be seen) scale where values close to 0.0 indicate observations that are less certain to be seen and values close to 1.0 indicate observations that are more certain to be seen (a value of .5 indicates an even chance that an observation or event will or will not be seen – a state of maximum uncertainty). Statisticians often interpret a probability as the likelihood of observing an event or type of individual in the population.

In the QCI database, we noted that the relative frequency of observing males was .52 and for females was .46. If we take these relative frequencies as estimates of the proportions of each gender in the population of inspectors, then .52 and .46 represent the probability of observing a male or female inspector, respectively.

Statisticians would state this as “the probability of observing a male quality control inspector is .52” or in a more commonly used shorthand code, the likelihood of observing a male quality control inspector is p = .52 (p for probability). For some, probabilities make more sense if they are converted to percentages (by multiplying by 100%). Thus, p = .52 can also understood as a 52% chance of observing a male quality control inspector.

We have seen that relative frequency is a sample statistic that can be used to estimate the population probability. Our estimate will get more precise as we use larger and larger samples (technically, as the size of our samples more closely approximates the size of our population). In most behavioural research, we never have access to entire populations so we must always estimate our probabilities.

In some very special populations, having a known number of fixed possible outcomes, such as results of coin tosses or rolls of a die, we can analytically establish event probabilities without doing an infinite number of observations; all we must do is assume that we have a fair coin or die. Thus, with a fair coin, the probability of observing a H or a T on any single coin toss is ½ or .5 or 50%; the probability of observing a 6 on any single throw of a die is 1/6 or .16667 or 16.667%. With behavioural data, though, we can never measure all possible behavioural outcomes, which thereby forces researchers to depend on samples of observations in order to make estimates of population values.

The concept of probability is central to much of what is done in the statistical analysis of behavioural data. Whenever a behavioural scientist wishes to establish whether a particular relationship exists between variables or whether two groups, treated differently, actually show different behaviours, he/she is playing a probability game. Given a sample of observations, the behavioural scientist must decide whether what he/she has observed is providing sufficient information to conclude something about the population from which the sample was drawn.

This decision always has a non-zero probability of being in error simply because in samples that are much smaller than the population, there is always the chance or probability that we are observing something rare and atypical instead of something which is indicative of a consistent population trend. Thus, the concept of probability forms the cornerstone for statistical inference about which we will have more to say later (see Fundamental Concept 10.1007/978-981-15-2537-7_7#Sec6). Probability also plays an important role in helping us to understand theoretical statistical distributions (e.g. the normal distribution) and what they can tell us about our observations. We will explore this idea further in Fundamental Concept II .

The Concept of Conditional Probability

It is important to understand that the concept of probability as described above focuses upon the likelihood or chances of observing a specific event or type of observation for a specific variable relative to a population or sample of observations. However, many important behavioural research issues may focus on the question of the probability of observing a specific event given that the researcher has knowledge that some other event has occurred or been observed (this latter event is usually measured by a second variable). Here, the focus is on the potential relationship or link between two variables or two events.

With respect to the QCI database, Maree could ask the quite reasonable question “what is the probability (estimated in the QCI sample by a relative frequency) of observing an inspector being female given that she knows that an inspector works for a Large Business Computer manufacturer.

To address this question, all she needs to know is:

• how many inspectors from Large Business Computer manufacturers are in the sample ( 22 ); and
• how many of those inspectors were female ( 7 ) (inspectors who were missing a score for either company or gender have been ignored here).

If she divides 7 by 22, she would obtain the probability that an inspector is female given that they work for a Large Business Computer manufacturer – that is, p = .32 .

This type of question points to the important concept of conditional probability (‘conditional’ because we are asking “what is the probability of observing one event conditional upon our knowledge of some other event”).

Continuing with the previous example, Maree would say that the conditional probability of observing a female inspector working for a Large Business Computer manufacturer is .32 or, equivalently, a 32% chance. Compare this conditional probability of p  = .32 to the overall probability of observing a female inspector in the entire sample ( p  = .46 as shown above).

This means that there is evidence for a connection or relationship between gender and the type of company an inspector works for. That is, the chances are lower for observing a female inspector from a Large Business Computer manufacturer than they are for simply observing a female inspector at all.

Maree therefore has evidence suggesting that females may be relatively under-represented in Large Business Computer manufacturing companies compared to the overall population. Knowing something about the company an inspector works for therefore can help us make a better prediction about their likely gender.

Suppose, however, that Maree’s conditional probability had been exactly equal to p  = .46. This would mean that there was exactly the same chance of observing a female inspector working for a Large Business Computer manufacturer as there was of observing a female inspector in the general population. Here, knowing something about the company an inspector works doesn’t help Maree make any better prediction about their likely gender. This would mean that the two variables are statistically independent of each other.

A classic case of events that are statistically independent is two successive throws of a fair die: rolling a six on the first throw gives us no information for predicting how likely it will be that we would roll a six on the second throw. The conditional probability of observing a six on the second throw given that I have observed a six on the first throw is 0.16667 (= 1 divided by 6) which is the same as the simple probability of observing a six on any specific throw. This statistical independence also means that if we wanted to know what the probability of throwing two sixes on two successive throws of a fair die, we would just multiply the probabilities for each independent event (i.e., throw) together; that is, .16667 × .16667 = .02789 (this is known as the multiplication rule of probability, see, for example, Smithson 2000 , p. 114).

Finally, you should know that conditional probabilities are often asymmetric. This means that for many types of behavioural variables, reversing the conditional arrangement will change the story about the relationship. Bayesian statistics (see Fundamental Concept 10.1007/978-981-15-2537-7_7#Sec73) relies heavily upon this asymmetric relationship between conditional probabilities.

Maree has already learned that the conditional probability that an inspector is female given that they worked for a Large Business Computer manufacturer is p = .32. She could easily turn the conditional relationship around and ask what is the conditional probability that an inspector works for a Large Business Computer manufacturer given that the inspector is female?

From the QCI database, she can find that 51 inspectors in her total sample were female and of those 51, 7 worked for a Large Business Computer manufacturer. If she divided 7 by 51, she would get p = .14 (did you notice that all that changed was the number she divided by?). Thus, there is only a 14% chance of observing an inspector working for a Large Business Computer manufacturer given that the inspector is female – a rather different probability from p = .32, which tells a different story.

As you will see in Procedures 10.1007/978-981-15-2537-7_6#Sec14 and 10.1007/978-981-15-2537-7_7#Sec17, conditional relationships between categorical variables are precisely what crosstabulation contingency tables are designed to reveal.

Procedure 5.6: Exploratory Data Analysis

There are a variety of visual display methods for EDA, including stem & leaf displays, boxplots and violin plots. Each method reflects a specific way of displaying features of a distribution of scores or measurements and, of course, each has its own advantages and disadvantages. In addition, EDA displays are surprisingly flexible and can combine features in various ways to enhance the story conveyed by the plot.

Stem & Leaf Displays

The stem & leaf display is a simple data summary technique which not only rank orders the data points in a sample but presents them visually so that the shape of the data distribution is reflected. Stem & leaf displays are formed from data scores by splitting each score into two parts: the first part of each score serving as the ‘stem’, the second part as the ‘leaf’ (e.g. for 2-digit data values, the ‘stem’ is the number in the tens position; the ‘leaf’ is the number in the ones position). Each stem is then listed vertically, in ascending order, followed horizontally by all the leaves in ascending order associated with it. The resulting display thus shows all of the scores in the sample, but reorganised so that a rough idea of the shape of the distribution emerges. As well, extreme scores can be easily identified in a stem & leaf display.

Consider the accuracy and speed scores for the 112 quality control inspectors in the QCI sample. Figure 5.22 (produced by the R Commander Stem-and-leaf display … procedure) shows the stem & leaf displays for inspection accuracy (left display) and speed (right display) data.

Stem & leaf displays produced by R Commander

[The first six lines reflect information from R Commander about each display: lines 1 and 2 show the actual R command used to produce the plot (the variable name has been highlighted in bold); line 3 gives a warning indicating that inspectors with missing values (= NA in R ) on the variable have been omitted from the display; line 4 shows how the stems and leaves have been defined; line 5 indicates what a leaf unit represents in value; and line 6 indicates the total number (n) of inspectors included in the display).] In Fig. 5.22 , for the accuracy display on the left-hand side, the ‘stems’ have been split into ‘half-stems’—one (which is starred) associated with the ‘leaves’ 0 through 4 and the other associated with the ‘leaves’ 5 through 9—a strategy that gives the display better balance and visual appeal.

Notice how the left stem & leaf display conveys a fairly clear (yet sideways) picture of the shape of the distribution of accuracy scores. It has a rather symmetrical bell-shape to it with only a slight suggestion of negative skewness (toward the extreme score at the top). The right stem & leaf display clearly depicts the highly positively skewed nature of the distribution of speed scores. Importantly, we could reconstruct the entire sample of scores for each variable using its display, which means that unlike most other graphical procedures, we didn’t have to sacrifice any information to produce the visual summary.

Some programs, such as SYSTAT, embellish their stem & leaf displays by indicating in which stem or half-stem the ‘median’ (50th percentile), the ‘upper hinge score’ (75th percentile), and ‘lower hinge score’ (25th percentile) occur in the distribution (recall the discussion of interquartile range in Procedure 5.5 ). This is shown in Fig. 5.23 , produced by SYSTAT, where M and H indicate the stem locations for the median and hinge points, respectively. This stem & leaf display labels a single extreme accuracy score as an ‘outside value’ and clearly shows that this actual score was 57.

Stem & leaf display, produced by SYSTAT, of the accuracy QCI variable

Another important EDA technique is the boxplot or, as it is sometimes known, the box-and-whisker plot . This plot provides a symbolic representation that preserves less of the original nature of the data (compared to a stem & leaf display) but typically gives a better picture of the distributional characteristics. The basic boxplot, shown in Fig. 5.24 , utilises information about the median (50th percentile score) and the upper (75th percentile score) and lower (25th percentile score) hinge points in the construction of the ‘box’ portion of the graph (the ‘median’ defines the centre line in the box; the ‘upper’ and ‘lower hinge values’ define the end boundaries of the box—thus the box encompasses the middle 50% of data values).

Boxplots for the accuracy and speed QCI variables

Additionally, the boxplot utilises the IQR (recall Procedure 5.5 ) as a way of defining what are called ‘fences’ which are used to indicate score boundaries beyond which we would consider a score in a distribution to be an ‘outlier’ (or an extreme or unusual value). In SPSS, the inner fence is typically defined as 1.5 times the IQR in each direction and a ‘far’ outlier or extreme case is typically defined as 3 times the IQR in either direction (Field 2018 , p. 193). The ‘whiskers’ in a boxplot extend out to the data values which are closest to the upper and lower inner fences (in most cases, the vast majority of data values will be contained within the fences). Outliers beyond these ‘whiskers’ are then individually listed. ‘Near’ outliers are those lying just beyond the inner fences and ‘far’ outliers lie well beyond the inner fences.

Figure 5.24 shows two simple boxplots (produced using SPSS), one for the accuracy QCI variable and one for the speed QCI variable. The accuracy plot shows a median value of about 83, roughly 50% of the data fall between about 77 and 89 and there is one outlier, inspector 83, in the lower ‘tail’ of the distribution. The accuracy boxplot illustrates data that are relatively symmetrically distributed without substantial skewness. Such data will tend to have their median in the middle of the box, whiskers of roughly equal length extending out from the box and few or no outliers.

The speed plot shows a median value of about 4 s, roughly 50% of the data fall between 2 s and 6 s and there are four outliers, inspectors 7, 62, 65 and 75 (although inspectors 65 and 75 fall at the same place and are rather difficult to read), all falling in the slow speed ‘tail’ of the distribution. Inspectors 65, 75 and 7 are shown as ‘near’ outliers (open circles) whereas inspector 62 is shown as a ‘far’ outlier (asterisk). The speed boxplot illustrates data which are asymmetrically distributed because of skewness in one direction. Such data may have their median offset from the middle of the box and/or whiskers of unequal length extending out from the box and outliers in the direction of the longer whisker. In the speed boxplot, the data are clearly positively skewed (the longer whisker and extreme values are in the slow speed ‘tail’).

Boxplots are very versatile representations in that side-by-side displays for sub-groups of data within a sample can permit easy visual comparisons of groups with respect to central tendency and variability. Boxplots can also be modified to incorporate information about error bands associated with the median producing what is called a ‘notched boxplot’. This helps in the visual detection of meaningful subgroup differences, where boxplot ‘notches’ don’t overlap.

Figure 5.25 (produced using NCSS), compares the distributions of accuracy and speed scores for QCI inspectors from the five types of companies, plotted side-by-side.

Comparisons of the accuracy (regular boxplots) and speed (notched boxplots) QCI variables for different types of companies

Focus first on the left graph in Fig. 5.25 which plots the distribution of accuracy scores broken down by company using regular boxplots. This plot clearly shows the differing degree of skewness in each type of company (indicated by one or more outliers in one ‘tail’, whiskers which are not the same length and/or the median line being offset from the centre of a box), the differing variability of scores within each type of company (indicated by the overall length of each plot—box and whiskers), and the differing central tendency in each type of company (the median lines do not all fall at the same level of accuracy score). From the left graph in Fig. 5.25 , we could conclude that: inspection accuracy scores are most variable in PC and Large Electrical Appliance manufacturing companies and least variable in the Large Business Computer manufacturing companies; Large Business Computer and PC manufacturing companies have the highest median level of inspection accuracy; and inspection accuracy scores tend to be negatively skewed (many inspectors toward higher levels, relatively fewer who are poorer in inspection performance) in the Automotive manufacturing companies. One inspector, working for an Automotive manufacturing company, shows extremely poor inspection accuracy performance.

The right display compares types of companies in terms of their inspection speed scores, using’ notched’ boxplots. The notches define upper and lower error limits around each median. Aside from the very obvious positive skewness for speed scores (with a number of slow speed outliers) in every type of company (least so for Large Electrical Appliance manufacturing companies), the story conveyed by this comparison is that inspectors from Large Electrical Appliance and Automotive manufacturing companies have substantially faster median decision speeds compared to inspectors from Large Business Computer and PC manufacturing companies (i.e. their ‘notches’ do not overlap, in terms of speed scores, on the display).

Boxplots can also add interpretive value to other graphical display methods through the creation of hybrid displays. Such displays might combine a standard histogram with a boxplot along the X-axis to provide an enhanced picture of the data distribution as illustrated for the mentabil variable in Fig. 5.26 (produced using NCSS). This hybrid plot also employs a data ‘smoothing’ method called a density trace to outline an approximate overall shape for the data distribution. Any one graphical method would tell some of the story, but combined in the hybrid display, the story of a relatively symmetrical set of mentabil scores becomes quite visually compelling.

A hybrid histogram-density-boxplot of the mentabil QCI variable

Violin Plots

Violin plots are a more recent and interesting EDA innovation, implemented in the NCSS software package (Hintze 2012 ). The violin plot gets its name from the rough shape that the plots tend to take on. Violin plots are another type of hybrid plot, this time combining density traces (mirror-imaged right and left so that the plots have a sense of symmetry and visual balance) with boxplot-type information (median, IQR and upper and lower inner ‘fences’, but not outliers). The goal of the violin plot is to provide a quick visual impression of the shape, central tendency and variability of a distribution (the length of the violin conveys a sense of the overall variability whereas the width of the violin conveys a sense of the frequency of scores occurring in a specific region).

Figure 5.27 (produced using NCSS), compares the distributions of speed scores for QCI inspectors across the five types of companies, plotted side-by-side. The violin plot conveys a similar story to the boxplot comparison for speed in the right graph of Fig. 5.25 . However, notice that with the violin plot, unlike with a boxplot, you also get a sense of distributions that have ‘clumps’ of scores in specific areas. Some violin plots, like that for Automobile manufacturing companies in Fig. 5.27 , have a shape suggesting a multi-modal distribution (recall Procedure 5.4 and the discussion of the fact that a distribution may have multiple modes). The violin plot in Fig. 5.27 has also been produced to show where the median (solid line) and mean (dashed line) would fall within each violin. This facilitates two interpretations: (1) a relative comparison of central tendency across the five companies and (2) relative degree of skewness in the distribution for each company (indicated by the separation of the two lines within a violin; skewness is particularly bad for the Large Business Computer manufacturing companies).

Violin plot comparisons of the speed QCI variable for different types of companies

EDA methods (of which we have illustrated only a small subset; we have not reviewed dot density diagrams, for example) provide summary techniques for visually displaying certain characteristics of a set of data. The advantage of the EDA methods over more traditional graphing techniques such as those described in Procedure 5.2 is that as much of the original integrity of the data is maintained as possible while maximising the amount of summary information available about distributional characteristics.

Stem & leaf displays maintain the data in as close to their original form as possible whereas boxplots and violin plots provide more symbolic and flexible representations. EDA methods are best thought of as communication devices designed to facilitate quick visual impressions and they can add interest to any statistical story being conveyed about a sample of data. NCSS, SYSTAT, STATGRAPHICS and R Commander generally offer more options and flexibility in the generation of EDA displays than SPSS.

EDA methods tend to get cumbersome if a great many variables or groups need to be summarised. In such cases, using numerical summary statistics (such as means and standard deviations) will provide a more economical and efficient summary. Boxplots or violin plots are generally more space efficient summary techniques than stem & leaf displays.

Often, EDA techniques are used as data screening devices, which are typically not reported in actual write-ups of research (we will discuss data screening in more detail in Procedure 10.1007/978-981-15-2537-7_8#Sec11). This is a perfectly legitimate use for the methods although there is an argument for researchers to put these techniques to greater use in published literature.

Software packages may use different rules for constructing EDA plots which means that you might get rather different looking plots and different information from different programs (you saw some evidence of this in Figs. 5.22 and 5.23 ). It is important to understand what the programs are using as decision rules for locating fences and outliers so that you are clear on how best to interpret the resulting plot—such information is generally contained in the user’s guides or manuals for NCSS (Hintze 2012 ), SYSTAT (SYSTAT Inc. 2009a , b ), STATGRAPHICS (StatPoint Technologies Inc. 2010 ) and SPSS (Norušis 2012 ).

Virtually any research design which produces numerical measures (even to the extent of just counting the number of occurrences of several events) provides opportunities for employing EDA displays which may help to clarify data characteristics or relationships. One extremely important use of EDA methods is as data screening devices for detecting outliers and other data anomalies, such as non-normality and skewness, before proceeding to parametric statistical analyses. In some cases, EDA methods can help the researcher to decide whether parametric or nonparametric statistical tests would be best to apply to his or her data because critical data characteristics such as distributional shape and spread are directly reflected.

Procedure 5.7: Standard ( z ) Scores

In certain practical situations in behavioural research, it may be desirable to know where a specific individual’s score lies relative to all other scores in a distribution. A convenient measure is to observe how many standard deviations (see Procedure 5.5 ) above or below the sample mean a specific score lies. This measure is called a standard score or z -score . Very simply, any raw score can be converted to a z -score by subtracting the sample mean from the raw score and dividing that result by the sample’s standard deviation. z -scores can be positive or negative and their sign simply indicates whether the score lies above (+) or below (−) the mean in value. A z -score has a very simple interpretation: it measures the number of standard deviations above or below the sample mean a specific raw score lies.

In the QCI database, we have a sample mean for speed scores of 4.48 s, a standard deviation for speed scores of 2.89 s (recall Table 5.4 in Procedure 5.5 ). If we are interested in the z -score for Inspector 65’s raw speed score of 11.94 s, we would obtain a z -score of +2.58 using the method described above (subtract 4.48 from 11.94 and divide the result by 2.89). The interpretation of this number is that a raw decision speed score of 11.94 s lies about 2.9 standard deviations above the mean decision speed for the sample.

z -scores have some interesting properties. First, if one converts (statisticians would say ‘transforms’) every available raw score in a sample to z -scores, the mean of these z -scores will always be zero and the standard deviation of these z -scores will always be 1.0. These two facts about z -scores (mean = 0; standard deviation = 1) will be true no matter what sample you are dealing with and no matter what the original units of measurement are (e.g. seconds, percentages, number of widgets assembled, amount of preference for a product, attitude rating, amount of money spent). This is because transforming raw scores to z -scores automatically changes the measurement units from whatever they originally were to a new system of measurements expressed in standard deviation units.

Suppose Maree was interested in the performance statistics for the top 25% most accurate quality control inspectors in the sample. Given a sample size of 112, this would mean finding the top 28 inspectors in terms of their accuracy scores. Since Maree is interested in performance statistics, speed scores would also be of interest. Table 5.5 (generated using the SPSS Descriptives … procedure, listed using the Case Summaries … procedure and formatted for presentation using Excel) shows accuracy and speed scores for the top 28 inspectors in descending order of accuracy scores. The z -score transformation for each of these scores is also shown (last two columns) as are the type of company, education level and gender for each inspector.

Listing of the 28 (top 25%) most accurate QCI inspectors’ accuracy and speed scores as well as standard ( z ) score transformations for each score

There are three inspectors (8, 9 and 14) who scored maximum accuracy of 100%. Such accuracy converts to a z -score of +1.95. Thus 100% accuracy is 1.95 standard deviations above the sample’s mean accuracy level. Interestingly, all three inspectors worked for PC manufacturers and all three had only high school-level education. The least accurate inspector in the top 25% had a z -score for accuracy that was .75 standard deviations above the sample mean.

Interestingly, the top three inspectors in terms of accuracy had decision speeds that fell below the sample’s mean speed; inspector 8 was the fastest inspector of the three with a speed just over 1 standard deviation ( z  = −1.03) below the sample mean. The slowest inspector in the top 25% was inspector 75 (case #28 in the list) with a speed z -score of +2.62; i.e., he was over two and a half standard deviations slower in making inspection decisions relative to the sample’s mean speed.

The fact that z -scores always have a common measurement scale having a mean of 0 and a standard deviation of 1.0 leads to an interesting application of standard scores. Suppose we focus on inspector number 65 (case #8 in the list) in Table 5.5 . It might be of interest to compare this inspector’s quality control performance in terms of both his decision accuracy and decision speed. Such a comparison is impossible using raw scores since the inspector’s accuracy score and speed scores are different measures which have differing means and standard deviations expressed in fundamentally different units of measurement (percentages and seconds). However, if we are willing to assume that the score distributions for both variables are approximately the same shape and that both accuracy and speed are measured with about the same level of reliability or consistency (see Procedure 10.1007/978-981-15-2537-7_8#Sec1), we can compare the inspector’s two scores by first converting them to z -scores within their own respective distributions as shown in Table 5.5 .

Inspector 65 looks rather anomalous in that he demonstrated a relatively high level of accuracy (raw score = 94%; z  = +1.29) but took a very long time to make those accurate decisions (raw score = 11.94 s; z  = +2.58). Contrast this with inspector 106 (case #17 in the list) who demonstrated a similar level of accuracy (raw score = 92%; z  = +1.08) but took a much shorter time to make those accurate decisions (raw score = 1.70 s; z  = −.96). In terms of evaluating performance, from a company perspective, we might conclude that inspector 106 is performing at an overall higher level than inspector 65 because he can achieve a very high level of accuracy but much more quickly; accurate and fast is more cost effective and efficient than accurate and slow.

Note: We should be cautious here since we know from our previous explorations of the speed variable in Procedure 5.6 , that accuracy scores look fairly symmetrical and speed scores are positively skewed, so assuming that the two variables have the same distribution shape, so that z -score comparisons are permitted, would be problematic.

You might have noticed that as you scanned down the two columns of z -scores in Table 5.5 , there was a suggestion of a pattern between the signs attached to the respective z -scores for each person. There seems to be a very slight preponderance of pairs of z -scores where the signs are reversed (12 out of 22 pairs). This observation provides some very preliminary evidence to suggest that there may be a relationship between inspection accuracy and decision speed, namely that a more accurate decision tends to be associated with a faster decision speed. Of course, this pattern would be better verified using the entire sample rather than the top 25% of inspectors. However, you may find it interesting to learn that it is precisely this sort of suggestive evidence (about agreement or disagreement between z -score signs for pairs of variable scores throughout a sample) that is captured and summarised by a single statistical indicator called a ‘correlation coefficient’ (see Fundamental Concept 10.1007/978-981-15-2537-7_6#Sec1 and Procedure 10.1007/978-981-15-2537-7_6#Sec4).

z -scores are not the only type of standard score that is commonly used. Three other types of standard scores are: stanines (standard nines), IQ scores and T-scores (not to be confused with the t -test described in Procedure 10.1007/978-981-15-2537-7_7#Sec22). These other types of scores have the advantage of producing only positive integer scores rather than positive and negative decimal scores. This makes interpretation somewhat easier for certain applications. However, you should know that almost all other types of standard scores come from a specific transformation of z -scores. This is because once you have converted raw scores into z -scores, they can then be quite readily transformed into any other system of measurement by simply multiplying a person’s z -score by the new desired standard deviation for the measure and adding to that product the new desired mean for the measure.

T-scores are simply z-scores transformed to have a mean of 50.0 and a standard deviation of 10.0; IQ scores are simply z-scores transformed to have a mean of 100 and a standard deviation of 15 (or 16 in some systems). For more information, see Fundamental Concept II .

Standard scores are useful for representing the position of each raw score within a sample distribution relative to the mean of that distribution. The unit of measurement becomes the number of standard deviations a specific score is away from the sample mean. As such, z -scores can permit cautious comparisons across samples or across different variables having vastly differing means and standard deviations within the constraints of the comparison samples having similarly shaped distributions and roughly equivalent levels of measurement reliability. z -scores also form the basis for establishing the degree of correlation between two variables. Transforming raw scores into z -scores does not change the shape of a distribution or rank ordering of individuals within that distribution. For this reason, a z -score is referred to as a linear transformation of a raw score. Interestingly, z -scores provide an important foundational element for more complex analytical procedures such as factor analysis ( Procedure 10.1007/978-981-15-2537-7_6#Sec36), cluster analysis ( Procedure 10.1007/978-981-15-2537-7_6#Sec41) and multiple regression analysis (see, for example, Procedure 10.1007/978-981-15-2537-7_6#Sec27 and 10.1007/978-981-15-2537-7_7#Sec86).

While standard scores are useful indices, they are subject to restrictions if used to compare scores across samples or across different variables. The samples must have similar distribution shapes for the comparisons to be meaningful and the measures must have similar levels of reliability in each sample. The groups used to generate the z -scores should also be similar in composition (with respect to age, gender distribution, and so on). Because z -scores are not an intuitively meaningful way of presenting scores to lay-persons, many other types of standard score schemes have been devised to improve interpretability. However, most of these schemes produce scores that run a greater risk of facilitating lay-person misinterpretations simply because their connection with z -scores is hidden or because the resulting numbers ‘look’ like a more familiar type of score which people do intuitively understand.

It is extremely rare for a T-score to exceed 100 or go below 0 because this would mean that the raw score was in excess of 5 standard deviations away from the sample mean. This unfortunately means that T-scores are often misinterpreted as percentages because they typically range between 0 and 100 and therefore ‘look’ like percentages. However, T-scores are definitely not percentages.

Finally, a common misunderstanding of z -scores is that transforming raw scores into z -scores makes them follow a normal distribution (see Fundamental Concept II ). This is not the case. The distribution of z -scores will have exactly the same shape as that for the raw scores; if the raw scores are positively skewed, then the corresponding z -scores will also be positively skewed.

z -scores are particularly useful in evaluative studies where relative performance indices are of interest. Whenever you compute a correlation coefficient ( Procedure 10.1007/978-981-15-2537-7_6#Sec4), you are implicitly transforming the two variables involved into z -scores (which equates the variables in terms of mean and standard deviation), so that only the patterning in the relationship between the variables is represented. z -scores are also useful as a preliminary step to more advanced parametric statistical methods when variables differing in scale, range and/or measurement units must be equated for means and standard deviations prior to analysis.

Fundamental Concept II: The Normal Distribution

Arguably the most fundamental distribution used in the statistical analysis of quantitative data in the behavioural and social sciences is the normal distribution (also known as the Gaussian or bell-shaped distribution ). Many behavioural phenomena, if measured on a large enough sample of people, tend to produce ‘normally distributed’ variable scores. This includes most measures of ability, performance and productivity, personality characteristics and attitudes. The normal distribution is important because it is the one form of distribution that you must assume describes the scores of a variable in the population when parametric tests of statistical inference are undertaken. The standard normal distribution is defined as having a population mean of 0.0 and a population standard deviation of 1.0. The normal distribution is also important as a means of interpreting various types of scoring systems.

Figure 5.28 displays the standard normal distribution (mean = 0; standard deviation = 1.0) and shows that there is a clear link between z -scores and the normal distribution. Statisticians have analytically calculated the probability (also expressed as percentages or percentiles) that observations will fall above or below any specific z -score in the theoretical standard normal distribution. Thus, a z -score of +1.0 in the standard normal distribution will have 84.13% (equals a probability of .8413) of observations in the population falling at or below one standard deviation above the mean and 15.87% falling above that point. A z -score of −2.0 will have 2.28% of observations falling at that point or below and 97.72% of observations falling above that point. It is clear then that, in a standard normal distribution, z -scores have a direct relationship with percentiles .

The normal (bell-shaped or Gaussian) distribution

Figure 5.28 also shows how T-scores relate to the standard normal distribution and to z -scores. The mean T-score falls at 50 and each increment or decrement of 10 T-score units means a movement of another standard deviation away from this mean of 50. Thus, a T-score of 80 corresponds to a z -score of +3.0—a score 3 standard deviations higher than the mean of 50.

Of special interest to behavioural researchers are the values for z -scores in a standard normal distribution that encompass 90% of observations ( z  = ±1.645—isolating 5% of the distribution in each tail), 95% of observations ( z  = ±1.96—isolating 2.5% of the distribution in each tail), and 99% of observations ( z  = ±2.58—isolating 0.5% of the distribution in each tail).

Depending upon the degree of certainty required by the researcher, these bands describe regions outside of which one might define an observation as being atypical or as perhaps not belonging to a distribution being centred at a mean of 0.0. Most often, what is taken as atypical or rare in the standard normal distribution is a score at least two standard deviations away from the mean, in either direction. Why choose two standard deviations? Since in the standard normal distribution, only about 5% of observations will fall outside a band defined by z -scores of ±1.96 (rounded to 2 for simplicity), this equates to data values that are 2 standard deviations away from their mean. This can give us a defensible way to identify outliers or extreme values in a distribution.

Thinking ahead to what you will encounter in Chap. 10.1007/978-981-15-2537-7_7, this ‘banding’ logic can be extended into the world of statistics (like means and percentages) as opposed to just the world of observations. You will frequently hear researchers speak of some statistic estimating a specific value (a parameter ) in a population, plus or minus some other value.

A survey organisation might report political polling results in terms of a percentage and an error band, e.g. 59% of Australians indicated that they would vote Labour at the next federal election, plus or minus 2%.

Most commonly, this error band (±2%) is defined by possible values for the population parameter that are about two standard deviations (or two standard errors—a concept discussed further in Fundamental Concept 10.1007/978-981-15-2537-7_7#Sec14) away from the reported or estimated statistical value. In effect, the researcher is saying that on 95% of the occasions he/she would theoretically conduct his/her study, the population value estimated by the statistic being reported would fall between the limits imposed by the endpoints of the error band (the official name for this error band is a confidence interval ; see Procedure 10.1007/978-981-15-2537-7_8#Sec18). The well-understood mathematical properties of the standard normal distribution are what make such precise statements about levels of error in statistical estimates possible.

Checking for Normality

It is important to understand that transforming the raw scores for a variable to z -scores (recall Procedure 5.7 ) does not produce z -scores which follow a normal distribution; rather they will have the same distributional shape as the original scores. However, if you are willing to assume that the normal distribution is the correct reference distribution in the population, then you are justified is interpreting z -scores in light of the known characteristics of the normal distribution.

In order to justify this assumption, not only to enhance the interpretability of z -scores but more generally to enhance the integrity of parametric statistical analyses, it is helpful to actually look at the sample frequency distributions for variables (using a histogram (illustrated in Procedure 5.2 ) or a boxplot (illustrated in Procedure 5.6 ), for example), since non-normality can often be visually detected. It is important to note that in the social and behavioural sciences as well as in economics and finance, certain variables tend to be non-normal by their very nature. This includes variables that measure time taken to complete a task, achieve a goal or make decisions and variables that measure, for example, income, occurrence of rare or extreme events or organisational size. Such variables tend to be positively skewed in the population, a pattern that can often be confirmed by graphing the distribution.

If you cannot justify an assumption of ‘normality’, you may be able to force the data to be normally distributed by using what is called a ‘normalising transformation’. Such transformations will usually involve a nonlinear mathematical conversion (such as computing the logarithm, square root or reciprocal) of the raw scores. Such transformations will force the data to take on a more normal appearance so that the assumption of ‘normality’ can be reasonably justified, but at the cost of creating a new variable whose units of measurement and interpretation are more complicated. [For some non-normal variables, such as the occurrence of rare, extreme or catastrophic events (e.g. a 100-year flood or forest fire, coronavirus pandemic, the Global Financial Crisis or other type of financial crisis, man-made or natural disaster), the distributions cannot be ‘normalised’. In such cases, the researcher needs to model the distribution as it stands. For such events, extreme value theory (e.g. see Diebold et al. 2000 ) has proven very useful in recent years. This theory uses a variation of the Pareto or Weibull distribution as a reference, rather than the normal distribution, when making predictions.]

Figure 5.29 displays before and after pictures of the effects of a logarithmic transformation on the positively skewed speed variable from the QCI database. Each graph, produced using NCSS, is of the hybrid histogram-density trace-boxplot type first illustrated in Procedure 5.6 . The left graph clearly shows the strong positive skew in the speed scores and the right graph shows the result of taking the log 10 of each raw score.

Combined histogram-density trace-boxplot graphs displaying the before and after effects of a ‘normalising’ log 10 transformation of the speed variable

Notice how the long tail toward slow speed scores is pulled in toward the mean and the very short tail toward fast speed scores is extended away from the mean. The result is a more ‘normal’ appearing distribution. The assumption would then be that we could assume normality of speed scores, but only in a log 10 format (i.e. it is the log of speed scores that we assume is normally distributed in the population). In general, taking the logarithm of raw scores provides a satisfactory remedy for positively skewed distributions (but not for negatively skewed ones). Furthermore, anything we do with the transformed speed scores now has to be interpreted in units of log 10 (seconds) which is a more complex interpretation to make.

Another visual method for detecting non-normality is to graph what is called a normal Q-Q plot (the Q-Q stands for Quantile-Quantile). This plots the percentiles for the observed data against the percentiles for the standard normal distribution (see Cleveland 1995 for more detailed discussion; also see Lane 2007 , http://onlinestatbook.com/2/advanced_graphs/ q-q_plots.html) . If the pattern for the observed data follows a normal distribution, then all the points on the graph will fall approximately along a diagonal line.

Figure 5.30 shows the normal Q-Q plots for the original speed variable and the transformed log-speed variable, produced using the SPSS Explore... procedure. The diagnostic diagonal line is shown on each graph. In the left-hand plot, for speed , the plot points clearly deviate from the diagonal in a way that signals positive skewness. The right-hand plot, for log_speed, shows the plot points generally falling along the diagonal line thereby conforming much more closely to what is expected in a normal distribution.

Normal Q-Q plots for the original speed variable and the new log_speed variable

In addition to visual ways of detecting non-normality, there are also numerical ways. As highlighted in Chap. 10.1007/978-981-15-2537-7_1, there are two additional characteristics of any distribution, namely skewness (asymmetric distribution tails) and kurtosis (peakedness of the distribution). Both have an associated statistic that provides a measure of that characteristic, similar to the mean and standard deviation statistics. In a normal distribution, the values for the skewness and kurtosis statistics are both zero (skewness = 0 means a symmetric distribution; kurtosis = 0 means a mesokurtic distribution). The further away each statistic is from zero, the more the distribution deviates from a normal shape. Both the skewness statistic and the kurtosis statistic have standard errors (see Fundamental Concept 10.1007/978-981-15-2537-7_7#Sec14) associated with them (which work very much like the standard deviation, only for a statistic rather than for observations); these can be routinely computed by almost any statistical package when you request a descriptive analysis. Without going into the logic right now (this will come in Fundamental Concept 10.1007/978-981-15-2537-7_7#Sec1), a rough rule of thumb you can use to check for normality using the skewness and kurtosis statistics is to do the following:

• Prepare : Take the standard error for the statistic and multiply it by 2 (or 3 if you want to be more conservative).
• Interval : Add the result from the Prepare step to the value of the statistic and subtract the result from the value of the statistic. You will end up with two numbers, one low - one high, that define the ends of an interval (what you have just created approximates what is called a ‘confidence interval’, see Procedure 10.1007/978-981-15-2537-7_8#Sec18).
• Check : If zero falls inside of this interval (i.e. between the low and high endpoints from the Interval step), then there is likely to be no significant issue with that characteristic of the distribution. If zero falls outside of the interval (i.e. lower than the low value endpoint or higher than the high value endpoint), then you likely have an issue with non-normality with respect to that characteristic.

Visually, we saw in the left graph in Fig. 5.29 that the speed variable was highly positively skewed. What if Maree wanted to check some numbers to support this judgment? She could ask SPSS to produce the skewness and kurtosis statistics for both the original speed variable and the new log_speed variable using the Frequencies... or the Explore... procedure. Table 5.6 shows what SPSS would produce if the Frequencies ... procedure were used.

Skewness and kurtosis statistics and their standard errors for both the original speed variable and the new log_speed variable

Using the 3-step check rule described above, Maree could roughly evaluate the normality of the two variables as follows:

• skewness : [Prepare] 2 × .229 = .458 ➔ [Interval] 1.487 − .458 = 1.029 and 1.487 + .458 = 1.945 ➔ [Check] zero does not fall inside the interval bounded by 1.029 and 1.945, so there appears to be a significant problem with skewness. Since the value for the skewness statistic (1.487) is positive, this means the problem is positive skewness, confirming what the left graph in Fig. 5.29 showed.
• kurtosis : [Prepare] 2 × .455 = .91 ➔ [Interval] 3.071 − .91 = 2.161 and 3.071 + .91 = 3.981 ➔ [Check] zero does not fall in interval bounded by 2.161 and 3.981, so there appears to be a significant problem with kurtosis. Since the value for the kurtosis statistic (1.487) is positive, this means the problem is leptokurtosis—the peakedness of the distribution is too tall relative to what is expected in a normal distribution.
• skewness : [Prepare] 2 × .229 = .458 ➔ [Interval] −.050 − .458 = −.508 and −.050 + .458 = .408 ➔ [Check] zero falls within interval bounded by −.508 and .408, so there appears to be no problem with skewness. The log transform appears to have corrected the problem, confirming what the right graph in Fig. 5.29 showed.
• kurtosis : [Prepare] 2 × .455 = .91 ➔ [Interval] −.672 – .91 = −1.582 and −.672 + .91 = .238 ➔ [Check] zero falls within interval bounded by −1.582 and .238, so there appears to be no problem with kurtosis. The log transform appears to have corrected this problem as well, rendering the distribution more approximately mesokurtic (i.e. normal) in shape.

There are also more formal tests of significance (see Fundamental Concept 10.1007/978-981-15-2537-7_7#Sec1) that one can use to numerically evaluate normality, such as the Kolmogorov-Smirnov test and the Shapiro-Wilk’s test . Each of these tests, for example, can be produced by SPSS on request, via the Explore... procedure.

1 For more information, see Chap. 10.1007/978-981-15-2537-7_1 – The language of statistics .

References for Procedure 5.1

• Allen P, Bennett K, Heritage B. SPSS statistics: A practical guide. 4. South Melbourne, VIC: Cengage Learning Australia Pty; 2019. [ Google Scholar ]
• George D, Mallery P. IBM SPSS statistics 25 step by step: A simple guide and reference. 15. New York: Routledge; 2019. [ Google Scholar ]

Useful Additional Readings for Procedure 5.1

• Agresti A. Statistical methods for the social sciences. 5. Boston: Pearson; 2018. [ Google Scholar ]
• Argyrous G. Statistics for research: With a guide to SPSS. 3. London: Sage; 2011. [ Google Scholar ]
• De Vaus D. Analyzing social science data: 50 key problems in data analysis. London: Sage; 2002. [ Google Scholar ]
• Glass GV, Hopkins KD. Statistical methods in education and psychology. 3. Upper Saddle River, NJ: Pearson; 1996. [ Google Scholar ]
• Gravetter FJ, Wallnau LB. Statistics for the behavioural sciences. 10. Belmont, CA: Wadsworth Cengage; 2017. [ Google Scholar ]
• Steinberg WJ. Statistics alive. 2. Los Angeles: Sage; 2011. [ Google Scholar ]

References for Procedure 5.2

• Chang W. R graphics cookbook: Practical recipes for visualizing data. 2. Sebastopol, CA: O’Reilly Media; 2019. [ Google Scholar ]
• Jacoby WG. Statistical graphics for univariate and bivariate data. Thousand Oaks, CA: Sage; 1997. [ Google Scholar ]
• McCandless D. Knowledge is beautiful. London: William Collins; 2014. [ Google Scholar ]
• Smithson MJ. Statistics with confidence. London: Sage; 2000. [ Google Scholar ]
• Toseland M, Toseland S. Infographica: The world as you have never seen it before. London: Quercus Books; 2012. [ Google Scholar ]
• Wilkinson L. Cognitive science and graphic design. In: SYSTAT Software Inc, editor. SYSTAT 13: Graphics. Chicago, IL: SYSTAT Software Inc; 2009. pp. 1–21. [ Google Scholar ]

Useful Additional Readings for Procedure 5.2

• Field A. Discovering statistics using SPSS for windows. 5. Los Angeles: Sage; 2018. [ Google Scholar ]
• George D, Mallery P. IBM SPSS statistics 25 step by step: A simple guide and reference. 15. Boston, MA: Pearson Education; 2019. [ Google Scholar ]
• Hintze JL. NCSS 8 help system: Graphics. Kaysville, UT: Number Cruncher Statistical Systems; 2012. [ Google Scholar ]
• StatPoint Technologies, Inc . STATGRAPHICS Centurion XVI user manual. Warrenton, VA: StatPoint Technologies Inc.; 2010. [ Google Scholar ]
• SYSTAT Software Inc . SYSTAT 13: Graphics. Chicago, IL: SYSTAT Software Inc; 2009. [ Google Scholar ]

References for Procedure 5.3

• Cleveland WR. Visualizing data. Summit, NJ: Hobart Press; 1995. [ Google Scholar ]
• Jacoby WJ. Statistical graphics for visualizing multivariate data. Thousand Oaks, CA: Sage; 1998. [ Google Scholar ]

Useful Additional Readings for Procedure 5.3

• Kirk A. Data visualisation: A handbook for data driven design. Los Angeles: Sage; 2016. [ Google Scholar ]
• Knaflic CN. Storytelling with data: A data visualization guide for business professionals. Hoboken, NJ: Wiley; 2015. [ Google Scholar ]
• Tufte E. The visual display of quantitative information. 2. Cheshire, CN: Graphics Press; 2001. [ Google Scholar ]

Reference for Procedure 5.4

Useful additional readings for procedure 5.4.

• Rosenthal R, Rosnow RL. Essentials of behavioral research: Methods and data analysis. 2. New York: McGraw-Hill Inc; 1991. [ Google Scholar ]

References for Procedure 5.5

Useful additional readings for procedure 5.5.

• Gravetter FJ, Wallnau LB. Statistics for the behavioural sciences. 9. Belmont, CA: Wadsworth Cengage; 2012. [ Google Scholar ]

References for Fundamental Concept I

Useful additional readings for fundamental concept i.

• Howell DC. Statistical methods for psychology. 8. Belmont, CA: Cengage Wadsworth; 2013. [ Google Scholar ]

References for Procedure 5.6

• Norušis MJ. IBM SPSS statistics 19 guide to data analysis. Upper Saddle River, NJ: Prentice Hall; 2012. [ Google Scholar ]
• Field A. Discovering statistics using SPSS for Windows. 5. Los Angeles: Sage; 2018. [ Google Scholar ]
• Hintze JL. NCSS 8 help system: Introduction. Kaysville, UT: Number Cruncher Statistical System; 2012. [ Google Scholar ]
• SYSTAT Software Inc . SYSTAT 13: Statistics - I. Chicago, IL: SYSTAT Software Inc; 2009. [ Google Scholar ]

Useful Additional Readings for Procedure 5.6

• Hartwig F, Dearing BE. Exploratory data analysis. Beverly Hills, CA: Sage; 1979. [ Google Scholar ]
• Leinhardt G, Leinhardt L. Exploratory data analysis. In: Keeves JP, editor. Educational research, methodology, and measurement: An international handbook. 2. Oxford: Pergamon Press; 1997. pp. 519–528. [ Google Scholar ]
• Rosenthal R, Rosnow RL. Essentials of behavioral research: Methods and data analysis. 2. New York: McGraw-Hill, Inc.; 1991. [ Google Scholar ]
• Tukey JW. Exploratory data analysis. Reading, MA: Addison-Wesley Publishing; 1977. [ Google Scholar ]
• Velleman PF, Hoaglin DC. ABC’s of EDA. Boston: Duxbury Press; 1981. [ Google Scholar ]

Useful Additional Readings for Procedure 5.7

References for fundemental concept ii.

• Diebold FX, Schuermann T, Stroughair D. Pitfalls and opportunities in the use of extreme value theory in risk management. The Journal of Risk Finance. 2000; 1 (2):30–35. doi: 10.1108/eb043443. [ CrossRef ] [ Google Scholar ]
• Lane D. Online statistics education: A multimedia course of study. Houston, TX: Rice University; 2007. [ Google Scholar ]

Useful Additional Readings for Fundemental Concept II

• Keller DK. The tao of statistics: A path to understanding (with no math) Thousand Oaks, CA: Sage; 2006. [ Google Scholar ]

• Skip to main content
• Skip to primary sidebar
• Skip to footer
• QuestionPro

• Solutions Industries Gaming Automotive Sports and events Education Government Travel & Hospitality Financial Services Healthcare Cannabis Technology Use Case AskWhy Communities Audience Contactless surveys Mobile LivePolls Member Experience GDPR Positive People Science 360 Feedback Surveys
• Resources Blog eBooks Survey Templates Case Studies Training Help center

Home Market Research

Descriptive Research: Definition, Characteristics, Methods + Examples

Suppose an apparel brand wants to understand the fashion purchasing trends among New York’s buyers, then it must conduct a demographic survey of the specific region, gather population data, and then conduct descriptive research on this demographic segment.

The study will then uncover details on “what is the purchasing pattern of New York buyers,” but will not cover any investigative information about “ why ” the patterns exist. Because for the apparel brand trying to break into this market, understanding the nature of their market is the study’s main goal. Let’s talk about it.

What is descriptive research?

Descriptive research is a research method describing the characteristics of the population or phenomenon studied. This descriptive methodology focuses more on the “what” of the research subject than the “why” of the research subject.

The method primarily focuses on describing the nature of a demographic segment without focusing on “why” a particular phenomenon occurs. In other words, it “describes” the research subject without covering “why” it happens.

Characteristics of descriptive research

The term descriptive research then refers to research questions, the design of the study, and data analysis conducted on that topic. We call it an observational research method because none of the research study variables are influenced in any capacity.

Some distinctive characteristics of descriptive research are:

• Quantitative research: It is a quantitative research method that attempts to collect quantifiable information for statistical analysis of the population sample. It is a popular market research tool that allows us to collect and describe the demographic segment’s nature.
• Uncontrolled variables: In it, none of the variables are influenced in any way. This uses observational methods to conduct the research. Hence, the nature of the variables or their behavior is not in the hands of the researcher.
• Cross-sectional studies: It is generally a cross-sectional study where different sections belonging to the same group are studied.
• The basis for further research: Researchers further research the data collected and analyzed from descriptive research using different research techniques. The data can also help point towards the types of research methods used for the subsequent research.

Applications of descriptive research with examples

A descriptive research method can be used in multiple ways and for various reasons. Before getting into any survey , though, the survey goals and survey design are crucial. Despite following these steps, there is no way to know if one will meet the research outcome. How to use descriptive research? To understand the end objective of research goals, below are some ways organizations currently use descriptive research today:

• Define respondent characteristics: The aim of using close-ended questions is to draw concrete conclusions about the respondents. This could be the need to derive patterns, traits, and behaviors of the respondents. It could also be to understand from a respondent their attitude, or opinion about the phenomenon. For example, understand millennials and the hours per week they spend browsing the internet. All this information helps the organization researching to make informed business decisions.
• Measure data trends: Researchers measure data trends over time with a descriptive research design’s statistical capabilities. Consider if an apparel company researches different demographics like age groups from 24-35 and 36-45 on a new range launch of autumn wear. If one of those groups doesn’t take too well to the new launch, it provides insight into what clothes are like and what is not. The brand drops the clothes and apparel that customers don’t like.
• Conduct comparisons: Organizations also use a descriptive research design to understand how different groups respond to a specific product or service. For example, an apparel brand creates a survey asking general questions that measure the brand’s image. The same study also asks demographic questions like age, income, gender, geographical location, geographic segmentation , etc. This consumer research helps the organization understand what aspects of the brand appeal to the population and what aspects do not. It also helps make product or marketing fixes or even create a new product line to cater to high-growth potential groups.
• Validate existing conditions: Researchers widely use descriptive research to help ascertain the research object’s prevailing conditions and underlying patterns. Due to the non-invasive research method and the use of quantitative observation and some aspects of qualitative observation , researchers observe each variable and conduct an in-depth analysis . Researchers also use it to validate any existing conditions that may be prevalent in a population.
• Conduct research at different times: The analysis can be conducted at different periods to ascertain any similarities or differences. This also allows any number of variables to be evaluated. For verification, studies on prevailing conditions can also be repeated to draw trends.

Advantages of descriptive research

Some of the significant advantages of descriptive research are:

• Data collection: A researcher can conduct descriptive research using specific methods like observational method, case study method, and survey method. Between these three, all primary data collection methods are covered, which provides a lot of information. This can be used for future research or even for developing a hypothesis for your research object.
• Varied: Since the data collected is qualitative and quantitative, it gives a holistic understanding of a research topic. The information is varied, diverse, and thorough.
• Natural environment: Descriptive research allows for the research to be conducted in the respondent’s natural environment, which ensures that high-quality and honest data is collected.
• Quick to perform and cheap: As the sample size is generally large in descriptive research, the data collection is quick to conduct and is inexpensive.

Descriptive research methods

There are three distinctive methods to conduct descriptive research. They are:

Observational method

The observational method is the most effective method to conduct this research, and researchers make use of both quantitative and qualitative observations.

A quantitative observation is the objective collection of data primarily focused on numbers and values. It suggests “associated with, of or depicted in terms of a quantity.” Results of quantitative observation are derived using statistical and numerical analysis methods. It implies observation of any entity associated with a numeric value such as age, shape, weight, volume, scale, etc. For example, the researcher can track if current customers will refer the brand using a simple Net Promoter Score question .

Qualitative observation doesn’t involve measurements or numbers but instead just monitoring characteristics. In this case, the researcher observes the respondents from a distance. Since the respondents are in a comfortable environment, the characteristics observed are natural and effective. In a descriptive research design, the researcher can choose to be either a complete observer, an observer as a participant, a participant as an observer, or a full participant. For example, in a supermarket, a researcher can from afar monitor and track the customers’ selection and purchasing trends. This offers a more in-depth insight into the purchasing experience of the customer.

Case study method

Case studies involve in-depth research and study of individuals or groups. Case studies lead to a hypothesis and widen a further scope of studying a phenomenon. However, case studies should not be used to determine cause and effect as they can’t make accurate predictions because there could be a bias on the researcher’s part. The other reason why case studies are not a reliable way of conducting descriptive research is that there could be an atypical respondent in the survey. Describing them leads to weak generalizations and moving away from external validity.

Survey research

In survey research, respondents answer through surveys or questionnaires or polls . They are a popular market research tool to collect feedback from respondents. A study to gather useful data should have the right survey questions. It should be a balanced mix of open-ended questions and close ended-questions . The survey method can be conducted online or offline, making it the go-to option for descriptive research where the sample size is enormous.

Examples of descriptive research

Some examples of descriptive research are:

• A specialty food group launching a new range of barbecue rubs would like to understand what flavors of rubs are favored by different people. To understand the preferred flavor palette, they conduct this type of research study using various methods like observational methods in supermarkets. By also surveying while collecting in-depth demographic information, offers insights about the preference of different markets. This can also help tailor make the rubs and spreads to various preferred meats in that demographic. Conducting this type of research helps the organization tweak their business model and amplify marketing in core markets.
• Another example of where this research can be used is if a school district wishes to evaluate teachers’ attitudes about using technology in the classroom. By conducting surveys and observing their comfortableness using technology through observational methods, the researcher can gauge what they can help understand if a full-fledged implementation can face an issue. This also helps in understanding if the students are impacted in any way with this change.

Some other research problems and research questions that can lead to descriptive research are:

• Market researchers want to observe the habits of consumers.
• A company wants to evaluate the morale of its staff.
• A school district wants to understand if students will access online lessons rather than textbooks.
• To understand if its wellness questionnaire programs enhance the overall health of the employees.

LEARN MORE         FREE TRIAL

MORE LIKE THIS

Age Gating: Effective Strategies for Online Content Control

Aug 23, 2024

Customer Experience Lessons from 13,000 Feet — Tuesday CX Thoughts

Aug 20, 2024

Insight: Definition & meaning, types and examples

Aug 19, 2024

Employee Loyalty: Strategies for Long-Term Business Success 

Other categories.

• Academic Research
• Artificial Intelligence
• Assessments
• Brand Awareness
• Case Studies
• Communities
• Consumer Insights
• Customer effort score
• Customer Engagement
• Customer Experience
• Customer Loyalty
• Customer Research
• Customer Satisfaction
• Employee Benefits
• Employee Engagement
• Employee Retention
• Friday Five
• General Data Protection Regulation
• Insights Hub
• Life@QuestionPro
• Market Research
• Mobile diaries
• Mobile Surveys
• New Features
• Online Communities
• Question Types
• Questionnaire
• QuestionPro Products
• Release Notes
• Research Tools and Apps
• Revenue at Risk
• Survey Templates
• Training Tips
• Tuesday CX Thoughts (TCXT)
• Uncategorized
• What’s Coming Up
• Workforce Intelligence

Root out friction in every digital experience, super-charge conversion rates, and optimize digital self-service

Uncover insights from any interaction, deliver AI-powered agent coaching, and reduce cost to serve

Increase revenue and loyalty with real-time insights and recommendations delivered to teams on the ground

Know how your people feel and empower managers to improve employee engagement, productivity, and retention

Take action in the moments that matter most along the employee journey and drive bottom line growth

Whatever they’re are saying, wherever they’re saying it, know exactly what’s going on with your people

Get faster, richer insights with qual and quant tools that make powerful market research available to everyone

Run concept tests, pricing studies, prototyping + more with fast, powerful studies designed by UX research experts

Track your brand performance 24/7 and act quickly to respond to opportunities and challenges in your market

Explore the platform powering Experience Management

• Free Account
• Product Demos
• For Digital
• For Customer Care
• For Human Resources
• For Researchers
• Financial Services
• All Industries

Popular Use Cases

• Customer Experience
• Employee Experience
• Net Promoter Score
• Voice of Customer
• Customer Success Hub
• Product Documentation
• Training & Certification
• XM Institute
• Popular Resources
• Customer Stories
• Artificial Intelligence

Market Research

• Partnerships
• Marketplace

The annual gathering of the experience leaders at the world’s iconic brands building breakthrough business results, live in Salt Lake City.

• English/AU & NZ
• Español/Europa
• Español/América Latina
• Português Brasileiro
• REQUEST DEMO
• Experience Management
• Descriptive Research

Try Qualtrics for free

Descriptive research: what it is and how to use it.

8 min read Understanding the who, what and where of a situation or target group is an essential part of effective research and making informed business decisions.

For example you might want to understand what percentage of CEOs have a bachelor’s degree or higher. Or you might want to understand what percentage of low income families receive government support – or what kind of support they receive.

Descriptive research is what will be used in these types of studies.

In this guide we’ll look through the main issues relating to descriptive research to give you a better understanding of what it is, and how and why you can use it.

Free eBook: 2024 global market research trends report

What is descriptive research?

Descriptive research is a research method used to try and determine the characteristics of a population or particular phenomenon.

Using descriptive research you can identify patterns in the characteristics of a group to essentially establish everything you need to understand apart from why something has happened.

Market researchers use descriptive research for a range of commercial purposes to guide key decisions.

For example you could use descriptive research to understand fashion trends in a given city when planning your clothing collection for the year. Using descriptive research you can conduct in depth analysis on the demographic makeup of your target area and use the data analysis to establish buying patterns.

Conducting descriptive research wouldn’t, however, tell you why shoppers are buying a particular type of fashion item.

Descriptive research design

Descriptive research design uses a range of both qualitative research and quantitative data (although quantitative research is the primary research method) to gather information to make accurate predictions about a particular problem or hypothesis.

As a survey method, descriptive research designs will help researchers identify characteristics in their target market or particular population.

These characteristics in the population sample can be identified, observed and measured to guide decisions.

Descriptive research characteristics

While there are a number of descriptive research methods you can deploy for data collection, descriptive research does have a number of predictable characteristics.

Here are a few of the things to consider:

Measure data trends with statistical outcomes

Descriptive research is often popular for survey research because it generates answers in a statistical form, which makes it easy for researchers to carry out a simple statistical analysis to interpret what the data is saying.

Descriptive research design is ideal for further research

Because the data collection for descriptive research produces statistical outcomes, it can also be used as secondary data for another research study.

Plus, the data collected from descriptive research can be subjected to other types of data analysis .

Uncontrolled variables

A key component of the descriptive research method is that it uses random variables that are not controlled by the researchers. This is because descriptive research aims to understand the natural behavior of the research subject.

It’s carried out in a natural environment

Descriptive research is often carried out in a natural environment. This is because researchers aim to gather data in a natural setting to avoid swaying respondents.

Data can be gathered using survey questions or online surveys.

For example, if you want to understand the fashion trends we mentioned earlier, you would set up a study in which a researcher observes people in the respondent’s natural environment to understand their habits and preferences.

Descriptive research allows for cross sectional study

Because of the nature of descriptive research design and the randomness of the sample group being observed, descriptive research is ideal for cross sectional studies – essentially the demographics of the group can vary widely and your aim is to gain insights from within the group.

This can be highly beneficial when you’re looking to understand the behaviors or preferences of a wider population.

Descriptive research advantages

There are many advantages to using descriptive research, some of them include:

Cost effectiveness

Because the elements needed for descriptive research design are not specific or highly targeted (and occur within the respondent’s natural environment) this type of study is relatively cheap to carry out.

Multiple types of data can be collected

A big advantage of this research type, is that you can use it to collect both quantitative and qualitative data. This means you can use the stats gathered to easily identify underlying patterns in your respondents’ behavior.

Descriptive research disadvantages

Potential reliability issues.

When conducting descriptive research it’s important that the initial survey questions are properly formulated.

If not, it could make the answers unreliable and risk the credibility of your study.

Potential limitations

As we’ve mentioned, descriptive research design is ideal for understanding the what, who or where of a situation or phenomenon.

However, it can’t help you understand the cause or effect of the behavior. This means you’ll need to conduct further research to get a more complete picture of a situation.

Descriptive research methods

Because descriptive research methods include a range of quantitative and qualitative research, there are several research methods you can use.

Use case studies

Case studies in descriptive research involve conducting in-depth and detailed studies in which researchers get a specific person or case to answer questions.

Case studies shouldn’t be used to generate results, rather it should be used to build or establish hypothesis that you can expand into further market research .

For example you could gather detailed data about a specific business phenomenon, and then use this deeper understanding of that specific case.

Use observational methods

This type of study uses qualitative observations to understand human behavior within a particular group.

By understanding how the different demographics respond within your sample you can identify patterns and trends.

As an observational method, descriptive research will not tell you the cause of any particular behaviors, but that could be established with further research.

Use survey research

Surveys are one of the most cost effective ways to gather descriptive data.

An online survey or questionnaire can be used in descriptive studies to gather quantitative information about a particular problem.

Survey research is ideal if you’re using descriptive research as your primary research.

Descriptive research examples

Descriptive research is used for a number of commercial purposes or when organizations need to understand the behaviors or opinions of a population.

One of the biggest examples of descriptive research that is used in every democratic country, is during elections.

Using descriptive research, researchers will use surveys to understand who voters are more likely to choose out of the parties or candidates available.

Using the data provided, researchers can analyze the data to understand what the election result will be.

In a commercial setting, retailers often use descriptive research to figure out trends in shopping and buying decisions.

By gathering information on the habits of shoppers, retailers can get a better understanding of the purchases being made.

Another example that is widely used around the world, is the national census that takes place to understand the population.

The research will provide a more accurate picture of a population’s demographic makeup and help to understand changes over time in areas like population age, health and education level.

Where Qualtrics helps with descriptive research

Whatever type of research you want to carry out, there’s a survey type that will work.

Qualtrics can help you determine the appropriate method and ensure you design a study that will deliver the insights you need.

Our experts can help you with your market research needs , ensuring you get the most out of Qualtrics market research software to design, launch and analyze your data to guide better, more accurate decisions for your organization.

Related resources

Market intelligence 10 min read, marketing insights 11 min read, ethnographic research 11 min read, qualitative vs quantitative research 13 min read, qualitative research questions 11 min read, qualitative research design 12 min read, primary vs secondary research 14 min read, request demo.

Ready to learn more about Qualtrics?

Descriptive Research: Methods And Examples

A research project always begins with selecting a topic. The next step is for researchers to identify the specific areas…

A research project always begins with selecting a topic. The next step is for researchers to identify the specific areas of interest. After that, they tackle the key component of any research problem: how to gather enough quality information. If we opt for a descriptive research design we have to ask the correct questions to access the right information. 

For instance, researchers may choose to focus on why people invest in cryptocurrency, knowing how dynamic the market is rather than asking why the market is so shaky. These are completely different questions that require different research approaches. Adopting the descriptive method can help capitalize on trends the information reveals. Descriptive research examples show the thorough research involved in such a study. 

Get to know more about descriptive research design .

Descriptive Research Meaning

Features of descriptive research design, types of descriptive research, descriptive research methods, applications of descriptive research, descriptive research examples.

A descriptive method of research is one that describes the characteristics of a phenomenon, situation or population. It uses quantitative and qualitative approaches to describe problems with little relevant information. Descriptive research accurately describes a research problem without asking why a particular event happened. By researching market patterns, the descriptive method answers how patterns change, what caused the change and when the change occurred, instead of dwelling on why the change happened.

Descriptive research refers to questions, study design and analysis of data conducted on a particular topic. It is a strictly observational research methodology with no influence on variables. Some distinctive features of descriptive research are:

• It’s a research method that collects quantifiable information for statistical analysis of a sample. It’s a quantitative market research tool that can analyze the nature of a demographic
• In a descriptive method of research , the nature of research study variables is determined with observation, without influence from the researcher
• Descriptive research is cross-sectional and different sections of a group can be studied
• The analyzed data is collected and serves as information for other search techniques. In this way, a descriptive research design becomes the basis of further research

To understand the descriptive research meaning , data collection methods, examples and application, we need a deeper understanding of its features.

Different ways of approaching the descriptive method help break it down further. Let’s look at the different types of descriptive research :

Descriptive Survey

Descriptive normative survey, descriptive status.

This type of research quantitatively describes real-life situations. For example, to understand the relation between wages and performance, research on employee salaries and their respective performances can be conducted.

Descriptive Analysis

This technique analyzes a subject further. Once the relation between wages and performance has been established, an organization can further analyze employee performance by researching the output of those who work from an office with those who work from home.

Descriptive Classification

Descriptive classification is mainly used in the field of biological science. It helps researchers classify species once they have studied the data collected from different search stations.

Descriptive Comparative

Comparing two variables can show if one is better than the other. Doing this through tests or surveys can reveal all the advantages and disadvantages associated with the two. For example, this technique can be used to find out if paper ballots are better than electronic voting devices.

Correlative Survey

The researcher has to effectively interpret the area of the problem and then decide the appropriate technique of descriptive research design . 

A researcher can choose one of the following methods to solve research problems and meet research goals:

Observational Method

With this method, a researcher observes the behaviors, mannerisms and characteristics of the participants. It is widely used in psychology and market research and does not require the participants to be involved directly. It’s an effective method and can be both qualitative and quantitative for the sheer volume and variety of data that is generated.

Survey Research

It’s a popular method of data collection in research. It follows the principle of obtaining information quickly and directly from the main source. The idea is to use rigorous qualitative and quantitative research methods and ask crucial questions essential to the business for the short and long term.

Case Study Method

Case studies tend to fall short in situations where researchers are dealing with highly diverse people or conditions. Surveys and observations are carried out effectively but the time of execution significantly differs between the two. 

There are multiple applications of descriptive research design but executives must learn that it’s crucial to clearly define the research goals first. Here’s how organizations use descriptive research to meet their objectives:

• As a tool to analyze participants : It’s important to understand the behaviors, traits and patterns of the participants to draw a conclusion about them. Close-ended questions can reveal their opinions and attitudes. Descriptive research can help understand the participant and assist in making strategic business decisions
• Designed to measure data trends : It’s a statistically capable research design that, over time, allows organizations to measure data trends. A survey can reveal unfavorable scenarios and give an organization the time to fix unprofitable moves
• Scope of comparison: Surveys and research can allow an organization to compare two products across different groups. This can provide a detailed comparison of the products and an opportunity for the organization to capitalize on a large demographic
• Conducting research at any time: An analysis can be conducted at any time and any number of variables can be evaluated. It helps to ascertain differences and similarities

Descriptive research is widely used due to its non-invasive nature. Quantitative observations allow in-depth analysis and a chance to validate any existing condition.

There are several different descriptive research examples that highlight the types, applications and uses of this research method. Let’s look at a few:

• Before launching a new line of gym wear, an organization chose more than one descriptive method to gather vital information. Their objective was to find the kind of gym clothes people like wearing and the ones they would like to see in the market. The organization chose to conduct a survey by recording responses in gyms, sports shops and yoga centers. As a second method, they chose to observe members of different gyms and fitness institutions. They collected volumes of vital data such as color and design preferences and the amount of money they’re willing to spend on it .
• To get a good idea of people’s tastes and expectations, an organization conducted a survey by offering a new flavor of the sauce and recorded people’s responses by gathering data from store owners. This let them understand how people reacted, whether they found the product reasonably priced, whether it served its purpose and their overall general preferences. Based on this, the brand tweaked its core marketing strategies and made the product widely acceptable .

Descriptive research can be used by an organization to understand the spending patterns of customers as well as by a psychologist who has to deal with mentally ill patients. In both these professions, the individuals will require thorough analyses of their subjects and large amounts of crucial data to develop a plan of action.

Every method of descriptive research can provide information that is diverse, thorough and varied. This supports future research and hypotheses. But although they can be quick, cheap and easy to conduct in the participants’ natural environment, descriptive research design can be limited by the kind of information it provides, especially with case studies. Trying to generalize a larger population based on the data gathered from a smaller sample size can be futile. Similarly, a researcher can unknowingly influence the outcome of a research project due to their personal opinions and biases. In any case, a manager has to be prepared to collect important information in substantial quantities and have a balanced approach to prevent influencing the result. 

Harappa’s Thinking Critically program harnesses the power of information to strengthen decision-making skills. It’s a growth-driven course for young professionals and managers who want to be focused on their strategies, outperform targets and step up to assume the role of leader in their organizations. It’s for any professional who wants to lay a foundation for a successful career and business owners who’re looking to take their organizations to new heights.

Explore Harappa Diaries to learn more about topics such as Main Objectives of Research , Examples of Experimental Research , Methods Of Ethnographic Research , and How To Use Blended Learning to upgrade your knowledge and skills.

• > Statistics

Types of Descriptive Analysis: Examples & Steps

• Hrithik Saini
• Aug 17, 2022

The study of statistics involves gathering, categorizing, analyzing, interpreting, and presenting quantitative facts and numbers. Statistics is a branch of math. It is beneficial when working with populations that are too big and diverse for precise, in-depth measurements. Statistics are essential when extrapolating broad inferences about a database from a test dataset.

Two different categories of analytics are descriptive and inferential. Today, we'll take a closer look at the descriptive analysis , including their definition, many types, and how they vary from inferential statistics. Let’s get started.

What is Descriptive Analysis ?

The practice of utilizing analytical techniques to characterize or summarize a data collection is known as descriptive analysis, sometimes referred to as descriptive analytics or descriptive statistics. 

Descriptive analysis, one of the main aspects of data analysis, is well-liked for its capacity to produce understandable insights from unrecognizable data.

The descriptive analysis somehow doesn't seek to make predictions about the future, in contrast to other methods of data analysis . Instead, it only uses historical data that has been altered to make sense of it in order to draw conclusions.

Also Read | Descriptive Statistics in R

How Does Descriptive Analysis Work?

Data analysis requires businesses to first gather and consolidate raw data from multiple sources, then transform it into a standard format for analysis. They may now begin analyzing the data. 

Many businesses employ data intelligence, which is a collection of techniques and instruments for gathering and analyzing data, then drawing conclusions and formulating plans of action based on the results. Others add simple descriptive analytics to the combined data using spreadsheet formulae, producing KPIs and other statistics which are subsequently included in presentations.

Integrated ERP systems may hold all of the company's business information in a centralized database, which greatly simplifies descriptive analytics. Professional suites also come with integrated analysis tools to aid with data narrative, which is the process of creating a narrative around data using visuals to communicate the significance of the data in an engaging manner. 

Common KPIs can be provided with real-time data combined into dashboards, charts, and reports using ERP-integrated business intelligence tools.

Difference Between Descriptive Analysis & Inferential Analysis

Descriptive statistics and inferential statistics, or what you're doing with the data, vary considerably. Let's take a look to learn more about the two terms.

In contrast to how the final result is presented in probabilities in descriptive statistics, the final outcome has a graphical representation of a tabulated format.

Although inferential statistics describes the likelihood of the risk occurring, descriptive statistics depicts a condition.

To synthesize the selection, descriptive statistics describe the data that is previously known. In contrast, inferential statistics seek to draw inferences about populations that are outside the scope of the data at hand.

Also Read | Frequency Distribution in Data Statistics

Types of Descriptive Analysis

There are several types, traits, or metrics of descriptive statistics. According to some experts, there are two sorts. Some others claim three or even four. We shall stick with four kinds for the sake of dealing with statistics.

Measures of Frequency

The frequency distribution in statistics indicates the responses or frequency of the possible possibilities in a data collection or sample, which are used for covering quantitative and qualitative research. Typically, the frequency distribution is shown in a graphical format. The counts or frequency of the values' repetitions within an interval, range, or particular group are provided alongside each item in the table or graph.

A representation or overview of categorical variables that have been divided into mutually exclusive groups and the number of instances in each class is called a frequency distribution. It enables the presentation of raw data in a more organized and orderly manner.

Bar charts, histograms, pie charts, and line graphs are examples of common charts and graphs used in frequency distribution presentation and visualization.

Central Tendency

A dataset's descriptive overview utilizing a single number that represents the center of the distribution of the data is referred to as having a central tendency. Statistical measures placement are another name for measures of central tendency. The measurements of central tendency are indeed the mean, median, and mode.

The standard or most frequent number in data collection is known as the mean, which is regarded as the most widely used measure of central tendency. The average score for data collection in ascending order is referred to as the median. The score or value that appears most frequently in a data collection is referred to as the mode.

Measures of Dispersion

Understanding how facts are dispersed throughout a range could be useful at times. Take the average stature of a sample of two persons to demonstrate this. The average size is six feet if both people are six feet tall. 

The average height is still six feet even if one person is five feet in height another is seven feet tall. Measures of variability like ranging or measure of dispersion can be used to quantify this type of distribution.

Variability

A summary statistic that reflects the level of sample variation is known as a measure of variability. How far away the measured values obviously fall from the center is determined by the variability measurements.

The length between the greatest and lowest frequencies within a data collection is idealized as the range, which shows the degree of dispersion. The standard deviation is used to calculate the average variance in a collection of data and gives information about how far a value from a data set is from the average value with the same given dataset. The variance, which is just an average of the squared deviations, represents the extent of the dispersion.

Example of Descriptive Analysis

Every part of the business, from finance to manufacturing and sales, has examples of descriptive analytics, some of which are included below.

Accounting entries receivable and payable, working capital, inventory, and output are all included in business reports.

Measures of the economy and other business Examples of descriptive analytics include KPIs. These include figures like the profitability ratio, current ratio, and return on capital employed that measure the strength and worth of a company.

Involvement in social media: Descriptive analytics offers measures like an increase in followers, audience engagement, and income related to certain social media platforms that assist in assessing the return on social networking operations.

Surveys: Descriptive analytics creates representations of the outcomes of internal and external surveys, such as customer satisfaction scores.

Importance of Descriptive Analytics in Business

Everyone in the organization benefits from using descriptive analytics to make better decisions that steer the company's operations in the correct direction. Managers can quickly assess how well the company is doing and where adjustments might be needed since it shows trends that would otherwise be concealed in raw data.

Additionally, descriptive analytics enables firms to share information internally and externally. Before they decide to participate in a company, potential lenders and investors, for instance, would want to carefully examine figures for sales, profit, cash flow , and debt.

Benefits & Drawbacks of Descriptive Analysis

There are several benefits to descriptive analytics. It may be carried out using commonly available instruments and doesn't need a thorough grasp of analytical or statistical approaches . 

It can respond to a lot of the often asked inquiries regarding how well a company is doing, such as whether or not sales last quarter met targets. This assists the company in identifying areas that require improvement.

Descriptive analytics' main flaw is that it only recounts what has occurred without seeking to understand its causes or foresee what will happen later. Additionally, it is typically restricted to relatively straightforward studies that focus on the interactions between two or three variables.

Also Read | Advantages of Business Intelligence in Finance

5 Steps of Descriptive Analysis

Determining the statistics you want to output is typically the first step in applying advanced statistics, and delivering them in the proper manner is the final step. The procedures to produce your own descriptive analytics are listed below.

State Business Metrics

Finding the metrics you want to produce is the first step. These need to represent the main corporate objectives of each segment or the organization as a whole. 

For instance, a business that is focused on growth may measure quarterly revenue growth, while its accounts receivable department might keep track of indicators like days sales outstanding and others that show how long it takes to recover money from consumers.

Identity the Necessary Data

Find the information you require to generate the necessary stats. The data may be dispersed over several programs and files at certain businesses. Businesses that utilize ERP systems can already have the majority of all of the data they require in the databases of their programs. 

Some indicators could also need information from other sources, such as social networking sites, e-commerce websites, and datasets used for industry evaluation.

Data Extraction and Preparation

Extracting, integrating, and preparing the data for analysis when it originates from numerous sources is a time-consuming but essential process to guarantee accuracy. This process could entail translating data into a format compatible with analytical tools as well as data cleansing to remove discrepancies and inaccuracies in data from various sources. 

Data modeling is a technique used by advanced data analytics to assist prepare, shaping, and arranging corporate data. A framework for defining and formatting data inside information systems is called data modeling.

Examining Data

Businesses may use descriptive analytics using a range of technologies, including spreadsheets and business intelligence (BI) software. Applying elementary mathematical computations to one or more parameters is a common step in descriptive analytics. 

Sales representatives could, for instance, keep tabs on the typical income per sale or the monthly revenue from new clients. Financial measures like profitability ratio , or the ratio of gross profit to sales, may be monitored by executives and financial experts.

Current Data

Stakeholders are frequently more likely to grasp data when it is presented in visually appealing ways like pie charts, bar charts, and line graphs. However, certain individuals, such as financial experts, might prefer information to be presented in the form of statistics and tables.

Popular data analysis techniques include descriptive analysis. Given that its sole purpose is to describe and summarize historical data, it is frequently carried out before diagnostics or predictive analysis.

A range of statistical methods, including measurements of incidence, internal consistency, distribution, and location, are used in descriptive analysis to achieve this. Descriptive analysis may be done in a variety of ways depending on your objectives, but the process often includes gathering, cleaning, and then evaluating data.

Share Blog :

Be a part of our Instagram community

Trending blogs

5 Factors Influencing Consumer Behavior

Elasticity of Demand and its Types

An Overview of Descriptive Analysis

What is PESTLE Analysis? Everything you need to know about it

What is Managerial Economics? Definition, Types, Nature, Principles, and Scope

5 Factors Affecting the Price Elasticity of Demand (PED)

6 Major Branches of Artificial Intelligence (AI)

Scope of Managerial Economics

Dijkstra’s Algorithm: The Shortest Path Algorithm

Different Types of Research Methods

Latest Comments

mitchell21600

Am Robert Mitchell USA , How i purchased Willy Wonka Golden Ticket from Wal-Mart #2605 in Gallipolis and won $15,000, It still feels incredible that my life has changed and I thank Dr Prince  everyday for his help. It is the best feeling in the world knowing that I am financially secure.Dr.Prince has proved that all the comment that i have read about him are all true, I am saying this now because before i contacted Dr.Prince i was having doubts if all what i have read about Dr.Prince are true but after contacting him, i believed that Dr.Price  is truly powerful and his spell has the capability to Win all kinds of lottery All thanks Dr prince, contact him today via [email protected]  His website https://obinnaspelltemple.com/ call Dr or Text him +16466652077

What can I say to you Dr Ayoola for what you have done for me, I’m here to say thank you Dr Ayoola, I’m a man that love playing Lottery. I have been playing lottery for over 15 years now and I have not won any good money because of the way my life was, I was having challenges in my financial life I was owning a lot of people around me because of what my wife put me through and don’t know what to do, I was confuse and frustrated I didnt know what to do, I was just researching on how I can win lottery when I got so many testimonies from people that Dr Ayoola has helped in the past and they were able to win a good money with the help of this man call Dr Ayoola I was overwhelmed and I contacted him as well for help I was so surprised he got back to me saying he will help me, that was how we started working together he promised me that I will win which I believe because of the way he spoke to me, today I’m here to tell the world that I’m a living testimony of his good works. Dr Ayoola helped me to win the sum of 50 million euro I was shocked because I have been playing this same lottery for over 15 years, Dr Ayoola was God sent to me I’m here testifying about him for you to know just in case you want help so you can contact him as well via website Drayoolatemple.com or [email protected] or https://www.facebook.com/Dr-Ayoola-105640401516053/ text or call +14809032128

bryankrauss345

I am very happy to recommend Dr. Wale to everyone that truly needs help to fix his or her broken relationship and marriage. I found Dr. Wale online. I was desperately in need of help to bring my ex Wife back. She left me for another man. It all happened so fast and I had nothing to say in the situation at all. She just left me after 3 years of our marriage without any explanation. I was very worried and could not eat till I went online and I found testimonies on Dr. Wale so I decided to contact Dr. Wale through his WhatsApp and I explain everything to him so he helps me cast a love spell to help us get back together. Shortly after he did the spell, my wife started texting and calling me again. She said that she was sorry and said that I was the most important person in her life and she knows that now. you can also contact him now for urgent help. WhatsApp/Text him: +1(978) 406-9575 or Email him:[email protected] or visit his website https://everlastingspellcaster.website2.me/

brenwright30

THIS IS HOW YOU CAN RECOVER YOUR LOST CRYPTO? Are you a victim of Investment, BTC, Forex, NFT, Credit card, etc Scam? Do you want to investigate a cheating spouse? Do you desire credit repair (all bureaus)? Contact Hacker Steve (Funds Recovery agent) asap to get started. He specializes in all cases of ethical hacking, cryptocurrency, fake investment schemes, recovery scam, credit repair, stolen account, etc. Stay safe out there! [email protected] https://hackersteve.great-site.net/

• MS in the Learning Sciences
• Tuition & Financial Aid

Qualitative vs. quantitative data analysis: How do they differ?

Learning analytics have become the cornerstone for personalizing student experiences and enhancing learning outcomes. In this data-informed approach to education there are two distinct methodologies: qualitative and quantitative analytics. These methods, which are typical to data analytics in general, are crucial to the interpretation of learning behaviors and outcomes. This blog will explore the nuances that distinguish qualitative and quantitative research, while uncovering their shared roles in learning analytics, program design and instruction.

What is qualitative data?

Qualitative data is descriptive and includes information that is non numerical. Qualitative research is used to gather in-depth insights that can't be easily measured on a scale like opinions, anecdotes and emotions. In learning analytics qualitative data could include in depth interviews, text responses to a prompt, or a video of a class period. 1

What is quantitative data?

Quantitative data is information that has a numerical value. Quantitative research is conducted to gather measurable data used in statistical analysis. Researchers can use quantitative studies to identify patterns and trends. In learning analytics quantitative data could include test scores, student demographics, or amount of time spent in a lesson. 2

Key difference between qualitative and quantitative data

It's important to understand the differences between qualitative and quantitative data to both determine the appropriate research methods for studies and to gain insights that you can be confident in sharing.

Data Types and Nature

Examples of qualitative data types in learning analytics:

• Observational data of human behavior from classroom settings such as student engagement, teacher-student interactions, and classroom dynamics
• Textual data from open-ended survey responses, reflective journals, and written assignments
• Feedback and discussions from focus groups or interviews
• Content analysis from various media

Examples of quantitative data types:

• Standardized test, assessment, and quiz scores
• Grades and grade point averages
• Attendance records
• Time spent on learning tasks
• Data gathered from learning management systems (LMS), including login frequency, online participation, and completion rates of assignments

Methods of Collection

Qualitative and quantitative research methods for data collection can occasionally seem similar so it's important to note the differences to make sure you're creating a consistent data set and will be able to reliably draw conclusions from your data.

Qualitative research methods

Because of the nature of qualitative data (complex, detailed information), the research methods used to collect it are more involved. Qualitative researchers might do the following to collect data:

• Conduct interviews to learn about subjective experiences
• Host focus groups to gather feedback and personal accounts
• Observe in-person or use audio or video recordings to record nuances of human behavior in a natural setting
• Distribute surveys with open-ended questions

Quantitative research methods

Quantitative data collection methods are more diverse and more likely to be automated because of the objective nature of the data. A quantitative researcher could employ methods such as:

• Surveys with close-ended questions that gather numerical data like birthdates or preferences
• Observational research and record measurable information like the number of students in a classroom
• Automated numerical data collection like information collected on the backend of a computer system like button clicks and page views

Analysis techniques

Qualitative and quantitative data can both be very informative. However, research studies require critical thinking for productive analysis.

Qualitative data analysis methods

Analyzing qualitative data takes a number of steps. When you first get all your data in one place you can do a review and take notes of trends you think you're seeing or your initial reactions. Next, you'll want to organize all the qualitative data you've collected by assigning it categories. Your central research question will guide your data categorization whether it's by date, location, type of collection method (interview vs focus group, etc), the specific question asked or something else. Next, you'll code your data. Whereas categorizing data is focused on the method of collection, coding is the process of identifying and labeling themes within the data collected to get closer to answering your research questions. Finally comes data interpretation. To interpret the data you'll take a look at the information gathered including your coding labels and see what results are occurring frequently or what other conclusions you can make. 3

Quantitative analysis techniques

The process to analyze quantitative data can be time-consuming due to the large volume of data possible to collect. When approaching a quantitative data set, start by focusing in on the purpose of your evaluation. Without making a conclusion, determine how you will use the information gained from analysis; for example: The answers of this survey about study habits will help determine what type of exam review session will be most useful to a class. 4

Next, you need to decide who is analyzing the data and set parameters for analysis. For example, if two different researchers are evaluating survey responses that rank preferences on a scale from 1 to 5, they need to be operating with the same understanding of the rankings. You wouldn't want one researcher to classify the value of 3 to be a positive preference while the other considers it a negative preference. It's also ideal to have some type of data management system to store and organize your data, such as a spreadsheet or database. Within the database, or via an export to data analysis software, the collected data needs to be cleaned of things like responses left blank, duplicate answers from respondents, and questions that are no longer considered relevant. Finally, you can use statistical software to analyze data (or complete a manual analysis) to find patterns and summarize your findings. 4

Qualitative and quantitative research tools

From the nuanced, thematic exploration enabled by tools like NVivo and ATLAS.ti, to the statistical precision of SPSS and R for quantitative analysis, each suite of data analysis tools offers tailored functionalities that cater to the distinct natures of different data types.

Qualitative research software:

NVivo: NVivo is qualitative data analysis software that can do everything from transcribe recordings to create word clouds and evaluate uploads for different sentiments and themes. NVivo is just one tool from the company Lumivero, which offers whole suites of data processing software. 5

ATLAS.ti: Similar to NVivo, ATLAS.ti allows researchers to upload and import data from a variety of sources to be tagged and refined using machine learning and presented with visualizations and ready for insert into reports. 6

SPSS: SPSS is a statistical analysis tool for quantitative research, appreciated for its user-friendly interface and comprehensive statistical tests, which makes it ideal for educators and researchers. With SPSS researchers can manage and analyze large quantitative data sets, use advanced statistical procedures and modeling techniques, predict customer behaviors, forecast market trends and more. 7

R: R is a versatile and dynamic open-source tool for quantitative analysis. With a vast repository of packages tailored to specific statistical methods, researchers can perform anything from basic descriptive statistics to complex predictive modeling. R is especially useful for its ability to handle large datasets, making it ideal for educational institutions that generate substantial amounts of data. The programming language offers flexibility in customizing analysis and creating publication-quality visualizations to effectively communicate results. 8

Applications in Educational Research

Both quantitative and qualitative data can be employed in learning analytics to drive informed decision-making and pedagogical enhancements. In the classroom, quantitative data like standardized test scores and online course analytics create a foundation for assessing and benchmarking student performance and engagement. Qualitative insights gathered from surveys, focus group discussions, and reflective student journals offer a more nuanced understanding of learners' experiences and contextual factors influencing their education. Additionally feedback and practical engagement metrics blend these data types, providing a holistic view that informs curriculum development, instructional strategies, and personalized learning pathways. Through these varied data sets and uses, educators can piece together a more complete narrative of student success and the impacts of educational interventions.

Master Data Analysis with an M.S. in Learning Sciences From SMU

Whether it is the detailed narratives unearthed through qualitative data or the informative patterns derived from quantitative analysis, both qualitative and quantitative data can provide crucial information for educators and researchers to better understand and improve learning. Dive deeper into the art and science of learning analytics with SMU's online Master of Science in the Learning Sciences program . At SMU, innovation and inquiry converge to empower the next generation of educators and researchers. Choose the Learning Analytics Specialization to learn how to harness the power of data science to illuminate learning trends, devise impactful strategies, and drive educational innovation. You could also find out how advanced technologies like augmented reality (AR), virtual reality (VR), and artificial intelligence (AI) can revolutionize education, and develop the insight to apply embodied cognition principles to enhance learning experiences in the Learning and Technology Design Specialization , or choose your own electives to build a specialization unique to your interests and career goals.

For more information on our curriculum and to become part of a community where data drives discovery, visit SMU's MSLS program website or schedule a call with our admissions outreach advisors for any queries or further discussion. Take the first step towards transforming education with data today.

• Retrieved on August 8, 2024, from nnlm.gov/guides/data-glossary/qualitative-data
• Retrieved on August 8, 2024, from nnlm.gov/guides/data-glossary/quantitative-data
• Retrieved on August 8, 2024, from cdc.gov/healthyyouth/evaluation/pdf/brief19.pdf
• Retrieved on August 8, 2024, from cdc.gov/healthyyouth/evaluation/pdf/brief20.pdf
• Retrieved on August 8, 2024, from lumivero.com/solutions/
• Retrieved on August 8, 2024, from atlasti.com/
• Retrieved on August 8, 2024, from ibm.com/products/spss-statistics
• Retrieved on August 8, 2024, from cran.r-project.org/doc/manuals/r-release/R-intro.html#Introduction-and-preliminaries

Return to SMU Online Learning Sciences Blog

Southern Methodist University has engaged Everspring , a leading provider of education and technology services, to support select aspects of program delivery.

This will only take a moment