statistical analysis research example

Table of Contents

Types of statistical analysis, importance of statistical analysis, benefits of statistical analysis, statistical analysis process, statistical analysis methods, statistical analysis software, statistical analysis examples, career in statistical analysis, choose the right program, become proficient in statistics today, what is statistical analysis types, methods and examples.

Statistical analysis is the process of collecting and analyzing data in order to discern patterns and trends. It is a method for removing bias from evaluating data by employing numerical analysis. This technique is useful for collecting the interpretations of research, developing statistical models, and planning surveys and studies.

Statistical analysis is a scientific tool in AI and ML that helps collect and analyze large amounts of data to identify common patterns and trends to convert them into meaningful information. In simple words, statistical analysis is a data analysis tool that helps draw meaningful conclusions from raw and unstructured data. 

The conclusions are drawn using statistical analysis facilitating decision-making and helping businesses make future predictions on the basis of past trends. It can be defined as a science of collecting and analyzing data to identify trends and patterns and presenting them. Statistical analysis involves working with numbers and is used by businesses and other institutions to make use of data to derive meaningful information. 

Given below are the 6 types of statistical analysis:

Descriptive Analysis

Descriptive statistical analysis involves collecting, interpreting, analyzing, and summarizing data to present them in the form of charts, graphs, and tables. Rather than drawing conclusions, it simply makes the complex data easy to read and understand.

Inferential Analysis

The inferential statistical analysis focuses on drawing meaningful conclusions on the basis of the data analyzed. It studies the relationship between different variables or makes predictions for the whole population.

Predictive Analysis

Predictive statistical analysis is a type of statistical analysis that analyzes data to derive past trends and predict future events on the basis of them. It uses machine learning algorithms, data mining , data modelling , and artificial intelligence to conduct the statistical analysis of data.

Prescriptive Analysis

The prescriptive analysis conducts the analysis of data and prescribes the best course of action based on the results. It is a type of statistical analysis that helps you make an informed decision. 

Exploratory Data Analysis

Exploratory analysis is similar to inferential analysis, but the difference is that it involves exploring the unknown data associations. It analyzes the potential relationships within the data. 

Causal Analysis

The causal statistical analysis focuses on determining the cause and effect relationship between different variables within the raw data. In simple words, it determines why something happens and its effect on other variables. This methodology can be used by businesses to determine the reason for failure. 

Statistical analysis eliminates unnecessary information and catalogs important data in an uncomplicated manner, making the monumental work of organizing inputs appear so serene. Once the data has been collected, statistical analysis may be utilized for a variety of purposes. Some of them are listed below:

• The statistical analysis aids in summarizing enormous amounts of data into clearly digestible chunks.
• The statistical analysis aids in the effective design of laboratory, field, and survey investigations.
• Statistical analysis may help with solid and efficient planning in any subject of study.
• Statistical analysis aid in establishing broad generalizations and forecasting how much of something will occur under particular conditions.
• Statistical methods, which are effective tools for interpreting numerical data, are applied in practically every field of study. Statistical approaches have been created and are increasingly applied in physical and biological sciences, such as genetics.
• Statistical approaches are used in the job of a businessman, a manufacturer, and a researcher. Statistics departments can be found in banks, insurance businesses, and government agencies.
• A modern administrator, whether in the public or commercial sector, relies on statistical data to make correct decisions.
• Politicians can utilize statistics to support and validate their claims while also explaining the issues they address.

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Statistical analysis can be called a boon to mankind and has many benefits for both individuals and organizations. Given below are some of the reasons why you should consider investing in statistical analysis:

• It can help you determine the monthly, quarterly, yearly figures of sales profits, and costs making it easier to make your decisions.
• It can help you make informed and correct decisions.
• It can help you identify the problem or cause of the failure and make corrections. For example, it can identify the reason for an increase in total costs and help you cut the wasteful expenses.
• It can help you conduct market analysis and make an effective marketing and sales strategy.
• It helps improve the efficiency of different processes.

Given below are the 5 steps to conduct a statistical analysis that you should follow:

• Step 1: Identify and describe the nature of the data that you are supposed to analyze.
• Step 2: The next step is to establish a relation between the data analyzed and the sample population to which the data belongs. 
• Step 3: The third step is to create a model that clearly presents and summarizes the relationship between the population and the data.
• Step 4: Prove if the model is valid or not.
• Step 5: Use predictive analysis to predict future trends and events likely to happen. 

Although there are various methods used to perform data analysis, given below are the 5 most used and popular methods of statistical analysis:

Mean or average mean is one of the most popular methods of statistical analysis. Mean determines the overall trend of the data and is very simple to calculate. Mean is calculated by summing the numbers in the data set together and then dividing it by the number of data points. Despite the ease of calculation and its benefits, it is not advisable to resort to mean as the only statistical indicator as it can result in inaccurate decision making. 

Standard Deviation

Standard deviation is another very widely used statistical tool or method. It analyzes the deviation of different data points from the mean of the entire data set. It determines how data of the data set is spread around the mean. You can use it to decide whether the research outcomes can be generalized or not. 

Regression is a statistical tool that helps determine the cause and effect relationship between the variables. It determines the relationship between a dependent and an independent variable. It is generally used to predict future trends and events.

Hypothesis Testing

Hypothesis testing can be used to test the validity or trueness of a conclusion or argument against a data set. The hypothesis is an assumption made at the beginning of the research and can hold or be false based on the analysis results. 

Sample Size Determination

Sample size determination or data sampling is a technique used to derive a sample from the entire population, which is representative of the population. This method is used when the size of the population is very large. You can choose from among the various data sampling techniques such as snowball sampling, convenience sampling, and random sampling. 

Everyone can't perform very complex statistical calculations with accuracy making statistical analysis a time-consuming and costly process. Statistical software has become a very important tool for companies to perform their data analysis. The software uses Artificial Intelligence and Machine Learning to perform complex calculations, identify trends and patterns, and create charts, graphs, and tables accurately within minutes. 

Look at the standard deviation sample calculation given below to understand more about statistical analysis.

The weights of 5 pizza bases in cms are as follows:

Calculation of Mean = (9+2+5+4+12)/5 = 32/5 = 6.4

Calculation of mean of squared mean deviation = (6.76+19.36+1.96+5.76+31.36)/5 = 13.04

Sample Variance = 13.04

Standard deviation = √13.04 = 3.611

A Statistical Analyst's career path is determined by the industry in which they work. Anyone interested in becoming a Data Analyst may usually enter the profession and qualify for entry-level Data Analyst positions right out of high school or a certificate program — potentially with a Bachelor's degree in statistics, computer science, or mathematics. Some people go into data analysis from a similar sector such as business, economics, or even the social sciences, usually by updating their skills mid-career with a statistical analytics course.

Statistical Analyst is also a great way to get started in the normally more complex area of data science. A Data Scientist is generally a more senior role than a Data Analyst since it is more strategic in nature and necessitates a more highly developed set of technical abilities, such as knowledge of multiple statistical tools, programming languages, and predictive analytics models.

Aspiring Data Scientists and Statistical Analysts generally begin their careers by learning a programming language such as R or SQL. Following that, they must learn how to create databases, do basic analysis, and make visuals using applications such as Tableau. However, not every Statistical Analyst will need to know how to do all of these things, but if you want to advance in your profession, you should be able to do them all.

Based on your industry and the sort of work you do, you may opt to study Python or R, become an expert at data cleaning, or focus on developing complicated statistical models.

You could also learn a little bit of everything, which might help you take on a leadership role and advance to the position of Senior Data Analyst. A Senior Statistical Analyst with vast and deep knowledge might take on a leadership role leading a team of other Statistical Analysts. Statistical Analysts with extra skill training may be able to advance to Data Scientists or other more senior data analytics positions.

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Hope this article assisted you in understanding the importance of statistical analysis in every sphere of life. Artificial Intelligence (AI) can help you perform statistical analysis and data analysis very effectively and efficiently. 

If you are a science wizard and fascinated by the role of AI in statistical analysis, check out this amazing Caltech Post Graduate Program in AI & ML course in collaboration with Caltech. With a comprehensive syllabus and real-life projects, this course is one of the most popular courses and will help you with all that you need to know about Artificial Intelligence. 

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What Is Statistical Analysis?

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment. 

In its simplest form, statistical analysis answers questions about:

• Quantification — how big/small/tall/wide is it?
• Variability — growth, increase, decline
• The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

• Descriptive Statistics:  Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 
• Inferential Statistics:  Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

More From Abdishakur Hassan The 7 Best Thematic Map Types for Geospatial Data

Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential. 

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range). 

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests. 

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .  

Statistical Analysis Steps  

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem. 

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it. 

The third stage involves data collection, understanding the data and checking its quality. 

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations.  You also develop and scrutinize your hypothesis in this stage of analysis. 

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

• Statistical quality control and analysis in product development 
• Clinical trials
• Customer satisfaction surveys and customer experience research 
• Marketing operations management
• Process improvement and optimization
• Training needs 

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative. 

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

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What is Statistical Analysis? Types, Methods, Software, Examples

Appinio Research · 29.02.2024 · 31min read

Ever wondered how we make sense of vast amounts of data to make informed decisions? Statistical analysis is the answer. In our data-driven world, statistical analysis serves as a powerful tool to uncover patterns, trends, and relationships hidden within data. From predicting sales trends to assessing the effectiveness of new treatments, statistical analysis empowers us to derive meaningful insights and drive evidence-based decision-making across various fields and industries. In this guide, we'll explore the fundamentals of statistical analysis, popular methods, software tools, practical examples, and best practices to help you harness the power of statistics effectively. Whether you're a novice or an experienced analyst, this guide will equip you with the knowledge and skills to navigate the world of statistical analysis with confidence.

What is Statistical Analysis?

Statistical analysis is a methodical process of collecting, analyzing, interpreting, and presenting data to uncover patterns, trends, and relationships. It involves applying statistical techniques and methodologies to make sense of complex data sets and draw meaningful conclusions.

Importance of Statistical Analysis

Statistical analysis plays a crucial role in various fields and industries due to its numerous benefits and applications:

• Informed Decision Making : Statistical analysis provides valuable insights that inform decision-making processes in business, healthcare, government, and academia. By analyzing data, organizations can identify trends, assess risks, and optimize strategies for better outcomes.
• Evidence-Based Research : Statistical analysis is fundamental to scientific research, enabling researchers to test hypotheses, draw conclusions, and validate theories using empirical evidence. It helps researchers quantify relationships, assess the significance of findings, and advance knowledge in their respective fields.
• Quality Improvement : In manufacturing and quality management, statistical analysis helps identify defects, improve processes, and enhance product quality. Techniques such as Six Sigma and Statistical Process Control (SPC) are used to monitor performance, reduce variation, and achieve quality objectives.
• Risk Assessment : In finance, insurance, and investment, statistical analysis is used for risk assessment and portfolio management. By analyzing historical data and market trends, analysts can quantify risks, forecast outcomes, and make informed decisions to mitigate financial risks.
• Predictive Modeling : Statistical analysis enables predictive modeling and forecasting in various domains, including sales forecasting, demand planning, and weather prediction. By analyzing historical data patterns, predictive models can anticipate future trends and outcomes with reasonable accuracy.
• Healthcare Decision Support : In healthcare, statistical analysis is integral to clinical research, epidemiology, and healthcare management. It helps healthcare professionals assess treatment effectiveness, analyze patient outcomes, and optimize resource allocation for improved patient care.

Statistical Analysis Applications

Statistical analysis finds applications across diverse domains and disciplines, including:

• Business and Economics : Market research , financial analysis, econometrics, and business intelligence.
• Healthcare and Medicine : Clinical trials, epidemiological studies, healthcare outcomes research, and disease surveillance.
• Social Sciences : Survey research, demographic analysis, psychology experiments, and public opinion polls.
• Engineering : Reliability analysis, quality control, process optimization, and product design.
• Environmental Science : Environmental monitoring, climate modeling, and ecological research.
• Education : Educational research, assessment, program evaluation, and learning analytics.
• Government and Public Policy : Policy analysis, program evaluation, census data analysis, and public administration.
• Technology and Data Science : Machine learning, artificial intelligence, data mining, and predictive analytics.

These applications demonstrate the versatility and significance of statistical analysis in addressing complex problems and informing decision-making across various sectors and disciplines.

Fundamentals of Statistics

Understanding the fundamentals of statistics is crucial for conducting meaningful analyses. Let's delve into some essential concepts that form the foundation of statistical analysis.

Basic Concepts

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions or conclusions. To embark on your statistical journey, familiarize yourself with these fundamental concepts:

• Population vs. Sample : A population comprises all the individuals or objects of interest in a study, while a sample is a subset of the population selected for analysis. Understanding the distinction between these two entities is vital, as statistical analyses often rely on samples to draw conclusions about populations.
• Independent Variables : Variables that are manipulated or controlled in an experiment.
• Dependent Variables : Variables that are observed or measured in response to changes in independent variables.
• Parameters vs. Statistics : Parameters are numerical measures that describe a population, whereas statistics are numerical measures that describe a sample. For instance, the population mean is denoted by μ (mu), while the sample mean is denoted by x̄ (x-bar).

Descriptive Statistics

Descriptive statistics involve methods for summarizing and describing the features of a dataset. These statistics provide insights into the central tendency, variability, and distribution of the data. Standard measures of descriptive statistics include:

• Mean : The arithmetic average of a set of values, calculated by summing all values and dividing by the number of observations.
• Median : The middle value in a sorted list of observations.
• Mode : The value that appears most frequently in a dataset.
• Range : The difference between the maximum and minimum values in a dataset.
• Variance : The average of the squared differences from the mean.
• Standard Deviation : The square root of the variance, providing a measure of the average distance of data points from the mean.
• Graphical Techniques : Graphical representations, including histograms, box plots, and scatter plots, offer visual insights into the distribution and relationships within a dataset. These visualizations aid in identifying patterns, outliers, and trends.

Inferential Statistics

Inferential statistics enable researchers to draw conclusions or make predictions about populations based on sample data. These methods allow for generalizations beyond the observed data. Fundamental techniques in inferential statistics include:

• Null Hypothesis (H0) : The hypothesis that there is no significant difference or relationship.
• Alternative Hypothesis (H1) : The hypothesis that there is a significant difference or relationship.
• Confidence Intervals : Confidence intervals provide a range of plausible values for a population parameter. They offer insights into the precision of sample estimates and the uncertainty associated with those estimates.
• Regression Analysis : Regression analysis examines the relationship between one or more independent variables and a dependent variable. It allows for the prediction of the dependent variable based on the values of the independent variables.
• Sampling Methods : Sampling methods, such as simple random sampling, stratified sampling, and cluster sampling , are employed to ensure that sample data are representative of the population of interest. These methods help mitigate biases and improve the generalizability of results.

Probability Distributions

Probability distributions describe the likelihood of different outcomes in a statistical experiment. Understanding these distributions is essential for modeling and analyzing random phenomena. Some common probability distributions include:

• Normal Distribution : The normal distribution, also known as the Gaussian distribution, is characterized by a symmetric, bell-shaped curve. Many natural phenomena follow this distribution, making it widely applicable in statistical analysis.
• Binomial Distribution : The binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials. It is commonly used to model binary outcomes, such as success or failure, heads or tails.
• Poisson Distribution : The Poisson distribution models the number of events occurring in a fixed interval of time or space. It is often used to analyze rare or discrete events, such as the number of customer arrivals in a queue within a given time period.

Types of Statistical Analysis

Statistical analysis encompasses a diverse range of methods and approaches, each suited to different types of data and research questions. Understanding the various types of statistical analysis is essential for selecting the most appropriate technique for your analysis. Let's explore some common distinctions in statistical analysis methods.

Parametric vs. Non-parametric Analysis

Parametric and non-parametric analyses represent two broad categories of statistical methods, each with its own assumptions and applications.

• Parametric Analysis : Parametric methods assume that the data follow a specific probability distribution, often the normal distribution. These methods rely on estimating parameters (e.g., means, variances) from the data. Parametric tests typically provide more statistical power but require stricter assumptions. Examples of parametric tests include t-tests, ANOVA, and linear regression.
• Non-parametric Analysis : Non-parametric methods make fewer assumptions about the underlying distribution of the data. Instead of estimating parameters, non-parametric tests rely on ranks or other distribution-free techniques. Non-parametric tests are often used when data do not meet the assumptions of parametric tests or when dealing with ordinal or non-normal data. Examples of non-parametric tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, and Spearman correlation.

Descriptive vs. Inferential Analysis

Descriptive and inferential analyses serve distinct purposes in statistical analysis, focusing on summarizing data and making inferences about populations, respectively.

• Descriptive Analysis : Descriptive statistics aim to describe and summarize the features of a dataset. These statistics provide insights into the central tendency, variability, and distribution of the data. Descriptive analysis techniques include measures of central tendency (e.g., mean, median, mode), measures of dispersion (e.g., variance, standard deviation), and graphical representations (e.g., histograms, box plots).
• Inferential Analysis : Inferential statistics involve making inferences or predictions about populations based on sample data. These methods allow researchers to generalize findings from the sample to the larger population. Inferential analysis techniques include hypothesis testing, confidence intervals, regression analysis, and sampling methods. These methods help researchers draw conclusions about population parameters, such as means, proportions, or correlations, based on sample data.

Exploratory vs. Confirmatory Analysis

Exploratory and confirmatory analyses represent two different approaches to data analysis, each serving distinct purposes in the research process.

• Exploratory Analysis : Exploratory data analysis (EDA) focuses on exploring data to discover patterns, relationships, and trends. EDA techniques involve visualizing data, identifying outliers, and generating hypotheses for further investigation. Exploratory analysis is particularly useful in the early stages of research when the goal is to gain insights and generate hypotheses rather than confirm specific hypotheses.
• Confirmatory Analysis : Confirmatory data analysis involves testing predefined hypotheses or theories based on prior knowledge or assumptions. Confirmatory analysis follows a structured approach, where hypotheses are tested using appropriate statistical methods. Confirmatory analysis is common in hypothesis-driven research, where the goal is to validate or refute specific hypotheses using empirical evidence. Techniques such as hypothesis testing, regression analysis, and experimental design are often employed in confirmatory analysis.

Methods of Statistical Analysis

Statistical analysis employs various methods to extract insights from data and make informed decisions. Let's explore some of the key methods used in statistical analysis and their applications.

Hypothesis Testing

Hypothesis testing is a fundamental concept in statistics, allowing researchers to make decisions about population parameters based on sample data. The process involves formulating null and alternative hypotheses, selecting an appropriate test statistic, determining the significance level, and interpreting the results. Standard hypothesis tests include:

• t-tests : Used to compare means between two groups.
• ANOVA (Analysis of Variance) : Extends the t-test to compare means across multiple groups.
• Chi-square test : Assessing the association between categorical variables.

Regression Analysis

Regression analysis explores the relationship between one or more independent variables and a dependent variable. It is widely used in predictive modeling and understanding the impact of variables on outcomes. Key types of regression analysis include:

• Simple Linear Regression : Examines the linear relationship between one independent variable and a dependent variable.
• Multiple Linear Regression : Extends simple linear regression to analyze the relationship between multiple independent variables and a dependent variable.
• Logistic Regression : Used for predicting binary outcomes or modeling probabilities.

Analysis of Variance (ANOVA)

ANOVA is a statistical technique used to compare means across two or more groups. It partitions the total variability in the data into components attributable to different sources, such as between-group differences and within-group variability. ANOVA is commonly used in experimental design and hypothesis testing scenarios.

Time Series Analysis

Time series analysis deals with analyzing data collected or recorded at successive time intervals. It helps identify patterns, trends, and seasonality in the data. Time series analysis techniques include:

• Trend Analysis : Identifying long-term trends or patterns in the data.
• Seasonal Decomposition : Separating the data into seasonal, trend, and residual components.
• Forecasting : Predicting future values based on historical data.

Survival Analysis

Survival analysis is used to analyze time-to-event data, such as time until death, failure, or occurrence of an event of interest. It is widely used in medical research, engineering, and social sciences to analyze survival probabilities and hazard rates over time.

Factor Analysis

Factor analysis is a statistical method used to identify underlying factors or latent variables that explain patterns of correlations among observed variables. It is commonly used in psychology, sociology, and market research to uncover underlying dimensions or constructs.

Cluster Analysis

Cluster analysis is a multivariate technique that groups similar objects or observations into clusters or segments based on their characteristics. It is widely used in market segmentation, image processing, and biological classification.

Principal Component Analysis (PCA)

PCA is a dimensionality reduction technique used to transform high-dimensional data into a lower-dimensional space while preserving most of the variability in the data. It identifies orthogonal axes (principal components) that capture the maximum variance in the data. PCA is useful for data visualization, feature selection, and data compression.

How to Choose the Right Statistical Analysis Method?

Selecting the appropriate statistical method is crucial for obtaining accurate and meaningful results from your data analysis.

Understanding Data Types and Distribution

Before choosing a statistical method, it's essential to understand the types of data you're working with and their distribution. Different statistical methods are suitable for different types of data:

• Continuous vs. Categorical Data : Determine whether your data are continuous (e.g., height, weight) or categorical (e.g., gender, race). Parametric methods such as t-tests and regression are typically used for continuous data , while non-parametric methods like chi-square tests are suitable for categorical data.
• Normality : Assess whether your data follows a normal distribution. Parametric methods often assume normality, so if your data are not normally distributed, non-parametric methods may be more appropriate.

Assessing Assumptions

Many statistical methods rely on certain assumptions about the data. Before applying a method, it's essential to assess whether these assumptions are met:

• Independence : Ensure that observations are independent of each other. Violations of independence assumptions can lead to biased results.
• Homogeneity of Variance : Verify that variances are approximately equal across groups, especially in ANOVA and regression analyses. Levene's test or Bartlett's test can be used to assess homogeneity of variance.
• Linearity : Check for linear relationships between variables, particularly in regression analysis. Residual plots can help diagnose violations of linearity assumptions.

Considering Research Objectives

Your research objectives should guide the selection of the appropriate statistical method.

• What are you trying to achieve with your analysis? : Determine whether you're interested in comparing groups, predicting outcomes, exploring relationships, or identifying patterns.
• What type of data are you analyzing? : Choose methods that are suitable for your data type and research questions.
• Are you testing specific hypotheses or exploring data for insights? : Confirmatory analyses involve testing predefined hypotheses, while exploratory analyses focus on discovering patterns or relationships in the data.

Consulting Statistical Experts

If you're unsure about the most appropriate statistical method for your analysis, don't hesitate to seek advice from statistical experts or consultants:

• Collaborate with Statisticians : Statisticians can provide valuable insights into the strengths and limitations of different statistical methods and help you select the most appropriate approach.
• Utilize Resources : Take advantage of online resources, forums, and statistical software documentation to learn about different methods and their applications.
• Peer Review : Consider seeking feedback from colleagues or peers familiar with statistical analysis to validate your approach and ensure rigor in your analysis.

By carefully considering these factors and consulting with experts when needed, you can confidently choose the suitable statistical method to address your research questions and obtain reliable results.

Statistical Analysis Software

Choosing the right software for statistical analysis is crucial for efficiently processing and interpreting your data. In addition to statistical analysis software, it's essential to consider tools for data collection, which lay the foundation for meaningful analysis.

What is Statistical Analysis Software?

Statistical software provides a range of tools and functionalities for data analysis, visualization, and interpretation. These software packages offer user-friendly interfaces and robust analytical capabilities, making them indispensable tools for researchers, analysts, and data scientists.

• Graphical User Interface (GUI) : Many statistical software packages offer intuitive GUIs that allow users to perform analyses using point-and-click interfaces. This makes statistical analysis accessible to users with varying levels of programming expertise.
• Scripting and Programming : Advanced users can leverage scripting and programming capabilities within statistical software to automate analyses, customize functions, and extend the software's functionality.
• Visualization : Statistical software often includes built-in visualization tools for creating charts, graphs, and plots to visualize data distributions, relationships, and trends.
• Data Management : These software packages provide features for importing, cleaning, and manipulating datasets, ensuring data integrity and consistency throughout the analysis process.

Popular Statistical Analysis Software

Several statistical software packages are widely used in various industries and research domains. Some of the most popular options include:

• R : R is a free, open-source programming language and software environment for statistical computing and graphics. It offers a vast ecosystem of packages for data manipulation, visualization, and analysis, making it a popular choice among statisticians and data scientists.
• Python : Python is a versatile programming language with robust libraries like NumPy, SciPy, and pandas for data analysis and scientific computing. Python's simplicity and flexibility make it an attractive option for statistical analysis, particularly for users with programming experience.
• SPSS : SPSS (Statistical Package for the Social Sciences) is a comprehensive statistical software package widely used in social science research, marketing, and healthcare. It offers a user-friendly interface and a wide range of statistical procedures for data analysis and reporting.
• SAS : SAS (Statistical Analysis System) is a powerful statistical software suite used for data management, advanced analytics, and predictive modeling. SAS is commonly employed in industries such as healthcare, finance, and government for data-driven decision-making.
• Stata : Stata is a statistical software package that provides tools for data analysis, manipulation, and visualization. It is popular in academic research, economics, and social sciences for its robust statistical capabilities and ease of use.
• MATLAB : MATLAB is a high-level programming language and environment for numerical computing and visualization. It offers built-in functions and toolboxes for statistical analysis, machine learning, and signal processing.

Data Collection Software

In addition to statistical analysis software, data collection software plays a crucial role in the research process. These tools facilitate data collection, management, and organization from various sources, ensuring data quality and reliability.

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How to Choose the Right Statistical Analysis Software?

When selecting software for statistical analysis and data collection, consider the following factors:

• Compatibility : Ensure the software is compatible with your operating system, hardware, and data formats.
• Usability : Choose software that aligns with your level of expertise and provides features that meet your analysis and data collection requirements.
• Integration : Consider whether the software integrates with other tools and platforms in your workflow, such as data visualization software or data storage systems.
• Cost and Licensing : Evaluate the cost of licensing or subscription fees, as well as any additional costs for training, support, or maintenance.

By carefully evaluating these factors and considering your specific analysis and data collection needs, you can select the right software tools to support your research objectives and drive meaningful insights from your data.

Statistical Analysis Examples

Understanding statistical analysis methods is best achieved through practical examples. Let's explore three examples that demonstrate the application of statistical techniques in real-world scenarios.

Example 1: Linear Regression

Scenario : A marketing analyst wants to understand the relationship between advertising spending and sales revenue for a product.

Data : The analyst collects data on monthly advertising expenditures (in dollars) and corresponding sales revenue (in dollars) over the past year.

Analysis : Using simple linear regression, the analyst fits a regression model to the data, where advertising spending is the independent variable (X) and sales revenue is the dependent variable (Y). The regression analysis estimates the linear relationship between advertising spending and sales revenue, allowing the analyst to predict sales based on advertising expenditures.

Result : The regression analysis reveals a statistically significant positive relationship between advertising spending and sales revenue. For every additional dollar spent on advertising, sales revenue increases by an estimated amount (slope coefficient). The analyst can use this information to optimize advertising budgets and forecast sales performance.

Example 2: Hypothesis Testing

Scenario : A pharmaceutical company develops a new drug intended to lower blood pressure. The company wants to determine whether the new drug is more effective than the existing standard treatment.

Data : The company conducts a randomized controlled trial (RCT) involving two groups of participants: one group receives the new drug, and the other receives the standard treatment. Blood pressure measurements are taken before and after the treatment period.

Analysis : The company uses hypothesis testing, specifically a two-sample t-test, to compare the mean reduction in blood pressure between the two groups. The null hypothesis (H0) states that there is no difference in the mean reduction in blood pressure between the two treatments, while the alternative hypothesis (H1) suggests that the new drug is more effective.

Result : The t-test results indicate a statistically significant difference in the mean reduction in blood pressure between the two groups. The company concludes that the new drug is more effective than the standard treatment in lowering blood pressure, based on the evidence from the RCT.

Example 3: ANOVA

Scenario : A researcher wants to compare the effectiveness of three different teaching methods on student performance in a mathematics course.

Data : The researcher conducts an experiment where students are randomly assigned to one of three groups: traditional lecture-based instruction, active learning, or flipped classroom. At the end of the semester, students' scores on a standardized math test are recorded.

Analysis : The researcher performs an analysis of variance (ANOVA) to compare the mean test scores across the three teaching methods. ANOVA assesses whether there are statistically significant differences in mean scores between the groups.

Result : The ANOVA results reveal a significant difference in mean test scores between the three teaching methods. Post-hoc tests, such as Tukey's HSD (Honestly Significant Difference), can be conducted to identify which specific teaching methods differ significantly from each other in terms of student performance.

These examples illustrate how statistical analysis techniques can be applied to address various research questions and make data-driven decisions in different fields. By understanding and applying these methods effectively, researchers and analysts can derive valuable insights from their data to inform decision-making and drive positive outcomes.

Statistical Analysis Best Practices

Statistical analysis is a powerful tool for extracting insights from data, but it's essential to follow best practices to ensure the validity, reliability, and interpretability of your results.

• Clearly Define Research Questions : Before conducting any analysis, clearly define your research questions or objectives . This ensures that your analysis is focused and aligned with the goals of your study.
• Choose Appropriate Methods : Select statistical methods suitable for your data type, research design , and objectives. Consider factors such as data distribution, sample size, and assumptions of the chosen method.
• Preprocess Data : Clean and preprocess your data to remove errors, outliers, and missing values. Data preprocessing steps may include data cleaning, normalization, and transformation to ensure data quality and consistency.
• Check Assumptions : Verify that the assumptions of the chosen statistical methods are met. Assumptions may include normality, homogeneity of variance, independence, and linearity. Conduct diagnostic tests or exploratory data analysis to assess assumptions.
• Transparent Reporting : Document your analysis procedures, including data preprocessing steps, statistical methods used, and any assumptions made. Transparent reporting enhances reproducibility and allows others to evaluate the validity of your findings.
• Consider Sample Size : Ensure that your sample size is sufficient to detect meaningful effects or relationships. Power analysis can help determine the minimum sample size required to achieve adequate statistical power.
• Interpret Results Cautiously : Interpret statistical results with caution and consider the broader context of your research. Be mindful of effect sizes, confidence intervals, and practical significance when interpreting findings.
• Validate Findings : Validate your findings through robustness checks, sensitivity analyses, or replication studies. Cross-validation and bootstrapping techniques can help assess the stability and generalizability of your results.
• Avoid P-Hacking and Data Dredging : Guard against p-hacking and data dredging by pre-registering hypotheses, conducting planned analyses, and avoiding selective reporting of results. Maintain transparency and integrity in your analysis process.

By following these best practices, you can conduct rigorous and reliable statistical analyses that yield meaningful insights and contribute to evidence-based decision-making in your field.

Conclusion for Statistical Analysis

Statistical analysis is a vital tool for making sense of data and guiding decision-making across diverse fields. By understanding the fundamentals of statistical analysis, including concepts like hypothesis testing, regression analysis, and data visualization, you gain the ability to extract valuable insights from complex datasets. Moreover, selecting the appropriate statistical methods, choosing the right software, and following best practices ensure the validity and reliability of your analyses. In today's data-driven world, the ability to conduct rigorous statistical analysis is a valuable skill that empowers individuals and organizations to make informed decisions and drive positive outcomes. Whether you're a researcher, analyst, or decision-maker, mastering statistical analysis opens doors to new opportunities for understanding the world around us and unlocking the potential of data to solve real-world problems.

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Statistical Analysis | 5 Steps & Examples

Statistical analysis involves the exploration of trends, patterns, and relationships through quantitative data. It serves as a crucial research tool for scientists, governments, businesses, and various organizations.

To draw valid conclusions, careful planning is essential from the inception of the research process. This includes specifying hypotheses and making decisions regarding research design, sample size, and sampling procedures.

After collecting data from the sample, the information can be organized and summarized using descriptive statistics. Subsequently, inferential statistics can be employed to formally test hypotheses and make estimates about the population. Finally, the findings can be interpreted and generalized.

This article serves as an introduction to statistical analysis for students and researchers, guiding them through the steps using two research examples.

The first example delves into a correlational research question, investigating the relationship between parental income and college grade point average (GPA).

The second example explores a potential cause-and-effect relationship, examining whether meditation can enhance exam performance in teenagers.

Covariate in Statistics: Examples

How to calculate the sample size for randomized controlled trials (rct), what is primary data collection types, advantages, and disadvantages, how do you avoid common mistakes in statistics, how to build a pls-sem model using amos, understanding standard deviation: a deep dive into the key concepts.

Table of Contents

Steps of Statistical Analysis Process

Step 1: develop your research design and hypotheses.

To gather valid data for statistical analysis, it’s crucial to develop hypotheses and outline the research design.

Formulating Statistical Hypotheses

Formulating Statistical Hypotheses Research often aims to explore relationships between variables within a population. The process begins with a prediction, and statistical analysis is employed to test that prediction.

A statistical hypothesis is a formal expression of a prediction about a population. Each research prediction is translated into null and alternative hypotheses, which can be tested using sample data.

The null hypothesis consistently posits no effect or relationship between variables, while the alternative hypothesis presents the research prediction of an effect or relationship.

Example: Hypotheses for Testing a Correlation

• Null hypothesis: There is no relationship between family income and GPA in university students.
• Alternative hypothesis: In university students, there is a positive relationship between family income and GPA.

Example: Hypotheses for Testing an Effect

• Null hypothesis: Teenagers’ math test scores will not be impacted by a 10-minute meditation activity.
• Alternative hypothesis: Teenagers who practice meditation for ten minutes will perform better on math tests.

Developing Research Design

Your research design is the comprehensive strategy for data collection and analysis, shaping the statistical tests applicable to test your hypotheses later.

Begin by determining whether your research will adopt a descriptive, correlational, or experimental design. Experiments exert direct influence on variables, whereas descriptive and correlational studies merely measure variables.

correlational design

In a correlational design, you can investigate relationships between variables (e.g., family income and GPA) without assuming causality, utilizing correlation coefficients and significance tests.

experimental design

In an experimental design, you can evaluate cause-and-effect relationships (e.g., the impact of meditation on test scores) using statistical tests of comparison or regression.

descriptive design

In a descriptive design, you can scrutinize the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.K. university students) and draw inferences from sample data using statistical tests.

Your research design will also address whether you will compare participants at the group, individual, or both levels.

between-subjects design

Group-level outcomes of individuals exposed to various treatments (e.g., those who undertook an exercise in meditation vs. those who did not) are compared in a between-subjects design.

within-subjects design

You compare repeated measures from participants participating in all treatments (e.g., scores before and after a meditation exercise) in a within-subjects design.

mixed design

One variable (e.g., pretest and posttest scores from participants who either did or did not undertake a meditation exercise) is manipulated between subjects in a mixed design, while another variable is manipulated within subjects.

Example: Correlational Research Design

In a correlational study, the objective is to explore the relationship between family income and GPA in graduating university students. To gather data, participants will be asked to complete a survey, self-reporting their parents’ incomes and their own GPA.

Unlike experimental designs, there are no distinct dependent or independent variables in this study. The focus is on measuring variables without actively influencing them. The aim is to examine the natural associations between family income and GPA without any experimental interventions.

Example: Experimental Research Design

Imagine designing a within-subjects experiment to investigate whether a 10-minute meditation exercise can enhance math test scores. Your study involves taking repeated measures from a single group of participants.

Here’s the process:

• Obtain baseline test scores from participants.
• Have participants engage in a 10-minute meditation exercise.
• Record participants’ scores from a second math test.

The 10-minute meditation exercise acts as the independent variable in this experiment, and the math test scores obtained both before and after the intervention act as the dependent variable.

A Glance At Derivatives & Formulas!

Principal Components Analysis (PCA) using SPSS

What is Multivariate Analysis?

Using Different Statistical Tools: A Guide to Choosing the Right Tool for Data Analysis

Type I vs Type II error in Hypothesis Testing

operationalizing your variables

When devising a research design, it’s crucial to operationalize your variables and determine precisely how you will measure them.

For statistical analysis, the level of measurement of your variables is a key consideration, indicating the nature of the data they encompass:

• Groupings can be nominal or ordinal in categorical data.
• Quantitative data is a representation of amounts that can be on an interval or ratio scale.

Variables may be measured at different levels of precision. For instance, age data can be either quantitative (e.g., 9 years old) or categorical (e.g., young). The numerical coding of a variable (e.g., a rating from 1–5 indicating the level of agreement) does not automatically determine its measurement level.

Choosing the right statistical methods and hypothesis testing requires knowing the measurement level. For example, with quantitative data, you can determine a mean score, but not with categorical data.

In addition to measuring variables of interest, data on relevant participant characteristics is frequently collected in a research study.

Measurement of Scale | Examples | PPT

Mixed Method Research: What It Is & Why You Should Use It

Types of Validity in Research | Examples | PPT

Example: nature of variables in Correlational Study

In a correlational study, the nature of the variables determines the test used for a correlation coefficient. When dealing with quantitative data, a parametric correlation test can be used; however, if one of the variables is ordinal, a non-parametric correlation test must be conducted.

Example: nature of variables in Experiment

While categorical variables can be used to determine groupings for comparison tests, quantitative age or test score data can be subjected to a number of calculations.

Step 2: Data Collection from a Sample

In most instances, it is impractical or costly to collect data from every individual in the population under study. Consequently, data is often gathered from a sample.

Statistical analysis allows for the extrapolation of findings beyond the sample as long as appropriate sampling procedures are employed. The goal is to have a sample that accurately represents the population.

Two primary approaches are employed in sample selection:

• Probability Sampling: Each member of the population has an equal chance of being chosen through random selection.
• Non-Probability Sampling: Certain members of the population are more likely to be chosen on the basis of convenient or voluntary self-selection criteria.

In theory, for highly generalizable results, probability sampling is preferred. Random selection minimizes various forms of research bias, like sampling bias, ensuring that the sample data is genuinely representative of the population. Parametric tests can then be used for robust statistical inferences.

However, in practice, it’s often challenging to achieve an ideal sample. Non-probability samples are more susceptible to biases like self-selection bias, but they are more accessible for recruitment and data collection. Non-parametric tests are suitable for non-probability samples, although they lead to weaker inferences about the population.

If you wish to employ parametric tests for non-probability samples, you need to argue:

• Your sample is a true representation of the population you aim to generalize your findings to.
• Your sample is devoid of systematic bias.

It is important to understand that applying external validity requires you to limit the generalization of findings to individuals who possess similar characteristics to your sample. For instance, findings from samples that are Western, educated, Industrialized, Rich, and Democratic cannot be generalized to all non-WEIRD populations.

When applying parametric tests to data from non-probability samples, it’s essential to discuss the limitations of generalizing your results in the discussion section.

Difference between Descriptive and Inferential Statistics

Friedman Test: Example, and Assumptions

T-test | Example, Formula | When to Use a T-test

Chi-Square Test (Χ²) || Examples, Types, and Assumptions

Develop an Effective Sampling Strategy

Decide how you will recruit participants based on the resources available for your research.

• Will you have the means to advertise your research broadly, even outside of the confines of your university?
• Will you be able to assemble a representative sample of the entire population that is diverse?
• Are you able to follow up with members of groups who are difficult to reach?

The primary population of interest is male university students in the United States. To gather participants, you utilize social media advertising and target senior-year male university students from a more specific subpopulation—namely, seven universities in the Boston area. In this scenario, participants willingly volunteer for the survey, indicating that this is a non-probability sample.

The focus is on the population of university students in your city. To recruit participants, you reach out to three private schools and seven public schools across different districts within the city, intending to conduct your experiment with bachelor’s students. The participants in this case are self-selected through their universities. Despite the use of a non-probability sample, efforts are made to ensure a diverse and representative sample.

Determine the Appropriate Sample Size

Before initiating the participant recruitment process, establish the sample size for your study. This can be accomplished by reviewing existing studies in your field or utilizing statistical methods. It’s crucial to avoid a sample that is too small, as it may not accurately represent the population, while an excessively large sample can incur unnecessary costs.

Several online sample size calculators are available, each using different formulas depending on factors such as the presence of subgroups or the desired rigor of the study (e.g., in clinical research). A general guideline is to have a minimum of 30 units per subgroup. To utilize these calculators effectively, you need to comprehend and input key components:

• Significance level (alpha): This is the risk of incorrectly rejecting a true null hypothesis, typically set at 5%.
• Population standard deviation: This is an estimate of the population parameter derived from a previous study or a pilot study conducted for your research.
• Expected effect size: This is a standardized measure of the anticipated magnitude of the study’s results, often based on similar studies.
• Statistical power: This is the likelihood that your study will detect an effect of a certain size if it exists, usually set at 80% or higher.

Step 3: Summarize Your Data Using Descriptive Statistics

After gathering all your data, the next step is to examine and summarize them using descriptive statistics.

Analyzing Data

• Organize Data: Create frequency distribution tables for each variable.
• Visual Representation: Use bar charts to illustrate the distribution of responses for a key variable.
• Explore Relationships: Utilize scatter plots to visualize the relationship between two variables.

By presenting your data in tables and graphs, you can evaluate whether the data exhibit a skewed or normal distribution and identify any outliers or missing data.

A normal distribution indicates that the data are symmetrically distributed around a central point, with the majority of values clustered there and tapering off towards the tail ends.

In contrast, a skewed distribution is asymmetrical and exhibits more values on one end than the other. Understanding the distribution’s shape is crucial because certain descriptive statistics are more suitable for skewed distributions.

The presence of extreme outliers can also distort statistics, necessitating a systematic approach to handling such values.

Determine Central Tendency Measures

Measures of central tendency indicate where the majority of values in a data set are concentrated.

The three primary measures are:

• Mode: The most frequent response or value in the data set.
• Median: The middle value when the data set is ordered from low to high.
• Mean: The sum of all values divided by the number of values.

However, the appropriateness of these measures depends on the distribution’s shape and the level of measurement. For instance, demographic characteristics may be described using the mode or proportions, while variables like reaction time may lack a mode.

Measures of Variability

Measures of variability convey how dispersed the values in a data set are. Four main measures are commonly reported:

• Range: The difference between the highest and lowest values in the data set.
• Interquartile Range: The range of the middle half of the data set.
• Standard Deviation: The average distance between each value in the data set and the mean.
• Variance: The square of the standard deviation.

Once again, the choice of variability statistics should be guided by the distribution’s shape and the level of measurement. The interquartile range is preferable for skewed distributions, while standard deviation and variance offer optimal information for normal distributions.

Example: Correlational Study

Following the collection of data from 567 students, descriptive statistics for annual family income and GPA are tabulated.

It is crucial to verify whether there is a broad range of data points. Insufficient variation in data points may result in skewness toward specific groups (e.g., high academic achievers), limiting the generalizability of inferences about a relationship.

Next, the computation of a correlation coefficient and the performance of a statistical test will provide insights into the significance of the relationship between the variables in the population.

Example: Experiment

Following the collection of pretest and posttest data from 30 students across the city, descriptive statistics are calculated. Given the normal distribution of data on an interval scale, the mean, standard deviation, variance, and range are tabulated.

It is crucial to examine whether the units of descriptive statistics are comparable for pretest and posttest scores using the table. Specifically, one should assess whether the variance levels are similar across the groups and identify any extreme values. If extreme outliers are present, they may need identification and removal from the dataset, or data transformation may be required before conducting a statistical test.

This table shows that following the meditation exercise, the mean score increased, and the variances of the two scores are similar. To find out if this increase in test scores is statistically significant throughout the population, a statistical test must be performed.

Step 4: Use Inferential Statistics to Test Hypotheses or Make Estimates

A numerical description of a sample is termed a statistic, while a number characterizing a population is referred to as a parameter. Inferential statistics enable drawing conclusions about population parameters based on sample statistics.

Researchers commonly employ two primary methods concurrently for statistical inferences:

• Estimation: This involves calculating population parameters based on sample statistics.
• Hypothesis Testing: It is a formal process for assessing research predictions about the population using samples.

There are two types of estimates for population parameters derived from sample statistics:

• Point Estimate: A single value representing the best guess of the exact parameter.
• Interval Estimate: A range of values representing the best guess of the parameter’s location.

In cases where the goal is to infer and report population characteristics from sample data, utilizing both point and interval estimates is advisable.

A sample statistic can serve as a point estimate for the population parameter when dealing with a representative sample. For instance, in a broad public opinion poll, the proportion of a sample supporting the current government is considered the population proportion of government supporters.

As estimation inherently involves error, providing a confidence interval as an interval estimate is essential to illustrate the variability around a point estimate. A confidence interval utilizes the standard error and the z-score from the standard normal distribution to indicate the range where the population parameter is likely to be found most of the time.

Hypothesis Testing

Testing hypotheses includes using data from a sample to assess hypotheses regarding the relationships between variables in the population. The null hypothesis is first assumed to be true for the population, and statistical tests are then used to see if the null hypothesis can be rejected.

Statistical tests ascertain where your sample data would fall on an expected distribution of sample data under the assumption that the null hypothesis is true. These tests yield two primary outcomes:

• Test Statistic: Indicates the extent to which your data deviates from the null hypothesis.
• p-value: Represents the likelihood of obtaining your results if the null hypothesis is indeed true in the population.

Statistical tests fall into three main categories:

• Regression Tests: Evaluate cause-and-effect relationships between variables.
• Comparison Tests: Assess group differences in outcomes.
• Correlation Tests: Examine relationships between variables without assuming causation.

A number of factors, such as the research questions, sampling method, research design, and data characteristics, influence the choice of statistical test.

Parametric Tests

Parametric tests enable robust inferences about the population based on sample data. However, certain assumptions must be met, and only specific types of variables can be used. If these assumptions are violated, appropriate data transformations or alternative non-parametric tests should be considered.

• Simple Linear Regression: Involves one predictor variable and one outcome variable.
• Multiple Linear Regression: Incorporates two or more predictor variables and one outcome variable.
• t-test: Applicable for 1 or 2 groups with a small sample size (30 or less).
• z-test: Suitable for 1 or 2 groups with a large sample size.
• ANOVA: Used when comparing means across 3 or more groups.

The z and t tests come with various subtypes based on the number and types of samples, as well as the hypotheses being tested:

• One-Sample Test: Applied when you have only one sample that you want to compare to a population mean.
• Dependent (Paired) Samples Test: Utilized for paired measurements in a within-subjects design.
• Independent (Unpaired) Samples Test: Employed when dealing with completely separate measurements from two unmatched groups in a between-subjects design.
• One-Tailed Test: Preferable if you expect a difference between groups in a specific direction.
• Two-Tailed Test: Suitable when you don’t have expectations for the direction of a difference between groups.

For parametric correlation testing, Pearson’s r is the primary tool. This correlation coefficient (r) gauges the strength of a linear relationship between two quantitative variables.

To assess whether the correlation in the sample holds significance in the population, a significance test of the correlation coefficient is conducted, usually using a t test, to obtain a p-value. This test leverages the sample size to determine how much the correlation coefficient deviates from zero in the population.

Example: Significance Test with Correlation Coefficient:

In investigating the relationship between family income and GPA, Pearson’s r is employed to quantify the strength of the linear correlation within the sample. The calculated Pearson’s r value of 0.12 indicates a small correlation observed in the sample.

While Pearson’s r serves as a test statistic, it alone does not provide insights into the significance of the correlation in the broader population. To ascertain whether this sample correlation is substantial enough to reflect a correlation in the population, a t-test is conducted. In this scenario, anticipating a positive correlation between parental income and GPA, a one-sample, one-tailed t-test is utilized. The results of the t-test are as follows:

• t Value: 3.08
• p Value: 0.001

These outcomes from the statistical test offer insights into the significance of the correlation, helping determine if the observed correlation in the sample holds importance in the broader population.

Example: Experimental Research Using Paired T-Tests:

In the context of a within-subjects experiment design, where both pretest and posttest measurements originate from the same group, a dependent (paired) t-test is employed. Given the anticipation of a change in a specific direction (an enhancement in test scores), a one-tailed test is deemed necessary.

For instance, let’s consider a study evaluating the impact of a meditation exercise on math test scores. Using a dependent-samples, one-tailed t-test, the following results are obtained:

• t Value (Test Statistic): 3.00
• p Value: 0.0028

These outcomes from the statistical test help determine whether the meditation exercise had a statistically significant effect on improving math test scores.

Step 5: Interpretation of the Results

The last step of statistical analysis involves the interpretation of your findings.

Statistically significant

In hypothesis testing, statistical significance stands as the principal criterion for drawing conclusions. The assessment involves comparing the obtained p value with a predetermined significance level, typically set at 0.05. This evaluation determines whether your results hold statistical significance or are deemed non-significant.

Results are deemed statistically significant when the likelihood of their occurrence due to chance alone is exceptionally low. Such outcomes suggest a minimal probability of the null hypothesis being true in the broader population, reinforcing the credibility of the observed results.

Example: Interpret Your Correlational Study Results

Upon comparing the obtained p value of 0.001 with the significance threshold set at 0.05, it is evident that the p value falls below this threshold. Consequently, you can reject the null hypothesis, signifying a statistically significant correlation between parental income and GPA in male college students.

It is essential to acknowledge that correlation does not inherently imply causation. Complex variables like GPA are often influenced by numerous underlying factors. A correlation between two variables may be due to a third variable impacting both or indirect connections between the two variables.

Additionally, it’s crucial to recognize that a large sample size can strongly influence the statistical significance of a correlation coefficient, potentially making even small correlations appear significant.

Example: interpret your experiment’s results

Upon scrutinizing the obtained p value of 0.0027 and comparing it to the predetermined significance threshold of 0.05, you discover that the p value is lower. Consequently, you opt to reject the null hypothesis, establishing your results as statistically significant.

This implies that, in your interpretation, the observed elevation in test scores is attributed to the meditation intervention rather than random factors.

Effect Size

While statistical significance provides information about the likelihood of chance influencing your results, it doesn’t inherently convey the practical importance or clinical relevance of your findings.

On the other hand, the effect size shows how useful your conclusions are in real-world situations. For a comprehensive understanding of your findings, it’s critical to include effect sizes in addition to your inferential statistics. In an APA style paper, you should additionally include interval estimates of the effect sizes.

Example: effect size of the correlation coefficient

When evaluating the effect size of the correlation coefficient, you reference Cohen’s effect size criteria with your Pearson’s r value. Falling between 0.1 and 0.3, your discovery of a correlation between family income and GPA indicates a very small effect, suggesting limited practical significance.

Example: Effect Size of the Experimental Research

In assessing the impact of the meditation exercise on test scores, you compute Cohen’s d, revealing a value of 0.72. This denotes a medium to high level of practical significance, indicating a substantial difference between pretest and posttest scores attributable to the meditation intervention.

Type I and Type II errors

In research conclusions, mistakes can occur in the form of Type I and Type II errors. A Type I error involves rejecting the null hypothesis when it is, in fact, true, while a Type II error occurs when the null hypothesis is not rejected when it is false.

Making sure there is high power and choosing the ideal significance level are crucial steps in reducing the possibility of these errors. But there is a trade-off between the two types of errors, so one needs to consider them carefully.

Bayesian Statistics versus Frequentist statistics

Frequentist statistics has traditionally focused on testing the significance of the null hypothesis and started with the assumption that the null hypothesis is true. In contrast, Bayesian statistics have become more prevalent as an alternative approach.

In Bayesian statistics, previous research is used to continuously update hypotheses based on expectations and observations.

In Bayesian statistics, the Bayes factor is a fundamental concept that compares the relative strength of evidence supporting the alternative hypothesis against the null hypothesis without necessarily concluding that the null hypothesis should be rejected.

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Statistical Analysis in Research: Meaning, Methods and Types

Home » Videos » Statistical Analysis in Research: Meaning, Methods and Types

The scientific method is an empirical approach to acquiring new knowledge by making skeptical observations and analyses to develop a meaningful interpretation. It is the basis of research and the primary pillar of modern science. Researchers seek to understand the relationships between factors associated with the phenomena of interest. In some cases, research works with vast chunks of data, making it difficult to observe or manipulate each data point. As a result, statistical analysis in research becomes a means of evaluating relationships and interconnections between variables with tools and analytical techniques for working with large data. Since researchers use statistical power analysis to assess the probability of finding an effect in such an investigation, the method is relatively accurate. Hence, statistical analysis in research eases analytical methods by focusing on the quantifiable aspects of phenomena.

What is Statistical Analysis in Research? A Simplified Definition

Statistical analysis uses quantitative data to investigate patterns, relationships, and patterns to understand real-life and simulated phenomena. The approach is a key analytical tool in various fields, including academia, business, government, and science in general. This statistical analysis in research definition implies that the primary focus of the scientific method is quantitative research. Notably, the investigator targets the constructs developed from general concepts as the researchers can quantify their hypotheses and present their findings in simple statistics.

When a business needs to learn how to improve its product, they collect statistical data about the production line and customer satisfaction. Qualitative data is valuable and often identifies the most common themes in the stakeholders’ responses. On the other hand, the quantitative data creates a level of importance, comparing the themes based on their criticality to the affected persons. For instance, descriptive statistics highlight tendency, frequency, variation, and position information. While the mean shows the average number of respondents who value a certain aspect, the variance indicates the accuracy of the data. In any case, statistical analysis creates simplified concepts used to understand the phenomenon under investigation. It is also a key component in academia as the primary approach to data representation, especially in research projects, term papers and dissertations. 

Most Useful Statistical Analysis Methods in Research

Using statistical analysis methods in research is inevitable, especially in academic assignments, projects, and term papers. It’s always advisable to seek assistance from your professor or you can try research paper writing by CustomWritings before you start your academic project or write statistical analysis in research paper. Consulting an expert when developing a topic for your thesis or short mid-term assignment increases your chances of getting a better grade. Most importantly, it improves your understanding of research methods with insights on how to enhance the originality and quality of personalized essays. Professional writers can also help select the most suitable statistical analysis method for your thesis, influencing the choice of data and type of study.

Descriptive Statistics

Descriptive statistics is a statistical method summarizing quantitative figures to understand critical details about the sample and population. A description statistic is a figure that quantifies a specific aspect of the data. For instance, instead of analyzing the behavior of a thousand students, research can identify the most common actions among them. By doing this, the person utilizes statistical analysis in research, particularly descriptive statistics.

• Measures of central tendency . Central tendency measures are the mean, mode, and media or the averages denoting specific data points. They assess the centrality of the probability distribution, hence the name. These measures describe the data in relation to the center.
• Measures of frequency . These statistics document the number of times an event happens. They include frequency, count, ratios, rates, and proportions. Measures of frequency can also show how often a score occurs.
• Measures of dispersion/variation . These descriptive statistics assess the intervals between the data points. The objective is to view the spread or disparity between the specific inputs. Measures of variation include the standard deviation, variance, and range. They indicate how the spread may affect other statistics, such as the mean.
• Measures of position . Sometimes researchers can investigate relationships between scores. Measures of position, such as percentiles, quartiles, and ranks, demonstrate this association. They are often useful when comparing the data to normalized information.

Inferential Statistics

Inferential statistics is critical in statistical analysis in quantitative research. This approach uses statistical tests to draw conclusions about the population. Examples of inferential statistics include t-tests, F-tests, ANOVA, p-value, Mann-Whitney U test, and Wilcoxon W test. This

Common Statistical Analysis in Research Types

Although inferential and descriptive statistics can be classified as types of statistical analysis in research, they are mostly considered analytical methods. Types of research are distinguishable by the differences in the methodology employed in analyzing, assembling, classifying, manipulating, and interpreting data. The categories may also depend on the type of data used.

Predictive Analysis

Predictive research analyzes past and present data to assess trends and predict future events. An excellent example of predictive analysis is a market survey that seeks to understand customers’ spending habits to weigh the possibility of a repeat or future purchase. Such studies assess the likelihood of an action based on trends.

Prescriptive Analysis

On the other hand, a prescriptive analysis targets likely courses of action. It’s decision-making research designed to identify optimal solutions to a problem. Its primary objective is to test or assess alternative measures.

Causal Analysis

Causal research investigates the explanation behind the events. It explores the relationship between factors for causation. Thus, researchers use causal analyses to analyze root causes, possible problems, and unknown outcomes.

Mechanistic Analysis

This type of research investigates the mechanism of action. Instead of focusing only on the causes or possible outcomes, researchers may seek an understanding of the processes involved. In such cases, they use mechanistic analyses to document, observe, or learn the mechanisms involved.

Exploratory Data Analysis

Similarly, an exploratory study is extensive with a wider scope and minimal limitations. This type of research seeks insight into the topic of interest. An exploratory researcher does not try to generalize or predict relationships. Instead, they look for information about the subject before conducting an in-depth analysis.

The Importance of Statistical Analysis in Research

As a matter of fact, statistical analysis provides critical information for decision-making. Decision-makers require past trends and predictive assumptions to inform their actions. In most cases, the data is too complex or lacks meaningful inferences. Statistical tools for analyzing such details help save time and money, deriving only valuable information for assessment. An excellent statistical analysis in research example is a randomized control trial (RCT) for the Covid-19 vaccine. You can download a sample of such a document online to understand the significance such analyses have to the stakeholders. A vaccine RCT assesses the effectiveness, side effects, duration of protection, and other benefits. Hence, statistical analysis in research is a helpful tool for understanding data.

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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What Is Statistical Analysis: Types, Methods, Steps & Examples

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Statistical analysis is the process of analyzing data in an effort to recognize patterns, relationships, and trends. It involves collecting, arranging and interpreting numerical data and using statistical techniques to draw conclusions.

Statistical analysis in research is a powerful tool used in various fields to make sense of quantitative data. Numbers speak for themselves and help you make assumptions on what may or may not happen if you take a certain course of action.

For example, let's say that you run an ecommerce business that sells coffee. By analyzing the amount of sales and the quantity of coffee produced, you can guess how much more coffee you should manufacture in order to increase sales.

In this blog by dissertation services , we will explore the basics of statistical analysis, including its types, methods, and steps on how to analyze statistical data. We will also provide examples to help you understand how statistical analysis methods are applied in different contexts.

What Is Statistical Analysis: Definition

Statistical analysis is a set of techniques used to analyze data and draw inferences about the population being studied. It involves organizing data, summarizing key patterns , and calculating the probability that observations could have occurred randomly. Statistics help to test hypotheses and determine the link between independent and dependent variables .

It is widely used to optimize processes, products, and services in various fields, including:

• Social sciences, etc.

The ultimate goal of statistical analysis is to extract meaningful insights from data and make predictions about causal relationships. It can also allow researchers to make generalizations about entire populations.

Types of Statistical Analysis

In general, there are 7 different types of statistical analysis, with descriptive, inferential and predictive ones being the most commonly used.

• Summarizes data in tables, charts, or graphs to help you find patterns.
• Includes calculating averages, percentages, mean, median and standard deviation.
• Draws inferences from a sample and estimates characteristics of a population, generalizing insights from a smaller group to a larger one.
• Includes hypothesis testing and confidence intervals.
• Uses data to oversee future trends and patterns.
• Relies on regression analysis and machine learning techniques.
• Uses data to make informed decisions and suggest actions.
• Comprises optimization models and network analysis.
• Investigates data and discovers relationships between variables.
• Requires cluster analysis, principal component analysis, and factor analysis.
• Examines the effect of one or more independent variables on a dependent variable.
• Implies experiments, surveys, and interviews.
• Studies how different variables interact and affect each other.
• Includes mathematical models and simulations.

What Are Statistics Used for?

People apply statistics for a variety of purposes across numerous fields, including research, business and even everyday life. Researchers most frequently opt for statistical methods in research in such cases:

• To scrutinize a dataset in experimental and non-experimental research designs and describe the core features
• To test the validity of a claim and determine whether occurring outcomes are due to an actual effect
• To model a causal connection between variables and foresee potential links
• To monitor and improve the quality of products or services by spotting trends
• To assess and manage potential risks.

As you can see, we can avail from statistical analysis tools in literally any area of our life to interpret our surroundings and observe tendencies. Any assumptions that we make after studying a sample can either make or break our research efforts. And a meticulous statistical analysis will ensure that you are making the best guess.

Statistical Analysis Methods

There is no shortage of statistical methods and techniques that can be exercised to make assumptions. When done right, these methods will streamline your research and enlighten you with meaningful insights into the correlation between various factors or processes.

As a student or researcher, you will most likely deal with the following statistical methods of data analysis in your studies:

• Mean: average value of a dataset.
• Standard deviation: measure of variability in data.
• Regression: predicting one variable based on another.
• Hypothesis testing: statistical testing of a hypothesis.
• Sample size: number of individuals to be observed.

Let's discuss each of these statistical analysis techniques in more detail.

Imagine that you need to figure out the standard value in a set of numbers. Mean is a common type of statistical research methods that gives a measure of the average value.

The mean value is calculated by summing up all data points and then dividing it by the number of individuals. It's a useful method for exploratory analysis as it shows how much of the data fall close to the average.

You want to calculate the average age of 500 people working in your enterprise. You would add up the ages of all 500 people and divide by 500 to calculate the mean age: (25+31+27+28+34...)/500=27.

Standard Deviation

Sometimes, you will need to figure out how your data is distributed. That's where a standard deviation comes in! The standard deviation is a statistical method that gives a clue of how far your data is located from the average value (mean).

A higher standard deviation indicates that the data is more spread out from the mean, while a lower standard deviation indicates that the data is more tightly clustered around the mean.

Let's take the same example as above and calculate how much the ages fluctuate from the average value, which is 27. You would subtract each age from the mean and then square the result. Then you add up all results and divide them by 500 (the number of individuals). You would end up with the standard deviation of your data set.

Regression is one of the most powerful types of statistical methods, as it allows you to make accurate predictions based on existing data. It showcases the link between two or more variables and allows you to estimate any unknown values. By using regression, you can measure how one factor impacts another one and forecast future values of the dependent variable.

You want to predict the price of a house based on its size. You would retrieve details on the size and price of several houses in a given district. You would then use regression analysis to determine if the size affects pricing. After recognizing a positive correlation between variables, you could then develop an equation that will allow to prognose the price of a house based on its size.

Hypothesis Testing

Hypothesis testing is another statistical analysis tool which allows you to ascertain if your assumptions hold true or not. By conducting tests, you can prove or disprove your hypothesis.

You are testing a new drug and would like to know if it has any effect on lowering cholesterol level. You can use hypothesis testing to compare the results of your treatment group and control group . Significant difference between results would imply that the drug can decrease cholesterol levels.

Sample Size

In order to draw reliable conclusions from your data analysis, you need to have a sample size large enough to provide you with accurate results. The size of the sample can greatly influence the reliability of your analysis, so it's important to decide on the right number of individuals.

You want to conduct a survey about customer satisfaction in your business. The sample size should be broad enough to offer you representative results. You would need to question as many clients as possible to obtain insightful information.

These are just a few examples of statistical analysis and its methods. By using them wisely, you will be able to make accurate verdicts.

Statistical Analysis Process

Now that you are familiar with the most essential methods and tools for statistical analysis, you are ready to get started with the process itself. Below we will explain how to perform statistical analysis in the right order. Stick to our detailed steps to run a foolproof study like a professional statistical analyst.

1. Prepare Your Hypotheses

Before you start digging into the numbers, it's important to formulate a hypothesis . 

Generally, there are two types of hypotheses that you will need to divide – a null hypothesis and an alternative hypothesis. The null assumption implies that the studied phenomenon is not true, while the alternative one suggests that it’s actually true.

First, detect a research question or problem that you want to investigate. Then, you should build 2 opposite statements that outline the relationship between variables in your study.

For example if you want to check how some specific exercise influences a person's resting heart rate, your hypotheses might look like this:

Null hypothesis: The exercise has no effect on resting heart rate. Alternative hypothesis:  The exercise reduces resting heart rate.

2. Collect Data

Your next step in conducting statistical data analysis is to make sure that you are working with the right data. After all, you don't want to realize that the information you obtained doesn't fit your research design .

To choose appropriate data for your study, keep a few key points in mind. First, you'll want to identify a trustworthy data source. This could be data from the primary source – a survey, poll or experiment you've conducted, or the secondary source – from existing databases, research articles, or other scholarly publications. If you are running an authentic research, most likely you will need to organize your own experimental study or survey.

You should also have enough data to work with. Decide on an adequate sample size or a sufficient time period. This will help make your data analysis applicable to broader populations.

As you're gathering data , don't forget to check its format and accessibility. You'll want the data to be in a usable form, so you might need to convert or aggregate it as needed.

Sampling Techniques for Data Analysis

Now, let's ensure that you are acquainted with the sampling methods. In general, they fall into 2 main categories: probability and non-probability sampling.

If you are performing a survey to investigate the shopping behaviors of people living in the USA, you can use simple random sampling. This means that you will randomly select individuals from a larger population.

3. Arrange and Clean Your Data

The information you retrieve from a sample may be inconsistent and contain errors. Before doing further manipulations, you will need to preprocess data. This is a crucial step in the process of statistical analysis as it allows us to prepare information for the next step.

Arrange your data in a logical fashion and see if you can detect any discrepancies. At this stage, you will need to look for potential missing values or duplicate entries. Here are some typical issues researchers deal with when digesting their data for a statistical study:

• Handling missing values Sometimes, certain entries might be absent. To fix this, you can either remove the entries with missing values or fill in the blanks based on already available data.
• Transforming variables In some cases, you might need to change the way a variable is measured or presented to make it more suitable for your data analysis. This can involve adjusting the scale of the variable or making its distribution more "normal."
• Resampling data Resampling is a technique used to alter data organization, like taking a smaller sample from a larger dataset or rearranging data points to create a new sample. This way, you will be able to enhance the accuracy of your analysis or test different scenarios.

Once your data is shovel-ready, you are ready to select statistical tools for data analysis and scrutinize the information.

4. Perform Data Analysis

Finally, we got to the most important stage – conducting data analysis. You will be surprised by the abundance of statistical methods. Your choice should largely depend on the type and scope of your research proposal or project. Keep in mind that there is no one-size-fits-all approach and your preference should be tailored to your particular research objective.

In some cases, descriptive statistics may be sufficient to answer the research question or hypothesis. For example, if you want to describe the characteristics of a population, such as the average income or education level, then descriptive statistics alone may be appropriate.

In other cases, you may need to use both descriptive and inferential statistics. For example, if you want to compare the means of 2 or more groups, such as the average income of men and women, then you would need to develop predictive models using inferential statistics or run hypothesis tests.

We will go through all scenarios so you can pick the right statistical methods for your specific instance.

Summing Up Data With Descriptive Statistics

To perform efficient statistical analysis, you need to see how numbers create a bigger picture. Some patterns aren't apparent from the first glance and may be hidden deep in raw data.

That's why your data should be presented in a clear manner. Descriptive statistics is the best way to handle this task.

Using Graphs

Your departure point is categorizing your information. Divide data into logical groups and think how to further visualize it. There are various graphical methods to uncover patterns:

• Bar charts: present relative frequencies of different groups
• Line charts: demonstrate how different variables change over time
• Scatter plots: show the connection between two variables
• Histograms: enable to detect the shape of data distribution
• Pie charts: provide visual representation of relative frequencies
• Box plots: help to identify significant outliers.

Imagine that you are analyzing the relationship between a person's age and their income. You have collected data on the age and income of 50 individuals, and you want to confirm if there is any relationship. You decide to use a scatter plot with age on x-axis and income on y-axis. When you look at the scatter plot, you might notice that there is a general trend of income increasing with age. This might indicate that older individuals tend to have higher incomes. However, there may be some variation in data, with some people having higher or lower incomes than you expected.

Calculating Averages

Based on how your data is distributed, you will need to calculate your averages, otherwise known as measures of central tendency. There are 3 methods allowing to analyze statistical data:

• Mean: useful when data is normally distributed.
• Median: a better measure in data sets with extreme outliers.
• Mode: handy when looking for the most common value in a data set.

Assessing Variability

In addition to measures of central tendency, statistical analysts often want to assess the spread or variability of their data. There are several measures of variability popular in statistical analysis:

• Range: Difference between the maximum and minimum values.
• Interquartile range (IQR): Difference between the 75th percentile and 25th percentile.
• Standard deviation: Measure of how widely values are dispersed from the mean.
• Variance: Measure of how far a set of numbers is spread out.

While range is the simplest one, it can be influenced by extreme values. The variance and standard deviation require additional calculations, but they are more robust in terms of showing the distance of each data point from the mean.

Testing Hypotheses with Inferential Statistics

After conducting descriptive statistics, researchers can use inferential statistics to build assumptions about a larger population.

One common method of inferential statistics is hypothesis testing. This involves determining the probability that the null hypothesis is correct. If the probability is low, the null hypothesis can be denied and the alternative hypothesis is accepted. When testing hypotheses, it is important to pick the appropriate statistical test (test statistic or p value) and consider factors such as sample size, statistical significance, and effect size.

Researchers test whether a new medication is effective at treating a medical condition by randomly assigning patients to a treatment group and a control group. They measure the outcome of interest and use a t-test to determine whether the medication is effective. As a result of calculation, researchers reveal that their t-value is less than the critical value. This indicates that the difference between the treatment and control groups is not statistically significant and the null hypothesis cannot be denied. As a result, researchers can conclude that the new medication is not effective at treating this medical condition.

Another method of inferential statistics is confidence intervals, which estimate the range of values that the true population parameter is likely to fall within.

If certain conditions for variables are satisfied, you can draw statistical inference using regression analysis. This technique helps researchers devise a scheme of how variables are interconnected in a study. There are different types of regression depending on the variables you're working with:

• Linear regression: used for predicting the value of a continuous variable.
• Logistic regression: chosen if scientists work with categorical data.
• Multiple regression: used to determine the relationship between several independent variables and a single outcome variable.

As you can see, there are various approaches in statistical analytics. Depending on the kind of data you are processing, you have to choose the right type of statistical analysis.

5. Interpret the Outcomes

After conducting the statistical analysis, it is important to interpret the results. This includes determining whether a hypothesis was accepted or rejected. If the hypothesis is accepted, it means that the data supports the original claim. You should further assess if data followed any patterns, and if so, what those patterns mean.

It is also important to consider any errors that could have occurred during the analysis, such as measurement error or sampling bias. These errors can affect your results and can lead to incorrect interpretations if not accounted for.

Make sure you communicate the results effectively to others. This may involve creating reports, or giving a presentation to other members of your research team. The choice of format for presenting the results will depend on the intended audience and the goals of your statistical analysis. You may also need to check the guidelines of any specific paper format you are working with. For example, if you are writing in APA style , you might need to learn more about reporting statistics in APA . 

After conducting a regression analysis, you found that there is a statistically significant positive relationship between the number of hours spent studying and the exam scores. Specifically, for every additional hour of studying, the exam score increased by an average of 5 points (β = 5.0, p < 0.001). Based on these results, you can conclude that the more time students spend studying, the higher their exam scores tend to be. However, it's important to note that there may be other factors that could also be influencing the exam scores, such as prior knowledge or natural ability. Therefore, you should account for these confounding variables when interpreting the results.

Benefits of Statistical Analysis

Statistics in research is a solid instrument for understanding numerical data in a quantitative study . Here are some of the key benefits of statistical analysis:

• Identifying patterns and relationships
• Testing hypotheses
• Making assumptions and forecasts
• Measuring uncertainty
• Comparing data.

Statistics Drawbacks

Statistical analysis can be powerful and useful, but it also has some limitations. Some of the key cons of statistics include:

• Reliance on data accuracy and quality
• Inability to provide complete explanations for results
• Chance of incorrect interpretation or application of results
• Need for specialized knowledge or software
• Complexity of analysis.

Bottom Line on Statistical Analysis

Statistical analysis is an essential tool for any researcher, scientist, or student who are coping with quantitative data. However, accuracy of data is paramount in any statistical analysis – if the data fails, then the results can be misleading. Therefore, you should be aware of how to do statistics and account for potential errors to obtain dependable results.

Entrust your task to proficient academic writers and have your project done quickly and efficiently. Whether you need research paper or thesis help , you can rely on our experts 24/7.

FAQ About Statistics

1. what is a statistical method.

A statistical method is a set of techniques used to analyze data and draw conclusions about a population. Statistical methods involve using mathematical formulas, models, or algorithms to summarize data and  investigate causal relationships. They are also utilized to estimate population parameters and make predictions.

2. What is the importance of statistical analysis?

Statistical analysis is important because it allows us to make sense of data and draw conclusions that are supported by evidence, rather than relying solely on intuition. It helps us to understand the relationships between variables, test hypotheses and make predictions, which can further drive progress in various fields of study. Additionally, statistical analysis can provide a means of objectively evaluating the effectiveness of interventions, policies, or programs.

3. How can I ensure the validity of my statistical analysis results?

To ensure the validity of statistical analysis results, it's essential to use techniques that are appropriate for your research question and data type. Most statistical methods assume certain conditions about the data. Verify whether the assumptions are met before applying any method. Outliers can also significantly affect the results of statistical analysis. Remove them if they are due to data entry errors, or analyze them separately if they are legitimate data points.

4. What is the difference between statistical analysis and data analysis?

Statistical analysis is a type of data analysis that uses statistical methods, while data analysis is a broader process of examining data using various techniques. Statistical analysis is just one tool used in data analysis.

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An Introduction to Statistics: Choosing the Correct Statistical Test

Priya ranganathan.

1 Department of Anaesthesiology, Critical Care and Pain, Tata Memorial Centre, Homi Bhabha National Institute, Mumbai, Maharashtra, India

The choice of statistical test used for analysis of data from a research study is crucial in interpreting the results of the study. This article gives an overview of the various factors that determine the selection of a statistical test and lists some statistical testsused in common practice.

How to cite this article: Ranganathan P. An Introduction to Statistics: Choosing the Correct Statistical Test. Indian J Crit Care Med 2021;25(Suppl 2):S184–S186.

In a previous article in this series, we looked at different types of data and ways to summarise them. 1 At the end of the research study, statistical analyses are performed to test the hypothesis and either prove or disprove it. The choice of statistical test needs to be carefully performed since the use of incorrect tests could lead to misleading conclusions. Some key questions help us to decide the type of statistical test to be used for analysis of study data. 2

W hat is the R esearch H ypothesis ?

Sometimes, a study may just describe the characteristics of the sample, e.g., a prevalence study. Here, the statistical analysis involves only descriptive statistics . For example, Sridharan et al. aimed to analyze the clinical profile, species distribution, and susceptibility pattern of patients with invasive candidiasis. 3 They used descriptive statistics to express the characteristics of their study sample, including mean (and standard deviation) for normally distributed data, median (with interquartile range) for skewed data, and percentages for categorical data.

Studies may be conducted to test a hypothesis and derive inferences from the sample results to the population. This is known as inferential statistics . The goal of inferential statistics may be to assess differences between groups (comparison), establish an association between two variables (correlation), predict one variable from another (regression), or look for agreement between measurements (agreement). Studies may also look at time to a particular event, analyzed using survival analysis.

A re the C omparisons M atched (P aired ) or U nmatched (U npaired )?

Observations made on the same individual (before–after or comparing two sides of the body) are usually matched or paired . Comparisons made between individuals are usually unpaired or unmatched . Data are considered paired if the values in one set of data are likely to be influenced by the other set (as can happen in before and after readings from the same individual). Examples of paired data include serial measurements of procalcitonin in critically ill patients or comparison of pain relief during sequential administration of different analgesics in a patient with osteoarthritis.

W hat are the T ype of D ata B eing M easured ?

The test chosen to analyze data will depend on whether the data are categorical (and whether nominal or ordinal) or numerical (and whether skewed or normally distributed). Tests used to analyze normally distributed data are known as parametric tests and have a nonparametric counterpart that is used for data, which is distribution-free. 4 Parametric tests assume that the sample data are normally distributed and have the same characteristics as the population; nonparametric tests make no such assumptions. Parametric tests are more powerful and have a greater ability to pick up differences between groups (where they exist); in contrast, nonparametric tests are less efficient at identifying significant differences. Time-to-event data requires a special type of analysis, known as survival analysis.

H ow M any M easurements are B eing C ompared ?

The choice of the test differs depending on whether two or more than two measurements are being compared. This includes more than two groups (unmatched data) or more than two measurements in a group (matched data).

T ests for C omparison

( Table 1 lists the tests commonly used for comparing unpaired data, depending on the number of groups and type of data. As an example, Megahed and colleagues evaluated the role of early bronchoscopy in mechanically ventilated patients with aspiration pneumonitis. 5 Patients were randomized to receive either early bronchoscopy or conventional treatment. Between groups, comparisons were made using the unpaired t test for normally distributed continuous variables, the Mann–Whitney U -test for non-normal continuous variables, and the chi-square test for categorical variables. Chowhan et al. compared the efficacy of left ventricular outflow tract velocity time integral (LVOTVTI) and carotid artery velocity time integral (CAVTI) as predictors of fluid responsiveness in patients with sepsis and septic shock. 6 Patients were divided into three groups— sepsis, septic shock, and controls. Since there were three groups, comparisons of numerical variables were done using analysis of variance (for normally distributed data) or Kruskal–Wallis test (for skewed data).

Tests for comparison of unpaired data

A common error is to use multiple unpaired t -tests for comparing more than two groups; i.e., for a study with three treatment groups A, B, and C, it would be incorrect to run unpaired t -tests for group A vs B, B vs C, and C vs A. The correct technique of analysis is to run ANOVA and use post hoc tests (if ANOVA yields a significant result) to determine which group is different from the others.

( Table 2 lists the tests commonly used for comparing paired data, depending on the number of groups and type of data. As discussed above, it would be incorrect to use multiple paired t -tests to compare more than two measurements within a group. In the study by Chowhan, each parameter (LVOTVTI and CAVTI) was measured in the supine position and following passive leg raise. These represented paired readings from the same individual and comparison of prereading and postreading was performed using the paired t -test. 6 Verma et al. evaluated the role of physiotherapy on oxygen requirements and physiological parameters in patients with COVID-19. 7 Each patient had pretreatment and post-treatment data for heart rate and oxygen supplementation recorded on day 1 and day 14. Since data did not follow a normal distribution, they used Wilcoxon's matched pair test to compare the prevalues and postvalues of heart rate (numerical variable). McNemar's test was used to compare the presupplemental and postsupplemental oxygen status expressed as dichotomous data in terms of yes/no. In the study by Megahed, patients had various parameters such as sepsis-related organ failure assessment score, lung injury score, and clinical pulmonary infection score (CPIS) measured at baseline, on day 3 and day 7. 5 Within groups, comparisons were made using repeated measures ANOVA for normally distributed data and Friedman's test for skewed data.

Tests for comparison of paired data

T ests for A ssociation between V ariables

( Table 3 lists the tests used to determine the association between variables. Correlation determines the strength of the relationship between two variables; regression allows the prediction of one variable from another. Tyagi examined the correlation between ETCO 2 and PaCO 2 in patients with chronic obstructive pulmonary disease with acute exacerbation, who were mechanically ventilated. 8 Since these were normally distributed variables, the linear correlation between ETCO 2 and PaCO 2 was determined by Pearson's correlation coefficient. Parajuli et al. compared the acute physiology and chronic health evaluation II (APACHE II) and acute physiology and chronic health evaluation IV (APACHE IV) scores to predict intensive care unit mortality, both of which were ordinal data. Correlation between APACHE II and APACHE IV score was tested using Spearman's coefficient. 9 A study by Roshan et al. identified risk factors for the development of aspiration pneumonia following rapid sequence intubation. 10 Since the outcome was categorical binary data (aspiration pneumonia— yes/no), they performed a bivariate analysis to derive unadjusted odds ratios, followed by a multivariable logistic regression analysis to calculate adjusted odds ratios for risk factors associated with aspiration pneumonia.

Tests for assessing the association between variables

T ests for A greement between M easurements

( Table 4 outlines the tests used for assessing agreement between measurements. Gunalan evaluated concordance between the National Healthcare Safety Network surveillance criteria and CPIS for the diagnosis of ventilator-associated pneumonia. 11 Since both the scores are examples of ordinal data, Kappa statistics were calculated to assess the concordance between the two methods. In the previously quoted study by Tyagi, the agreement between ETCO 2 and PaCO 2 (both numerical variables) was represented using the Bland–Altman method. 8

Tests for assessing agreement between measurements

T ests for T ime-to -E vent D ata (S urvival A nalysis )

Time-to-event data represent a unique type of data where some participants have not experienced the outcome of interest at the time of analysis. Such participants are considered to be “censored” but are allowed to contribute to the analysis for the period of their follow-up. A detailed discussion on the analysis of time-to-event data is beyond the scope of this article. For analyzing time-to-event data, we use survival analysis (with the Kaplan–Meier method) and compare groups using the log-rank test. The risk of experiencing the event is expressed as a hazard ratio. Cox proportional hazards regression model is used to identify risk factors that are significantly associated with the event.

Hasanzadeh evaluated the impact of zinc supplementation on the development of ventilator-associated pneumonia (VAP) in adult mechanically ventilated trauma patients. 12 Survival analysis (Kaplan–Meier technique) was used to calculate the median time to development of VAP after ICU admission. The Cox proportional hazards regression model was used to calculate hazard ratios to identify factors significantly associated with the development of VAP.

The choice of statistical test used to analyze research data depends on the study hypothesis, the type of data, the number of measurements, and whether the data are paired or unpaired. Reviews of articles published in medical specialties such as family medicine, cytopathology, and pain have found several errors related to the use of descriptive and inferential statistics. 12 – 15 The statistical technique needs to be carefully chosen and specified in the protocol prior to commencement of the study, to ensure that the conclusions of the study are valid. This article has outlined the principles for selecting a statistical test, along with a list of tests used commonly. Researchers should seek help from statisticians while writing the research study protocol, to formulate the plan for statistical analysis.

Priya Ranganathan https://orcid.org/0000-0003-1004-5264

Source of support: Nil

Conflict of interest: None

R eferences

Statistical Research Questions: Five Examples for Quantitative Analysis

Table of contents, introduction.

How are statistical research questions for quantitative analysis written? This article provides five examples of statistical research questions that will allow statistical analysis to take place.

In quantitative research projects, writing statistical research questions requires a good understanding and the ability to discern the type of data that you will analyze. This knowledge is elemental in framing research questions that shall guide you in identifying the appropriate statistical test to use in your research.

Thus, before writing your statistical research questions and reading the examples in this article, read first the article that enumerates the  four types of measurement scales . Knowing the four types of measurement scales will enable you to appreciate the formulation or structuring of research questions.

Once you feel confident that you can correctly identify the nature of your data, the following examples of statistical research questions will strengthen your understanding. Asking these questions can help you unravel unexpected outcomes or discoveries particularly while doing exploratory data analysis .

Five Examples of Statistical Research Questions

In writing the statistical research questions, I provide a topic that shows the variables of the study, the study description, and a link to the original scientific article to give you a glimpse of the real-world examples.

Topic 1: Physical Fitness and Academic Achievement

A study was conducted to determine the relationship between physical fitness and academic achievement. The subjects of the study include school children in urban schools.

Statistical Research Question No. 1

Is there a significant relationship between physical fitness and academic achievement?

Notice that this study correlated two variables, namely 1) physical fitness, and 2) academic achievement.

To allow statistical analysis to take place, there is a need to define what is physical fitness, as well as academic achievement. The researchers measured physical fitness in terms of  the number of physical fitness tests  that the students passed during their physical education class. It’s simply counting the ‘number of PE tests passed.’

On the other hand, the researchers measured academic achievement in terms of a passing score in Mathematics and English. The variable is the  number of passing scores  in both Mathematics and English.

Both variables are ratio variables. 

Given the statistical research question, the appropriate statistical test can be applied to determine the relationship. A Pearson correlation coefficient test will test the significance and degree of the relationship. But the more sophisticated higher level statistical test can be applied if there is a need to correlate with other variables.

In the particular study mentioned, the researchers used  multivariate logistic regression analyses  to assess the probability of passing the tests, controlling for students’ weight status, ethnicity, gender, grade, and socioeconomic status. For the novice researcher, this requires further study of multivariate (or many variables) statistical tests. You may study it on your own.

Most of what I discuss in the statistics articles I wrote came from self-study. It’s easier to understand concepts now as there are a lot of resource materials available online. Videos and ebooks from places like Youtube, Veoh, The Internet Archives, among others, provide free educational materials. Online education will be the norm of the future. I describe this situation in my post about  Education 4.0 .

The following video sheds light on the frequently used statistical tests and their selection. It is an excellent resource for beginners. Just maintain an open mind to get rid of your dislike for numbers; that is, if you are one of those who have a hard time understanding mathematical concepts. My ebook on  statistical tests and their selection  provides many examples.

Source: Chomitz et al. (2009)

Topic 2: Climate Conditions and Consumption of Bottled Water

This study attempted to correlate climate conditions with the decision of people in Ecuador to consume bottled water, including the volume consumed. Specifically, the researchers investigated if the increase in average ambient temperature affects the consumption of bottled water.

Statistical Research Question No. 2

Is there a significant relationship between average temperature and amount of bottled water consumed?

In this instance, the variables measured include the  average temperature in the areas studied  and the  volume of water consumed . Temperature is an  interval variable,  while volume is a  ratio variable .

In this example, the variables include the  average temperature  and  volume of bottled water . The first variable (average temperature) is an interval variable, and the latter (volume of water) is a ratio variable.

Now, it’s easy to identify the statistical test to analyze the relationship between the two variables. You may refer to my previous post titled  Parametric Statistics: Four Widely Used Parametric Tests and When to Use Them . Using the figure supplied in that article, the appropriate test to use is, again, Pearson’s Correlation Coefficient.

Source: Zapata (2021)

Topic 3: Nursing Home Staff Size and Number of COVID-19 Cases

An investigation sought to determine if the size of nursing home staff and the number of COVID-19 cases are correlated. Specifically, they looked into the number of unique employees working daily, and the outcomes include weekly counts of confirmed COVID-19 cases among residents and staff and weekly COVID-19 deaths among residents.

Statistical Research Question No. 3

Is there a significant relationship between the number of unique employees working in skilled nursing homes and the following:

• number of weekly confirmed COVID-19 cases among residents and staff, and
• number of weekly COVID-19 deaths among residents.

Note that this study on COVID-19 looked into three variables, namely 1) number of unique employees working in skilled nursing homes, 2) number of weekly confirmed cases among residents and staff, and 3) number of weekly COVID-19 deaths among residents.

We call the variable  number of unique employees  the  independent variable , and the other two variables ( number of weekly confirmed cases among residents and staff  and  number of weekly COVID-19 deaths among residents ) as the  dependent variables .

This correlation study determined if the number of staff members in nursing homes influences the number of COVID-19 cases and deaths. It aims to understand if staffing has got to do with the transmission of the deadly coronavirus. Thus, the study’s outcome could inform policy on staffing in nursing homes during the pandemic.

A simple Pearson test may be used to correlate one variable with another variable. But the study used multiple variables. Hence, they produced  regression models  that show how multiple variables affect the outcome. Some of the variables in the study may be redundant, meaning, those variables may represent the same attribute of a population.  Stepwise multiple regression models  take care of those redundancies. Using this statistical test requires further study and experience.

Source: McGarry et al. (2021)

Topic 4: Surrounding Greenness, Stress, and Memory

Scientific evidence has shown that surrounding greenness has multiple health-related benefits. Health benefits include better cognitive functioning or better intellectual activity such as thinking, reasoning, or remembering things. These findings, however, are not well understood. A study, therefore, analyzed the relationship between surrounding greenness and memory performance, with stress as a mediating variable.

Statistical Research Question No. 4

Is there a significant relationship between exposure to and use of natural environments, stress, and memory performance?

As this article is behind a paywall and we cannot see the full article, we can content ourselves with the knowledge that three major variables were explored in this study. These are 1) exposure to and use of natural environments, 2) stress, and 3) memory performance.

Referring to the abstract of this study,  exposure to and use of natural environments  as a variable of the study may be measured in terms of the days spent by the respondent in green surroundings. That will be a ratio variable as we can count it and has an absolute zero point. Stress levels can be measured using standardized instruments like the  Perceived Stress Scale . The third variable, i.e., memory performance in terms of short-term, working memory, and overall memory may be measured using a variety of  memory assessment tools as described by Murray (2016) .

As you become more familiar and well-versed in identifying the variables you would like to investigate in your study, reading studies like this requires reading the method or methodology section. This section will tell you how the researchers measured the variables of their study. Knowing how those variables are quantified can help you design your research and formulate the appropriate statistical research questions.

Source: Lega et al. (2021)

Topic 5: Income and Happiness

This recent finding is an interesting read and is available online. Just click on the link I provide as the source below. The study sought to determine if income plays a role in people’s happiness across three age groups: young (18-30 years), middle (31-64 years), and old (65 or older). The literature review suggests that income has a positive effect on an individual’s sense of happiness. That’s because more money increases opportunities to fulfill dreams and buy more goods and services.

Reading the abstract, we can readily identify one of the variables used in the study, i.e., money. It’s easy to count that. But for happiness, that is a largely subjective matter. Happiness varies between individuals. So how did the researcher measured happiness? As previously mentioned, we need to see the methodology portion to find out why.

If you click on the link to the full text of the paper on pages 10 and 11, you will read that the researcher measured happiness using a 10-point scale. The scale was categorized into three namely, 1) unhappy, 2) happy, and 3) very happy.

An investigation was conducted to determine if the size of nursing home staff and the number of COVID-19 cases are correlated. Specifically, they looked into the number of unique employees working daily, and the outcomes include weekly counts of confirmed COVID-19 cases among residents and staff and weekly COVID-19 deaths among residents.

Statistical Research Question No. 5

Is there a significant relationship between income and happiness?

Source: Måseide (2021)

Now the statistical test used by the researcher is, honestly, beyond me. I may be able to understand it how to use it but doing so requires further study. Although I have initially did some readings on logit models, ordered logit model and generalized ordered logit model are way beyond my self-study in statistics.

Anyhow, those variables found with asterisk (***, **, and **) on page 24 tell us that there are significant relationships between income and happiness. You just have to look at the probability values and refer to the bottom of the table for the level of significance of those relationships.

I do hope that upon reaching this part of the article, you are now well familiar on how to write statistical research questions. Practice makes perfect.

References:

Chomitz, V. R., Slining, M. M., McGowan, R. J., Mitchell, S. E., Dawson, G. F., & Hacker, K. A. (2009). Is there a relationship between physical fitness and academic achievement? Positive results from public school children in the northeastern United States.  Journal of School Health ,  79 (1), 30-37.

Lega, C., Gidlow, C., Jones, M., Ellis, N., & Hurst, G. (2021). The relationship between surrounding greenness, stress and memory.  Urban Forestry & Urban Greening ,  59 , 126974.

Måseide, H. (2021). Income and Happiness: Does the relationship vary with age?

McGarry, B. E., Gandhi, A. D., Grabowski, D. C., & Barnett, M. L. (2021). Larger Nursing Home Staff Size Linked To Higher Number Of COVID-19 Cases In 2020: Study examines the relationship between staff size and COVID-19 cases in nursing homes and skilled nursing facilities. Health Affairs, 40(8), 1261-1269.

Zapata, O. (2021). The relationship between climate conditions and consumption of bottled water: A potential link between climate change and plastic pollution. Ecological Economics, 187, 107090.

© P. A. Regoniel 12 October 2021 | Updated 08 January 2024

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How to write survey questions, about the author, patrick regoniel.

Dr. Regoniel, a faculty member of the graduate school, served as consultant to various environmental research and development projects covering issues and concerns on climate change, coral reef resources and management, economic valuation of environmental and natural resources, mining, and waste management and pollution. He has extensive experience on applied statistics, systems modelling and analysis, an avid practitioner of LaTeX, and a multidisciplinary web developer. He leverages pioneering AI-powered content creation tools to produce unique and comprehensive articles in this website.

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What the data says about crime in the U.S.

A growing share of Americans say reducing crime should be a top priority for the president and Congress to address this year. Around six-in-ten U.S. adults (58%) hold that view today, up from 47% at the beginning of Joe Biden’s presidency in 2021.

We conducted this analysis to learn more about U.S. crime patterns and how those patterns have changed over time.

The analysis relies on statistics published by the FBI, which we accessed through the Crime Data Explorer , and the Bureau of Justice Statistics (BJS), which we accessed through the  National Crime Victimization Survey data analysis tool .

To measure public attitudes about crime in the U.S., we relied on survey data from Pew Research Center and Gallup.

Additional details about each data source, including survey methodologies, are available by following the links in the text of this analysis.

With the issue likely to come up in this year’s presidential election, here’s what we know about crime in the United States, based on the latest available data from the federal government and other sources.

How much crime is there in the U.S.?

It’s difficult to say for certain. The  two primary sources of government crime statistics  – the Federal Bureau of Investigation (FBI) and the Bureau of Justice Statistics (BJS) – paint an incomplete picture.

The FBI publishes  annual data  on crimes that have been reported to law enforcement, but not crimes that haven’t been reported. Historically, the FBI has also only published statistics about a handful of specific violent and property crimes, but not many other types of crime, such as drug crime. And while the FBI’s data is based on information from thousands of federal, state, county, city and other police departments, not all law enforcement agencies participate every year. In 2022, the most recent full year with available statistics, the FBI received data from 83% of participating agencies .

BJS, for its part, tracks crime by fielding a  large annual survey of Americans ages 12 and older and asking them whether they were the victim of certain types of crime in the past six months. One advantage of this approach is that it captures both reported and unreported crimes. But the BJS survey has limitations of its own. Like the FBI, it focuses mainly on a handful of violent and property crimes. And since the BJS data is based on after-the-fact interviews with crime victims, it cannot provide information about one especially high-profile type of offense: murder.

All those caveats aside, looking at the FBI and BJS statistics side-by-side  does  give researchers a good picture of U.S. violent and property crime rates and how they have changed over time. In addition, the FBI is transitioning to a new data collection system – known as the National Incident-Based Reporting System – that eventually will provide national information on a much larger set of crimes , as well as details such as the time and place they occur and the types of weapons involved, if applicable.

Which kinds of crime are most and least common?

Property crime in the U.S. is much more common than violent crime. In 2022, the FBI reported a total of 1,954.4 property crimes per 100,000 people, compared with 380.7 violent crimes per 100,000 people.  

By far the most common form of property crime in 2022 was larceny/theft, followed by motor vehicle theft and burglary. Among violent crimes, aggravated assault was the most common offense, followed by robbery, rape, and murder/nonnegligent manslaughter.

BJS tracks a slightly different set of offenses from the FBI, but it finds the same overall patterns, with theft the most common form of property crime in 2022 and assault the most common form of violent crime.

How have crime rates in the U.S. changed over time?

Both the FBI and BJS data show dramatic declines in U.S. violent and property crime rates since the early 1990s, when crime spiked across much of the nation.

Using the FBI data, the violent crime rate fell 49% between 1993 and 2022, with large decreases in the rates of robbery (-74%), aggravated assault (-39%) and murder/nonnegligent manslaughter (-34%). It’s not possible to calculate the change in the rape rate during this period because the FBI  revised its definition of the offense in 2013 .

The FBI data also shows a 59% reduction in the U.S. property crime rate between 1993 and 2022, with big declines in the rates of burglary (-75%), larceny/theft (-54%) and motor vehicle theft (-53%).

Using the BJS statistics, the declines in the violent and property crime rates are even steeper than those captured in the FBI data. Per BJS, the U.S. violent and property crime rates each fell 71% between 1993 and 2022.

While crime rates have fallen sharply over the long term, the decline hasn’t always been steady. There have been notable increases in certain kinds of crime in some years, including recently.

In 2020, for example, the U.S. murder rate saw its largest single-year increase on record – and by 2022, it remained considerably higher than before the coronavirus pandemic. Preliminary data for 2023, however, suggests that the murder rate fell substantially last year .

How do Americans perceive crime in their country?

Americans tend to believe crime is up, even when official data shows it is down.

In 23 of 27 Gallup surveys conducted since 1993 , at least 60% of U.S. adults have said there is more crime nationally than there was the year before, despite the downward trend in crime rates during most of that period.

While perceptions of rising crime at the national level are common, fewer Americans believe crime is up in their own communities. In every Gallup crime survey since the 1990s, Americans have been much less likely to say crime is up in their area than to say the same about crime nationally.

Public attitudes about crime differ widely by Americans’ party affiliation, race and ethnicity, and other factors . For example, Republicans and Republican-leaning independents are much more likely than Democrats and Democratic leaners to say reducing crime should be a top priority for the president and Congress this year (68% vs. 47%), according to a recent Pew Research Center survey.

How does crime in the U.S. differ by demographic characteristics?

Some groups of Americans are more likely than others to be victims of crime. In the  2022 BJS survey , for example, younger people and those with lower incomes were far more likely to report being the victim of a violent crime than older and higher-income people.

There were no major differences in violent crime victimization rates between male and female respondents or between those who identified as White, Black or Hispanic. But the victimization rate among Asian Americans (a category that includes Native Hawaiians and other Pacific Islanders) was substantially lower than among other racial and ethnic groups.

The same BJS survey asks victims about the demographic characteristics of the offenders in the incidents they experienced.

In 2022, those who are male, younger people and those who are Black accounted for considerably larger shares of perceived offenders in violent incidents than their respective shares of the U.S. population. Men, for instance, accounted for 79% of perceived offenders in violent incidents, compared with 49% of the nation’s 12-and-older population that year. Black Americans accounted for 25% of perceived offenders in violent incidents, about twice their share of the 12-and-older population (12%).

As with all surveys, however, there are several potential sources of error, including the possibility that crime victims’ perceptions about offenders are incorrect.

How does crime in the U.S. differ geographically?

There are big geographic differences in violent and property crime rates.

For example, in 2022, there were more than 700 violent crimes per 100,000 residents in New Mexico and Alaska. That compares with fewer than 200 per 100,000 people in Rhode Island, Connecticut, New Hampshire and Maine, according to the FBI.

The FBI notes that various factors might influence an area’s crime rate, including its population density and economic conditions.

What percentage of crimes are reported to police? What percentage are solved?

Most violent and property crimes in the U.S. are not reported to police, and most of the crimes that  are  reported are not solved.

In its annual survey, BJS asks crime victims whether they reported their crime to police. It found that in 2022, only 41.5% of violent crimes and 31.8% of household property crimes were reported to authorities. BJS notes that there are many reasons why crime might not be reported, including fear of reprisal or of “getting the offender in trouble,” a feeling that police “would not or could not do anything to help,” or a belief that the crime is “a personal issue or too trivial to report.”

Most of the crimes that are reported to police, meanwhile,  are not solved , at least based on an FBI measure known as the clearance rate . That’s the share of cases each year that are closed, or “cleared,” through the arrest, charging and referral of a suspect for prosecution, or due to “exceptional” circumstances such as the death of a suspect or a victim’s refusal to cooperate with a prosecution. In 2022, police nationwide cleared 36.7% of violent crimes that were reported to them and 12.1% of the property crimes that came to their attention.

Which crimes are most likely to be reported to police? Which are most likely to be solved?

Around eight-in-ten motor vehicle thefts (80.9%) were reported to police in 2022, making them by far the most commonly reported property crime tracked by BJS. Household burglaries and trespassing offenses were reported to police at much lower rates (44.9% and 41.2%, respectively), while personal theft/larceny and other types of theft were only reported around a quarter of the time.

Among violent crimes – excluding homicide, which BJS doesn’t track – robbery was the most likely to be reported to law enforcement in 2022 (64.0%). It was followed by aggravated assault (49.9%), simple assault (36.8%) and rape/sexual assault (21.4%).

The list of crimes  cleared  by police in 2022 looks different from the list of crimes reported. Law enforcement officers were generally much more likely to solve violent crimes than property crimes, according to the FBI.

The most frequently solved violent crime tends to be homicide. Police cleared around half of murders and nonnegligent manslaughters (52.3%) in 2022. The clearance rates were lower for aggravated assault (41.4%), rape (26.1%) and robbery (23.2%).

When it comes to property crime, law enforcement agencies cleared 13.0% of burglaries, 12.4% of larcenies/thefts and 9.3% of motor vehicle thefts in 2022.

Are police solving more or fewer crimes than they used to?

Nationwide clearance rates for both violent and property crime are at their lowest levels since at least 1993, the FBI data shows.

Police cleared a little over a third (36.7%) of the violent crimes that came to their attention in 2022, down from nearly half (48.1%) as recently as 2013. During the same period, there were decreases for each of the four types of violent crime the FBI tracks:

• Police cleared 52.3% of reported murders and nonnegligent homicides in 2022, down from 64.1% in 2013.
• They cleared 41.4% of aggravated assaults, down from 57.7%.
• They cleared 26.1% of rapes, down from 40.6%.
• They cleared 23.2% of robberies, down from 29.4%.

The pattern is less pronounced for property crime. Overall, law enforcement agencies cleared 12.1% of reported property crimes in 2022, down from 19.7% in 2013. The clearance rate for burglary didn’t change much, but it fell for larceny/theft (to 12.4% in 2022 from 22.4% in 2013) and motor vehicle theft (to 9.3% from 14.2%).

Note: This is an update of a post originally published on Nov. 20, 2020.

• Criminal Justice

John Gramlich is an associate director at Pew Research Center

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#blacklivesmatter turns 10, support for the black lives matter movement has dropped considerably from its peak in 2020, fewer than 1% of federal criminal defendants were acquitted in 2022, before release of video showing tyre nichols’ beating, public views of police conduct had improved modestly, most popular.

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