importance of statistics in thesis writing

Statistics Made Easy

The Importance of Statistics in Research (With Examples)

The field of statistics is concerned with collecting, analyzing, interpreting, and presenting data.

In the field of research, statistics is important for the following reasons:

Reason 1 : Statistics allows researchers to design studies such that the findings from the studies can be extrapolated to a larger population.

Reason 2 : Statistics allows researchers to perform hypothesis tests to determine if some claim about a new drug, new procedure, new manufacturing method, etc. is true.

Reason 3 : Statistics allows researchers to create confidence intervals to capture uncertainty around population estimates.

In the rest of this article, we elaborate on each of these reasons.

Reason 1: Statistics Allows Researchers to Design Studies

Researchers are often interested in answering questions about populations like:

• What is the average weight of a certain species of bird?
• What is the average height of a certain species of plant?
• What percentage of citizens in a certain city support a certain law?

One way to answer these questions is to go around and collect data on every single individual in the population of interest.

However, this is typically too costly and time-consuming which is why researchers instead take a  sample  of the population and use the data from the sample to draw conclusions about the population as a whole.

There are many different methods researchers can potentially use to obtain individuals to be in a sample. These are known as  sampling methods .

There are two classes of sampling methods:

• Probability sampling methods : Every member in a population has an equal probability of being selected to be in the sample.
• Non-probability sampling methods : Not every member in a population has an equal probability of being selected to be in the sample.

By using probability sampling methods, researchers can maximize the chances that they obtain a sample that is representative of the overall population.

This allows researchers to extrapolate the findings from the sample to the overall population.

Read more about the two classes of sampling methods here .

Reason 2: Statistics Allows Researchers to Perform Hypothesis Tests

Another way that statistics is used in research is in the form of hypothesis tests .

These are tests that researchers can use to determine if there is a statistical significance between different medical procedures or treatments.

For example, suppose a scientist believes that a new drug is able to reduce blood pressure in obese patients. To test this, he measures the blood pressure of 30 patients before and after using the new drug for one month.

He then performs a paired samples t- test using the following hypotheses:

• H 0 : μ after = μ before (the mean blood pressure is the same before and after using the drug)
• H A : μ after < μ before (the mean blood pressure is less after using the drug)

If the p-value of the test is less than some significance level (e.g. α = .05), then he can reject the null hypothesis and conclude that the new drug leads to reduced blood pressure.

Note : This is just one example of a hypothesis test that is used in research. Other common tests include a one sample t-test , two sample t-test , one-way ANOVA , and two-way ANOVA .

Reason 3: Statistics Allows Researchers to Create Confidence Intervals

Another way that statistics is used in research is in the form of confidence intervals .

A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence.

For example, suppose researchers are interested in estimating the mean weight of a certain species of turtle.

Instead of going around and weighing every single turtle in the population, researchers may instead take a simple random sample of turtles with the following information:

• Sample size  n = 25
• Sample mean weight  x  = 300
• Sample standard deviation  s = 18.5

Using the confidence interval for a mean formula , researchers may then construct the following 95% confidence interval:

95% Confidence Interval:  300 +/-  1.96*(18.5/√ 25 ) =  [292.75, 307.25]

The researchers would then claim that they’re 95% confident that the true mean weight for this population of turtles is between 292.75 pounds and 307.25 pounds.

Additional Resources

The following articles explain the importance of statistics in other fields:

The Importance of Statistics in Healthcare The Importance of Statistics in Nursing The Importance of Statistics in Business The Importance of Statistics in Economics The Importance of Statistics in Education

Hey there. My name is Zach Bobbitt. I have a Master of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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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 he or she reads. 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 her 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 he or she is 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 his or her 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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What do senior theses in Statistics look like?

This is a brief overview of thesis writing; for more information, please see our  complete guide here . Senior theses in Statistics cover a wide range of topics, across the spectrum from applied to theoretical. Typically, senior theses are expected to have one of the following three flavors:                                                                                                            

1. Novel statistical theory or methodology, supported by extensive mathematical and/or simulation results, along with a clear account of how the research extends or relates to previous related work.

2. An analysis of a complex data set that advances understanding in a related field, such as public health, economics, government, or genetics. Such a thesis may rely entirely on existing methods, but should give useful results and insights into an interesting applied problem.                                                                                 

3. An analysis of a complex data set in which new methods or modifications of published methods are required. While the thesis does not necessarily contain an extensive mathematical study of the new methods, it should contain strong plausibility arguments or simulations supporting the use of the new methods.

A good thesis is clear, readable, and well-motivated, justifying the applicability of the methods used rather than, for example, mechanically running regressions without discussing the assumptions (and whether they are plausible), performing diagnostics, and checking whether the conclusions make sense. 

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Thesis life: 7 ways to tackle statistics in your thesis.

By Pranav Kulkarni

Thesis is an integral part of your Masters’ study in Wageningen University and Research. It is the most exciting, independent and technical part of the study. More often than not, most departments in WU expect students to complete a short term independent project or a part of big on-going project for their thesis assignment.

Source : www.coursera.org

This assignment involves proposing a research question, tackling it with help of some observations or experiments, analyzing these observations or results and then stating them by drawing some conclusions.

Since it is an immitigable part of your thesis, you can neither run from statistics nor cry for help.

The penultimate part of this process involves analysis of results which is very crucial for coherence of your thesis assignment.This analysis usually involve use of statistical tools to help draw inferences. Most students who don’t pursue statistics in their curriculum are scared by this prospect. Since it is an immitigable part of your thesis, you can neither run from statistics nor cry for help. But in order to not get intimidated by statistics and its “greco-latin” language, there are a few ways in which you can make your journey through thesis life a pleasant experience.

Make statistics your friend

The best way to end your fear of statistics and all its paraphernalia is to befriend it. Try to learn all that you can about the techniques that you will be using, why they were invented, how they were invented and who did this deed. Personifying the story of statistical techniques makes them digestible and easy to use. Each new method in statistics comes with a unique story and loads of nerdy anecdotes.

If you cannot make friends with statistics, at least make a truce

If you cannot still bring yourself about to be interested in the life and times of statistics, the best way to not hate statistics is to make an agreement with yourself. You must realise that although important, this is only part of your thesis. The better part of your thesis is something you trained for and learned. So, don’t bother to fuss about statistics and make you all nervous. Do your job, enjoy thesis to the fullest and complete the statistical section as soon as possible. At the end, you would have forgotten all about your worries and fears of statistics.

Visualize your data

The best way to understand the results and observations from your study/ experiments, is to visualize your data. See different trends, patterns, or lack thereof to understand what you are supposed to do. Moreover, graphics and illustrations can be used directly in your report. These techniques will also help you decide on which statistical analyses you must perform to answer your research question. Blind decisions about statistics can often influence your study and make it very confusing or worse, make it completely wrong!

Simplify with flowcharts and planning

Similar to graphical visualizations, making flowcharts and planning various steps of your study can prove beneficial to make statistical decisions. Human brain can analyse pictorial information faster than literal information. So, it is always easier to understand your exact goal when you can make decisions based on flowchart or any logical flow-plans.

Source: www.imindq.com

Find examples on internet

Although statistics is a giant maze of complicated terminologies, the internet holds the key to this particular maze. You can find tons of examples on the web. These may be similar to what you intend to do or be different applications of the similar tools that you wish to engage. Especially, in case of Statistical programming languages like R, SAS, Python, PERL, VBA, etc. there is a vast database of example codes, clarifications and direct training examples available on the internet. Various forums are also available for specialized statistical methodologies where different experts and students discuss the issues regarding their own projects.

Comparative studies

Much unlike blindly searching the internet for examples and taking word of advice from online faceless people, you can systematically learn which quantitative tests to perform by rigorously studying literature of relevant research. Since you came up with a certain problem to tackle in your field of study, chances are, someone else also came up with this issue or something quite similar. You can find solutions to many such problems by scouring the internet for research papers which address the issue. Nevertheless, you should be cautious. It is easy to get lost and disheartened when you find many heavy statistical studies with lots of maths and derivations with huge cryptic symbolical text.

When all else fails, talk to an expert

All the steps above are meant to help you independently tackle whatever hurdles you encounter over the course of your thesis. But, when you cannot tackle them yourself it is always prudent and most efficient to ask for help. Talking to students from your thesis ring who have done something similar is one way of help. Another is to make an appointment with your supervisor and take specific questions to him/ her. If that is not possible, you can contact some other teaching staff or researchers from your research group. Try not to waste their as well as you time by making a list of specific problems that you will like to discuss. I think most are happy to help in any way possible.

Talking to students from your thesis ring who have done something similar is one way of help.

Sometimes, with the help of your supervisor, you can make an appointment with someone from the “Biometris” which is the WU’s statistics department. These people are the real deal; chances are, these people can solve all your problems without any difficulty. Always remember, you are in the process of learning, nobody expects you to be an expert in everything. Ask for help when there seems to be no hope.

Apart from these seven ways to make your statistical journey pleasant, you should always engage in reading, watching, listening to stuff relevant to your thesis topic and talking about it to those who are interested. Most questions have solutions in the ether realm of communication. So, best of luck and break a leg!!!

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There are 4 comments.

A perfect approach in a very crisp and clear manner! The sequence suggested is absolutely perfect and will help the students very much. I particularly liked the idea of visualisation!

You are write! I get totally stuck with learning and understanding statistics for my Dissertation!

Statistics is a technical subject that requires extra effort. With the highlighted tips you already highlighted i expect it will offer the much needed help with statistics analysis in my course.

this is so much relevant to me! Don’t forget one more point: try to enrol specific online statistics course (in my case, I’m too late to join any statistic course). The hardest part for me actually to choose what type of statistical test to choose among many options

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What is research data?

Research data are the evidence that underpins the answer to your research question and can support the findings or outputs of your research. Research data takes many different forms. They may include for example, statistics, digital images, sound recordings, films, transcripts of interviews, survey data, artworks, published texts or manuscripts, or fieldwork observations. The term 'data' is more familiar to researchers in Science, Technology, Engineering and Mathematics (STEM), but any outputs from research could be considered data. For example, Humanities, Arts and Social Sciences (HASS) researchers might create data in the form of presentations, spreadsheets, documents, images, works of art, or musical scores. The Research Data Management Team in the University Library aim to help you plan, create, organise, share, and look after your research materials, whatever form they take. For more information about the Research data Management Team, visit their website .

Data Management Plans

Research Data Management is a complex issue, but if done correctly from the start, could save you a lot of time and hassle when you are writing up your thesis. We advise all students to consider data management as early as possible and create a Data Management Plan (DMP). The Research Data Management Team offer help in creating your DMP and can offer advice and training on how to do this. There are some departments that have joined a pilot project to include Data Management Plans in the registration reviews of PhD students. As part of the pilot, students are asked to complete a brief Data Management Plan (DMP) and supervisors and assessors ensure that the student has thought about all the issues and their responses are reasonable. If your department is taking part in the pilot or would like to, see the Data Management Plans for Pilot for Cambridge PhD Students page. The Research Data Management Team will provide support for any students, supervisors or assessors that are in need.

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If you have created data that is connected to your thesis and the data is in a format separate to the thesis file itself, we recommend that you deposit it in the data repository and make it open access to improve discoverability. We will accept data that either does not contain third party copyright, or contains third party copyright that has been cleared and is data of the following types:

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If you have created a research output which is not one of those listed above, please contact us on the [email protected] address and we will advise whether you should deposit this with your thesis, or separately in the data repository. If you are ready to deposit your data in the data repository, please do so via symplectic elements. More information on how to deposit can be found on the Research Data Management pages . If you wish to cite your data in your thesis, we can arranged for placeholder DOIs to be created in the data repository before your thesis is submitted. For further information, please email:  [email protected]  

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For an explanation of what is third party copyright, please see the OSC third party copyright page . If your data is based on, or contains third party copyright you will need to obtain clearance to make your data open access in the data repository. It is possible to apply a 12 month embargo to datasets while clearance is obtained if you need extra time to do this. However, if it is not possible to clear the third party copyrighted material, it is not possible to deposit your data in the data repository. In these cases, it might be preferable to deposit your data with your thesis instead, under controlled access, but this can be complicated if you wish to deposit the thesis itself under a different access level. Please email [email protected] with any queries and we can advise on the best solution.

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Statistical Methods in Theses: Guidelines and Explanations

Signed August 2018 Naseem Al-Aidroos, PhD, Christopher Fiacconi, PhD Deborah Powell, PhD, Harvey Marmurek, PhD, Ian Newby-Clark, PhD, Jeffrey Spence, PhD, David Stanley, PhD, Lana Trick, PhD

Version:  2.00

This document is an organizational aid, and workbook, for students. We encourage students to take this document to meetings with their advisor and committee. This guide should enhance a committee’s ability to assess key areas of a student’s work. 

In recent years a number of well-known and apparently well-established findings have  failed to replicate , resulting in what is commonly referred to as the replication crisis. The APA Publication Manual 6 th Edition notes that “The essence of the scientific method involves observations that can be repeated and verified by others.” (p. 12). However, a systematic investigation of the replicability of psychology findings published in  Science  revealed that over half of psychology findings do not replicate (see a related commentary in  Nature ). Even more disturbing, a  Bayesian reanalysis of the reproducibility project  showed that 64% of studies had sample sizes so small that strong evidence for or against the null or alternative hypotheses did not exist. Indeed, Morey and Lakens (2016) concluded that most of psychology is statistically unfalsifiable due to small sample sizes and correspondingly low power (see  article ). Our discipline’s reputation is suffering. News of the replication crisis has reached the popular press (e.g.,  The Atlantic ,   The Economist ,   Slate , Last Week Tonight ).

An increasing number of psychologists have responded by promoting new research standards that involve open science and the elimination of  Questionable Research Practices . The open science perspective is made manifest in the  Transparency and Openness Promotion (TOP) guidelines  for journal publications. These guidelines were adopted some time ago by the  Association for Psychological Science . More recently, the guidelines were adopted by American Psychological Association journals ( see details ) and journals published by Elsevier ( see details ). It appears likely that, in the very near future, most journals in psychology will be using an open science approach. We strongly advise readers to take a moment to inspect the  TOP Guidelines Summary Table . 

A key aspect of open science and the TOP guidelines is the sharing of data associated with published research (with respect to medical research, see point #35 in the  World Medical Association Declaration of Helsinki ). This practice is viewed widely as highly important. Indeed, open science is recommended by  all G7 science ministers . All Tri-Agency grants must include a data-management plan that includes plans for sharing: “ research data resulting from agency funding should normally be preserved in a publicly accessible, secure and curated repository or other platform for discovery and reuse by others.”  Moreover, a 2017 editorial published in the  New England Journal of Medicine announced that the  International Committee of Medical Journal Editors believes there is  “an ethical obligation to responsibly share data.”  As of this writing,  60% of highly ranked psychology journals require or encourage data sharing .

The increasing importance of demonstrating that findings are replicable is reflected in calls to make replication a requirement for the promotion of faculty (see details in  Nature ) and experts in open science are now refereeing applications for tenure and promotion (see details at the  Center for Open Science  and  this article ). Most dramatically, in one instance, a paper resulting from a dissertation was retracted due to misleading findings attributable to Questionable Research Practices. Subsequent to the retraction, the Ohio State University’s Board of Trustees unanimously revoked the PhD of the graduate student who wrote the dissertation ( see details ). Thus, the academic environment is changing and it is important to work toward using new best practices in lieu of older practices—many of which are synonymous with Questionable Research Practices. Doing so should help you avoid later career regrets and subsequent  public mea culpas . One way to achieve your research objectives in this new academic environment is  to incorporate replications into your research . Replications are becoming more common and there are even websites dedicated to helping students conduct replications (e.g.,  Psychology Science Accelerator ) and indexing the success of replications (e.g., Curate Science ). You might even consider conducting a replication for your thesis (subject to committee approval).

As early-career researchers, it is important to be aware of the changing academic environment. Senior principal investigators may be  reluctant to engage in open science  (see this student perspective in a  blog post  and  podcast ) and research on resistance to data sharing indicates that one of the barriers to sharing data is that researchers do not feel that they have knowledge of  how to share data online . This document is an educational aid and resource to provide students with introductory knowledge of how to participate in open science and online data sharing to start their education on these subjects. 

Guidelines and Explanations

In light of the changes in psychology, faculty members who teach statistics/methods have reviewed the literature and generated this guide for graduate students. The guide is intended to enhance the quality of student theses by facilitating their engagement in open and transparent research practices and by helping them avoid Questionable Research Practices, many of which are now deemed unethical and covered in the ethics section of textbooks.

This document is an informational tool.

How to Start

In order to follow best practices, some first steps need to be followed. Here is a list of things to do:

• Get an Open Science account. Registration at  osf.io  is easy!
• If conducting confirmatory hypothesis testing for your thesis, pre-register your hypotheses (see Section 1-Hypothesizing). The Open Science Foundation website has helpful  tutorials  and  guides  to get you going.
• Also, pre-register your data analysis plan. Pre-registration typically includes how and when you will stop collecting data, how you will deal with violations of statistical assumptions and points of influence (“outliers”), the specific measures you will use, and the analyses you will use to test each hypothesis, possibly including the analysis script. Again, there is a lot of help available for this. 

Exploratory and Confirmatory Research Are Both of Value, But Do Not Confuse the Two

We note that this document largely concerns confirmatory research (i.e., testing hypotheses). We by no means intend to devalue exploratory research. Indeed, it is one of the primary ways that hypotheses are generated for (possible) confirmation. Instead, we emphasize that it is important that you clearly indicate what of your research is exploratory and what is confirmatory. Be clear in your writing and in your preregistration plan. You should explicitly indicate which of your analyses are exploratory and which are confirmatory. Please note also that if you are engaged in exploratory research, then Null Hypothesis Significance Testing (NHST) should probably be avoided (see rationale in  Gigerenzer  (2004) and  Wagenmakers et al., (2012) ). 

This document is structured around the stages of thesis work:  hypothesizing, design, data collection, analyses, and reporting – consistent with the headings used by Wicherts et al. (2016). We also list the Questionable Research Practices associated with each stage and provide suggestions for avoiding them. We strongly advise going through all of these sections during thesis/dissertation proposal meetings because a priori decisions need to be made prior to data collection (including analysis decisions). 

To help to ensure that the student has informed the committee about key decisions at each stage, there are check boxes at the end of each section.

How to Use This Document in a Proposal Meeting

• Print off a copy of this document and take it to the proposal meeting.
• During the meeting, use the document to seek assistance from faculty to address potential problems.
• Revisit responses to issues raised by this document (especially the Analysis and Reporting Stages) when you are seeking approval to proceed to defense.

Consultation and Help Line

Note that the Center for Open Science now has a help line (for individual researchers and labs) you can call for help with open science issues. They also have training workshops. Please see their  website  for details.

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Effective Use of Statistics in Research – Methods and Tools for Data Analysis

Remember that impending feeling you get when you are asked to analyze your data! Now that you have all the required raw data, you need to statistically prove your hypothesis. Representing your numerical data as part of statistics in research will also help in breaking the stereotype of being a biology student who can’t do math.

Statistical methods are essential for scientific research. In fact, statistical methods dominate the scientific research as they include planning, designing, collecting data, analyzing, drawing meaningful interpretation and reporting of research findings. Furthermore, the results acquired from research project are meaningless raw data unless analyzed with statistical tools. Therefore, determining statistics in research is of utmost necessity to justify research findings. In this article, we will discuss how using statistical methods for biology could help draw meaningful conclusion to analyze biological studies.

Table of Contents

Role of Statistics in Biological Research

Statistics is a branch of science that deals with collection, organization and analysis of data from the sample to the whole population. Moreover, it aids in designing a study more meticulously and also give a logical reasoning in concluding the hypothesis. Furthermore, biology study focuses on study of living organisms and their complex living pathways, which are very dynamic and cannot be explained with logical reasoning. However, statistics is more complex a field of study that defines and explains study patterns based on the sample sizes used. To be precise, statistics provides a trend in the conducted study.

Biological researchers often disregard the use of statistics in their research planning, and mainly use statistical tools at the end of their experiment. Therefore, giving rise to a complicated set of results which are not easily analyzed from statistical tools in research. Statistics in research can help a researcher approach the study in a stepwise manner, wherein the statistical analysis in research follows –

1. Establishing a Sample Size

Usually, a biological experiment starts with choosing samples and selecting the right number of repetitive experiments. Statistics in research deals with basics in statistics that provides statistical randomness and law of using large samples. Statistics teaches how choosing a sample size from a random large pool of sample helps extrapolate statistical findings and reduce experimental bias and errors.

2. Testing of Hypothesis

When conducting a statistical study with large sample pool, biological researchers must make sure that a conclusion is statistically significant. To achieve this, a researcher must create a hypothesis before examining the distribution of data. Furthermore, statistics in research helps interpret the data clustered near the mean of distributed data or spread across the distribution. These trends help analyze the sample and signify the hypothesis.

3. Data Interpretation Through Analysis

When dealing with large data, statistics in research assist in data analysis. This helps researchers to draw an effective conclusion from their experiment and observations. Concluding the study manually or from visual observation may give erroneous results; therefore, thorough statistical analysis will take into consideration all the other statistical measures and variance in the sample to provide a detailed interpretation of the data. Therefore, researchers produce a detailed and important data to support the conclusion.

Types of Statistical Research Methods That Aid in Data Analysis

Statistical analysis is the process of analyzing samples of data into patterns or trends that help researchers anticipate situations and make appropriate research conclusions. Based on the type of data, statistical analyses are of the following type:

1. Descriptive Analysis

The descriptive statistical analysis allows organizing and summarizing the large data into graphs and tables . Descriptive analysis involves various processes such as tabulation, measure of central tendency, measure of dispersion or variance, skewness measurements etc.

2. Inferential Analysis

The inferential statistical analysis allows to extrapolate the data acquired from a small sample size to the complete population. This analysis helps draw conclusions and make decisions about the whole population on the basis of sample data. It is a highly recommended statistical method for research projects that work with smaller sample size and meaning to extrapolate conclusion for large population.

3. Predictive Analysis

Predictive analysis is used to make a prediction of future events. This analysis is approached by marketing companies, insurance organizations, online service providers, data-driven marketing, and financial corporations.

4. Prescriptive Analysis

Prescriptive analysis examines data to find out what can be done next. It is widely used in business analysis for finding out the best possible outcome for a situation. It is nearly related to descriptive and predictive analysis. However, prescriptive analysis deals with giving appropriate suggestions among the available preferences.

5. Exploratory Data Analysis

EDA is generally the first step of the data analysis process that is conducted before performing any other statistical analysis technique. It completely focuses on analyzing patterns in the data to recognize potential relationships. EDA is used to discover unknown associations within data, inspect missing data from collected data and obtain maximum insights.

6. Causal Analysis

Causal analysis assists in understanding and determining the reasons behind “why” things happen in a certain way, as they appear. This analysis helps identify root cause of failures or simply find the basic reason why something could happen. For example, causal analysis is used to understand what will happen to the provided variable if another variable changes.

7. Mechanistic Analysis

This is a least common type of statistical analysis. The mechanistic analysis is used in the process of big data analytics and biological science. It uses the concept of understanding individual changes in variables that cause changes in other variables correspondingly while excluding external influences.

Important Statistical Tools In Research

Researchers in the biological field find statistical analysis in research as the scariest aspect of completing research. However, statistical tools in research can help researchers understand what to do with data and how to interpret the results, making this process as easy as possible.

1. Statistical Package for Social Science (SPSS)

It is a widely used software package for human behavior research. SPSS can compile descriptive statistics, as well as graphical depictions of result. Moreover, it includes the option to create scripts that automate analysis or carry out more advanced statistical processing.

2. R Foundation for Statistical Computing

This software package is used among human behavior research and other fields. R is a powerful tool and has a steep learning curve. However, it requires a certain level of coding. Furthermore, it comes with an active community that is engaged in building and enhancing the software and the associated plugins.

3. MATLAB (The Mathworks)

It is an analytical platform and a programming language. Researchers and engineers use this software and create their own code and help answer their research question. While MatLab can be a difficult tool to use for novices, it offers flexibility in terms of what the researcher needs.

4. Microsoft Excel

Not the best solution for statistical analysis in research, but MS Excel offers wide variety of tools for data visualization and simple statistics. It is easy to generate summary and customizable graphs and figures. MS Excel is the most accessible option for those wanting to start with statistics.

5. Statistical Analysis Software (SAS)

It is a statistical platform used in business, healthcare, and human behavior research alike. It can carry out advanced analyzes and produce publication-worthy figures, tables and charts .

6. GraphPad Prism

It is a premium software that is primarily used among biology researchers. But, it offers a range of variety to be used in various other fields. Similar to SPSS, GraphPad gives scripting option to automate analyses to carry out complex statistical calculations.

This software offers basic as well as advanced statistical tools for data analysis. However, similar to GraphPad and SPSS, minitab needs command over coding and can offer automated analyses.

Use of Statistical Tools In Research and Data Analysis

Statistical tools manage the large data. Many biological studies use large data to analyze the trends and patterns in studies. Therefore, using statistical tools becomes essential, as they manage the large data sets, making data processing more convenient.

Following these steps will help biological researchers to showcase the statistics in research in detail, and develop accurate hypothesis and use correct tools for it.

There are a range of statistical tools in research which can help researchers manage their research data and improve the outcome of their research by better interpretation of data. You could use statistics in research by understanding the research question, knowledge of statistics and your personal experience in coding.

Have you faced challenges while using statistics in research? How did you manage it? Did you use any of the statistical tools to help you with your research data? Do write to us or comment below!

Frequently Asked Questions

Statistics in research can help a researcher approach the study in a stepwise manner: 1. Establishing a sample size 2. Testing of hypothesis 3. Data interpretation through analysis

Statistical methods are essential for scientific research. In fact, statistical methods dominate the scientific research as they include planning, designing, collecting data, analyzing, drawing meaningful interpretation and reporting of research findings. Furthermore, the results acquired from research project are meaningless raw data unless analyzed with statistical tools. Therefore, determining statistics in research is of utmost necessity to justify research findings.

Statistical tools in research can help researchers understand what to do with data and how to interpret the results, making this process as easy as possible. They can manage large data sets, making data processing more convenient. A great number of tools are available to carry out statistical analysis of data like SPSS, SAS (Statistical Analysis Software), and Minitab.

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What’s the Importance of Using Statistics in Writing Research Papers?

For effective numerical data analysis aimed at drawing meaningful interpretation/ conclusion, understanding, and using quantitative research findings appropriately, students and scholars must understand why use statistics in writing research papers .

A quantitative research paper entails collecting, preparing, organizing, analyzing, and interpreting data containing quantitative variables using statistical tools to draw valid conclusions; and preparing a research report accordingly. Statistics can be divided into descriptive and inferential statistics .

Descriptive statistics involves collecting data points and interpreting them in terms of distribution, relationships between and among variables, and measurements. Examples include the measures of central tendency such as mean, median, mode, measures of variability such as standard deviation and variance, and frequency distribution. Inferential statistics entails making inferences about a particular population by analyzing data drawn from a sample group.

They involve null hypothesis significance testing against an alternative hypothesis and comprise the parametric and non-parametric tests. The type of statistical test to perform depend on the nature of the variables and whether the data are normally distributed or not. This article contains a detailed discussion on the importance of using statistics in writing research papers .

Reasons for Using Statistics When Writing Research Papers

Informed use of statistics is fundamental to quantitative research, not only in data collection but also in its analysis and interpretation. The correct statistical analysis of research data leads to accurate, believable, and useful results.

Students and scholars conduct medical, market, or clinical research projects with various goals and objectives. Statistics help them in using the most appropriate research design, methods, and tools to collect data, analyze and interpret it, and present the findings based on the research questions being answered. The reasons for using statistics in writing research papers include:

1. Drawing meaningful conclusions using numerical evidence

Statistics involves using a particular statistical package to learn from data in an attempt to answer a specific research question. It produces quantitative evidence with which a scholar can evaluate arguments, claims, and the quality of conclusions.

2. Researchers use statistics to produce accurate results

The correct use of statistical analysis tools and procedures leads to the production of accurate results. To produce accurate, valid, and trustworthy results, statisticians must ensure the correct methods are used to collect reliable data, analyze it appropriately, and draw logical conclusions.

3. Statistical techniques help in designing studies

Through statistics, researchers can establish study designs in which findings from sample data can be generalized to the general population from which the subset was drawn. Samples can be obtained through probability and non-probability sampling methods.

4. Statistics help in conducting hypothesis tests

Statistics help in conducting statistical tests to find out whether or not provided data supports what an alternative hypothesis states in a study or if the conclusions drawn are statistically significant or by chance. Testing statistical hypotheses can be performed using statistical analyses such as the one sample t-tests, paired sample t-test statistic, analysis of variance (ANOVA), analysis of covariance (ANCOVA), regression analysis , and correlations among others. Additionally, the tests can also be used to determine the statistical significance of findings.

5. It helps in creating confidence intervals for population parameters

Confidence intervals are fundamental in statistical hypothesis testing where observations about particular population parameters are based on collected data. It indicates the variability between specific estimated parameters within a group. Moreover, the confidence interval scale can be used to determine the extent of uncertainty within estimates of a particular population parameter.

6. Testing significance of relationships between variables

With correlation coefficients, one can measure the direction, stability, and strength of relationships between two or more variables. The independent variable must be defined alongside the dependent variable to perform the right statistical test.

7. Establishing a sample size for a research study

Statistics help in calculating the appropriate sample size for a research study depending on defined requirements. By determining the appropriate sample size, researchers can reduce loss of data by minimizing unnecessary inclusion. Analyzing sample data can be helpful in inferring the population from which it was drawn.

8. The c orrect interpretation of data

Statistical data analysis assists researchers and scholars to draw meaningful interpretations and conclusions from their observations or experiments. Statistics also facilitate data visualization through which research findings can be understood and interpreted better. Graphs, tables, infographics, and other visuals plotted using statistical packages are helpful in condensing large volumes of data into manageable pieces of information.

9. Avoidance of common mistakes that can compromise the findings

The overall quality of research results is dependent on the entire study process. With statistics, researchers can avoid mistakes or errors that could compromise the quality and accuracy of the findings such as:

• Issues with the accuracy and precision of the measurement system.
• Biased samples that can lead to incorrect inferences/conclusions.
• The limitation of overgeneralization.
• Errors in defining causality relationships.
• Incorrect analysis of data.
• Violating the assumptions of a particular type of analysis.

To correctly use statistics in a research paper, one should be sure of:

• The type of research question to answer.
• The types of data and variables to analyze to produce valid research conclusions.
• The type of variables in the data set.
• Whether the data follows a non-normal or normal distribution.
• Whether the data has outliers, missing, or extreme values.
• Adhering to all relevant assumptions regarding a particular statistic.

The correct use of statistical methods is essential not only in communicating research findings with accuracy but also in giving credibility to the methodologies used to reach such findings and conclusions. Students, researchers, scholars, businesses, consumers, specialists in medical sciences, and all other interested persons can use statistics to evaluate the credibility and usefulness of information to make excellent decisions within their unique settings.

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The mean, the mode, the median, the range, and the standard deviation are all examples of descriptive statistics. Descriptive statistics are used because in most cases, it isn't possible to present all of your data in any form that your reader will be able to quickly interpret.

Generally, when writing descriptive statistics, you want to present at least one form of central tendency (or average), that is, either the mean, median, or mode. In addition, you should present one form of variability , usually the standard deviation.

Measures of Central Tendency and Other Commonly Used Descriptive Statistics

The mean, median, and the mode are all measures of central tendency. They attempt to describe what the typical data point might look like. In essence, they are all different forms of 'the average.' When writing statistics, you never want to say 'average' because it is difficult, if not impossible, for your reader to understand if you are referring to the mean, the median, or the mode.

The mean is the most common form of central tendency, and is what most people usually are referring to when the say average. It is simply the total sum of all the numbers in a data set, divided by the total number of data points. For example, the following data set has a mean of 4: {-1, 0, 1, 16}. That is, 16 divided by 4 is 4. If there isn't a good reason to use one of the other forms of central tendency, then you should use the mean to describe the central tendency.

The median is simply the middle value of a data set. In order to calculate the median, all values in the data set need to be ordered, from either highest to lowest, or vice versa. If there are an odd number of values in a data set, then the median is easy to calculate. If there is an even number of values in a data set, then the calculation becomes more difficult. Statisticians still debate how to properly calculate a median when there is an even number of values, but for most purposes, it is appropriate to simply take the mean of the two middle values. The median is useful when describing data sets that are skewed or have extreme values. Incomes of baseballs players, for example, are commonly reported using a median because a small minority of baseball players makes a lot of money, while most players make more modest amounts. The median is less influenced by extreme scores than the mean.

The mode is the most commonly occurring number in the data set. The mode is best used when you want to indicate the most common response or item in a data set. For example, if you wanted to predict the score of the next football game, you may want to know what the most common score is for the visiting team, but having an average score of 15.3 won't help you if it is impossible to score 15.3 points. Likewise, a median score may not be very informative either, if you are interested in what score is most likely.

Standard Deviation

The standard deviation is a measure of variability (it is not a measure of central tendency). Conceptually it is best viewed as the 'average distance that individual data points are from the mean.' Data sets that are highly clustered around the mean have lower standard deviations than data sets that are spread out.

For example, the first data set would have a higher standard deviation than the second data set:

Notice that both groups have the same mean (5) and median (also 5), but the two groups contain different numbers and are organized much differently. This organization of a data set is often referred to as a distribution. Because the two data sets above have the same mean and median, but different standard deviation, we know that they also have different distributions. Understanding the distribution of a data set helps us understand how the data behave.

Making Sense of Learning pp 385–410 Cite as

Making Sense of Statistics

How Statistics Can Help Us Forward in Education

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• Asma Amanat Ali 4  
• First Online: 26 August 2020

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Statistics can be seen as a tool to enable us to make some sense of much data. Statistics now underpins many areas of modern life today and is widely used across many academic disciplines. It has a powerful role in helping us to interpret research data in education. In this chapter, we seek to unfold and explain some key statistical ideas. We then move on to show how these ideas can be very useful and insightful in interpreting different kinds of data. Statistics has a central place in educationalresearch but it also has an important making senserole in of all kinds of measurements made regularly in schools and universities today.

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write . H. G. Wells

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Sometimes, spreadsheets give the answer to the calculations to huge numbers of decimal places. This generates considerable confusion. It is necessary to reduce the number of numbers after the decimal point and this can be adjusted (the methods to do this varying between software packages).

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Reid, N., Amanat Ali, A. (2020). Making Sense of Statistics. In: Making Sense of Learning. Springer Texts in Education. Springer, Cham. https://doi.org/10.1007/978-3-030-53677-0_16

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How to Present Data and Statistics in Your Research Paper: Language Matters 

Statistics is an inexact science as it is based on probabilities rather than certainties. However, the language used to present data and statistics in your thesis or research paper needs to be accurate to avoid misunderstandings when your work is read by others. If the written descriptions of your data and statistics are not clear and accurate, experienced researchers may lose confidence in your entire study and dismiss your results, no matter how compelling they may be. 

The presentation of data in research and effective communication of statistical results requires writers to be very careful in their word choices. You must be confident that you understand the analysis you performed and the meaning of the results to really know how to present the data and statistics in your research paper effectively. Here are some terms and concepts that are often misused and may be confusing to early career researchers. 

Averages, the measures of the central tendency of a dataset, can be calculated in several different ways. The word “average” in non-scholarly writings typically refers to the arithmetic mean. However, the median and mode are two other frequently used measures. In your research paper, it is critical to state exactly what measure you are using. Therefore, don’t report an average but a mean, median, or mode. 

Percentages

Percentages are commonly used in presentations of data in research. They can indicate concentrations, probabilities, or comparisons, and they are frequently used to report changes in values. For example, the annual crime rate increased by 25%. However, unless you have a basis for this number, it’s difficult to judge the meaningfulness of this increase 1 . Did the number of crimes increase from 4 incidents to 5 or from 4,000 incidents to 5,000? Be sure to include enough information for the reader to understand the context.  

In addition, when used for comparison, make sure your comparison is complete. For instance, if the temperature was 17% higher in 2022, be sure to include that it was 17% higher than the temperature in 2017. 

Descriptive vs. inferential statistics

Descriptive statistics deal with populations, while inferential statistics deal with samples. A population is a group of objects or measurements that includes all possible instances, and a sample is a subset of that population. For example, you measure the mass of all the 1.1 kg jars of peanut butter at your favorite grocery store and report the mean and standard deviation. These are descriptive statistics for this population of peanut butter jars. However, if you then say that this is the mean of all such jars of peanut butter produced, you are engaging in inferential statistics because you now have measured only a sample of jars. You are inferring a characteristic of a population based on a sample. Inferential statistics are usually reported with a margin of error or confidence interval, such as 1.1 ± .02 kg. 

A hypothesis is a testable statement about the relationship between two or more groups or variables that forms the basis of the scientific method. The appropriate language around the topic of hypotheses and hypothesis testing can be confusing for even seasoned researchers. 

The alternative hypothesis is generally the researcher’s prediction for the study, and the null hypothesis is the negation of the alternative hypothesis. The aim of the study is to find evidence to reject the null hypothesis, which supports the truth of the alternative hypothesis. 

When writing up the results of your hypothesis test, it is important to understand exactly what the results mean. Remember, hypothesis testing can never “prove” anything – it merely provides evidence for either rejecting or not rejecting the null hypothesis. Also, be careful that you don’t overgeneralize the meaning of the results. Just because you find evidence that the null hypothesis can be rejected in this case does not mean the same is true under all conditions. 

Tips for effectively presenting statistics in academic writing

Presenting your data and statistical results can be very challenging. For researchers without extensive experience or statistical training, writing this part of the study report can be especially daunting. Here are some things to keep in mind when presenting your data and statistical results 1 . 

• If you don’t completely understand a statistical procedure, do not attempt to write it up without guidance from an expert. This is the most important thing you can do. 
• Keep your audience in mind. When you present your data and statistical results, think about how familiar your readers may be with the analysis and include the amount of detail needed for them to be comfortable 2 .  
• Use tables and graphics to illustrate your results more clearly and make your writing more understandable. 

We hope the points above help answer the question of how to present data and statistics in your research paper correctly. All the best! 

• The University of North Carolina at Chapel Hill Writing Center. Statistics. https://writingcenter.unc.edu/tips-and-tools/statistics/ [Accessed October 10, 2022] 
• Purdue University Online Writing Lab. Writing with statistics. https://owl.purdue.edu/owl/research_and_citation/using_research/writing_with_statistics/index.html [Accessed October 10, 2022] 

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While Sandel argues that pursuing perfection through genetic engineering would decrease our sense of humility, he claims that the sense of solidarity we would lose is also important.

This thesis summarizes several points in Sandel’s argument, but it does not make a claim about how we should understand his argument. A reader who read Sandel’s argument would not also need to read an essay based on this descriptive thesis.  

Broad thesis (arguable, but difficult to support with evidence) 

Michael Sandel’s arguments about genetic engineering do not take into consideration all the relevant issues.

This is an arguable claim because it would be possible to argue against it by saying that Michael Sandel’s arguments do take all of the relevant issues into consideration. But the claim is too broad. Because the thesis does not specify which “issues” it is focused on—or why it matters if they are considered—readers won’t know what the rest of the essay will argue, and the writer won’t know what to focus on. If there is a particular issue that Sandel does not address, then a more specific version of the thesis would include that issue—hand an explanation of why it is important.  

Arguable thesis with analytical claim 

While Sandel argues persuasively that our instinct to “remake” (54) ourselves into something ever more perfect is a problem, his belief that we can always draw a line between what is medically necessary and what makes us simply “better than well” (51) is less convincing.

This is an arguable analytical claim. To argue for this claim, the essay writer will need to show how evidence from the article itself points to this interpretation. It’s also a reasonable scope for a thesis because it can be supported with evidence available in the text and is neither too broad nor too narrow.  

Arguable thesis with normative claim 

Given Sandel’s argument against genetic enhancement, we should not allow parents to decide on using Human Growth Hormone for their children.

This thesis tells us what we should do about a particular issue discussed in Sandel’s article, but it does not tell us how we should understand Sandel’s argument.  

Questions to ask about your thesis 

• Is the thesis truly arguable? Does it speak to a genuine dilemma in the source, or would most readers automatically agree with it?  
• Is the thesis too obvious? Again, would most or all readers agree with it without needing to see your argument?  
• Is the thesis complex enough to require a whole essay's worth of argument?  
• Is the thesis supportable with evidence from the text rather than with generalizations or outside research?  
• Would anyone want to read a paper in which this thesis was developed? That is, can you explain what this paper is adding to our understanding of a problem, question, or topic?
• picture_as_pdf Thesis

Developing a Thesis Statement

Many papers you write require developing a thesis statement. In this section you’ll learn what a thesis statement is and how to write one.

Keep in mind that not all papers require thesis statements . If in doubt, please consult your instructor for assistance.

What is a thesis statement?

A thesis statement . . .

• Makes an argumentative assertion about a topic; it states the conclusions that you have reached about your topic.
• Makes a promise to the reader about the scope, purpose, and direction of your paper.
• Is focused and specific enough to be “proven” within the boundaries of your paper.
• Is generally located near the end of the introduction ; sometimes, in a long paper, the thesis will be expressed in several sentences or in an entire paragraph.
• Identifies the relationships between the pieces of evidence that you are using to support your argument.

Not all papers require thesis statements! Ask your instructor if you’re in doubt whether you need one.

Identify a topic

Your topic is the subject about which you will write. Your assignment may suggest several ways of looking at a topic; or it may name a fairly general concept that you will explore or analyze in your paper.

Consider what your assignment asks you to do

Inform yourself about your topic, focus on one aspect of your topic, ask yourself whether your topic is worthy of your efforts, generate a topic from an assignment.

Below are some possible topics based on sample assignments.

Sample assignment 1

Analyze Spain’s neutrality in World War II.

Identified topic

Franco’s role in the diplomatic relationships between the Allies and the Axis

This topic avoids generalities such as “Spain” and “World War II,” addressing instead on Franco’s role (a specific aspect of “Spain”) and the diplomatic relations between the Allies and Axis (a specific aspect of World War II).

Sample assignment 2

Analyze one of Homer’s epic similes in the Iliad.

The relationship between the portrayal of warfare and the epic simile about Simoisius at 4.547-64.

This topic focuses on a single simile and relates it to a single aspect of the Iliad ( warfare being a major theme in that work).

Developing a Thesis Statement–Additional information

Your assignment may suggest several ways of looking at a topic, or it may name a fairly general concept that you will explore or analyze in your paper. You’ll want to read your assignment carefully, looking for key terms that you can use to focus your topic.

Sample assignment: Analyze Spain’s neutrality in World War II Key terms: analyze, Spain’s neutrality, World War II

After you’ve identified the key words in your topic, the next step is to read about them in several sources, or generate as much information as possible through an analysis of your topic. Obviously, the more material or knowledge you have, the more possibilities will be available for a strong argument. For the sample assignment above, you’ll want to look at books and articles on World War II in general, and Spain’s neutrality in particular.

As you consider your options, you must decide to focus on one aspect of your topic. This means that you cannot include everything you’ve learned about your topic, nor should you go off in several directions. If you end up covering too many different aspects of a topic, your paper will sprawl and be unconvincing in its argument, and it most likely will not fulfull the assignment requirements.

For the sample assignment above, both Spain’s neutrality and World War II are topics far too broad to explore in a paper. You may instead decide to focus on Franco’s role in the diplomatic relationships between the Allies and the Axis , which narrows down what aspects of Spain’s neutrality and World War II you want to discuss, as well as establishes a specific link between those two aspects.

Before you go too far, however, ask yourself whether your topic is worthy of your efforts. Try to avoid topics that already have too much written about them (i.e., “eating disorders and body image among adolescent women”) or that simply are not important (i.e. “why I like ice cream”). These topics may lead to a thesis that is either dry fact or a weird claim that cannot be supported. A good thesis falls somewhere between the two extremes. To arrive at this point, ask yourself what is new, interesting, contestable, or controversial about your topic.

As you work on your thesis, remember to keep the rest of your paper in mind at all times . Sometimes your thesis needs to evolve as you develop new insights, find new evidence, or take a different approach to your topic.

Derive a main point from topic

Once you have a topic, you will have to decide what the main point of your paper will be. This point, the “controlling idea,” becomes the core of your argument (thesis statement) and it is the unifying idea to which you will relate all your sub-theses. You can then turn this “controlling idea” into a purpose statement about what you intend to do in your paper.

Look for patterns in your evidence

Compose a purpose statement.

Consult the examples below for suggestions on how to look for patterns in your evidence and construct a purpose statement.

• Franco first tried to negotiate with the Axis
• Franco turned to the Allies when he couldn’t get some concessions that he wanted from the Axis

Possible conclusion:

Spain’s neutrality in WWII occurred for an entirely personal reason: Franco’s desire to preserve his own (and Spain’s) power.

Purpose statement

This paper will analyze Franco’s diplomacy during World War II to see how it contributed to Spain’s neutrality.

• The simile compares Simoisius to a tree, which is a peaceful, natural image.
• The tree in the simile is chopped down to make wheels for a chariot, which is an object used in warfare.

At first, the simile seems to take the reader away from the world of warfare, but we end up back in that world by the end.

This paper will analyze the way the simile about Simoisius at 4.547-64 moves in and out of the world of warfare.

Derive purpose statement from topic

To find out what your “controlling idea” is, you have to examine and evaluate your evidence . As you consider your evidence, you may notice patterns emerging, data repeated in more than one source, or facts that favor one view more than another. These patterns or data may then lead you to some conclusions about your topic and suggest that you can successfully argue for one idea better than another.

For instance, you might find out that Franco first tried to negotiate with the Axis, but when he couldn’t get some concessions that he wanted from them, he turned to the Allies. As you read more about Franco’s decisions, you may conclude that Spain’s neutrality in WWII occurred for an entirely personal reason: his desire to preserve his own (and Spain’s) power. Based on this conclusion, you can then write a trial thesis statement to help you decide what material belongs in your paper.

Sometimes you won’t be able to find a focus or identify your “spin” or specific argument immediately. Like some writers, you might begin with a purpose statement just to get yourself going. A purpose statement is one or more sentences that announce your topic and indicate the structure of the paper but do not state the conclusions you have drawn . Thus, you might begin with something like this:

• This paper will look at modern language to see if it reflects male dominance or female oppression.
• I plan to analyze anger and derision in offensive language to see if they represent a challenge of society’s authority.

At some point, you can turn a purpose statement into a thesis statement. As you think and write about your topic, you can restrict, clarify, and refine your argument, crafting your thesis statement to reflect your thinking.

As you work on your thesis, remember to keep the rest of your paper in mind at all times. Sometimes your thesis needs to evolve as you develop new insights, find new evidence, or take a different approach to your topic.

Compose a draft thesis statement

If you are writing a paper that will have an argumentative thesis and are having trouble getting started, the techniques in the table below may help you develop a temporary or “working” thesis statement.

Begin with a purpose statement that you will later turn into a thesis statement.

Assignment: Discuss the history of the Reform Party and explain its influence on the 1990 presidential and Congressional election.

Purpose Statement: This paper briefly sketches the history of the grassroots, conservative, Perot-led Reform Party and analyzes how it influenced the economic and social ideologies of the two mainstream parties.

Question-to-Assertion

If your assignment asks a specific question(s), turn the question(s) into an assertion and give reasons why it is true or reasons for your opinion.

Assignment : What do Aylmer and Rappaccini have to be proud of? Why aren’t they satisfied with these things? How does pride, as demonstrated in “The Birthmark” and “Rappaccini’s Daughter,” lead to unexpected problems?

Beginning thesis statement: Alymer and Rappaccinni are proud of their great knowledge; however, they are also very greedy and are driven to use their knowledge to alter some aspect of nature as a test of their ability. Evil results when they try to “play God.”

Write a sentence that summarizes the main idea of the essay you plan to write.

Main idea: The reason some toys succeed in the market is that they appeal to the consumers’ sense of the ridiculous and their basic desire to laugh at themselves.

Make a list of the ideas that you want to include; consider the ideas and try to group them.

• nature = peaceful
• war matériel = violent (competes with 1?)
• need for time and space to mourn the dead
• war is inescapable (competes with 3?)

Use a formula to arrive at a working thesis statement (you will revise this later).

• although most readers of _______ have argued that _______, closer examination shows that _______.
• _______ uses _______ and _____ to prove that ________.
• phenomenon x is a result of the combination of __________, __________, and _________.

What to keep in mind as you draft an initial thesis statement

Beginning statements obtained through the methods illustrated above can serve as a framework for planning or drafting your paper, but remember they’re not yet the specific, argumentative thesis you want for the final version of your paper. In fact, in its first stages, a thesis statement usually is ill-formed or rough and serves only as a planning tool.

As you write, you may discover evidence that does not fit your temporary or “working” thesis. Or you may reach deeper insights about your topic as you do more research, and you will find that your thesis statement has to be more complicated to match the evidence that you want to use.

You must be willing to reject or omit some evidence in order to keep your paper cohesive and your reader focused. Or you may have to revise your thesis to match the evidence and insights that you want to discuss. Read your draft carefully, noting the conclusions you have drawn and the major ideas which support or prove those conclusions. These will be the elements of your final thesis statement.

Sometimes you will not be able to identify these elements in your early drafts, but as you consider how your argument is developing and how your evidence supports your main idea, ask yourself, “ What is the main point that I want to prove/discuss? ” and “ How will I convince the reader that this is true? ” When you can answer these questions, then you can begin to refine the thesis statement.

Refine and polish the thesis statement

To get to your final thesis, you’ll need to refine your draft thesis so that it’s specific and arguable.

• Ask if your draft thesis addresses the assignment
• Question each part of your draft thesis
• Clarify vague phrases and assertions
• Investigate alternatives to your draft thesis

Consult the example below for suggestions on how to refine your draft thesis statement.

Sample Assignment

Choose an activity and define it as a symbol of American culture. Your essay should cause the reader to think critically about the society which produces and enjoys that activity.

• Ask The phenomenon of drive-in facilities is an interesting symbol of american culture, and these facilities demonstrate significant characteristics of our society.This statement does not fulfill the assignment because it does not require the reader to think critically about society.

Drive-ins are an interesting symbol of American culture because they represent Americans’ significant creativity and business ingenuity.

Among the types of drive-in facilities familiar during the twentieth century, drive-in movie theaters best represent American creativity, not merely because they were the forerunner of later drive-ins and drive-throughs, but because of their impact on our culture: they changed our relationship to the automobile, changed the way people experienced movies, and changed movie-going into a family activity.

While drive-in facilities such as those at fast-food establishments, banks, pharmacies, and dry cleaners symbolize America’s economic ingenuity, they also have affected our personal standards.

While drive-in facilities such as those at fast- food restaurants, banks, pharmacies, and dry cleaners symbolize (1) Americans’ business ingenuity, they also have contributed (2) to an increasing homogenization of our culture, (3) a willingness to depersonalize relationships with others, and (4) a tendency to sacrifice quality for convenience.

This statement is now specific and fulfills all parts of the assignment. This version, like any good thesis, is not self-evident; its points, 1-4, will have to be proven with evidence in the body of the paper. The numbers in this statement indicate the order in which the points will be presented. Depending on the length of the paper, there could be one paragraph for each numbered item or there could be blocks of paragraph for even pages for each one.

Complete the final thesis statement

The bottom line.

As you move through the process of crafting a thesis, you’ll need to remember four things:

• Context matters! Think about your course materials and lectures. Try to relate your thesis to the ideas your instructor is discussing.
• As you go through the process described in this section, always keep your assignment in mind . You will be more successful when your thesis (and paper) responds to the assignment than if it argues a semi-related idea.
• Your thesis statement should be precise, focused, and contestable ; it should predict the sub-theses or blocks of information that you will use to prove your argument.
• Make sure that you keep the rest of your paper in mind at all times. Change your thesis as your paper evolves, because you do not want your thesis to promise more than your paper actually delivers.

In the beginning, the thesis statement was a tool to help you sharpen your focus, limit material and establish the paper’s purpose. When your paper is finished, however, the thesis statement becomes a tool for your reader. It tells the reader what you have learned about your topic and what evidence led you to your conclusion. It keeps the reader on track–well able to understand and appreciate your argument.

Writing Process and Structure

This is an accordion element with a series of buttons that open and close related content panels.

Getting Started with Your Paper

Interpreting Writing Assignments from Your Courses

Generating Ideas for

Creating an Argument

Thesis vs. Purpose Statements

Architecture of Arguments

Working with Sources

Quoting and Paraphrasing Sources

Using Literary Quotations

Citing Sources in Your Paper

Drafting Your Paper

Generating Ideas for Your Paper

Introductions

Paragraphing

Developing Strategic Transitions

Conclusions

Revising Your Paper

Peer Reviews

Reverse Outlines

Revising an Argumentative Paper

Revision Strategies for Longer Projects

Finishing Your Paper

Twelve Common Errors: An Editing Checklist

How to Proofread your Paper

Writing Collaboratively

Collaborative and Group Writing

School of Music

Madeline Yankell brings the bubbly Vesta to life in the Hancher premiere of Fierce

Vesta―named after the Roman goddess of the Earth―is one of the four principal characters in Fierce , a new opera that follows four young girls (also referred to as “muses”) as they prepare for the next chapter of their lives. The opera—making its Iowa premiere—reflects the collaborative spirit of Performing Arts At Iowa and will be co-produced by the School of Music, the Performing Arts Production Unit, and Hancher Auditorium. Vesta, played by Madeline Yankell, is the youngest of the muses. She is naive, bubbly, and sometimes she takes refuge from life in a fantasy world full of otters.   

Yankell is a graduate student in music education who recently defended her MA thesis on movement and choral singing. She has previously performed in La Traviata and Dialogues des Carmelites .   

“I’m so excited to perform at Hancher. It’s a dream come true,” Yankell beams, “I’ve had the opportunity to perform on the Hancher stage a few times but the fact that I get to sing a song about otters on this huge stage is just kind of nuts.”  

Yankell grew up on the east coast in Moorestown, New Jersey, before pursuing her BA with a focus in music teacher education from Case Western Reserve University in Ohio. After graduating, she moved to Massachusetts, where she spent a few years teaching high school choir.   

“I applied to a lot of different grad programs in places all over the country,” Yankell explains what drew her to the University of Iowa. “UI really has the perfect combination of research and performing arts funding. I get to participate in operas, choirs, and be part of the performing arts but I also get to do music education research.”   

Since Yankell has been at the university, she’s enjoyed the collaborative environment encouraged in the School of Music and across Performing Arts At Iowa.   

When she was exploring her grad school options, Yankell says, “I just happened upon the performing arts scene in Iowa City. The Iowa City community is really strong and so supportive of the arts. Also, the School of Music, Hancher, and the theatre and dance departments have been working well together to create more collaborative experiences for students. The students also really support each other here.”  

Yankell is currently in the last semester of her master’s so, when the opportunity to audition for Fierce came around, she jumped at it.   

The new opera was composed for Cincinnati Opera by Dr. William Menefield, a UI assistant professor of Jazz Studies, in collaboration with librettist Sheila Williams. It premiered there in 2022. For the Hancher debut, Menefield will be taking on the role of director.    

“I knew Dr. Menefield was the leader of the Black Pop Ensemble and they’re such a great group,” Yankell says. “I really wanted to work with him, and this opera is so different from anything I’ve ever done.”  

The characters of the four muses were created by Williams, based on the real life stories and personalities of a group of Cincinnatti -area high school girls she talked with in a yearlong series of heart-to-heart conversations. These rich conversations spanned topics such as parental expectations, the best lipstick color, ethnic identity, and college admissions anxiety.   

Yankell is excited to bring the bubbly character of Vesta to life on the Hancher stage.   

“What I really love about playing Vesta is that she’s got these layers of sadness and depth,” Yankell explains her role. “There’s a great juxtaposition between her bubbly exclamations about how magical otters are, and the issues she faces at home with her parents. She also gets to be brave and bold. Behind her silliness there is so much wisdom and strength.”   

As Yankell has been rehearsing for Fierce , she has also been writing her master’s thesis. She is passionate about music education and would like to return to teaching high school students after graduation—with aspirations towards teaching at the collegiate level in the future.   

Yankell notes “Something I’ve enjoyed about working with Dr. Menefield and the production team is that they’ve fostered an environment of growth. We’ll often stop to discuss acting methods or vocal technique, which is so important because, at the end of the day, we’re a learning community.”  

“And it’s just a fun project because we have Dr. Menefield there and he wrote it,” she adds. “There are days where he’ll say he was channeling something specific, like Beyonce. It’s not often you get to channel Beyonce while working on an opera.”