essay about statistics

Introductory essay

Written by the educators who created Visualizing Data, a brief look at the key facts, tough questions and big ideas in their field. Begin this TED Study with a fascinating read that gives context and clarity to the material.

The reality of today

All of us now are being blasted by information design. It's being poured into our eyes through the Web, and we're all visualizers now; we're all demanding a visual aspect to our information...And if you're navigating a dense information jungle, coming across a beautiful graphic or a lovely data visualization, it's a relief, it's like coming across a clearing in the jungle. David McCandless

In today's complex 'information jungle,' David McCandless observes that "Data is the new soil." McCandless, a data journalist and information designer, celebrates data as a ubiquitous resource providing a fertile and creative medium from which new ideas and understanding can grow. McCandless's inspiration, statistician Hans Rosling, builds on this idea in his own TEDTalk with his compelling image of flowers growing out of data/soil. These 'flowers' represent the many insights that can be gleaned from effective visualization of data.

We're just learning how to till this soil and make sense of the mountains of data constantly being generated. As Gary King, Director of Harvard's Institute for Quantitative Social Science says in his New York Times article "The Age of Big Data":

It's a revolution. We're really just getting under way. But the march of quantification, made possible by enormous new sources of data, will sweep through academia, business and government. There is no area that is going to be untouched.

How do we deal with all this data without getting information overload? How do we use data to gain real insight into the world? Finding ways to pull interesting information out of data can be very rewarding, both personally and professionally. The managing editor of Financial Times observed on CNN's Your Money : "The people who are able to in a sophisticated and practical way analyze that data are going to have terrific jobs." Those who learn how to present data in effective ways will be valuable in every field.

Many people, when they think of data, think of tables filled with numbers. But this long-held notion is eroding. Today, we're generating streams of data that are often too complex to be presented in a simple "table." In his TEDTalk, Blaise Aguera y Arcas explores images as data, while Deb Roy uses audio, video, and the text messages in social media as data.

Some may also think that only a few specialized professionals can draw insights from data. When we look at data in the right way, however, the results can be fun, insightful, even whimsical — and accessible to everyone! Who knew, for example, that there are more relationship break-ups on Monday than on any other day of the week, or that the most break-ups (at least those discussed on Facebook) occur in mid-December? David McCandless discovered this by analyzing thousands of Facebook status updates.

Data, data, everywhere

There is more data available to us now than we can possibly process. Every minute , Internet users add the following to the big data pool (i):

• 204,166,667 email messages sent
• More than 2,000,000 Google searches
• 684,478 pieces of content added on Facebook
• $272,070 spent by consumers via online shopping
• More than 100,000 tweets on Twitter
• 47,000 app downloads from Apple
• 34,722 "likes" on Facebook for different brands and organizations
• 27,778 new posts on Tumblr blogs
• 3,600 new photos on Instagram
• 3,125 new photos on Flickr
• 2,083 check-ins on Foursquare
• 571 new websites created
• 347 new blog posts published on Wordpress
• 217 new mobile web users
• 48 hours of new video on YouTube

These numbers are almost certainly higher now, as you read this. And this just describes a small piece of the data being generated and stored by humanity. We're all leaving data trails — not just on the Internet, but in everything we do. This includes reams of financial data (from credit cards, businesses, and Wall Street), demographic data on the world's populations, meteorological data on weather and the environment, retail sales data that records everything we buy, nutritional data on food and restaurants, sports data of all types, and so on.

Governments are using data to search for terrorist plots, retailers are using it to maximize marketing strategies, and health organizations are using it to track outbreaks of the flu. But did you ever think of collecting data on every minute of your child's life? That's precisely what Deb Roy did. He recorded 90,000 hours of video and 140,000 hours of audio during his son's first years. That's a lot of data! He and his colleagues are using the data to understand how children learn language, and they're now extending this work to analyze publicly available conversations on social media, allowing them to take "the real-time pulse of a nation."

Data can provide us with new and deeper insight into our world. It can help break stereotypes and build understanding. But the sheer quantity of data, even in just any one small area of interest, is overwhelming. How can we make sense of some of this data in an insightful way?

The power of visualizing data

Visualization can help transform these mountains of data into meaningful information. In his TEDTalk, David McCandless comments that the sense of sight has by far the fastest and biggest bandwidth of any of the five senses. Indeed, about 80% of the information we take in is by eye. Data that seems impenetrable can come alive if presented well in a picture, graph, or even a movie. Hans Rosling tells us that "Students get very excited — and policy-makers and the corporate sector — when they can see the data."

It makes sense that, if we can effectively display data visually, we can make it accessible and understandable to more people. Should we worry, however, that by condensing data into a graph, we are simplifying too much and losing some of the important features of the data? Let's look at a fascinating study conducted by researchers Emre Soyer and Robin Hogarth . The study was conducted on economists, who are certainly no strangers to statistical analysis. Three groups of economists were asked the same question concerning a dataset:

• One group was given the data and a standard statistical analysis of the data; 72% of these economists got the answer wrong.
• Another group was given the data, the statistical analysis, and a graph; still 61% of these economists got the answer wrong.
• A third group was given only the graph, and only 3% got the answer wrong.

Visualizing data can sometimes be less misleading than using the raw numbers and statistics!

What about all the rest of us, who may not be professional economists or statisticians? Nathalie Miebach finds that making art out of data allows people an alternative entry into science. She transforms mountains of weather data into tactile physical structures and musical scores, adding both touch and hearing to the sense of sight to build even greater understanding of data.

Another artist, Chris Jordan, is concerned about our ability to comprehend big numbers. As citizens of an ever-more connected global world, we have an increased need to get useable information from big data — big in terms of the volume of numbers as well as their size. Jordan's art is designed to help us process such numbers, especially numbers that relate to issues of addiction and waste. For example, Jordan notes that the United States has the largest percentage of its population in prison of any country on earth: 2.3 million people in prison in the United States in 2005 and the number continues to rise. Jordan uses art, in this case a super-sized image of 2.3 million prison jumpsuits, to help us see that number and to help us begin to process the societal implications of that single data value. Because our brains can't truly process such a large number, his artwork makes it real.

The role of technology in visualizing data

The TEDTalks in this collection depend to varying degrees on sophisticated technology to gather, store, process, and display data. Handling massive amounts of data (e.g., David McCandless tracking 10,000 changes in Facebook status, Blaise Aguera y Arcas synching thousands of online images of the Notre Dame Cathedral, or Deb Roy searching for individual words in 90,000 hours of video tape) requires cutting-edge computing tools that have been developed specifically to address the challenges of big data. The ability to manipulate color, size, location, motion, and sound to discover and display important features of data in a way that makes it readily accessible to ordinary humans is a challenging task that depends heavily on increasingly sophisticated technology.

The importance of good visualization

There are good ways and bad ways of presenting data. Many examples of outstanding presentations of data are shown in the TEDTalks. However, sometimes visualizations of data can be ineffective or downright misleading. For example, an inappropriate scale might make a relatively small difference look much more substantial than it should be, or an overly complicated display might obfuscate the main relationships in the data. Statistician Kaiser Fung's blog Junk Charts offers many examples of poor representations of data (and some good ones) with descriptions to help the reader understand what makes a graph effective or ineffective. For more examples of both good and bad representations of data, see data visualization architect Andy Kirk's blog at visualisingdata.com . Both consistently have very current examples from up-to-date sources and events.

Creativity, even artistic ability, helps us see data in new ways. Magic happens when interesting data meets effective design: when statistician meets designer (sometimes within the same person). We are fortunate to live in a time when interactive and animated graphs are becoming commonplace, and these tools can be incredibly powerful. Other times, simpler graphs might be more effective. The key is to present data in a way that is visually appealing while allowing the data to speak for itself.

Changing perceptions through data

While graphs and charts can lead to misunderstandings, there is ultimately "truth in numbers." As Steven Levitt and Stephen Dubner say in Freakonomics , "[T]eachers and criminals and real-estate agents may lie, and politicians, and even C.I.A. analysts. But numbers don't." Indeed, consideration of data can often be the easiest way to glean objective insights. Again from Freakonomics : "There is nothing like the sheer power of numbers to scrub away layers of confusion and contradiction."

Data can help us understand the world as it is, not as we believe it to be. As Hans Rosling demonstrates, it's often not ignorance but our preconceived ideas that get in the way of understanding the world as it is. Publicly-available statistics can reshape our world view: Rosling encourages us to "let the dataset change your mindset."

Chris Jordan's powerful images of waste and addiction make us face, rather than deny, the facts. It's easy to hear and then ignore that we use and discard 1 million plastic cups every 6 hours on airline flights alone. When we're confronted with his powerful image, we engage with that fact on an entirely different level (and may never see airline plastic cups in the same way again).

The ability to see data expands our perceptions of the world in ways that we're just beginning to understand. Computer simulations allow us to see how diseases spread, how forest fires might be contained, how terror networks communicate. We gain understanding of these things in ways that were unimaginable only a few decades ago. When Blaise Aguera y Arcas demonstrates Photosynth, we feel as if we're looking at the future. By linking together user-contributed digital images culled from all over the Internet, he creates navigable "immensely rich virtual models of every interesting part of the earth" created from the collective memory of all of us. Deb Roy does somewhat the same thing with language, pulling in publicly available social media feeds to analyze national and global conversation trends.

Roy sums it up with these powerful words: "What's emerging is an ability to see new social structures and dynamics that have previously not been seen. ...The implications here are profound, whether it's for science, for commerce, for government, or perhaps most of all, for us as individuals."

Let's begin with the TEDTalk from David McCandless, a self-described "data detective" who describes how to highlight hidden patterns in data through its artful representation.

David McCandless

The beauty of data visualization.

i. Data obtained June 2012 from “How Much Data Is Created Every Minute?” on http://mashable.com/2012/06/22/data-created-every-minute/.

Relevant talks

Blaise Agüera y Arcas

How photosynth can connect the world's images.

Chris Jordan

Turning powerful stats into art.

The birth of a word

Hans Rosling

The magic washing machine.

Nathalie Miebach

Art made of storms.

There are lies, damned lies, and statistics. —Mark Twain

What this handout is about

The purpose of this handout is to help you use statistics to make your argument as effectively as possible.

Introduction

Numbers are power. Apparently freed of all the squishiness and ambiguity of words, numbers and statistics are powerful pieces of evidence that can effectively strengthen any argument. But statistics are not a panacea. As simple and straightforward as these little numbers promise to be, statistics, if not used carefully, can create more problems than they solve.

Many writers lack a firm grasp of the statistics they are using. The average reader does not know how to properly evaluate and interpret the statistics they read. The main reason behind the poor use of statistics is a lack of understanding about what statistics can and cannot do. Many people think that statistics can speak for themselves. But numbers are as ambiguous as words and need just as much explanation.

In many ways, this problem is quite similar to that experienced with direct quotes. Too often, quotes are expected to do all the work and are treated as part of the argument, rather than a piece of evidence requiring interpretation (see our handout on how to quote .) But if you leave the interpretation up to the reader, who knows what sort of off-the-wall interpretations may result? The only way to avoid this danger is to supply the interpretation yourself.

But before we start writing statistics, let’s actually read a few.

Reading statistics

As stated before, numbers are powerful. This is one of the reasons why statistics can be such persuasive pieces of evidence. However, this same power can also make numbers and statistics intimidating. That is, we too often accept them as gospel, without ever questioning their veracity or appropriateness. While this may seem like a positive trait when you plug them into your paper and pray for your reader to submit to their power, remember that before we are writers of statistics, we are readers. And to be effective readers means asking the hard questions. Below you will find a useful set of hard questions to ask of the numbers you find.

1. Does your evidence come from reliable sources?

This is an important question not only with statistics, but with any evidence you use in your papers. As we will see in this handout, there are many ways statistics can be played with and misrepresented in order to produce a desired outcome. Therefore, you want to take your statistics from reliable sources (for more information on finding reliable sources, please see our handout on evaluating print sources ). This is not to say that reliable sources are infallible, but only that they are probably less likely to use deceptive practices. With a credible source, you may not need to worry as much about the questions that follow. Still, remember that reading statistics is a bit like being in the middle of a war: trust no one; suspect everyone.

2. What is the data’s background?

Data and statistics do not just fall from heaven fully formed. They are always the product of research. Therefore, to understand the statistics, you should also know where they come from. For example, if the statistics come from a survey or poll, some questions to ask include:

• Who asked the questions in the survey/poll?
• What, exactly, were the questions?
• Who interpreted the data?
• What issue prompted the survey/poll?
• What (policy/procedure) potentially hinges on the results of the poll?
• Who stands to gain from particular interpretations of the data?

All these questions help you orient yourself toward possible biases or weaknesses in the data you are reading. The goal of this exercise is not to find “pure, objective” data but to make any biases explicit, in order to more accurately interpret the evidence.

3. Are all data reported?

In most cases, the answer to this question is easy: no, they aren’t. Therefore, a better way to think about this issue is to ask whether all data have been presented in context. But it is much more complicated when you consider the bigger issue, which is whether the text or source presents enough evidence for you to draw your own conclusion. A reliable source should not exclude data that contradicts or weakens the information presented.

An example can be found on the evening news. If you think about ice storms, which make life so difficult in the winter, you will certainly remember the newscasters warning people to stay off the roads because they are so treacherous. To verify this point, they tell you that the Highway Patrol has already reported 25 accidents during the day. Their intention is to scare you into staying home with this number. While this number sounds high, some studies have found that the number of accidents actually goes down on days with severe weather. Why is that? One possible explanation is that with fewer people on the road, even with the dangerous conditions, the number of accidents will be less than on an “average” day. The critical lesson here is that even when the general interpretation is “accurate,” the data may not actually be evidence for the particular interpretation. This means you have no way to verify if the interpretation is in fact correct.

There is generally a comparison implied in the use of statistics. How can you make a valid comparison without having all the facts? Good question. You may have to look to another source or sources to find all the data you need.

4. Have the data been interpreted correctly?

If the author gives you their statistics, it is always wise to interpret them yourself. That is, while it is useful to read and understand the author’s interpretation, it is merely that—an interpretation. It is not the final word on the matter. Furthermore, sometimes authors (including you, so be careful) can use perfectly good statistics and come up with perfectly bad interpretations. Here are two common mistakes to watch out for:

• Confusing correlation with causation. Just because two things vary together does not mean that one of them is causing the other. It could be nothing more than a coincidence, or both could be caused by a third factor. Such a relationship is called spurious.The classic example is a study that found that the more firefighters sent to put out a fire, the more damage the fire did. Yikes! I thought firefighters were supposed to make things better, not worse! But before we start shutting down fire stations, it might be useful to entertain alternative explanations. This seemingly contradictory finding can be easily explained by pointing to a third factor that causes both: the size of the fire. The lesson here? Correlation does not equal causation. So it is important not only to think about showing that two variables co-vary, but also about the causal mechanism.
• Ignoring the margin of error. When survey results are reported, they frequently include a margin of error. You might see this written as “a margin of error of plus or minus 5 percentage points.” What does this mean? The simple story is that surveys are normally generated from samples of a larger population, and thus they are never exact. There is always a confidence interval within which the general population is expected to fall. Thus, if I say that the number of UNC students who find it difficult to use statistics in their writing is 60%, plus or minus 4%, that means, assuming the normal confidence interval of 95%, that with 95% certainty we can say that the actual number is between 56% and 64%.

Why does this matter? Because if after introducing this handout to the students of UNC, a new poll finds that only 56%, plus or minus 3%, are having difficulty with statistics, I could go to the Writing Center director and ask for a raise, since I have made a significant contribution to the writing skills of the students on campus. However, she would no doubt point out that a) this may be a spurious relationship (see above) and b) the actual change is not significant because it falls within the margin of error for the original results. The lesson here? Margins of error matter, so you cannot just compare simple percentages.

Finally, you should keep in mind that the source you are actually looking at may not be the original source of your data. That is, if you find an essay that quotes a number of statistics in support of its argument, often the author of the essay is using someone else’s data. Thus, you need to consider not only your source, but the author’s sources as well.

Writing statistics

As you write with statistics, remember your own experience as a reader of statistics. Don’t forget how frustrated you were when you came across unclear statistics and how thankful you were to read well-presented ones. It is a sign of respect to your reader to be as clear and straightforward as you can be with your numbers. Nobody likes to be played for a fool. Thus, even if you think that changing the numbers just a little bit will help your argument, do not give in to the temptation.

As you begin writing, keep the following in mind. First, your reader will want to know the answers to the same questions that we discussed above. Second, you want to present your statistics in a clear, unambiguous manner. Below you will find a list of some common pitfalls in the world of statistics, along with suggestions for avoiding them.

1. The mistake of the “average” writer

Nobody wants to be average. Moreover, nobody wants to just see the word “average” in a piece of writing. Why? Because nobody knows exactly what it means. There are not one, not two, but three different definitions of “average” in statistics, and when you use the word, your reader has only a 33.3% chance of guessing correctly which one you mean.

For the following definitions, please refer to this set of numbers: 5, 5, 5, 8, 12, 14, 21, 33, 38

• Mean (arithmetic mean) This may be the most average definition of average (whatever that means). This is the weighted average—a total of all numbers included divided by the quantity of numbers represented. Thus the mean of the above set of numbers is 5+5+5+8+12+14+21+33+38, all divided by 9, which equals 15.644444444444 (Wow! That is a lot of numbers after the decimal—what do we do about that? Precision is a good thing, but too much of it is over the top; it does not necessarily make your argument any stronger. Consider the reasonable amount of precision based on your input and round accordingly. In this case, 15.6 should do the trick.)
• Median Depending on whether you have an odd or even set of numbers, the median is either a) the number midway through an odd set of numbers or b) a value halfway between the two middle numbers in an even set. For the above set (an odd set of 9 numbers), the median is 12. (5, 5, 5, 8 < 12 < 14, 21, 33, 38)
• Mode The mode is the number or value that occurs most frequently in a series. If, by some cruel twist of fate, two or more values occur with the same frequency, then you take the mean of the values. For our set, the mode would be 5, since it occurs 3 times, whereas all other numbers occur only once.

As you can see, the numbers can vary considerably, as can their significance. Therefore, the writer should always inform the reader which average they are using. Otherwise, confusion will inevitably ensue.

2. Match your facts with your questions

Be sure that your statistics actually apply to the point/argument you are making. If we return to our discussion of averages, depending on the question you are interesting in answering, you should use the proper statistics.

Perhaps an example would help illustrate this point. Your professor hands back the midterm. The grades are distributed as follows:

The professor felt that the test must have been too easy, because the average (median) grade was a 95.

When a colleague asked her about how the midterm grades came out, she answered, knowing that her classes were gaining a reputation for being “too easy,” that the average (mean) grade was an 80.

When your parents ask you how you can justify doing so poorly on the midterm, you answer, “Don’t worry about my 63. It is not as bad as it sounds. The average (mode) grade was a 58.”

I will leave it up to you to decide whether these choices are appropriate. Selecting the appropriate facts or statistics will help your argument immensely. Not only will they actually support your point, but they will not undermine the legitimacy of your position. Think about how your parents will react when they learn from the professor that the average (median) grade was 95! The best way to maintain precision is to specify which of the three forms of “average” you are using.

3. Show the entire picture

Sometimes, you may misrepresent your evidence by accident and misunderstanding. Other times, however, misrepresentation may be slightly less innocent. This can be seen most readily in visual aids. Do not shape and “massage” the representation so that it “best supports” your argument. This can be achieved by presenting charts/graphs in numerous different ways. Either the range can be shortened (to cut out data points which do not fit, e.g., starting a time series too late or ending it too soon), or the scale can be manipulated so that small changes look big and vice versa. Furthermore, do not fiddle with the proportions, either vertically or horizontally. The fact that USA Today seems to get away with these techniques does not make them OK for an academic argument.

Charts A, B, and C all use the same data points, but the stories they seem to be telling are quite different. Chart A shows a mild increase, followed by a slow decline. Chart B, on the other hand, reveals a steep jump, with a sharp drop-off immediately following. Conversely, Chart C seems to demonstrate that there was virtually no change over time. These variations are a product of changing the scale of the chart. One way to alleviate this problem is to supplement the chart by using the actual numbers in your text, in the spirit of full disclosure.

Another point of concern can be seen in Charts D and E. Both use the same data as charts A, B, and C for the years 1985-2000, but additional time points, using two hypothetical sets of data, have been added back to 1965. Given the different trends leading up to 1985, consider how the significance of recent events can change. In Chart D, the downward trend from 1990 to 2000 is going against a long-term upward trend, whereas in Chart E, it is merely the continuation of a larger downward trend after a brief upward turn.

One of the difficulties with visual aids is that there is no hard and fast rule about how much to include and what to exclude. Judgment is always involved. In general, be sure to present your visual aids so that your readers can draw their own conclusions from the facts and verify your assertions. If what you have cut out could affect the reader’s interpretation of your data, then you might consider keeping it.

4. Give bases of all percentages

Because percentages are always derived from a specific base, they are meaningless until associated with a base. So even if I tell you that after this reading this handout, you will be 23% more persuasive as a writer, that is not a very meaningful assertion because you have no idea what it is based on—23% more persuasive than what?

Let’s look at crime rates to see how this works. Suppose we have two cities, Springfield and Shelbyville. In Springfield, the murder rate has gone up 75%, while in Shelbyville, the rate has only increased by 10%. Which city is having a bigger murder problem? Well, that’s obvious, right? It has to be Springfield. After all, 75% is bigger than 10%.

Hold on a second, because this is actually much less clear than it looks. In order to really know which city has a worse problem, we have to look at the actual numbers. If I told you that Springfield had 4 murders last year and 7 this year, and Shelbyville had 30 murders last year and 33 murders this year, would you change your answer? Maybe, since 33 murders are significantly more than 7. One would certainly feel safer in Springfield, right?

Not so fast, because we still do not have all the facts. We have to make the comparison between the two based on equivalent standards. To do that, we have to look at the per capita rate (often given in rates per 100,000 people per year). If Springfield has 700 residents while Shelbyville has 3.3 million, then Springfield has a murder rate of 1,000 per 100,000 people, and Shelbyville’s rate is merely 1 per 100,000. Gadzooks! The residents of Springfield are dropping like flies. I think I’ll stick with nice, safe Shelbyville, thank you very much.

Percentages are really no different from any other form of statistics: they gain their meaning only through their context. Consequently, percentages should be presented in context so that readers can draw their own conclusions as you emphasize facts important to your argument. Remember, if your statistics really do support your point, then you should have no fear of revealing the larger context that frames them.

Important questions to ask (and answer) about statistics

• Is the question being asked relevant?
• Do the data come from reliable sources?
• Margin of error/confidence interval—when is a change really a change?
• Are all data reported, or just the best/worst?
• Are the data presented in context?
• Have the data been interpreted correctly?
• Does the author confuse correlation with causation?

Now that you have learned the lessons of statistics, you have two options. Use this knowledge to manipulate your numbers to your advantage, or use this knowledge to better understand and use statistics to make accurate and fair arguments. The choice is yours. Nine out of ten writers, however, prefer the latter, and the other one later regrets their decision.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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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 organizations.

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 organize and summarize 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 generalize 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: summarize your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, other interesting articles.

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 operationalize 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.

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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 generalizable findings, you should use a probability sampling method. Random selection reduces several types of research bias , like 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 at risk for biases like self-selection bias , 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 generalizing your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalize your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialized, 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 generalized 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 standardized 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 summarize them.

Inspect your data

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

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

By visualizing 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 minimize 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 emphasizes 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.

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

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval

Methodology

• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hostile attribution bias
• Affect heuristic

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Statistics By Jim

Making statistics intuitive

The Importance of Statistics

By Jim Frost 51 Comments

The field of statistics is the science of learning from data. Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions. Statistics allows you to understand a subject much more deeply.

Personally, I think statistics is an exciting field about the thrill of discovery, learning, and challenging your assumptions. Statistics facilitates the creation of new knowledge. Bit by bit, we push back the frontier of what is known. To learn more about my passion for statistics as an experienced statistician, read about my experiences and challenges early in my scientific research career .

For a contrast, read about qualitative research , which uses non-numeric data and does not perform statistical analyses.

Statistics Uses Numerical Evidence to Draw Valid Conclusions

Statistics are not just numbers and facts. You know, things like 4 out of 5 dentists prefer a specific toothpaste. Instead, it’s an array of knowledge and procedures that allow you to learn from data reliably. Statistics allow you to evaluate claims based on quantitative evidence and help you differentiate between reasonable and dubious conclusions. That aspect is particularly vital these days because data are so plentiful along with interpretations presented by people with unknown motivations.

Statisticians offer critical guidance in producing trustworthy analyses and predictions. Along the way, statisticians can help investigators avoid a wide variety of analytical traps.

When analysts use statistical procedures correctly, they tend to produce accurate results. In fact, statistical analyses account for uncertainty and error in the results. Statisticians ensure that all aspects of a study follow the appropriate methods to produce trustworthy results. These methods include:

• Producing reliable data.
• Analyzing the data appropriately.
• Drawing reasonable conclusions.

Statisticians Know How to Avoid Common Pitfalls

Using statistical analyses to produce findings for a study is the culmination of a long process. This process includes constructing the study design, selecting and measuring the variables, devising the sampling technique and sample size , cleaning the data, and determining the analysis methodology among numerous other issues. In some cases, you might want to take the raw data and use it to cluster observations in similar groups by using patterns in the data to help target your research or interventions. The overall quality of the results depends on the entire chain of events. A single weak link might produce unreliable results. The following list provides a small taste of potential problems and analytical errors that can affect a study.

Accuracy and Precision : Before collecting data, you must ascertain the accuracy and precision of your measurement system. After all, if you can’t trust your data, you can’t trust the results!

Biased samples: An incorrectly drawn sample can bias the conclusions from the start. For example, if a study uses human subjects, the subjects might be different than non-subjects in a way that affects the results. See: Populations, Parameters, and Samples in Inferential Statistics .

Overgeneralization: Findings from one population might not apply to another population. Unfortunately, it’s not necessarily clear what differentiates one population from another. Statistical inferences are always limited, and you must understand the limitations.

Causality: How do you determine when X causes a change in Y? Statisticians need tight standards to assume causality whereas others accept causal relationships more easily. When A precedes B, and A is correlated with B, many mistakenly believe it is a causal connection! However, you’ll need to use an experimental design that includes random assignment to assume confidently that the results represent causality. Learn how to determine whether you’re observing causation or correlation !

Incorrect analysis: Are you analyzing a multivariate study area with only one variable? Or, using an inadequate set of variables? Perhaps you’re assessing the mean when the median might be a better ? Or, did you fit a linear relationship to data that are nonlinear ? You can use a wide range of analytical tools, but not all of them are correct for a specific situation.

Violating the assumptions for an analysis: Most statistical analyses have assumptions. These assumptions often involve properties of the sample, variables, data, and the model. Adding to the complexity, you can waive some assumptions under specific conditions—sometimes thanks to the central limit theorem . When you violate an important assumption, you risk producing misleading results.

Data mining : Even when analysts do everything else correctly, they can produce falsely significant results by investigating a dataset for too long. When analysts conduct many tests, some will be statistically significant due to chance patterns in the data. Fastidious statisticians track the number of tests performed during a study and place the results in the proper context.

Numerous considerations must be correct to produce trustworthy conclusions. Unfortunately, there are many ways to mess up analyses and produce misleading results. Statisticians can guide others through this swamp! Without these guides, you might unintentionally end up p-hacking your results .

Use Statistics to Make an Impact in Your Field

Statistical analyses are used in almost all fields to make sense of the vast amount of data that are available. Even if the field of statistics is not your primary field of study, it can help you make an impact in your chosen field. Chances are very high that you’ll need working knowledge of statistical methodology both to produce new findings in your field and to understand the work of others.

Conversely, as a statistician, there is a high demand for your skills in a wide variety of areas: universities, research labs, government, industry, etc. Furthermore, statistical careers often pay quite well. One of my favorite quotes about statistics is the following by John Tukey:

“The best thing about being a statistician is that you get to play in everyone else’s backyard.”

My interests are quite broad, and statistical knowledge provides the tools to understand all of them.

Lies, Damned Lies, and Statistics: Use Statistical Knowledge to Protect Yourself

I’m sure you’re familiar with the expression about damned lies and statistics, which was spread by Mark Twain among others. Is it true?

Unscrupulous analysts can use incorrect methodology to draw unwarranted conclusions. That long list of accidental pitfalls can quickly become a source of techniques to produce misleading analyses intentionally. But, how do you know? If you’re not familiar with statistics, these manipulations can be hard to detect. Statistical knowledge is the solution to this problem. Use it to protect yourself from manipulation and to react to information intelligently.

Learn how anecdotal evidence is the opposite of statistical methodology and how it can lead you astray!

Using statistics in a scientific study requires a lot of planning. To learn more about this process, read 5 Steps for Conducting Scientific Studies with Statistical Analyses .

The world today produces more data and more analyses designed to influence you than ever before. Are you ready for it?

If you’re learning about statistics and like the approach I use in my blog, check out my Introduction to Statistics book! It’s available at Amazon and other retailers.

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Reader Interactions

July 11, 2022 at 2:25 am

Your are Awesome Jim I like your Blog’s Thanks It’s Very Helpful for me!

July 11, 2022 at 2:33 am

Thanks so much! You’re too kind! I’m really glad my blog has been helpful too! 🙂

June 7, 2022 at 1:40 pm

Please pardon my ignorance and the possibility that I’m some sort of Philistine but I’m trying to help my teenager with statistics revision and my brain is fried. I’m not lacking in intelligence (my favourite subject is physics) but I’m struggling to see the point in the subject when I imagine that there are computer programs that one can put data into in order to find out statistics. I even typed ‘statistics for idiots’ into Google search and the results I got have made me even more confused.

June 8, 2022 at 9:02 pm

There are definitely computer programs in which you can enter the data and it’ll display some numbers. However, there is a lot more to it than that. There are many pitfalls that the untrained can fall into without realizing. Those pitfalls can completely invalidate the results. So, yes, you can enter data into statistical software, and it’ll display some results. However, garbage in –> garbage out. And there are various cases where you won’t realize it’s garbage. The analyses have various assumptions that you need to check. If you don’t check and satisfy the assumptions, you can’t trust the results. Do you know what statistical test is correct for your specific data?

Then there are all the experimental design issues before you even get to measuring data that will help ensure valid results. And, if you want to show causation, how do you do that? There’s the old and true saying that “correlation doesn’t necessarily imply causation.” So, how do you tell? How do you show causation?

Those are just a few of the possible issues. There are many others! Some I discuss in this vary blog post!

Statistics isn’t just the numbers and calculations. It’s understanding the proper methods and procedures, and how to use them correctly so you can both collect and analyze data that will answer your research questions. There’s a whole chain of events that starts during the design phase (well before data collection) and goes through to the analysis phase that needs to be just right for you to be able to trust the results you see in your statistical software. And, if your software says the results are statistically significant, what does that even mean? And not mean? There’s a lot of specialized knowledge that is required throughout that process.

March 31, 2022 at 10:55 am

Thank you so much! It would be a great help. Appreciate it!

March 27, 2022 at 6:21 am

Hello Sir. may I ask on how to ensure that the statistical tools will be used in the study are aligned with the research objectives? Thank you so much!

March 28, 2022 at 9:23 pm

That’s question that requires a very long and complex answer. I’ve written three books about that and there are many more!

However, I’ve written a post that discusses the key considerations and it’ll answer your questions: Conducting Scientific Studies with Statistical Analyses

February 2, 2022 at 3:01 pm

Pls sir, I want to ask a question, What is the importance of statistics in mass communication

February 3, 2022 at 4:03 pm

Imagine you’re communicating with many people about scientific findings. You’ll need to know how to interpret the results of a statistical study. Sometimes knowing exactly what a study is concluding and, importantly, unable to conclude is crucial. Additionally, you should understand the strength of the study. Are there any shortcomings or weaknesses that should make you question the results? By being able to read the statistical results of the study and having a full awareness of the implications of the study’s design, you’ll be better able to present only the credible results to your audience and able to convey them accurately without either incorrectly exaggerating or diminishing their importance beyond their true value.

September 20, 2021 at 12:37 pm

What is statistics and the Importance sir please this is an assignment given to me thank you sir.

September 20, 2021 at 3:49 pm

You’re in the right place. Read this article to answer your questions. There’s no reason for me to retype what I’ve already written in the article in the comments sections! It’s all there!

February 5, 2021 at 3:22 am

Hello sir Jim, your articles is very interesting and very much helpful.

Knowing about statistics sir, I have personal question: How do you apply statistics in the research process?

February 5, 2021 at 9:58 pm

I happen to have written a blog post exactly about that topic! 5 Steps for Conducting Studies with Statistics

Please read that post and if you have more specific questions about a part of the process, you can post them there.

Thanks for writing!

December 1, 2020 at 4:16 am

what year was this made? im planning to use it as a reference to my paper

December 1, 2020 at 11:39 pm

Hi Saegiru,

For online resources, you typically don’t use the publication data because it can change over time. Instead, you generally use the data you accessed the URL. Perdue University’s Online Writing Lab (OWL) has a great web page for how to reference websites and URLs . Please see their guidelines.

November 6, 2020 at 6:18 am

THANK YOU FOR THIS ‘VERY HELPFUL’

September 27, 2020 at 11:38 am

When are ur articles publisehd?

September 28, 2020 at 2:16 pm

I post new articles every 2-4 weeks. You can subscribe to receive an email every time I post a new article. Look in the right side bar, partway down for the place to enter your email address. I do not send spam or sell your email.

August 7, 2020 at 11:06 am

Jim. What a champion you are. Than you so much. May God Bless.

June 15, 2020 at 7:02 pm

Achei incrível, maravilhoso texto!!! Trabalhar com estatística, a Bioestatística em particular é desafiador.

June 15, 2020 at 10:24 pm

Obrigado! Estou feliz que meu site seja útil!

June 13, 2020 at 5:30 am

I’m really grateful for this explanation. You clarified everything, more knowledge I pray.

March 2, 2020 at 1:44 pm

Thank you sir ,for your selfless services,your text really help me. more knowledge I pray 🙏.

February 16, 2020 at 7:18 pm

Thanks a lot, Jim. I found very useful, your article in the preparation of my research work. I highly appreciate your work.

December 7, 2019 at 2:57 pm

Hi Jim, I am elated to run into your website. You clearly explain confusing subjects. As I have decided to embark on learning data science, statistics is the number one area that pops up in every online course. I am curious of your perspective on how linear regression machine learning algorithms differs from the linear regression in statistics. I would love your explanation to draw the connection between the two. Moreover, it would be so amazing if you could educate on all of these algorithms. We need SMEs like yourself to talk in layman’s terms. Thank you!

November 17, 2019 at 11:25 pm

And the year this article was published is when sir? Or the date published. Thank you

November 18, 2019 at 11:28 am

Hello Najihah,

To cite this page as a reference, please see the Electronic Sources guidelines from Purdue University. Look in the “A Page on a Website” section. Typically, you use the access date. For this post, you can use the following citation (change the date as needed):

Frost, Jim. “The Importance of Statistics” Statistics By Jim , https://statisticsbyjim.com/basics/importance-statistics/ . Accessed 18 November 2019.

November 11, 2019 at 8:31 am

Thank you sir for your well explained notes. This one has really helped me a lot to complete my assignment

October 2, 2019 at 4:10 am

Please can you help me in writing a reference to your article?

October 2, 2019 at 5:09 pm

For this type of request, I always refer people to Purdue’s excellent resource about citing electronic sources. This first section on their web page is titled “Webpage or Piece of Online Content” and has several examples that you can use.

Purdue’s Reference List: Electronic Sources

For the author’s name (mine), you can use “Frost, J.”

September 7, 2019 at 9:16 am

how does statistics widen the scope of knowledge

June 18, 2019 at 6:08 am

Thanks for the information, it’s quite interesting.

May 15, 2019 at 4:23 am

i found your article is so usefull for me writing my thesis. may I know when you wrote this article?

May 17, 2019 at 10:30 am

Hi Geovani,

Thank you and I’m glad that you found the article to be helpful! I’m not sure exactly when I wrote it. It goes back quite a ways. However, to reference a webpage, you really need the retrieved from URL date because webpages can change overtime. Read here to learn How to cite a website .

Best of luck with your thesis!

April 30, 2019 at 7:22 am

I have found your article very informative and interesting. I appreciate your points of view and I agree with so many. You’ve done a great job with making this clear enough for anyone to understand.

April 30, 2019 at 11:07 pm

Thank you so much, Steav! I really appreciate that!

March 28, 2019 at 2:13 am

In social science, statistics cover all the jobs which is necessary in social sciences for planning, estimating,working, facilitating and most important point is that through statistics all information, observation and data are collected into a single page.

December 6, 2018 at 10:26 am

what is your thought about the importance of statistics in social science?

December 1, 2018 at 11:05 pm

I have a baseball data sets with 30 independent variables. In this data set, I have one variable which is a combination of the summation 3 variables from the data set. For example, x8=x3+x4+x5. I need to build a multiple linear regression model, if i include x8 in my model should i remove x3,x4,x5. Could you please advise with this

December 2, 2018 at 12:35 am

Yes, you should remove those variables!

October 23, 2018 at 2:07 pm

thanks for sharing your knowledge with us thankss you sir

September 15, 2018 at 4:20 am

My notes on statistics are incomplete because I don’t know the importance of statistics .but u help me a lot in completing my notes .thanku so much sir

September 15, 2018 at 4:17 pm

You’re super welcome! I’m glad it was helpful!

June 27, 2018 at 12:26 pm

its really awesome as it helped me a lot in completing my class 11 notes thank you sir thank you very much for such a wonderful explanation

June 27, 2018 at 2:30 pm

Hi Cera, It makes me happy to hear that my website helped you! Best of luck with your studies!

March 21, 2018 at 1:56 am

Hi,very well explain in simple language , I expect more blogs from you’r side. especially ,how much sample is required for particular analysis and what are criteria should be consider before collecting the sample.

Thank you.Jim..

March 21, 2018 at 1:49 pm

Hi Gopala, I’m very happy to hear that you’re finding my blogs to helpful! I have just written one about determining a good sample size ! I think you’ll find that one to be helpful too.

March 14, 2018 at 6:53 am

Hi. Thanks for posting this. This really helped me with my research for the upcoming quiz.

March 14, 2018 at 11:02 am

Hi Madison, you’re very welcome! I’m glad it helped!

December 11, 2017 at 1:46 am

1. The hanging comma (the second one in “Lies, Damned Lies, and Statistics”) gives this a totally different sense.

2. We are in the age of information quality. This is beyond traditional statistics. See https://www.facebook.com/infoQbook/

December 11, 2017 at 2:06 am

Hi Ron, thanks for you thoughtful comment.

The full expression is: “There are three kinds of lies: lies, damned lies, and statistics.” And, the Wikipedia article includes the final comma. I believe it accurately reflects the intention of the quote that statistics are worse than both lies and damn lies!

I’d argue that the field of statistics is very concerned about the quality of the information that goes into analyses. However, it looks like you and your book are taking it to another level. Congratulations!

Comments and Questions Cancel reply

Statistics, Its Importance and Application Essay

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Importance of Statistics

Examples of how statistics can be used.

Statistics is a science that helps businesses in decision-making. It entails the collection of data, tabulation, and inference making. In essence, Statistics is widely used in businesses to make forecasts, research on the market conditions, and ensure the quality of products. The importance of statistics is to determine the type of data required, how it is collected, and the way it is analyzed to get factual answers.

Statistics is the collection of numerical facts and figures on such things as population, education, economy, incomes, etc. Figures collected are referred to as data. The collection, analysis, and interpretation of data are referred to as statistical methods (Lind, Marchal, & Wathen, 2011).

Two subdivisions of the statistical method are:

• Descriptive statistics: Deals with compilation and presentation of data in various forms such as tables, graphs, and diagrams from which conclusions can be drawn and decisions made. Businesses, for example, use descriptive statistics when presenting their annual accounts and reports.
• Mathematical/inferential/inductive statistics: This deals with the tools of statistics. These are the techniques that are used to analyze, make estimates, inferences, and conclude the data collected (McClave, Benson, & Sincish, 2011).

Statistics have been collected since the earliest times in history. Rulers needed to have data on population and wealth so that taxes could be levied to maintain the state and the courts. Details on the composition of the population were necessary to determine the strength of the nation. With the growth of the population and the advent of the industrial revolution in the 18 th and 19 th centuries, there was a need for greater volumes of statistics in an increasing variety of subjects such as production, expenditure, incomes, imports, and exports. In the 19 th and 20 th centuries, governments worldwide took more control in economic activities such as education and health. This led to the enormous expansion of statistics collected by governments (Lind, Marchal, & Wathen, 2011).

The government’s economic activities have expanded in the last three centuries and so have the companies/businesses grown, as well. Indeed, some have grown to such an extent that their annual turnover is greater than the annual budgets of some governments. Big firms have to make decisions based on data. The companies collect data on their own other than these sources to establish:

• Competition
• Customer needs
• Production and personnel costs
• Accounting reports on liabilities, assets, losses, and income

The tools of statistics are important for companies in areas such as planning, forecasting, and quality control (McClave, Benson, & Sincish, 2011).

To Ensure Quality

A continuous check into quality using programs is very helpful in ensuring that only quality products come out of production firms. This, in turn, ensures that there is minimum wastage or errors in the production of goods and services (McClave, Benson, & Sincish, 2011).

Making Connections

Statistics are good in revealing relationships between variables – a good example is when a company makes a close relationship between the numbers of dissatisfied customers and the turnover. Indeed, there is an inverse relationship between the number of dissatisfied customers and turnover.

Backing Judgment

With only a small sample of the population studied, the management can come up with a concrete understanding of how the customers will relate to their products. This, therefore, will help them decide on whether to or not continue with that line of production (Lind, Marchal, & Wathen, 2011).

Lind, D., Marchal, G., & Wathen, A. (2011). Basic statistics for business and economics (7 th ed.). New York, NY: McGraw-Hill/Irwin.

McClave, T., Benson, G., & Sincish, T. (2011). Statistics for business and economics (11 th ed.). Boston, MA: Pearson-Prentice Hall.

• Descriptive and Inferential Statistical Tests
• "Mindless Statistics" by Gerd Gigerenzer
• Descriptive Statistics in Nursing
• Descriptive Statistics Method: Household Income Analysis
• Statistical Process in Data Analysis
• Hypothesis Testing in Practical Statistics
• Applied Statistics for Healthcare Professionals
• Time Series and Causal Models in Forecasting
• Study Hours and Grades in Educational Institutions
• The Repeated-Measures ANOVA in a General Context
• Chicago (A-D)
• Chicago (N-B)

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Statistics - List of Free Essay Examples And Topic Ideas

Statistics, as the science of collecting, analyzing, and interpreting data, plays an indispensable role in modern decision-making and knowledge generation. Essays could explore the myriad applications of statistics across various fields including healthcare, economics, and social sciences. They might delve into key statistical concepts, methods, and tools, illustrating how they help in understanding complex phenomena, making predictions, and informing policy. Discussions might also extend to the ethical considerations inherent in statistical practices, such as data integrity, privacy, and the potential for misrepresentation or bias. The discourse may also touch on the evolving landscape of statistics amid the advent of big data and computational advancements, examining how these developments are expanding the capabilities and applications of statistical analysis. We have collected a large number of free essay examples about Statistics you can find at PapersOwl Website. You can use our samples for inspiration to write your own essay, research paper, or just to explore a new topic for yourself.

Gender Wage Inequaity in the United States: Statistics and Solutions

"There is a deeply ingrained ideology amongst people in our society that men are the movers and shakers in the business world. This refers to the point of view that men are limited to working in major companies and businesses, and women are limited to the domestic domain. This may have been a true reflection of life fifty years ago, but today a new trend is developing in American society. The levels of education amongst women are increasing, which leads […]

Same-Sex Marriage – Statistics

Marriage was determined to be a fundamental right in Baskin and Obergefell. With many fundamental rights, the right should be considered reversible. Individuals can defer their fundamental rights such as the rights to bear arms, speech, and religion. Therefore, deciding not to marry should also be seen as fundamental. Society has always had strong views on marriage. “Most people think it’s important for couples who intend to stay together to be married, but the number of single Americans who want […]

Hazard of Climate Changing

Sustainability is more than just a term, it's the logic of earth and methods/technique a businesses/people must follow to achieve goals that won't harm the environment in the meanwhile still good socially and increasing the economy. In my paper, I would like to discuss how could the climate change be harmful to sustainability and how it may have an affect on all aspects of the sustainability. According to Reed Karaim in his article about Climate change, he claims that climate […]

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Statistics on Adolescent Suicide

What are your fondest memories playing as a young child? Some of us will remember chasing after a soccer ball or throwing a football across the yard. Others may remember jumping up and down erupting with glee while pretending to be a cheerleader or hitting a baseball across the neighbor’s fence with an aluminum bat. However, a few might not remember playing outside or participating in any sports at all because their parents were engulfed with fear of them getting […]

The Effect of Coffee Consumption on the Risk of Hypertension

ABSTRACT BACKGROUND: hypertension can be defined as a disorder that makes the blood to exert some forces against the walls of the blood vessels. This force depends on the rate of heart beats as well as the resistance from the blood vessels. The medical guidelines define this disorder as pressure higher than 140 over 90 millimeters of mercury (mmHg). AIM: Caffeine compounds are present in coffee and tea. We aimed to evaluate the impact of chronic coffee or tea consumption […]

Inferential Stats Analysis for Psychology

Concerning the data collected, it means that it is easier to draw a valid conclusion regarding the manner in which their variable relates to each group. In this way, it was easier to determine or provide the means of testing the validity of the outcome as well as inferring their characteristics just from a small sample of the participants into a larger one (Goodwin & Goodwin, 2017). In so doing, it implies that it was easier to tell how the […]

Discuss the Importance of Data Management in Research

1. Definiton of Key terms Data management is a general term which refers to a part of research process involving organising, structuring, storage and care of data generated during the research process. It is of prime importance in that it is part of good research practice and it has a bearing on the quality of analysis and research output. The University of Edinburgh (2014) defines data management as a general term covering how you organize, structure, store and care for […]

The Relationship between Early Pregnancy and Wages

Abstract The purpose of this research is to investigate the existence of a possible relationship between early pregnancy and wages. Findings within my research may provide policymakers with critical information required to make decisions that may avert premature pregnancy. Furthermore, I hope the findings of my investigation can help motivate policymakers to focus their efforts on groups that are harmed more due to early pregnancy. The regression analyzes cross-sectional data from 2017 which includes all fifty states. Within the study, […]

College and African American Male: Basketball Athletes

As a freshman in college, I acknowledge and recognize the fact that college can be a challenging experience. The college experience can become even more challenging when you factor in sororities, clubs, fraternities, sports and other school activities. The article that I have decided to use for my analysis is, “College and the African American Male Athlete by Stephen Brown.” Stephen Brown’s main source comes from the book Closing the Education Achievement Gaps for African American Males by Theodore S. […]

Racial Stereotypes in Athletics

The article, Racial Athletic Stereotype Confirmation in College Football Recruiting, can be found in the Journal of Social Psychology and is written by Grant Thomas, Jessica J. Good, and Alexi R. Gross. This article was published in 2015 and it explores the topic of racial stereotypes in the context of college athletic recruitment. They were basically studying if a racial bias could play a role in college athletic recruitment. The researchers' first hypothesis was that coaches would rate black players […]

UNIVERSITY of SOUTH AUSTRALIA 

Introduction In quantitative methods a systematic empirical observation through statistical, mathematical and computational techniques are important components. Reliability of the data is important in quantitative methods. Data accuracy is affected by a variety of factors which range from the choice of the collection methods to biasness. Data is important in improving several aspects of business it is therefore imperative for any business to carry out quantitative research. The data provided in the appendices can is helpful in determining the relationships […]

Customer Success/Customer Engagement

Introduction Customer success and customer engagement are important concepts in every company or business-oriented organization. There are various concerns about the concepts of customer engagement and customer success, as well as their importance for various companies. However, studies have also taken a keen interest in various issues associated with customer engagement through different strategies. From this description, it is clear that customer engagement is a critical concern for every management team with regards to fulfilling the needs of the customers […]

Psychological Survey Study

Questions and Answers 1. How are families likely to view your age/gender/race/ethnicity/spirituality etc. and what cultural blind spots or considerations do you need to take into account when you start working with a family (or about a family that you know)?Families tend to view a person?'s ideas based on their age. In most cases young persons' ideas may be discriminated simply because they are young  therefore, family members tend to think that the younger you are, the less informed you […]

Racism: Unmasking Microaggressions and Discrimination

Reading through the article provided a vivid reflection on how racism becomes a serious issue in the today society. There are various types of racism the article brings out manifested in micro aggression form. The varied opinions in my mind provide a clear picture of the information relayed in the article through the following analysis. Discrimination concerning race will major in my analysis. First, let me talk about the black guy abused in the Saudi Arabia that has sparked public […]

New Insights into Modern Sports Narratives

In the realm of contemporary sports journalism a diverse array of compelling stories has surfaced each offering a distinct glimpse into the dynamic world of athletic competition and achievement. These articles go beyond mere statistics presenting nuanced narratives that resonate with the human spirit and captivate audiences worldwide. One particularly intriguing article profiles a seasoned tennis player whose remarkable comeback culminated in a historic triumph at a prestigious Grand Slam tournament. This narrative not only celebrates the athlete's perseverance and […]

John Elway’s Career in Numbers: a Comprehensive Analysis

John Elway, legendary figure in American football, separated a wonderful career certain his exceptional habits how a defender and his operating on a game. Born 28 of June, 1960, in Port Angeles, Washington, trip of Elway to forming of one of Nfl, portrait figures began early in his life. His statistics of career not only removes his individual mastery but and underlines his holding to the orders that he presented for these years. The professional career of Elway hugged with […]

Memphis Crime Rate: a Closer Look at the Statistics

In the annals of cultural heritage and musical genesis, Memphis stands as an emblem of profound resonance, heralded as the cradle of blues melody. Yet, amidst its illustrious tapestry, the city grapples with the stark limelight of crime statistics. A scrutiny of Memphis's crime metrics unveils a labyrinthine narrative, necessitating a discerning comprehension of the socio-economic and cultural dynamics at play. The city's crime landscape, particularly in the realm of violent transgressions, often eclipses the national benchmark, eliciting both trepidation […]

How to Write a Statistics Essay: Short Guide

Statistics is an incredibly useful subject, particularly in today's data-driven world, and it frequently goes hand in hand with tools. For example excel is renowned for its ability to handle a variety of complex calculations, making it an indispensable tool for students tackling statistical problems. However, mastering requires a solid foundation of knowledge, which some students may lack. This is where the integration of STEM-focused Excel courses in many universities becomes beneficial, providing students with the necessary skills to utilize effectively for statistical analysis. Nevertheless, when students encounter difficulties, PapersOwl presents a solution with excel help online.

Their experts are adept in both statistics, offering personalized assistance to students who struggle with using Excel for their statistical assignments.

Writing a statistics essay involves more than just presenting numbers and data. It requires a clear understanding of statistical methods, an ability to interpret results, and the skill to communicate findings effectively. This article provides a step-by-step guide on how to write a compelling statistics essay.

Understanding the Essay Question

Firstly, it's essential to comprehend the specific question or topic you are dealing with. A statistics essay could range from analyzing a set of data to discussing a particular statistical method. Understanding the scope, requirements, and objectives of the essay will guide your research and writing process.

Research and Data Collection

Begin by collecting relevant data for your essay. This could involve gathering existing data or conducting your own research. Ensure that your sources are credible and that your data is accurate. Additionally, familiarize yourself with the statistical methods that are appropriate for analyzing your data.

Planning Your Essay

Organize your thoughts and data before you start writing. This includes outlining the structure of your essay and deciding how you will present your data. A typical structure might include an introduction, a methodology section, a data analysis section, and a conclusion.

Writing the Introduction

Your introduction should set the context for your essay. Explain why the topic is important and how your essay addresses it. Introduce your thesis statement or the main argument of your essay.

Methodology

In this section, describe the methods used to collect and analyze your data. Be detailed so that readers understand how you arrived at your conclusions. This might include discussing sample sizes, variables, and statistical tests used.

Data Analysis

This is the core of your statistics essay. Present your data in a clear and structured manner. Use graphs, tables, and charts to illustrate your points. Interpret the results of your analysis, explaining what the data shows and why it is significant.

Discussing Results

Go beyond just presenting data. Discuss what the results mean in the context of your topic. Compare your findings with other studies and theories. Address any limitations in your study and suggest areas for further research.

Summarize the main points of your essay, restating your thesis in light of the evidence presented. Highlight the significance of your findings and how they contribute to the understanding of the topic.

Referencing and Citation

Accurately cite all the sources and data used in your essay. Follow the required citation style (APA, MLA, Chicago, etc.). Proper citation is essential to avoid plagiarism and to give credit to the original authors.

Proofreading and Editing

Finally, revise your essay. Check for grammatical and spelling errors, ensure clarity and flow, and verify that all data is accurately presented. Peer reviews can be helpful in identifying areas for improvement.

In conclusion, writing a statistics essay requires careful planning, thorough research, and clear presentation of data and findings. By following these guidelines, you can effectively communicate complex statistical information and insights, contributing meaningfully to the topic of discussion.

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13.7 Cosmos & Culture

How i learned to love statistics — and why you should, too.

I always hated statistics. I mean really, really, really hated it.

Recently though, I've had a change of heart about the subject. In response, I find statistics changing my mind, or at least changing my perspective.

Let me explain.

When I was an undergraduate physics major, lab classes were mandatory. One of the most important parts of lab was doing error analysis — and that meant applying basic statistical ideas like calculating averages and measures of variability (like standard deviations ).

After a few weeks of this, I happily changed my major from physics to math-physics. The latter, I learned, came mercifully without the lab and its statistics requirement.

The problem for me wasn't doing the statistical calculations. They were OK. Instead, it was the idea of statistics that bummed me out. What I loved about physics were its laws. They were timeless. They were eternal. Most of all, I believed they fully and exactly determined everything about the behavior of the cosmos.

Statistics, on the other hand, was about the imperfect world of imperfect equipment taking imperfect data. For me, that realm was just a crappy version of the pure domain of perfect laws I was interested in. Measurements, by their nature, would always be messy. A truck goes by and jiggles your equipment. The kid you paid to do the observations isn't really paying attention. The very need to account for those variations made me sad.

Now, however, I see things very differently. My change of heart can be expressed in just two words — Big Data. Over the last 10 years, I've been watching in awe as the information we have been inadvertently amassing has changed society for better and worse. There is so much power, promise and peril for everyone in this brave new world that I knew I had to get involved . That's where my new life in statistics began.

The whole point of Big Data is to understand how to quickly and intelligently shift through peta-bytes of information and extract relationships. That means applying statistics-based methods to the numbers, names and other quantities that are what we mean by "The Data."

But to get anywhere with Big Data, I need to learn everything I can about statistics as fast as I can. My first refresher and guide in this effort has been the Coursera Course of Matthijs Rooduijn and Emiel van Loon of the University of Amsterdam. So far, I've only made it through the first week of their online lectures, but my platonic-oriented mind is already being retuned. The thing that's really getting to me is pretty simple, so I hope you'll excuse my naïve enthusiasm.

The issue is the world that's out there, independent of us. With my platonic-theoretical-physicist glasses on, I have always been happy to claim that we already know the exact laws exactly governing that independent world. But really, a claim like that is kind of bull. The real, independent world is way more complex than my theoretical physics equations can handle. This is particularly true when it comes to biology or, even more to the point, human society with its economy and culture and politics and elections.

So what can we do to understand the complexity of economies, cultures, politics and elections? We can take data. We can go out and measure whatever we can get our hands on. And it's right there that the light snaps on and vaults me past in my old distaste for statistics.

The problem with taking data is you don't know what it's telling you. It's always only a partial representation of the thing you are trying to understand. That means there is only one way to make clear links between the data you have taken and what the world wants to understand. You have to be very clear and very clever about interrogating the data. You have to develop methods — statistical methods — that extract answers you can trust.

Even more important, you need methods — statistical methods — for knowing exactly what the limits of trust are. Without these methods we would literally be lost. We'd be unable to see what data to take, what that data can tell us and when the data can't tell us anything at all.

Of course, what I'm saying will elicit a giant snooze for anyone who has thought even a bit about statistics and their use. But for us statistic-haters, the deeper philosophical basis of its methods in representing the world are worth consideration. That's because the effectiveness of all those algorithms creeping into every aspect of our lives hinge exactly on understanding the essential gap between the data we collect and the world it's meant to describe.

So now, finally , I can see the great range and beauty in the ideas behind statistics. Better late than never, at least on average.

Adam Frank is a co-founder of the 13.7 blog, an astrophysics professor at the University of Rochester, a book author and a self-described "evangelist of science." You can keep up with more of what Adam is thinking on Facebook and Twitter: @adamfrank4

• theoretical physics

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Writing with Descriptive Statistics

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Usually there is no good way to write a statistic. It rarely sounds good, and often interrupts the structure or flow of your writing. Oftentimes the best way to write descriptive statistics is to be direct. If you are citing several statistics about the same topic, it may be best to include them all in the same paragraph or section.

The mean of exam two is 77.7. The median is 75, and the mode is 79. Exam two had a standard deviation of 11.6.

Overall the company had another excellent year. We shipped 14.3 tons of fertilizer for the year, and averaged 1.7 tons of fertilizer during the summer months. This is an increase over last year, where we shipped only 13.1 tons of fertilizer, and averaged only 1.4 tons during the summer months. (Standard deviations were as followed: this summer .3 tons, last summer .4 tons).

Some fields prefer to put means and standard deviations in parentheses like this:

If you have lots of statistics to report, you should strongly consider presenting them in tables or some other visual form. You would then highlight statistics of interest in your text, but would not report all of the statistics. See the section on statistics and visuals for more details.

If you have a data set that you are using (such as all the scores from an exam) it would be unusual to include all of the scores in a paper or article. One of the reasons to use statistics is to condense large amounts of information into more manageable chunks; presenting your entire data set defeats this purpose.

At the bare minimum, if you are presenting statistics on a data set, it should include the mean and probably the standard deviation. This is the minimum information needed to get an idea of what the distribution of your data set might look like. How much additional information you include is entirely up to you. In general, don't include information if it is irrelevant to your argument or purpose. If you include statistics that many of your readers would not understand, consider adding the statistics in a footnote or appendix that explains it in more detail.

Essays on Statistics

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Home — Essay Samples — Science — Mathematics in Everyday Life — The Benefits and Importance of Statistics in Daily Life

The Benefits and Importance of Statistics in Daily Life

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Finding Statistics

• Why are Statistics Important?

Statistics are important because they help people make informed decisions. Governments, organizations, and businesses all collect statistics to help them track progress, measure performance, analyze problems, and prioritize. For example, the U.S. Census Bureau collects information from people about where they live and their age. This information can help cities decide where they should build a new hospital if they find that there is a high elderly population in an area or a new school, if they find there are many families with young children.

On a personal level, statistics can be a great way to enhance your argument in a research paper or presentation. They show that there is evidence to back up your claim and can add credibility to your work. Statistics often create an emotional response in your audience. Think about how you feel when someone can back up their argument with statistics? Don't the statistics make you feel more strongly to the argument?

The below video by Ms. Emma Stevenson will help explain how statistics can help you in a research paper or project:

Misleading Statistics

Statistics are an excellent way to enhance an argument and persuade your audience; however, there are some considerations to keep in mind. Statistics can be misleading, because they are often taken out of context. Sometimes, important information is left out about how the statistic was collected in order to make it seem more dramatic, proving big ideas or generalizations that it wouldn't if the rest of the information was included. 

For example, let's say you found a statistic that said 5 out of 5 dentists recommend a certain brand of toothpaste. That sounds like this is a great brand of toothpaste that everyone should use. However, what if you found out that the dentists were all asked if they would recommend that brand of toothpaste or not brushing your teeth at all? Of course all of the dentists are going to pick the brand of toothpaste. This makes the 5 out of 5 recommendation basically meaningless. You might assume when you see this statistic that dentists were ranking this toothpaste brand over other toothpaste brands, instead of against not brushing your teeth at all; this makes the statistic misleading.

Another way statistics can be misleading is in the sample size that the data was collected in. For example, let's say you found a statistic that says 4 out of 5 women prefer wearing high heels over flats to work. However, when you start looking closer at the source the statistic came from, you find that this statistic came from someone asking 5 women they work with in a corporate law firm if they liked wearing heels or flats to work. This is a problem for several reasons.

First, the information was collected from a very small sample size (5 women who all work at the same place). These 5 women cannot represent all women and their opinions on high heels. Second, this sample is very biased, because all of the women work in the same corporate law firm. These women's opinions are not going to reflect all women's opinions, regardless of the number of women sampled, because the women are too similar to one another. If all women in all industries were surveyed for this question, the statistic would look very different. Because of this, it's always important to know the context of any statistic before you use it in your argument. Similarly, you want to be wary of statistics you find that don't have context or can't be tracked back to an original source.

Just like evaluating the credibility of your sources , you will want to do the same for when you want to use statistics in your research. Ask yourself the following questions:

• Can you find the original source that this statistic was published in? This will help you understand the context of the statistics.
• Who published the original source and where was it published?
• Who collected the information for the statistics? Do they have any kind of agenda/stake in the statistics?
• When was the information collected? Could it be out of date?
• How big was the sample size/how much data was collected? What were the demographics of the sample size? This will help you figure out if the statistics are representative of a certain group or area. 

Here is an article that goes deeper into how statistics can be misleading and ways to determine whether your statistics are misleading or not.

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Essay on Statistics: Meaning and Definition of Statistics

“Statistics”, that a word is often used, has been derived from the Latin word ‘Status’ that means a group of numbers or figures; those represent some information of our human interest.

We find statistics in everyday life, such as in books or other information papers or TV or newspapers.

Although, in the beginning it was used by Kings only for collecting information about states and other information which was needed about their people, their number, revenue of the state etc.

This was known as the science of the state because it was used only by the Kings. So it got its development as ‘Kings’ subject or ‘Science of Kings’ or we may call it as “Political Arithmetic’s”. It was for the first time, perhaps in Egypt to conduct census of population in 3050 B.C. because the king needed money to erect pyramids. But in India, it is thought, that, it started dating back to Chandra Gupta Maurya’s kingdom under Chankya to collect the data of births and deaths. TM has also been stated in Chankya’s Arthshastra.

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But now-a-days due to its pervading nature, its scope has increased and widened. It is now used in almost in all the fields of human knowledge and skills like Business, Commerce, Economics, Social Sciences, Politics, Planning, Medicine and other sciences, Physical as well as Natural.

Definition :

The term ‘Statistics’ has been defined in two senses, i.e. in Singular and in Plural sense.

“Statistics has two meanings, as in plural sense and in singular sense”.

—Oxford Dictionary

In plural sense, it means a systematic collection of numerical facts and in singular sense; it is the science of collecting, classifying and using statistics.

A. In the Plural Sense :

“Statistics are numerical statements of facts in any department of enquiry placed in relation to each other.” —A.L. Bowley

“The classified facts respecting the condition of the people in a state—especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.” —Webster

These definitions given above give a narrow meaning to the statistics as they do not indicate its various aspects as are witnessed in its practical applications. From the this point of view the definition given by Prof. Horace Sacrist appears to be the most comprehensive and meaningful:

“By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose, and placed in relation to each other.”—Horace Sacrist

B. In the Singular Sense :

“Statistics refers to the body of technique or methodology, which has been developed for the collection, presentation and analysis of quantitative data and for the use of such data in decision making.” —Ncttor and Washerman

“Statistics may rightly be called the science of averages.” —Bowleg

“Statistics may be defined as the collection, presentation, analysis, and interpretation of numerical data.” —Croxton and Cowden

Stages of Investigations :

1. Collection of Data:

It is the first stage of investigation and is regarding collection of data. It is determined that which method of collection is needed in this problem and then data are collected.

2. Organisation of Data:

It is second stage. The data are simplified and made comparative and are classified according to time and place.

3. Presentation of Data:

In this third stage, organised data are made simple and attractive. These are presented in the form of tables diagrams and graphs.

4. Analysis of Data:

Forth stage of investigation is analysis. To get correct results, analysis is necessary. It is often undertaken using Measures of central tendencies, Measures of dispersion, correlation, regression and interpolation etc.

5. Interpretation of Data:

In this last stage, conclusions are enacted. Use of comparisons is made. On this basis, forecasting is made.

Some Modern Definitions :

From the above two senses of statistics, modem definitions have emerged as given below:

“Statistics is a body of methods for making wise decisions on the face of uncertainty.” —Wallis and Roberts

“Statistics is a body of methods for obtaining and analyzing numerical data in order to make better decisions in an uncertain world.” —Edward N. Dubois

So, from above definitions we find that science of statistics also includes the methods of collecting, organising, presenting, analysing and interpreting numerical facts and decisions are taken on their basis.

The most proper definition of statistics can be given as following after analysing the various definitions of statistics.

“Statistics in the plural sense are numerical statements of facts capable of some meaningful analysis and interpretation, and in singular sense, it relates to the collection, classification, presentation and interpretation of numerical data.”

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probability and statistics , the branches of mathematics concerned with the laws governing random events, including the collection, analysis , interpretation, and display of numerical data. Probability has its origin in the study of gambling and insurance in the 17th century, and it is now an indispensable tool of both social and natural sciences. Statistics may be said to have its origin in census counts taken thousands of years ago; as a distinct scientific discipline , however, it was developed in the early 19th century as the study of populations, economies, and moral actions and later in that century as the mathematical tool for analyzing such numbers. For technical information on these subjects, see probability theory and statistics . See also conditional probability , probability density function , likelihood , and geometric distribution .

Early probability

The modern mathematics of chance is usually dated to a correspondence between the French mathematicians Pierre de Fermat and Blaise Pascal in 1654. Their inspiration came from a problem about games of chance, proposed by a remarkably philosophical gambler, the chevalier de Méré . De Méré inquired about the proper division of the stakes when a game of chance is interrupted. Suppose two players, A and B , are playing a three-point game, each having wagered 32 pistoles, and are interrupted after A has two points and B has one. How much should each receive?

Fermat and Pascal proposed somewhat different solutions, though they agreed about the numerical answer. Each undertook to define a set of equal or symmetrical cases, then to answer the problem by comparing the number for A with that for B . Fermat, however, gave his answer in terms of the chances, or probabilities. He reasoned that two more games would suffice in any case to determine a victory. There are four possible outcomes, each equally likely in a fair game of chance. A might win twice, A A ; or first A then B might win; or B then A ; or B B . Of these four sequences, only the last would result in a victory for B . Thus, the odds for A are 3:1, implying a distribution of 48 pistoles for A and 16 pistoles for B .

Pascal thought Fermat’s solution unwieldy, and he proposed to solve the problem not in terms of chances but in terms of the quantity now called “expectation.” Suppose B had already won the next round. In that case, the positions of A and B would be equal, each having won two games, and each would be entitled to 32 pistoles. A should receive his portion in any case. B ’s 32, by contrast, depend on the assumption that he had won the first round. This first round can now be treated as a fair game for this stake of 32 pistoles, so that each player has an expectation of 16. Hence A ’s lot is 32 + 16, or 48, and B ’s is just 16.

Games of chance such as this one provided model problems for the theory of chances during its early period, and indeed they remain staples of the textbooks. A posthumous work of 1665 by Pascal on the “arithmetic triangle” now linked to his name ( see binomial theorem ) showed how to calculate numbers of combinations and how to group them to solve elementary gambling problems. Fermat and Pascal were not the first to give mathematical solutions to problems such as these. More than a century earlier, the Italian mathematician, physician, and gambler Girolamo Cardano calculated odds for games of luck by counting up equally probable cases. His little book, however, was not published until 1663, by which time the elements of the theory of chances were already well known to mathematicians in Europe. It will never be known what would have happened had Cardano published in the 1520s. It cannot be assumed that probability theory would have taken off in the 16th century. When it began to flourish, it did so in the context of the “new science” of the 17th-century scientific revolution, when the use of calculation to solve tricky problems had gained a new credibility. Cardano, moreover, had no great faith in his own calculations of gambling odds, since he believed also in luck, particularly in his own. In the Renaissance world of monstrosities, marvels, and similitudes, chance—allied to fate—was not readily naturalized, and sober calculation had its limits.

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