how to write essay on statistics

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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How To Write a Statistical Analysis Essay

Home » Videos » How To Write a Statistical Analysis Essay

Statistical analysis is a powerful tool used to draw meaningful insights from data. It can be applied to almost any field and has been used in everything from natural sciences, economics, and sociology to sports analytics and business decisions. Writing a statistical analysis essay requires an understanding of the concepts behind it as well as proficiency with data manipulation techniques.

In this guide, we’ll look at the steps involved in writing a statistical analysis essay. Experts in research paper writing from https://domypaper.me/write-my-research-paper/ give detailed instructions on how to properly conduct a statistical analysis and make valid conclusions.

Overview of statistical analysis essays

A statistical analysis essay is an academic paper that involves analyzing quantitative data and interpreting the results. It is often used in social sciences, economics and business to draw meaningful conclusions from the data. The objective of a statistical analysis essay is to analyze a specific dataset or multiple datasets in order to answer a question or prove or disprove a hypothesis. To achieve this effectively, the information must be analyzed using appropriate statistical techniques such as descriptive statistics, inferential statistics, regression analysis and correlation analysis.

Researching the subject matter

Before writing your statistical analysis essay it is important to research the subject matter thoroughly so that you have an understanding of what you are dealing with. This can include collecting and organizing any relevant data sets as well as researching different types of statistical techniques available for analyzing them. Furthermore, it is important to become familiar with the terminology associated with statistical analysis such as mean, median and mode.

Structuring your statistical analysis essay

The structure of your essay will depend on the type of data you are analyzing and the research question or hypothesis that you are attempting to answer. Generally speaking, it should include an introduction which introduces the research question or hypothesis; a body section which includes an overview of relevant literature; a description of how the data was collected and analyzed and any conclusions drawn from it; and finally a conclusion which summarizes all findings.

Analyzing data and drawing conclusions from it

After collecting and organizing your data, you must analyze it in order to draw meaningful conclusions from it. This involves using appropriate statistical techniques such as descriptive statistics, inferential statistics, regression analysis and correlation analysis. It is important to understand the assumptions made when using each technique in order to analyze the data correctly and draw accurate conclusions from it. When choosing a statistical technique for your research, it is important to consult with an expert https://typemyessay.me/service/research-paper-writing-service who can guide you on the most appropriate approach for your study.

Interpreting results and writing a conclusion

Once you have analyzed the data successfully, you must interpret the results carefully in order to answer your research question or prove/disprove your hypothesis. This involves making sure that any conclusions drawn are soundly based on the evidence presented. After interpreting the results, you should write a conclusion which summarizes all of your findings.

Using sources in your analysis

In order to back up your claims and provide support for your arguments, it is important to use credible sources within your analysis. This could include peer-reviewed articles, journals and books which can provide evidence to support your conclusion. It is also important to cite all sources used in order to avoid plagiarism.

Proofreading and finalizing your work

Once you have written your essay it is important to proofread it carefully before submitting it. This involves checking for grammar, spelling and punctuation errors as well as ensuring that the flow of the essay makes sense. Additionally, make sure that any references cited are correct and up-to-date. If you find it hard to complete your research statistical paper, you may want to consider buying a research paper for sale . This service can save you time and money, allowing you to focus on other important tasks.

Tips for writing a successful statistical analysis essay

Here are some tips for writing a successful statistical analysis essay:

• Research your subject matter thoroughly before writing your essay.
• Structure your paper according to the type of data you are analyzing.
• Analyze your data using appropriate statistical techniques.
• Interpret and draw meaningful conclusions from your results.
• Use credible sources to back up any claims or arguments made.
• Proofread and finalize your work before submitting it.

These tips will help ensure that your essay is well researched, structured correctly and contains accurate information. Following these tips will help you write a successful statistical analysis essay which can be used to answer research questions or prove/disprove hypotheses.

Sources and links For the articles and videos I use different databases, such as Eurostat, OECD World Bank Open Data, Data Gov and others. You are free to use the video I have made on your site using the link or the embed code. If you have any questions, don’t hesitate to write to me!

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How To Write a Statistical Research Paper: Tips, Topics, Outline

Working on a research paper can be a bit challenging. Some people even opt for paying online writing companies to do the job for them. While this might seem like a better solution, it can cost you a lot of money. A cheaper option is to search online for the critical parts of your essay. Your data should come from reliable sources for your research paper to be authentic. You will also need to introduce your work to your readers. It should be straightforward and relevant to the topic.  With this in mind, here is a guideline to help you succeed in your research writing. But before that, let’s see what the outline should look like.

The Outline

Table of Contents

How to write a statistical analysis paper is a puzzle many people find difficult to crack. It’s not such a challenging task as you might think, especially if you learn some helpful tips to make the writing process easier. It’s just like working on any other essay. You only need to get the format and structure right and study the process. Here is what the general outline should look like:

• introduction;
• problem statement;
• objectives;
• methodology;
• data examination;
• discussion;
• conclusion and recommendations.

Let us now see some tips that can help you become a better statistical researcher.

• Top 99+ Trending Statistics Research Topics for Students

Tips for Writing Statistics Research Paper

If you are wondering how people write their papers, you are in the right place. We’ll take a look at a few pointers that can help you come up with amazing work.

Choose A Topic

Basically, this is the most important stage of your essay. Whether you want to pay for it or not, you need a simple and accessible topic to write about. Usually, the paid research papers have a well-formed and clear topic. It helps your paper to stand out. Start off by explaining to your audience what your papers are all about. Also, check whether there is enough data to support your idea. The weaker the topic is, the harder your work will be. Is the potential theme within the realm of statistics? Can the question at hand be solved with the help of the available data? These are some of the questions someone should answer first. In the end, the topic you opt for should provide sufficient space for independent information collection and analysis.

Collect Data

This stage relies heavily on the quantity of data sources and the method used to collect them. Keep in mind that you must stick to the chosen methodology throughout your essay. It is also important to explain why you opted for the data collection method used. Plus, be cautious when collecting information. One simple mistake can compromise the entire work. You can source your data from reliable sources like google, read published articles, or experiment with your own findings. However, if your instructor provides certain recommendations, follow them instead. Don’t twist the information to fit your interest to avoid losing originality. And in case no recommendations are given, ask your instructor to provide some.

Write Body Paragraphs

Use the information garnered to create the main body of your essay. After identifying an applicable area of interest, use the data to build your paragraphs. You can start off by making a rough draft of your findings and then use it as a guide for your main essay. The next step is to construe numerical figures and make conclusions. This stage requires your proficiency in interpreting statistics. Integrate your math engagement strategies to break down those figures and pinpoint only the most meaningful parts of them. Also, include some common counterpoints and support the information with specific examples.

Create Your Essay

Now that you have all the appropriate materials at hand, this section will be easy. Simply note down all the information gathered, citing your sources as well. Make sure not to copy and paste directly to avoid plagiarism. Your content should be unique and easy to read, too. We recommend proofreading and polishing your work before making it public. In addition, be on the lookout for any grammatical, spelling, or punctuation mistakes.

This section is a summary of all your findings. Explain the importance of what you are doing. You can also include suggestions for future work. Make sure to restate what you mentioned in the introduction and touch a little bit on the method used to collect and analyze your data. In short, sum up everything you’ve written in your essay.

How to Find Statistical Topics for your Paper

Statistics is a discipline that involves collecting, analyzing, organizing, presenting, and interpreting data. If you are looking for the right topic for your work, here are a few things to consider.

●   Start by finding out what topics have already been worked on and pick the remaining areas.

●   Consider recent developments in your field of study that may inspire a new topic.

●   Think about any specific questions or problems that you have come across on your own that could be explored further.

●   Ask your advisor or mentor for suggestions.

●   Review conference proceedings, journal articles, and other publications.

●   Try using a brainstorming technique. For instance, list out related keywords and combine them in different ways to generate new ideas.

Try out some of these tips. Be sure to find something that will work for you.

Working on a statistics paper can be quite challenging to work on. But with the right information sources, everything becomes easy. This guide will help you reveal the secret of preparing such essays. Also, don’t forget to do more reading to broaden your knowledge. You can find statistics research paper examples and refer to them for ideas. Nonetheless, if you’re still not confident enough, you can always hire a trustworthy writing company to get the job done.

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Using Statistics in Your Writing

• Writing with Statistics  The Purdue Online Writing Lab explains how to write with statistics including quick tips, writing descriptive statistics, writing inferential statistics, and using visuals with statistics. 
• This Statistics handout from The Writing Center, University of North Carolina at Chapel Hill, helps you to use statistics to make your argument as effectively as possible.
• For a better understanding of why and how to use statistics in your writing, read the chapter on "Arguing" in The Norton Field Guide to Writing , pages 397-417. Copies are on reserve at the Circulation Desk in Columbus Hall and are also available at the Reference Desk in Moeller Hall at the Delaware campus.  
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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.

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• Report Writing

How to Write a Statistical Report

Last Updated: June 12, 2024 Fact Checked

This article was reviewed by Grace Imson, MA and by wikiHow staff writer, Jennifer Mueller, JD . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 409,815 times.

A statistical report informs readers about a particular subject or project. You can write a successful statistical report by formatting your report properly and including all the necessary information your readers need. [1] X Research source

A Beginner’s Guide to Statistical Report Writing

Use other statistical reports as a guide to format your own. Type your report in an easy-to-read font, include all the information that your reader needs, and present your results in a table or graph.

Formatting Your Report

• If you're completing your report for a class, your instructor or professor may be willing to show you some reports submitted by previous students if you ask.
• University libraries also have copies of statistical reports created by students and faculty researchers on file. Ask the research librarian to help you locate one in your field of study.
• You also may be able to find statistical reports online that were created for business or marketing research, as well as those filed for government agencies.
• Be careful following samples exactly, particularly if they were completed for research in another field. Different fields of study have their own conventions regarding how a statistical report should look and what it should contain. For example, a statistical report by a mathematician may look incredibly different than one created by a market researcher for a retail business.

• You typically want to have 1-inch margins around all sides of your report. Be careful when adding visual elements such as charts and graphs to your report, and make sure they don't bleed over the margins or your report may not print properly and will look sloppy.
• You may want to have a 1.5-inch margin on the left-hand side of the page if you anticipate putting your study into a folder or binder, so all the words can be read comfortably when the pages are turned.
• Don't double-space your report unless you're writing it for a class assignment and the instructor or professor specifically tells you to do so.
• Use headers to add the page number to every page. You may also want to add your last name or the title of the study along with the page number.

• Citation methods typically are included in style manuals, which not only detail how you should cite your references but also have rules on acceptable punctuation and abbreviations, headings, and the general formatting of your report.
• For example, if you're writing a statistical report based on a psychological study, you typically must use the style manual published by the American Psychological Association (APA).
• Your citation method is all the more important if you anticipate your statistical report will be published in a particular trade or professional journal.

• If you're creating your statistical report for a class, a cover sheet may be required. Check with your instructor or professor or look on your assignment sheet to find out whether a cover sheet is required and what should be included on it.
• For longer statistical reports, you may also want to include a table of contents. You won't be able to format this until after you've finished the report, but it will list each section of your report and the page on which that section starts.

• If you decide to create section headings, they should be bold-faced and set off in such a way that they stand out from the rest of the text. For example, you may want to center bold-faced headings and use a slightly larger font size.
• Make sure a section heading doesn't fall at the bottom of the page. You should have at least a few lines of text, if not a full paragraph, below each section heading before the page break.

• Check the margins around visual elements and make sure the text lines up and is not too close to the visual element. You want it to be clear where the text ends and the words associated with the visual element (such as the axis labels for a graph) begin.
• Visual elements can cause your text to shift, so you'll need to double-check your section headings after your report is complete and make sure none of them are at the bottom of a page.
• Where possible, you also want to change your page breaks to eliminate situations in which the last line of a page is the first line of a paragraph, or the first line of a page is the last line of a paragraph. These are difficult to read.

Creating Your Content

• Avoid overly scientific or statistical language in your abstract as much as possible. Your abstract should be understandable to a larger audience than those who will be reading the entire report.
• It can help to think of your abstract as an elevator pitch. If you were in an elevator with someone and they asked you what your project was about, your abstract is what you would say to that person to describe your project.
• Even though your abstract appears first in your report, it's often easier to write it last, after you've completed the entire report.

• Aim for clear and concise language to set the tone for your report. Put your project in layperson's terms rather than using overly statistical language, regardless of the target audience of your report.
• If your report is based on a series of scientific experiments or data drawn from polls or demographic data, state your hypothesis or expectations going into the project.
• If other work has been done in the field regarding the same subject or similar questions, it's also appropriate to include a brief review of that work after your introduction. Explain why your work is different or what you hope to add to the existing body of work through your research.

• Include a description of any particular methods you used to track results, particularly if your experiments or studies were longer-term or observational in nature.
• If you had to make any adjustments during the development of the project, identify those adjustments and explain what required you to make them.
• List any software, resources, or other materials you used in the course of your research. If you used any textbook material, a reference is sufficient – there's no need to summarize that material in your report.

• Start with your main results, then include subsidiary results or interesting facts or trends you discovered.
• Generally you want to stay away from reporting results that have nothing to do with your original expectations or hypotheses. However, if you discovered something startling and unexpected through your research, you may want to at least mention it.
• This typically will be the longest section of your report, with the most detailed statistics. It also will be the driest and most difficult section for your readers to get through, especially if they are not statisticians.
• Small graphs or charts often show your results more clearly than you can write them in text.

• When you get to this section of your report, leave the heavy, statistical language behind. This section should be easy for anyone to understand, even if they skipped over your results section.
• If any additional research or study is necessary to further explore your hypotheses or answer questions that arose in the context of your project, describe that as well.

• It is often the case that you see things in hindsight that would have made data-gathering easier or more efficient. This is the place to discuss those. Since the scientific method is designed so that others can repeat your study, you want to pass on to future researchers your insights.
• Any speculation you have, or additional questions that came to mind over the course of your study, also are appropriate here. Just make sure you keep it to a minimum – you don't want your personal opinions and speculation to overtake the project itself.

• For example, if you compared your study to a similar study conducted in another city the year before yours, you would want to include a citation to that report in your references.
• Cite your references using the appropriate citation method for your discipline or field of study.
• Avoid citing any references that you did not mention in your report. For example, you may have done some background reading in preparation for your project. However, if you didn't end up directly citing any of those sources in your report, there's no need to list them in your references.

• Avoid trade "terms of art" or industry jargon if your report will be read mainly by people outside your particular industry.
• Make sure the terms of art and statistical terms that you do use in your report are used correctly. For example, you shouldn't use the word "average" in a statistical report because people often use that word to refer to different measures. Instead, use "mean," "median," or "mode" – whichever is correct.

Presenting Your Data

• This is particularly important if you're submitting your report for publication in a trade journal. If the pages are different sizes than the paper you print your report on, your visual elements won't line up the same way in the journal as they do in your manuscript.
• This also can be a factor if your report will be published online, since different display sizes can cause visual elements to display differently.
• The easiest way to label your visual elements is "Figure," followed by a number. Then you simply number each element sequentially in the order in which they appear in your report.
• Your title describes the information presented by the visual element. For example, if you've created a bar graph that shows the test scores of students on the chemistry class final, you might title it "Chemistry Final Test Scores, Fall 2016."

• Make sure each visual element is large enough in size that your readers can see everything they need to see without squinting. If you have to shrink down a graph to the point that readers can't make out the labels, it won't be very helpful to them.
• Create your visual elements using a format that you can easily import into your word-processing file. Importing using some graphics formats can distort the image or result in extremely low resolution.

• For example, if you have hundreds of samples, your x axis will be cluttered if you display each sample individually as a bar. However, you can move the measure on the y axis to the x axis, and use the y axis to measure the frequency.
• When your data include percentages, only go out to fractions of a percentage if your research demands it. If the smallest difference between your subjects is two percentage points, there's no need to display more than the whole percentage. However, if the difference between your subjects comes down to hundredths of a percent, you would need to display percentages to two decimal places so the graph would show the difference.
• For example, if your report includes a bar graph of the distribution of test scores for a chemistry class, and those scores are 97.56, 97.52, 97.46, and 97.61, your x axis would be each of the students and your y axis would start at 97 and go up to 98. This would highlight the differences in the students' scores.

• Be careful that your appendix does not overwhelm your report. You don't necessarily want to include every data sheet or other document you created over the course of your project.
• Rather, you only want to include documents that reasonably expand and lead to a further understanding of your report.
• For example, when describing your methods you state that a survey was conducted of students in a chemistry class to determine how they studied for the final exam. You might include a copy of the questions the students were asked in an appendix. However, you wouldn't necessarily need to include a copy of each student's answers to those questions.

Statistical Report Outline

Community Q&A

You Might Also Like

• ↑ https://www.ibm.com/docs/en/iotdm/11.3?topic=SSMLQ4_11.3.0/com.ibm.nex.optimd.dg.doc/11arcperf/oparcuse-r-statistical_reports.html
• ↑ https://www.examples.com/business/report/statistics-report.html
• ↑ https://collaboratory.ucr.edu/sites/g/files/rcwecm2761/files/2019-04/Final_Report_dan.pdf
• ↑ https://tex.stackexchange.com/questions/49386/what-is-the-recommended-font-to-use-for-a-statistical-table-in-an-academic-journ
• ↑ https://psychology.ucsd.edu/undergraduate-program/undergraduate-resources/academic-writing-resources/writing-research-papers/citing-references.html
• ↑ https://www.youtube.com/watch?v=kl3JOCmuil4

About This Article

Start your statistical report with an introduction explaining the purpose of your research. Then, dive into your research methods, how you collected data, and the experiments you conducted. Present you results with any necessary charts and graphs, but do not discuss or analyze the numbers -- in a statistical report, all analysis should happen in the conclusion. Once you’ve finished writing your report, draft a 200 word abstract and create a cover sheet with your name, the date, and the report title. Don’t forget to cite the appropriate references when necessary! For more formatting help, read on! Did this summary help you? Yes No

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

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

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

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

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

Table of contents

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

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

Writing statistical hypotheses

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

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

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

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

Planning your research design

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

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

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

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

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

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

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

Measuring variables

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

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

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

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

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

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

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

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

Sampling for statistical analysis

There are two main approaches to selecting a sample.

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

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

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

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

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

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

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

Create an appropriate sampling procedure

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

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

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

Calculate sufficient sample size

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

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

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

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

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

Inspect your data

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

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

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

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

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

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

Calculate measures of central tendency

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

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

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

Calculate measures of variability

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Hypothesis testing

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

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

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

Statistical tests come in three main varieties:

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

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

Parametric tests

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The final step of statistical analysis is interpreting your results.

Statistical significance

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

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

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

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

Effect size

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

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

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

Decision errors

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

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

Frequentist versus Bayesian statistics

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

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

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

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

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

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

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

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• Central Limit Theorem | Formula, Definition & Examples
• Central Tendency | Understanding the Mean, Median & Mode
• Correlation Coefficient | Types, Formulas & Examples
• Descriptive Statistics | Definitions, Types, Examples
• How to Calculate Standard Deviation (Guide) | Calculator & Examples
• How to Calculate Variance | Calculator, Analysis & Examples
• How to Find Degrees of Freedom | Definition & Formula
• How to Find Interquartile Range (IQR) | Calculator & Examples
• How to Find Outliers | Meaning, Formula & Examples
• How to Find the Geometric Mean | Calculator & Formula
• How to Find the Mean | Definition, Examples & Calculator
• How to Find the Median | Definition, Examples & Calculator
• How to Find the Range of a Data Set | Calculator & Formula
• Inferential Statistics | An Easy Introduction & Examples
• Levels of measurement: Nominal, ordinal, interval, ratio
• Missing Data | Types, Explanation, & Imputation
• Normal Distribution | Examples, Formulas, & Uses
• Null and Alternative Hypotheses | Definitions & Examples
• Poisson Distributions | Definition, Formula & Examples
• Skewness | Definition, Examples & Formula
• T-Distribution | What It Is and How To Use It (With Examples)
• The Standard Normal Distribution | Calculator, Examples & Uses
• Type I & Type II Errors | Differences, Examples, Visualizations
• Understanding Confidence Intervals | Easy Examples & Formulas
• Variability | Calculating Range, IQR, Variance, Standard Deviation
• What is Effect Size and Why Does It Matter? (Examples)
• What Is Interval Data? | Examples & Definition
• What Is Nominal Data? | Examples & Definition
• What Is Ordinal Data? | Examples & Definition
• What Is Ratio Data? | Examples & Definition
• What Is the Mode in Statistics? | Definition, Examples & Calculator

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

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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

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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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Writing With Statistics: Mistakes to Watch Out For

Numbers are power. Adding relevant statistics to your content can strengthen any argument. But if not used carefully, numbers create more problems than they solve.

I wrote a book for content writers called From Reads To Leads . You should check it out to learn what rules you need to follow to write content that converts readers into leads. One of these rules is about using statistics in writing. Go to my home page to get the book or read the first chapter.

Many writers pick up numbers off the street to make their messages more compelling. They aren’t looking to support their arguments or to make their stories more accurate. They aren’t looking for truth. 

Let's look at this example:

If 36 percent of Americans use food delivery services, does this mean that the popularity of these services is growing? To show growth in popularity, we would need to compare the percentage of Americans who used food delivery services in March 2019, for example, with the percentage who used them in March 2021. Growth can only be demonstrated over time. Since there’s nothing to which readers can compare this 36 percent, they might doubt whether the popularity of food delivery services is actually growing.

Let's look at another example:

Any percentage is meaningless to your readers unless you compare it against some base percentage. The stats in the example I've just mentioned look reasonable. The author compares Black Friday sales completed using mobile devices last year with sales completed using mobile devices a few years ago. But let’s think about it for a second. Don’t these statistics raise any questions? Firstly of all, they come from two different sources. They may have been collected using wildly different methodologies and by surveying entirely different demographics. There’s no way for the reader to know whether these percentages can reasonably be compared.

Sometimes a percentage might look high, but without context, it might not be telling the whole story. You need to dig deeper to uncover the truth:

The author did solid research to help her readers arrive at the conclusion that despite a seemingly large number of women-owned businesses, there’s still gender inequality in entrepreneurship.

How to write with statistics

As you use statistics in your writing, here are a few things you need to pay attention to:

1 . Numbers can be just as ambiguous as words and need just as much explanation.

For example:

Is 57 percent good or bad? This statement requires an explanation:

Now it’s clear that we’re making progress. 

2. Don’t just throw numbers everywhere you can because it’s considered a good SEO practice. Your statistics need to help you make your point . They can make your arguments believable. 

For example, let’s say our key message is “eating fat keeps you healthy.” One of the arguments we can use to support this message is that polyunsaturated fats can lower cholesterol levels, which, as a result, can lower the risk of heart disease and stroke. We can use statistics to make this argument believable:

‍ We didn’t use these stats to demonstrate expertise . We added them to support our key message.

3. When trying to prove your argument with statistics, you need to be sure that what you’re saying is true. I you have doubts, you need to look first at the numbers to help you shape your message and ideas. Don’t do it the other way round. 

If you’ve already shaped your message about something, you’ll be tempted to look for data to prove that you’re right. But the truth is, you might be wrong. You can find seemingly legitimate evidence to support any claim, but your argument won’t be convincing if it’s built on a shaky foundation. 

The next time you find yourself thinking that what you want to say might not be accurate, don’t head to Google to prove you’re right. Instead, look to answer the question with data. Good writing is about telling the truth, not trying to dupe the reader.

4. Numbers without context or specific details are just that—numbers. They don’t help readers arrive at conclusions.

Now let’s see how to author, uses details to communicate the gravity of the situation:

The statement “the cost of college increased by more than 25% in the last 10 years” doesn’t give readers a clear idea of the growing cost of higher education. But comparing what students paid (on average) for a college education in 1978, 2008, and today helps the reader realize that the costs of college are increasing at a breakneck pace and that something has to be done about it.

You need statistics to prove your arguments. And when citing statistics, you must obey the same rules of clarity you obey with words. Learn more about these rules in my book From Reads To Leads.

Watch it on YouTube:

Hope this article was useful! Thank you for reading and subscribing to my YouTube channel .

Every writer knows that proper writing flow makes a story feel connected and allows the reader to follow the thread of the argument. Yet creating a logical sequence is a trouble spot for many writers. Learn how to work on your writing flow to create a smooth experience for your readers.

People fall into one of five decision-making categories: charismatics, thinkers, skeptics, followers, or controllers. Let’s take a closer look at these personalities to understand how you can adapt your writing style and message to your type of reader.

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How to present data and statistics in your paper

In most academic fields, presenting stats and data is key. words like 'values', 'equations', 'numbers', and 'tests' are common in theses and papers. but how do you use these words; what other words do they usually combine with in this analysis, we explore what phrases authors use most often when they present data and statistics..

Our analysis

We built a data set of 300 million sentences from published papers. From these sentences, we extracted all three-word combinations following the pattern subject + verb + object (for example, 'data shows difference').

We then collected the 100 most frequent combinations and their frequency, and visualized these (see image below). The 3 most-used triples were 'equation have solution', 'data provide evidence', and 'test show difference'.

Note that all phrases are lemmatized: they reflect the total counts of all forms. For example, the phrase 'test show difference' includes 'tests showing differences', 'tests showed differences', and others. The combined words were also not necessarily adjacent in the original sentence; for instance, an occurrence of 'test show difference' might have been 'test A showed a small difference' in the original paper.

The image below shows the most frequently used word combinations. The subject is shown in bold, the verb in regular script, and the object in italics. The figure uses hierarchical clustering, with the phrases first being grouped by subject and then by verb.

Not surprisingly, ‘data’ is the most frequent subject. It is often combined with the verbs 'provide', 'show', and 'support'. For example, data 'provide' 'evidence', 'information', or 'insights'; data 'show' 'differences', 'increases', and 'correlations'; and data 'support' 'hypotheses', 'notions', and 'ideas'. The subject 'test' is also frequent, and most often followed by 'reveal', 'indicate', or 'show' '(a) difference'.

Next time you’re writing your methods or results section and you’re stuck for words, see if this image helps you! It might give you the words you’re looking for.

About the author

Hilde is Chief Applied Linguist at Writefull.

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The Beginner's Guide to Writing an Essay | Steps & Examples

An academic essay is a focused piece of writing that develops an idea or argument using evidence, analysis, and interpretation.

There are many types of essays you might write as a student. The content and length of an essay depends on your level, subject of study, and course requirements. However, most essays at university level are argumentative — they aim to persuade the reader of a particular position or perspective on a topic.

The essay writing process consists of three main stages:

• Preparation: Decide on your topic, do your research, and create an essay outline.
• Writing : Set out your argument in the introduction, develop it with evidence in the main body, and wrap it up with a conclusion.
• Revision:  Check your essay on the content, organization, grammar, spelling, and formatting of your essay.

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Table of contents

Essay writing process, preparation for writing an essay, writing the introduction, writing the main body, writing the conclusion, essay checklist, lecture slides, frequently asked questions about writing an essay.

The writing process of preparation, writing, and revisions applies to every essay or paper, but the time and effort spent on each stage depends on the type of essay .

For example, if you’ve been assigned a five-paragraph expository essay for a high school class, you’ll probably spend the most time on the writing stage; for a college-level argumentative essay , on the other hand, you’ll need to spend more time researching your topic and developing an original argument before you start writing.

Prevent plagiarism. Run a free check.

Before you start writing, you should make sure you have a clear idea of what you want to say and how you’re going to say it. There are a few key steps you can follow to make sure you’re prepared:

• Understand your assignment: What is the goal of this essay? What is the length and deadline of the assignment? Is there anything you need to clarify with your teacher or professor?
• Define a topic: If you’re allowed to choose your own topic , try to pick something that you already know a bit about and that will hold your interest.
• Do your research: Read  primary and secondary sources and take notes to help you work out your position and angle on the topic. You’ll use these as evidence for your points.
• Come up with a thesis:  The thesis is the central point or argument that you want to make. A clear thesis is essential for a focused essay—you should keep referring back to it as you write.
• Create an outline: Map out the rough structure of your essay in an outline . This makes it easier to start writing and keeps you on track as you go.

Once you’ve got a clear idea of what you want to discuss, in what order, and what evidence you’ll use, you’re ready to start writing.

The introduction sets the tone for your essay. It should grab the reader’s interest and inform them of what to expect. The introduction generally comprises 10–20% of the text.

1. Hook your reader

The first sentence of the introduction should pique your reader’s interest and curiosity. This sentence is sometimes called the hook. It might be an intriguing question, a surprising fact, or a bold statement emphasizing the relevance of the topic.

Let’s say we’re writing an essay about the development of Braille (the raised-dot reading and writing system used by visually impaired people). Our hook can make a strong statement about the topic:

The invention of Braille was a major turning point in the history of disability.

2. Provide background on your topic

Next, it’s important to give context that will help your reader understand your argument. This might involve providing background information, giving an overview of important academic work or debates on the topic, and explaining difficult terms. Don’t provide too much detail in the introduction—you can elaborate in the body of your essay.

3. Present the thesis statement

Next, you should formulate your thesis statement— the central argument you’re going to make. The thesis statement provides focus and signals your position on the topic. It is usually one or two sentences long. The thesis statement for our essay on Braille could look like this:

As the first writing system designed for blind people’s needs, Braille was a groundbreaking new accessibility tool. It not only provided practical benefits, but also helped change the cultural status of blindness.

4. Map the structure

In longer essays, you can end the introduction by briefly describing what will be covered in each part of the essay. This guides the reader through your structure and gives a preview of how your argument will develop.

The invention of Braille marked a major turning point in the history of disability. The writing system of raised dots used by blind and visually impaired people was developed by Louis Braille in nineteenth-century France. In a society that did not value disabled people in general, blindness was particularly stigmatized, and lack of access to reading and writing was a significant barrier to social participation. The idea of tactile reading was not entirely new, but existing methods based on sighted systems were difficult to learn and use. As the first writing system designed for blind people’s needs, Braille was a groundbreaking new accessibility tool. It not only provided practical benefits, but also helped change the cultural status of blindness. This essay begins by discussing the situation of blind people in nineteenth-century Europe. It then describes the invention of Braille and the gradual process of its acceptance within blind education. Subsequently, it explores the wide-ranging effects of this invention on blind people’s social and cultural lives.

Write your essay introduction

The body of your essay is where you make arguments supporting your thesis, provide evidence, and develop your ideas. Its purpose is to present, interpret, and analyze the information and sources you have gathered to support your argument.

Length of the body text

The length of the body depends on the type of essay. On average, the body comprises 60–80% of your essay. For a high school essay, this could be just three paragraphs, but for a graduate school essay of 6,000 words, the body could take up 8–10 pages.

Paragraph structure

To give your essay a clear structure , it is important to organize it into paragraphs . Each paragraph should be centered around one main point or idea.

That idea is introduced in a  topic sentence . The topic sentence should generally lead on from the previous paragraph and introduce the point to be made in this paragraph. Transition words can be used to create clear connections between sentences.

After the topic sentence, present evidence such as data, examples, or quotes from relevant sources. Be sure to interpret and explain the evidence, and show how it helps develop your overall argument.

Lack of access to reading and writing put blind people at a serious disadvantage in nineteenth-century society. Text was one of the primary methods through which people engaged with culture, communicated with others, and accessed information; without a well-developed reading system that did not rely on sight, blind people were excluded from social participation (Weygand, 2009). While disabled people in general suffered from discrimination, blindness was widely viewed as the worst disability, and it was commonly believed that blind people were incapable of pursuing a profession or improving themselves through culture (Weygand, 2009). This demonstrates the importance of reading and writing to social status at the time: without access to text, it was considered impossible to fully participate in society. Blind people were excluded from the sighted world, but also entirely dependent on sighted people for information and education.

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The conclusion is the final paragraph of an essay. It should generally take up no more than 10–15% of the text . A strong essay conclusion :

• Returns to your thesis
• Ties together your main points
• Shows why your argument matters

A great conclusion should finish with a memorable or impactful sentence that leaves the reader with a strong final impression.

What not to include in a conclusion

To make your essay’s conclusion as strong as possible, there are a few things you should avoid. The most common mistakes are:

• Including new arguments or evidence
• Undermining your arguments (e.g. “This is just one approach of many”)
• Using concluding phrases like “To sum up…” or “In conclusion…”

Braille paved the way for dramatic cultural changes in the way blind people were treated and the opportunities available to them. Louis Braille’s innovation was to reimagine existing reading systems from a blind perspective, and the success of this invention required sighted teachers to adapt to their students’ reality instead of the other way around. In this sense, Braille helped drive broader social changes in the status of blindness. New accessibility tools provide practical advantages to those who need them, but they can also change the perspectives and attitudes of those who do not.

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Checklist: Essay

My essay follows the requirements of the assignment (topic and length ).

My introduction sparks the reader’s interest and provides any necessary background information on the topic.

My introduction contains a thesis statement that states the focus and position of the essay.

I use paragraphs to structure the essay.

I use topic sentences to introduce each paragraph.

Each paragraph has a single focus and a clear connection to the thesis statement.

I make clear transitions between paragraphs and ideas.

My conclusion doesn’t just repeat my points, but draws connections between arguments.

I don’t introduce new arguments or evidence in the conclusion.

I have given an in-text citation for every quote or piece of information I got from another source.

I have included a reference page at the end of my essay, listing full details of all my sources.

My citations and references are correctly formatted according to the required citation style .

My essay has an interesting and informative title.

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An essay is a focused piece of writing that explains, argues, describes, or narrates.

In high school, you may have to write many different types of essays to develop your writing skills.

Academic essays at college level are usually argumentative : you develop a clear thesis about your topic and make a case for your position using evidence, analysis and interpretation.

The structure of an essay is divided into an introduction that presents your topic and thesis statement , a body containing your in-depth analysis and arguments, and a conclusion wrapping up your ideas.

The structure of the body is flexible, but you should always spend some time thinking about how you can organize your essay to best serve your ideas.

Your essay introduction should include three main things, in this order:

• An opening hook to catch the reader’s attention.
• Relevant background information that the reader needs to know.
• A thesis statement that presents your main point or argument.

The length of each part depends on the length and complexity of your essay .

A thesis statement is a sentence that sums up the central point of your paper or essay . Everything else you write should relate to this key idea.

The thesis statement is essential in any academic essay or research paper for two main reasons:

• It gives your writing direction and focus.
• It gives the reader a concise summary of your main point.

Without a clear thesis statement, an essay can end up rambling and unfocused, leaving your reader unsure of exactly what you want to say.

A topic sentence is a sentence that expresses the main point of a paragraph . Everything else in the paragraph should relate to the topic sentence.

At college level, you must properly cite your sources in all essays , research papers , and other academic texts (except exams and in-class exercises).

Add a citation whenever you quote , paraphrase , or summarize information or ideas from a source. You should also give full source details in a bibliography or reference list at the end of your text.

The exact format of your citations depends on which citation style you are instructed to use. The most common styles are APA , MLA , and Chicago .

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PrimoStats Blog

How to write statistics in your content.

Statistics help content marketers convey their perspectives to readers. It’s the extra support you need to compel your audience to take action. 

Sometimes, statistics can be tricky. You may not know when to add the stat or how to cite it in your blog post. There are even times when content marketers may accidentally use the stat in the wrong context. 

No worries. In this blog post, we’re highlighting how to properly write statistics in your blog post. That way, you can inform and persuade your readers. 

Why Statistics Matter in Your Content

Statistics serve as the backbone of compelling narratives and persuasive arguments. Understanding why statistics matter in your content is key to elevating your message and resonating with your audience.

Enhancing Credibility: Statistics provide a solid foundation of evidence that adds credibility to your content. When you back your statements with relevant and accurate statistical data, you position yourself as an informed and trustworthy source. This, in turn, instills confidence in your audience, making them more likely to engage with and believe in your message.

Supporting Claims and Arguments: Statistics serve as compelling evidence to support these claims. Whether you’re advocating for a particular viewpoint, showcasing the success of a product, or discussing industry trends, incorporating statistics reinforces your narrative and lends weight to your assertions.

Connecting with Your Audience: Numbers have a universal language that resonates with a diverse audience. Statistics can simplify complex concepts, making them more accessible and relatable. Whether you’re addressing a niche market or a broader audience, well-presented statistics bridge the gap between technical details and audience understanding, fostering a deeper connection.

Driving Decision-Making: Effective content often aims to influence the decisions of your audience. Data-driven insights provide a rational basis for decision-making, empowering your audience to take informed actions based on the information you present.

When to Add Statistics to Your Content

Oftentimes, statistics are part of your content checklist . As a result, content marketers feel compelled to find any ol’ stat and add it to their next article. But it’s important to remember to use stats as a way to inform your audience and give your thoughts credibility. 

Adding a bunch of stats to your blog post won’t make you an instant expert. Instead, add stats to your original thoughts to pique your readers’ interest.

Highlight specific ideas

Statistics help you get laser-focused on your ideas. They are best used when you want to show you agree or disagree with data. Your words coupled with stats will give the reader new concepts to consider as they continue reading your article. Stay away from using stats with vague ideas. You may confuse the reader with unfounded assumptions.

For instance, let’s say a report surveyed 500 marketers in Texas and found that 73% don’t enjoy attending marketing conferences outside the state. For this specific idea, you would state why the Texas marketers feel this way and offer an explanation on why you agree or disagree with the statistic.

Emphasize a particular circumstance

Statistics also exist to reinforce distinct situations. By using an authoritative source, you can offer your reader an inside perspective. 

In the excerpt below, Emanuel Petrescu begins his article with an overwhelming stat to grab the reader’s attention. It’s followed up with another stat that supports the circumstance. In the second paragraph, he stresses the impact of these statistics.

Add colorful language

Writers have limits to how vivid they can describe a specific situation. In those cases, it’s best to lean on the exact wording of your selected statistic. Quoting the stat word-for-word adds more credibility to your claim than paraphrasing what you read in the study or report. This notion is especially true when the stat includes scientific language or terms of art.

How to Add Statistics to Your Content

After selecting your stat, the next step is to add it to your content. You want the stat to provide your reader with more depth on the topic. Steer clear of adding a stat as filler text. Stats should add value, whether it’s credibility or a different viewpoint. Below are a few tips to help you.

1. Give context about the statistic

A statistic is only as good as the context around it. Help your readers understand the significance of the stat by giving them additional details about the concept. Your goal is to explain the circumstances without bias. You want the reader to understand why the stat matters within your content.

Take a look at the example below. This BigCommerce article offers context about jewelry sales and then leads into forecast stats. The final paragraph gives the reader more context of why these stats matter with real-world application.

2. Attribute the statistic to its source

Statistics hold more weight when you can cite the original source. You’ll want to name the source in your blog post and link to the actual report or to the lead generation page where readers can get the report. PrimoStats is a valuable resource to search for curated marketing stats with links to original sources.

How to Embed a Statistic Into Your Sentence

Now, it’s time to add the statistic to your sentence. The main rule is not to interrupt your words with standalone statistic. Remember, we want to give the reader context. Use the following examples as guidance.

Lead into the statistic with a colon

In grammar, the colon functions as a way to emphasize the text that follows. When embedding your stat, give the reader context preceding the colon, then follow it with the statistic.  

Professional development is important for marketers seeking career growth: “23% of marketers like to read career books in their spare time.”

Use the statistic within your sentence

Sometimes, it makes sense to mingle your words with the statistic. It helps with the flow of your sentence and gives the reader a complete concise thought. Your goal is to give clarity, so don’t be verbose. Here’s an example:

While “23% of marketers like to read career books in their spare time,” my research finds it imperative for marketers to participate in networking events, too.

Things You Should Avoid

Let’s face it. Mistakes will happen along the way as you add statistics to your content. You’re not going to get everything right 24/7. But that’s okay. It’s important to be aware of the common mistakes and to avoid them as you strive to write better content. 

Outdated Statistics

To maintain high-quality content , you should use the most updated statistics. New studies are published every year and can offer the latest data for you to share with your audience. Be mindful that “outdated” is a relative term depending on the industry standard. So, aim to highlight stats no more than three to five years from your published content.

The frustration is real amongst content marketers. On LinkedIn , writer Brooklin Nash expresses his concern about outdated statistics, and the post received more than 600 reactions and 100 comments.

Unknown Sources

Citing original sources is a key part of adding statistics to your content. It lends to the credibility of your claim. Rather than linking to a roundup post with a bunch of stats, you’ll want to find the original source of the stat. That way, your readers can learn more about the research or study.

Misusing Statistics

The goal of statistics is to give your words more credibility. Don’t misrepresent the stats you add to your content. It will only weaken your argument. So, aim to include the entire stat, even if it conflicts with your opinion. If your thoughts and the research don’t mesh, look at it as an opportunity to trailblaze a new way of thinking on the topic.

Statistical Terms You Need to Know

Population: A population refers to the entire group or set of individuals, objects, or events under study. It represents the complete collection of elements about which conclusions are drawn.

Sample: A sample is a subset of a population that is selected for analysis. It is chosen to represent the larger population accurately. Samples are often more feasible to collect and analyze compared to studying the entire population.

Descriptive Statistics: Descriptive statistics involve methods and techniques used to summarize and describe the main features of a dataset. It includes measures such as mean, median, mode, standard deviation, and range, which provide insights into the central tendency, variability, and distribution of the data.

Inferential Statistics: Inferential statistics is concerned with making predictions or inferences about a population based on sample data. It involves using statistical techniques to draw conclusions, estimate parameters, and test hypotheses. Inferential statistics allows us to make generalizations from the sample to the larger population.

Mean: The mean, also known as the average, is a measure of central tendency that represents the sum of all values in a dataset divided by the number of observations. It is often used to describe the typical value or the arithmetic average of a set of numbers.

Median: The median is another measure of central tendency. It is the middle value in an ordered dataset when arranged in ascending or descending order. The median is less sensitive to extreme values compared to the mean and provides a better representation of the data in skewed distributions.

Mode: The mode is the value or values that occur most frequently in a dataset. It represents the peak(s) of the distribution and can be used to describe the most common observation(s) in the data.

Standard Deviation: The standard deviation is a measure of the spread or variability of a dataset. It quantifies how much the individual data points deviate from the mean. A higher standard deviation indicates greater variability, while a lower standard deviation suggests less dispersion around the mean.

FAQs about Writing Statistics in Content

Q1: How recent should my statistics be to maintain relevance?

A1: Aim to use the most updated statistics available. While “recent” may vary by industry standards, try not to highlight stats more than three to five years from your published content to ensure accuracy and relevance.

Q2: Is it acceptable to use curated statistics from roundup posts?

A2: While curated stats can be convenient, it’s preferable to find and cite the original source for increased credibility. Directly linking to the original study or report allows readers to explore the research in-depth.

Q3: What if the statistic conflicts with my opinion?

A3: Embrace the diversity of perspectives. Include the entire stat even if it contradicts your opinion. This transparency strengthens your argument and opens the door for innovative thinking on the topic.

Q4: How do I ensure statistical literacy in my audience?

A4: Provide context around statistics to aid understanding. Explain the significance of the stat without bias, ensuring your audience comprehends why it matters within the context of your content.

Q5: Can I use statistics to evoke emotions in my audience?

A5: Absolutely. Statistics can evoke emotions by showcasing impact and significance. Craft your narrative to not only present numbers but also to tell a compelling story that resonates with your audience on an emotional level.

Be Thoughtful When Writing Statistics

Using statistics in your blog posts is an effective way to support your claim. When writing your stats, consider when you should one and how you should embed the stat into your content. By doing so, you’ll gain the trust of your audience.

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Statistics and Visuals

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Don't be afraid to use graphics. Statistics can contain a lot of information. Visuals can display a lot of information in a manner that can be quickly understood. The same thing applies to tables. For example:

It' s hard to read! Imagine trying to make sense of this. Instead, provide your data in a table for easy reading:

A table is much easier to read than blocks of text. It can help sort the information for both you and your readers. It also makes group comparisons easy. For example, suppose you want to point out to the reader the difference between group A and group D (perhaps this was a new weight training program comparing the number of 80 lbs. dumbbell reps).

Or, you could do this:

Don't be afraid to bold, use asterisks, or otherwise highlight important groups or comparisons.

Graphs are an excellent alternative to tables, and they are used by virtually everyone in every field. Papers and articles are like faces. Graphics are like makeup. Makeup is always good in small doses, but don't over apply, or you will end up looking worse than if you didn't use any make up at all. Use visuals, but be careful not to over use them. This is a good example of a visual using the data from the previous table:

Visual Graph of Data

Consider distributions of information for a moment. Imagine that we are teaching a class and displaying the students' first homework grades to the students for their benefit. This is one of the ways we could display their homework grades.

Poor example of a graph.

In this graph, each of these bars represents a student (each student gets a different color). This is an example of using too much make-up. While the graph does convey a lot of information, it is hard to read. The following graph is much better, and it actually gives you some useful information regarding the class:

Better graph of student scores

Now we can clearly see that one person did really poorly, but that most people were clustered between 70-90%. In the first graph of student scores, we can't really 'see' the distribution, but in this second graph we have a much clearer image of the distribution of scores.