what is the importance of statistics in research essay

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Finding Statistics

• Why are Statistics Important?

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

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

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

Misleading Statistics

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

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

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

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

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

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

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

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Statistics By Jim

Making statistics intuitive

The Importance of Statistics

By Jim Frost 51 Comments

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

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

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

Statistics Uses Numerical Evidence to Draw Valid Conclusions

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

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

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

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

Statisticians Know How to Avoid Common Pitfalls

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

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

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

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

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

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

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

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

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

Use Statistics to Make an Impact in Your Field

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

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

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

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

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

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

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

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

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

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

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

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Reader Interactions

July 11, 2022 at 2:25 am

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

July 11, 2022 at 2:33 am

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

June 7, 2022 at 1:40 pm

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

June 8, 2022 at 9:02 pm

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

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

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

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

March 31, 2022 at 10:55 am

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

March 27, 2022 at 6:21 am

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

March 28, 2022 at 9:23 pm

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

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

February 2, 2022 at 3:01 pm

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

February 3, 2022 at 4:03 pm

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

September 20, 2021 at 12:37 pm

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

September 20, 2021 at 3:49 pm

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

February 5, 2021 at 3:22 am

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

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

February 5, 2021 at 9:58 pm

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

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

Thanks for writing!

December 1, 2020 at 4:16 am

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

December 1, 2020 at 11:39 pm

Hi Saegiru,

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

November 6, 2020 at 6:18 am

THANK YOU FOR THIS ‘VERY HELPFUL’

September 27, 2020 at 11:38 am

When are ur articles publisehd?

September 28, 2020 at 2:16 pm

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

August 7, 2020 at 11:06 am

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

June 15, 2020 at 7:02 pm

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

June 15, 2020 at 10:24 pm

Obrigado! Estou feliz que meu site seja útil!

June 13, 2020 at 5:30 am

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

March 2, 2020 at 1:44 pm

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

February 16, 2020 at 7:18 pm

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

December 7, 2019 at 2:57 pm

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

November 17, 2019 at 11:25 pm

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

November 18, 2019 at 11:28 am

Hello Najihah,

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

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

November 11, 2019 at 8:31 am

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

October 2, 2019 at 4:10 am

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

October 2, 2019 at 5:09 pm

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

Purdue’s Reference List: Electronic Sources

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

September 7, 2019 at 9:16 am

how does statistics widen the scope of knowledge

June 18, 2019 at 6:08 am

Thanks for the information, it’s quite interesting.

May 15, 2019 at 4:23 am

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

May 17, 2019 at 10:30 am

Hi Geovani,

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

Best of luck with your thesis!

April 30, 2019 at 7:22 am

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

April 30, 2019 at 11:07 pm

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

March 28, 2019 at 2:13 am

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

December 6, 2018 at 10:26 am

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

December 1, 2018 at 11:05 pm

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

December 2, 2018 at 12:35 am

Yes, you should remove those variables!

October 23, 2018 at 2:07 pm

thanks for sharing your knowledge with us thankss you sir

September 15, 2018 at 4:20 am

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

September 15, 2018 at 4:17 pm

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

June 27, 2018 at 12:26 pm

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

June 27, 2018 at 2:30 pm

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

March 21, 2018 at 1:56 am

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

Thank you.Jim..

March 21, 2018 at 1:49 pm

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

March 14, 2018 at 6:53 am

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

March 14, 2018 at 11:02 am

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

December 11, 2017 at 1:46 am

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

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

December 11, 2017 at 2:06 am

Hi Ron, thanks for you thoughtful comment.

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

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

Comments and Questions Cancel reply

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

What this handout is about

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

Introduction

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

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

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

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

Reading statistics

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

1. Does your evidence come from reliable sources?

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

2. What is the data’s background?

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

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

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

3. Are all data reported?

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

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

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

4. Have the data been interpreted correctly?

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

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

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

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

Writing statistics

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

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

1. The mistake of the “average” writer

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

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

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

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

2. Match your facts with your questions

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

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

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

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

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

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

3. Show the entire picture

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

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

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

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

4. Give bases of all percentages

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

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

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

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

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

Important questions to ask (and answer) about statistics

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

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

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

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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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The importance of Statistics in Scientific Research and Development

Sentiments on statistics in research and academia have rarely been viewed in the positive light – at least at the very beginning. Often failing to disguise itself as anything but “more math”, budding students transitioning into tertiary education have attempted to evade statistics like the plague. A disregard and distaste for statistics however is undoubtedly disturbing for educators and industry professionals all around, particularly among the circles of STEM. How is something so critical in helping students develop quantitative reasoning skills, obtain tools to make inferences, assess limitations, detect errors and uncertainty from data, so that decisions and/or conclusions can be formed, be neglected?

One way statistics has eased into peoples good books is through the happy marriage of computer science and statistics . The world of statistics and computer science have collided and melded together as the practice of statistics has moved onto our electronic devices in the form of programming. Languages like R and Python rank as some of the fastest growing and most used programming languages in the last 5 years . The use of R has grown particularly in academic circles for statistical computing is a well sought out skill and proficiency in R or Python is now desired by many employers especially for those who are pursuing careers in STEM.  Statistical tests have come a long way since the beginning and harnessing the power and utility of computers will only see it advance and influence others more rapidly and efficiently.

Another way these bad vibes are being countered is the early inclusion of statistics to educational curriculums. In the USA, statistics has been introduced as one of the core components of K-12 Mathematics , highlighting the importance of the learning mathematical skills of induction, deduction, and communication of data. Such practices seem promising as this year alone we should have hit a 50% increase (approximately 200,000 individuals) of professional statisticians entering the workforce. Learning statistics earlier should provide educators a chance to cultivate an earlier appreciation of statistics and corresponding valuable analytical skills. Educators should not provide students with the illusion that pursuing a career in geology or nursing will end all affairs with statistics because the truth is the pervasiveness of data analysis is far-reaching and only increasing in importance as we rely on the data to advance into the future.

So having chosen to embrace statistics, where and who can we expect to be at the frontier of statistics? The truth is many of you will be at the heart of it before knowing it. As emphasized earlier, statistics is an interdisciplinary study. While often highlighted in sciences, it becomes absolutely relevant and paramount whenever there is a need for research and development. We ask questions, seek for improvements, develop new concepts and need a way to answer or see how these ideas come to life. The next step is to then perform experiments, develop prototypes, run tests, all the while tracking results, recording data. Statistics finally comes into play, helping you assess levels of uncertainty, % of success, project growth or sales rates, where to build houses, or mine Gold. Such is the nature of research and development that involves the application of scientific methods, processes, and systems in order to evaluate and interpret data. Data-driven-statistical- research now forms a fundamental piece of the puzzle when innovating, creating or attempting to progress forward – be it in medicine, academia, business, Information Technology, medicine, economics, or construction.

For example, a biostatistician may be involved in researching the rate of HIV spread and invasion throughout sub-saharan Africa to help identify the countries that will be hit the hardest. In medicine, statistical research may take the form of equivalence testing to compare, improve and examine the effectiveness of new drugs to aid depression. Astronomers may utilize statistical models to support research on the expansion of the universe, while an actuary may look for statistical models to predict risk of financial investments or business expansion. Mechanics and automotive industrialists can apply statistics to constantly improve the quality of their product by constantly minimizing the level of errors in the performance of their product. Perhaps a more familiar example is the collation of government statistics. For years, governments have gathered a wealth of enormous datasets and utilized the power of statistics to inform decisions and research improvements on housing, income, unemployment, minimum wage, healthcare, and education services.

So why is it so important to pair scientific research with the use of statistics ?

1. informs methods on data collection.

By pre-emptively identifying the statistical test(s) you want to employ to help answer your research question(s), hopefully you know what sort of data needs to be collected. Where statistics comes in handy is helping you identify key aspects you may not have considered in your chosen methods of data collection . Such may come in the form of identifying an additional variable of importance to collect data on. Another pitfall statistics can help you avoid is that of pseudoreplication. Pseudoreplication is particularly dangerous for several reasons: Firstly, it paints a false image of how large a sample size is and ignores the need for “true” replicated treatments (when applicable). Sample sizes are important as they determine the power of your statistical tests and therefore the confidence and scope of your conclusions based on the statistical results. Secondly it fails to highlight that some variables may not be independent. This may mask the true effects of the variables that you wish to be examining independently. Sampling bias can also be avoided when considering the statistical test you hope to use: for example research on the occurrence of domestic violence in households should investigate low-income, middle-income, and high-income neighbourhoods.

“To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of.”

— Ronald Fisher

2. Used to support or negate a hypothesis

Without statistical tests there would be no objective way to show whether the data are in support or in disagreement of research questions. Since the burden of evidence (for or against) lies in results of statistic tests, without the use of statistics in research, we would be buried in unknowns, more questions, open-ended conclusions, and more data than we can handle! Without statistical research, we would be unable to credit new discoveries, answer new questions, and confidently advance with new developments. Statistical tests form the basis on each we can trust what the data is saying and make sense of what the raw, volumes of data are communicating.

3.  Seeks out uncertainty, errors, and outliers in the data

Data is rarely squeaky clean and more often than not, data is messy, ugly and incomplete: Such is the nature of sampling data, there are answers people do not answer completely, truly, or circumstances beyond our control that prevent us to collect all the data points we desire: e.g. an inaccessible village of HIV+ patients trapped in a war zone, the premature death of chicks in a nest, apparatus failure, or the sudden crash in stocks. Truth of the matter is there is no way to collect ALL data points – this is where inferential statistics saves the day. Beyond those limitations, at the very minimum there is human error in data sampling or collection and with every tool, a measure of uncertainty. Errors can also arise due to uncontrollable circumstances as aforementioned, or due to a limitation of a statistical test. These errors can be accounted for to some degree in statistical models and tests so that we can cut through all the noise and assess our hypotheses honestly.

Using statistics can help us map out those outliers , identify the levels of uncertainty in our results, and help us deal fairly with those errors. No statistical test is perfect and neither is any dataset. Statistics allows us to draw conclusions openly by realizing these limitations from the start.  

4.  Aid interpretation, summarization, and communication of datasets:

Having utilized the appropriate statistical test, fair and objective conclusions, implications, can now be interpreted from the dataset. Statistical tests provide us with the means to interpret the dataset accurately so that we can make unbiased decisions on how to proceed knowing what the data is saying. It also guides the way we communicate our results and calls for us to defend why these statistical tests were chosen and how we arrived at our explanations based on a series of numbers. Statistics are also a great way of communicating and condensing large datasets into digestible, bitesize pieces of information easily understood by the masses. These summary statistics are helpful in providing people with an immediate idea of the big picture and whether your conclusions are valid.

5. Multivariate statistics and modelling

Without statistics we would be unable to tease apart the multitude of effects that may be influencing our dependent variable . Furthermore we would not be able to identify which factors are working in conjunction to produce a compounded effect on our dependent variable. Statistical modelling helps us deal with our multivariate statistical questions so that we can assess hypotheses from every possible angle. So for example, how do we know that domestic violence in neighbourhoods of various levels of income are not also affected by ethnicity, religion, and level of education? Some of the factors may be intertwined and using statistics helps us tease apart these details.

With all that being said, it is worth pointing out that statistics can’t solve everything and anything under the sun perfectly. Statistical tests/models are flawed and in themselves have limitations in the way they were designed and formulated. Even using the wrong statistical test can lead to serious erroneous conclusions and overlook the data completely. Statisticians have thus tried to create helpful guides , books , charts and keys to help advise students and working professionals alike how to identify the appropriate tests/models to apply to their data. These resources should help students be more vigilant and aid the appropriate use and digestion of statistics. Combined with a more positive outlook on statistics, early exposure, an abundance of tools, and the knowledge of a ubiquitous need for statistics in all forms of research and development, there is hope that statistics will be shunned no more. Surely if plants can sense and harness the value of statistics, so can we.

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.    —   George Box & Norman R. Draper

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Use of Statistics in Research

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Evaluating Statistics

Inclusion of erroneous statistical data can harm the credibility of your research. Therefore, it is very important to evaluate the source of your statistical information. The following questions will help you to evaluate the reliability of statistical information.

• Who is the author of the source that presents the statistics? What are the author's credentials? Is the author an authority on the subject? Could the author be presenting bias?
• What is the date of the statistics? How current are they? Are they relevant to the time period that you are interested in?
• Who is the intended audience?
• What type of publication is the data published in? And is the data clearly represented?
• Can the data be cross-checked in other reliable sources?
• Can the statistics be verified? Do the methods used and data presented seem valid?

Statistical data will lend credibility to your research by providing facts and figures supporting your position. Therefore, statistics may be important to include in your class assignments, research papers, and theses. However, statistical data is not always easy to find since there is no single source for this type of information. Statistics may come from scholarly journals, magazines, newspapers, reports, websites, books, statistical databases, and more.

It is important to keep in mind that the most current statistics may actually be a year old or more. Organizations publish reports and statistics according to the data collection cycle (not necessarily annual), the time it takes to analyze and report the data, and the public release schedule.

This guide outlines several techniques and resources for finding and evaluating statistical data. When searching, it is important to keep in mind that the precise information you need may not exist ; the data may never have been collected. In other cases, data might be held privately; not all data is available to the public. Be flexible and consider alternative measures to support your research.

Subject Statistics

• Health Statistics
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• Search Statista
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• Statista Help

The Statista database provides current statistics from private and government sources on a wide range of topics including technology, health, public opinion, and market research. For detailed information about the sources of statistics in Statista, click here .

You can access Statista by hovering over Research Resources on the Library homepage and clicking on A-Z Databases .

On the Statista home page, you may enter a keyword relating to your research topic to retrieve results for Statistics and Studies & Reports. A description of all content types available through the Library's subscription appears below. Note: NU does not subscribe to the Market Outlooks so content under the "Expert Tools" menu is unavailable.

• Statistics : Over 1,000,000 statistics from four different databases: German, English, French and Spanish*
• Forecasts & Surveys : 5-year forecasts on hot topics and exclusive surveys among consumers and experts
• Infographics : Easy and appealing visualization of topical events
• Topics : Over 80,000 topics are the ideal starting point for your research
• Studies & Reports : Studies database containing over 32,000 external studies
• Companies : Company database for over 5,000 companies

The search results screen defaults to displaying the most most relevant content first (based on a formula which has been specifically developed for this purpose). You may change the sort feature to Date of Publication or Popularity by using the "Sort by" drop-down menu under the search box.

Content from from the United States prioritized. This means that it ranks higher in your search results. You may change this prioritization to another country by using the "Location Focus" menu.

Below the content type filters on the left-hand menu, you can find more filter options, including Regions, Countries & Territories, Industry, Publication date, and Archive. The Archive feature allows you to view results from archived news entries which are no longer current, but still worth keeping in Statista.

The "Search accuracy" feature allows you to narrow your search down by using search specification parameters.

• Normal: searches for the entered terms by means of an AND connective
• Wide: searches for the entered terms by means of an OR connective
• High: displays only the most relevant results of a search for the entered terms using an AND connective

To view available all search commands in Statista (Boolean operators, phrase searching, wildcards, etc.), click here .

Additionally, you may browse Statista using the drop-down menu at the top of the screen. To browse by industry, recent and popular statistics, or by topic, hover over the Statistics menu, as shown below.

Note: NU does not subscribe to the Market Outlooks so content under the Outlooks menu is unavailable.

From the search results screen, simply click on the statistic you are interested in to view the full record.

You may download Statista charts in the form of a .png image, or as Excel, PowerPoint, or Adobe Arobat files. These charts are permitted for use in your papers and presentations, as long as you properly cite the original source of the data in your research, not the Statista database. For details on properly citing Statista, see the next tab.

Download Formats:

• PNG: As an image file, the statistic, visualized in the way that is visible on the page, can be easily embedded into other documents. In this format, neither the data nor the visualization can be changed afterwards.
• PDF: PDF files are perfect for sharing via email. In this format, neither the data nor the visualization can be changed afterwards.
• XLS: The Excel file contains the raw data of the statistic. Use it if you want to further process the data according to your requirements and visualize it. The second sheet contains all information about the source, survey and release.
• PPT: As a PowerPoint slide you can embed the statistic into your presentation and apply your desired layout to it. The download includes a set of multiple slides, which provide you with a range of different visualizations. Simply use the slide that fits your presentation best.

Charts can be customized under settings. Click on the Gear icon to change the chart type and data labels. In case a chart looks overcrowded with data labels, you can, for instance, remove individual labels by clicking on them, before downloading the statistic by selecting Custom .

Charts can also be shared on social media or embedded in web pages. Click on the Share icon to select from the available options or to view the embed code.

Related statistics, topics, and studies may be found at the bottom of the screen.

Statista has a citation tool on the right-hand side of the screen under the download options. Simply select APA from the citation drop-down menu as shown in the image below.

It is important to note, however, that you will need to check for the correct format with the  Publication Manual of the American Psychological Association ,  Seventh Edition .  

Please note that this information only serves as guidance. Use the  Academic Success Center  website to  learn about coaching  and access  writing ,  statistics ,  editing , and  APA Style  resources. The Academic Success Center provides access to  Academic Writer ,  which provides over 150 sample references, as well as nearly 10 sample papers. It also incorporates all of the references and other content from the Publication Manual.

Please note that this information only serves as guidance. Use the Academic Success Center website to learn about coaching and access writing , statistics , editing , and APA Style resources.

• Statista Guided Tours All functions related to statistics explained with videos.
• Welcome to Statista This guide will show you how to benefit from all the hidden treasures of our platform and tell you how to effortlessly get more out of your search, structure your research or which of the many content types suit your needs best. Also includes frequently asked questions.

Additional Resources

• Journal Articles
• Search Engines
• U.S. Statistics
• International Statistics
• Specific Countries

Often you may obtain statistics from journal, magazine or newspaper articles on your research topic. The Library’s NavigatorSearch is a good starting point since it searches most of the Library’s databases in a single, simultaneous search. To access, go to the Library’s homepage and look for the box in the middle of the page titled NavigatorSearch. Click on the Advanced Search link to bring up more search options.

You may include the keywords (statistics OR ratio OR proportion OR rate) as part of your search string, as shown below. Additional keywords to consider are prevalence, percentage, numbers, increase, decrease, data, trends, polling, figures, and tables.

Conducting a search in Google or another internet search engine is also a good starting point for finding statistics related to your research topic. Reliable sources of statistics may include government and technical reports, scholarly journal articles, conference papers, white papers, and professional organizations.

When retrieving statistics from the internet, it is even more pertinent to evaluate the source as reliable and appropriate for use in scholarly research. Refer to the Evaluating Statistics section above for specific questions you should ask regarding the statistical source. The Website Evaluation page provides additional factors to consider before including online sources in your research.

Similar to a database search, in Google you may include the keyword statistics as part of your search string, as shown below. Additional keywords to consider are ratio, proportion, rate, percentage, prevalence, numbers, increase, decrease, data, trends, polling, figures, and tables. You may also want to try putting in the year in order to locate more recent statistics.

Government, agency and organizational websites are a great source of reliable statistical information.

• Association of Religion Data Archives Strives to democratize access to the best data on religion. Provides a collection of surveys, polls, and other data submitted by researchers.
• Bureau of Economic Analysis Source of accurate and objective data about the nation's economy.
• Bureau of Justice Statistics Provides information on crime, criminal offenders, victims of crime, and the operation of justice systems at all levels of government.
• Bureau of Labor Statistics Principal fact-finding agency for the Federal Government in the broad field of labor economics and statistics. The BLS is an independent national statistical agency that collects, processes, analyzes, and disseminates statistical information.
• Bureau of Transportation Statistics Statistics from the U.S. Department of Transportation are organized by transportation mode, region, or subject. Finding Transportation Statistics provides additional resources for statistics.
• Centers for Disease Control and Prevention: FastStats Provides quick access to statistics on topics of public health importance and is organized alphabetically.
• ChildStats.gov Provides statistics on children and families in the U.S. across a range of domains, including family and social environment, economic circumstances, health care, physical environment and safety, behavior, education and health.
• Data.gov The home of the U.S. Government's open data. Here you will find data, tools, and resources to conduct research, develop web and mobile applications, design data visualizations, and more.
• Data and Statistics about the United States Find data about the U.S., such as maps and population, demographic, and economic data.
• Department of Homeland Security: Data Provides statistical information on citizenship, immigration, FEMA, and more.
• FRED (Federal Reserve Economic Data) Download, graph, and track 765,000 US and international time series from 94 sources.
• Integrated Postsecondary Education Data System (IPEDS) Provides statistics related to postsecondary education, including admissions, tuition rates, enrollment numbers, demographics of students, and more.
• International Statistical Agencies Directory of international statistical agencies provided by the U.S. Census Bureau.
• IRS Tax Statistics Search Includes a wide range of tables, articles, and data that describe and measure elements of the U.S. tax system.
• National Center for Charitable Statistics National repository of data on the nonprofit sector in the United States; provides high quality data on nonprofit organizations and their activities.
• National Center for Education Statistics (NCES) Fulfills a Congressional mandate to collect, collate, analyze, and report complete statistics on the condition of American education; conduct and publish reports; and review and report on education activities internationally.
• National Center for Health Statistics Statistics from the U.S. Dept. of Health and Human Services.
• Organization for Economic Co-operation and Development Data on key economic indicators such as GDP, inflation, unemployment, government debt and deficit.
• Statistics on Child and Family Well-Being Resources provide State and national statistics on child and family well-being indicators, such as health, child care, education, income, and marriage.
• U.S. Census Bureau Data on population & housing, economy, and demographics. Easy Stats gives you quick and easy access to selected statistics collected by the U.S. Census Bureau through the American Community Survey.
• U.S. Department of Commerce Responsibilities of this Department include trade, economic development, technology, entrepreneurship and business development, environmental stewardship, and statistical research and analysis.
• U.S. Energy Information Administration Provides information and data covering energy production, stocks, demand, imports, exports, and prices.
• U.S. Statistical Abstract Authoritative and comprehensive summary of statistics on the social, political, and economic organization of the United States.
• USAGov Find data about the U.S., such as maps and population, demographic, and economic data.
• USDA Economic Research Service Mission is to anticipate trends and emerging issues in agriculture, food, the environment, and rural America and to conduct high-quality, objective economic research to inform and enhance public and private decision making.
• USDA National Agricultural Statistics Service Conducts hundreds of surveys every year and prepares reports covering virtually every aspect of U.S. agriculture. Production and supplies of food and fiber, prices paid and received by farmers, farm labor and wages, farm finances, chemical use, and changes in the demographics of U.S. producers are only a few examples.
• AidData Research lab at William & Mary's Global Research Institute that equips policymakers and practitioners with better evidence to improve how sustainable development investments are targeted, monitored, and evaluated.
• CIA World Factbook Provides information on the history, people, government, economy, geography, communications, transportation, military, and transnational issues for 267 world entities.
• DataBank Analysis and visualisation tool that contains collections of time series data on a variety of topics. You can create your own queries; generate tables, charts, and maps; and easily save, embed, and share them.
• EasyData Comprehensive collection of South African macroeconomic, industry, trade and regional indicators.
• Eurostat The statistical office of the European Union situated in Luxembourg. Its mission is to provide high quality statistics for Europe.
• FAOSTAT Provides free access to food and agriculture data for over 245 countries and territories and covers all FAO regional groupings from 1961 to the most recent year available.
• Food and Agricultural Organization of the United Nations Dedicated to collecting, analysing, interpreting and disseminating food and agriculture statistics that are relevant for decision-making.
• Gallup.com Global statistics on employee well-being and engagement, and trust in leadership of organizations as well as country leaders.
• Global Health Observatory World Health Organization's gateway to health-related statistics for more than 1000 indicators.
• Google Public Data Takes large data sets and makes them palatable for public consumption, taking numbers, figures and other data and turning them into bar graphs, line graphs, maps and bubbles.
• ILOSTAT Compiles and produces labor statistics, with the goal of disseminating internationally-comparable datasets through a variety of data tools.
• IMF Data International Monetary Fund Statistical Databases include International Financial Statistics, Direction of Trade Statistics, Government Finance Statistics, and Balance of Payments Statistics.
• International Computing Centre Leading provider of Information Technology and Communications (ICT) services within the United Nations System.
• International Data Base Find demographic indicators, population pyramids, and source information for countries and areas of the world with a population of 5,000 or more.
• International Energy Agency Work spans a variety of programs and initiatives, helping ensure energy security, tracking clean energy transitions, collecting data, or providing training around the world.
• International Labour Organization (ILO) Provides statistics for international labor market for a range of indicators by country.
• OECD Statistics Statistical online platform of the Organisation for Economic Co-operation and Development where users can search and access OECD’s statistical databases.
• Organization for Economic Cooperation and Development Works on establishing evidence-based international standards and finding solutions to a range of social, economic and environmental challenges.
• Trade Map Provides (in the form of tables, graphs and maps) indicators on export performance, international demand, alternative markets and competitive markets, as well as a directory of importing and exporting companies.
• UN Comtrade Database Free access to detailed global trade data. UN Comtrade is a repository of official international trade statistics and relevant analytical tables.
• UNdata Search a variety of statistical resources compiled by the United Nations (UN) statistical system and other international agencies. Covers a wide range of statistical themes including agriculture, crime, communication, development assistance, education, energy, environment, finance, gender, health, labour market, manufacturing, national accounts, population and migration, science and technology, tourism, transport and trade.
• UN Economic Commission for Europe (UNECE) Facilitates greater economic integration and cooperation among its member countries and promotes sustainable development and economic prosperity.
• UNESCO Institute for Statistics Official and trusted source of internationally-comparable data on education, science, culture and communication. Browse stats by theme, indicator, or country.
• UNIDO Statistics Data Portal Provides online access to different sets of data compiled by the UN Industrial Development Organization. While some data is available for the public, access to all datasets and variables is limited to registered users.
• World Bank Open Data Free and open access to global development data. Browser by indicator to view the Education statistics.
• World Statistics Site gives free and easy access to data provided by International Organisations, such as the World Bank, the United Nations and Eurostat.
• National Statistical Agencies of Other Countries Directory maintained by the U.S. Bureau of Labor Statistics.
• National Statistical Offices Websites Website directory maintained by the United Nations Statistics Division.
• United Nations Statistics Division: Country Profiles Central repository of country profiles of statistical systems. Includes a brief history of the country's statistical system, legal basis, the statistical programme and much more.

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• Indian J Crit Care Med
• v.23(Suppl 3); 2019 Sep

An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors

Priya ranganathan.

1 Department of Anesthesiology, Critical Care and Pain, Tata Memorial Hospital, Mumbai, Maharashtra, India

2 Department of Surgical Oncology, Tata Memorial Centre, Mumbai, Maharashtra, India

The second article in this series on biostatistics covers the concepts of sample, population, research hypotheses and statistical errors.

How to cite this article

Ranganathan P, Pramesh CS. An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors. Indian J Crit Care Med 2019;23(Suppl 3):S230–S231.

Two papers quoted in this issue of the Indian Journal of Critical Care Medicine report. The results of studies aim to prove that a new intervention is better than (superior to) an existing treatment. In the ABLE study, the investigators wanted to show that transfusion of fresh red blood cells would be superior to standard-issue red cells in reducing 90-day mortality in ICU patients. 1 The PROPPR study was designed to prove that transfusion of a lower ratio of plasma and platelets to red cells would be superior to a higher ratio in decreasing 24-hour and 30-day mortality in critically ill patients. 2 These studies are known as superiority studies (as opposed to noninferiority or equivalence studies which will be discussed in a subsequent article).

SAMPLE VERSUS POPULATION

A sample represents a group of participants selected from the entire population. Since studies cannot be carried out on entire populations, researchers choose samples, which are representative of the population. This is similar to walking into a grocery store and examining a few grains of rice or wheat before purchasing an entire bag; we assume that the few grains that we select (the sample) are representative of the entire sack of grains (the population).

The results of the study are then extrapolated to generate inferences about the population. We do this using a process known as hypothesis testing. This means that the results of the study may not always be identical to the results we would expect to find in the population; i.e., there is the possibility that the study results may be erroneous.

HYPOTHESIS TESTING

A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the “alternate” hypothesis, and the opposite is called the “null” hypothesis; every study has a null hypothesis and an alternate hypothesis. For superiority studies, the alternate hypothesis states that one treatment (usually the new or experimental treatment) is superior to the other; the null hypothesis states that there is no difference between the treatments (the treatments are equal). For example, in the ABLE study, we start by stating the null hypothesis—there is no difference in mortality between groups receiving fresh RBCs and standard-issue RBCs. We then state the alternate hypothesis—There is a difference between groups receiving fresh RBCs and standard-issue RBCs. It is important to note that we have stated that the groups are different, without specifying which group will be better than the other. This is known as a two-tailed hypothesis and it allows us to test for superiority on either side (using a two-sided test). This is because, when we start a study, we are not 100% certain that the new treatment can only be better than the standard treatment—it could be worse, and if it is so, the study should pick it up as well. One tailed hypothesis and one-sided statistical testing is done for non-inferiority studies, which will be discussed in a subsequent paper in this series.

STATISTICAL ERRORS

There are two possibilities to consider when interpreting the results of a superiority study. The first possibility is that there is truly no difference between the treatments but the study finds that they are different. This is called a Type-1 error or false-positive error or alpha error. This means falsely rejecting the null hypothesis.

The second possibility is that there is a difference between the treatments and the study does not pick up this difference. This is called a Type 2 error or false-negative error or beta error. This means falsely accepting the null hypothesis.

The power of the study is the ability to detect a difference between groups and is the converse of the beta error; i.e., power = 1-beta error. Alpha and beta errors are finalized when the protocol is written and form the basis for sample size calculation for the study. In an ideal world, we would not like any error in the results of our study; however, we would need to do the study in the entire population (infinite sample size) to be able to get a 0% alpha and beta error. These two errors enable us to do studies with realistic sample sizes, with the compromise that there is a small possibility that the results may not always reflect the truth. The basis for this will be discussed in a subsequent paper in this series dealing with sample size calculation.

Conventionally, type 1 or alpha error is set at 5%. This means, that at the end of the study, if there is a difference between groups, we want to be 95% certain that this is a true difference and allow only a 5% probability that this difference has occurred by chance (false positive). Type 2 or beta error is usually set between 10% and 20%; therefore, the power of the study is 90% or 80%. This means that if there is a difference between groups, we want to be 80% (or 90%) certain that the study will detect that difference. For example, in the ABLE study, sample size was calculated with a type 1 error of 5% (two-sided) and power of 90% (type 2 error of 10%) (1).

Table 1 gives a summary of the two types of statistical errors with an example

Statistical errors

In the next article in this series, we will look at the meaning and interpretation of ‘ p ’ value and confidence intervals for hypothesis testing.

Source of support: Nil

Conflict of interest: None

• Why Study Statistics?
• Descriptive & Inferential Statistics
• Fundamental Elements of Statistics
• Quantitative and Qualitative Data
• Measurement Data Levels
• Collecting Data
• Ethics in Statistics
• Describing Qualitative Data
• Describing Quantitative Data
• Stem-and-Leaf Plots
• Measures of Central Tendency
• Measures of Variability
• Describing Data using the Mean and Standard Deviation
• Measures of Position
• Counting Techniques
• Simple & Compound Events
• Independent and Dependent Events
• Mutually Exclusive and Non-Mutually Exclusive Events
• Permutations and Combinations
• Normal Distribution
• Central Limit Theorem
• Confidence Intervals
• Determining the Sample Size
• Hypothesis Testing
• Hypothesis Testing Process

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

Statistics is an exciting field about the thrill of discovery, learning, and challenging your assumptions. Statistics facilitates the creation of new knowledge. Bit by bit, we push back the frontier of what is known. 

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• URL: https://libraryguides.centennialcollege.ca/c.php?g=717168

Statistics, Its Importance and Application Essay

• To find inspiration for your paper and overcome writer’s block
• As a source of information (ensure proper referencing)
• As a template for you assignment

Importance of Statistics

Examples of how statistics can be used.

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

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

Two subdivisions of the statistical method are:

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

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

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

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

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

To Ensure Quality

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

Making Connections

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

Backing Judgment

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

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

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

• Descriptive and Inferential Statistical Tests
• Essentials of Statistics for the Behavioural Sciences
• Descriptive Statistics and Probability
• Descriptive Statistics in Nursing
• Descriptive Statistics Method: Household Income Analysis
• Hypothesis Testing in Practical Statistics
• Applied Statistics for Healthcare Professionals
• Time Series and Causal Models in Forecasting
• Study Hours and Grades in Educational Institutions
• The Repeated-Measures ANOVA in a General Context
• Chicago (A-D)
• Chicago (N-B)

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• Knowledge Base

An Easy Introduction to Statistical Significance (With Examples)

Published on January 7, 2021 by Pritha Bhandari . Revised on June 22, 2023.

If a result is statistically significant , that means it’s unlikely to be explained solely by chance or random factors. In other words, a statistically significant result has a very low chance of occurring if there were no true effect in a research study.

The p value , or probability value, tells you the statistical significance of a finding. In most studies, a p value of 0.05 or less is considered statistically significant, but this threshold can also be set higher or lower.

Table of contents

How do you test for statistical significance, what is a significance level, problems with relying on statistical significance, other types of significance in research, other interesting articles, frequently asked questions about statistical significance.

In quantitative research , data are analyzed through null hypothesis significance testing, or hypothesis testing. This is a formal procedure for assessing whether a relationship between variables or a difference between groups is statistically significant.

Null and alternative hypotheses

To begin, research predictions are rephrased into two main hypotheses: the null and alternative hypothesis .

• A null hypothesis ( H 0 ) always predicts no true effect, no relationship between variables , or no difference between groups.
• An alternative hypothesis ( H a or H 1 ) states your main prediction of a true effect, a relationship between variables, or a difference between groups.

Hypothesis testin g always starts with the assumption that the null hypothesis is true. Using this procedure, you can assess the likelihood (probability) of obtaining your results under this assumption. Based on the outcome of the test, you can reject or retain the null hypothesis.

• H 0 : There is no difference in happiness between actively smiling and not smiling.
• H a : Actively smiling leads to more happiness than not smiling.

Test statistics and p values

Every statistical test produces:

• A test statistic that indicates how closely your data match the null hypothesis.
• A corresponding p value that tells you the probability of obtaining this result if the null hypothesis is true.

The p value determines statistical significance. An extremely low p value indicates high statistical significance, while a high p value means low or no statistical significance.

Next, you perform a t test to see whether actively smiling leads to more happiness. Using the difference in average happiness between the two groups, you calculate:

• a t value (the test statistic) that tells you how much the sample data differs from the null hypothesis,
• a p value showing the likelihood of finding this result if the null hypothesis is true.

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The significance level , or alpha (α), is a value that the researcher sets in advance as the threshold for statistical significance. It is the maximum risk of making a false positive conclusion ( Type I error ) that you are willing to accept .

In a hypothesis test, the  p value is compared to the significance level to decide whether to reject the null hypothesis.

• If the p value is  higher than the significance level, the null hypothesis is not refuted, and the results are not statistically significant .
• If the p value is lower than the significance level, the results are interpreted as refuting the null hypothesis and reported as statistically significant .

Usually, the significance level is set to 0.05 or 5%. That means your results must have a 5% or lower chance of occurring under the null hypothesis to be considered statistically significant.

The significance level can be lowered for a more conservative test. That means an effect has to be larger to be considered statistically significant.

The significance level may also be set higher for significance testing in non-academic marketing or business contexts. This makes the study less rigorous and increases the probability of finding a statistically significant result.

As best practice, you should set a significance level before you begin your study. Otherwise, you can easily manipulate your results to match your research predictions.

It’s important to note that hypothesis testing can only show you whether or not to reject the null hypothesis in favor of the alternative hypothesis. It can never “prove” the null hypothesis, because the lack of a statistically significant effect doesn’t mean that absolutely no effect exists.

When reporting statistical significance, include relevant descriptive statistics about your data (e.g., means and standard deviations ) as well as the test statistic and p value.

There are various critiques of the concept of statistical significance and how it is used in research.

Researchers classify results as statistically significant or non-significant using a conventional threshold that lacks any theoretical or practical basis. This means that even a tiny 0.001 decrease in a p value can convert a research finding from statistically non-significant to significant with almost no real change in the effect.

On its own, statistical significance may also be misleading because it’s affected by sample size. In extremely large samples , you’re more likely to obtain statistically significant results, even if the effect is actually small or negligible in the real world. This means that small effects are often exaggerated if they meet the significance threshold, while interesting results are ignored when they fall short of meeting the threshold.

The strong emphasis on statistical significance has led to a serious publication bias and replication crisis in the social sciences and medicine over the last few decades. Results are usually only published in academic journals if they show statistically significant results—but statistically significant results often can’t be reproduced in high quality replication studies.

As a result, many scientists call for retiring statistical significance as a decision-making tool in favor of more nuanced approaches to interpreting results.

That’s why APA guidelines advise reporting not only p values but also  effect sizes and confidence intervals wherever possible to show the real world implications of a research outcome.

Aside from statistical significance, clinical significance and practical significance are also important research outcomes.

Practical significance shows you whether the research outcome is important enough to be meaningful in the real world. It’s indicated by the effect size of the study.

Clinical significance is relevant for intervention and treatment studies. A treatment is considered clinically significant when it tangibly or substantially improves the lives of patients.

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

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

A p -value , or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test .

P -values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p -value tables for the relevant test statistic .

P -values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.

If the test statistic is far from the mean of the null distribution, then the p -value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.

No. The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis .

If the p -value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.

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What Is Statistics?

• First Online: 10 December 2017

Cite this chapter

• Christopher J. Wild 4 ,
• Jessica M. Utts 5 &
• Nicholas J. Horton 6  

Part of the book series: Springer International Handbooks of Education ((SIHE))

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What is statistics? We attempt to answer this question as it relates to grounding research in statistics education. We discuss the nature of statistics as the science of learning from data, its history and traditions, what characterizes statistical thinking and how it differs from mathematics, connections with computing and data science, why learning statistics is essential, and what is most important. Finally, we attempt to gaze into the future, drawing upon what is known about the fast-growing demand for statistical skills and the portents of where the discipline is heading, especially those arising from data science and the promises and problems of big data.

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Wild, C.J., Utts, J.M., Horton, N.J. (2018). What Is Statistics?. In: Ben-Zvi, D., Makar, K., Garfield, J. (eds) International Handbook of Research in Statistics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-319-66195-7_1

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How to Write a Research Proposal: (with Examples & Templates)

Table of Contents

Before conducting a study, a research proposal should be created that outlines researchers’ plans and methodology and is submitted to the concerned evaluating organization or person. Creating a research proposal is an important step to ensure that researchers are on track and are moving forward as intended. A research proposal can be defined as a detailed plan or blueprint for the proposed research that you intend to undertake. It provides readers with a snapshot of your project by describing what you will investigate, why it is needed, and how you will conduct the research.  

Your research proposal should aim to explain to the readers why your research is relevant and original, that you understand the context and current scenario in the field, have the appropriate resources to conduct the research, and that the research is feasible given the usual constraints.  

This article will describe in detail the purpose and typical structure of a research proposal , along with examples and templates to help you ace this step in your research journey.  

What is a Research Proposal ?  

A research proposal¹ ,²  can be defined as a formal report that describes your proposed research, its objectives, methodology, implications, and other important details. Research proposals are the framework of your research and are used to obtain approvals or grants to conduct the study from various committees or organizations. Consequently, research proposals should convince readers of your study’s credibility, accuracy, achievability, practicality, and reproducibility.   

With research proposals , researchers usually aim to persuade the readers, funding agencies, educational institutions, and supervisors to approve the proposal. To achieve this, the report should be well structured with the objectives written in clear, understandable language devoid of jargon. A well-organized research proposal conveys to the readers or evaluators that the writer has thought out the research plan meticulously and has the resources to ensure timely completion.  

Purpose of Research Proposals  

A research proposal is a sales pitch and therefore should be detailed enough to convince your readers, who could be supervisors, ethics committees, universities, etc., that what you’re proposing has merit and is feasible . Research proposals can help students discuss their dissertation with their faculty or fulfill course requirements and also help researchers obtain funding. A well-structured proposal instills confidence among readers about your ability to conduct and complete the study as proposed.  

Research proposals can be written for several reasons:³  

• To describe the importance of research in the specific topic  
• Address any potential challenges you may encounter  
• Showcase knowledge in the field and your ability to conduct a study  
• Apply for a role at a research institute  
• Convince a research supervisor or university that your research can satisfy the requirements of a degree program  
• Highlight the importance of your research to organizations that may sponsor your project  
• Identify implications of your project and how it can benefit the audience  

What Goes in a Research Proposal?    

Research proposals should aim to answer the three basic questions—what, why, and how.  

The What question should be answered by describing the specific subject being researched. It should typically include the objectives, the cohort details, and the location or setting.  

The Why question should be answered by describing the existing scenario of the subject, listing unanswered questions, identifying gaps in the existing research, and describing how your study can address these gaps, along with the implications and significance.  

The How question should be answered by describing the proposed research methodology, data analysis tools expected to be used, and other details to describe your proposed methodology.   

Research Proposal Example  

Here is a research proposal sample template (with examples) from the University of Rochester Medical Center. 4 The sections in all research proposals are essentially the same although different terminology and other specific sections may be used depending on the subject.  

Structure of a Research Proposal  

If you want to know how to make a research proposal impactful, include the following components:¹  

1. Introduction  

This section provides a background of the study, including the research topic, what is already known about it and the gaps, and the significance of the proposed research.  

2. Literature review  

This section contains descriptions of all the previous relevant studies pertaining to the research topic. Every study cited should be described in a few sentences, starting with the general studies to the more specific ones. This section builds on the understanding gained by readers in the Introduction section and supports it by citing relevant prior literature, indicating to readers that you have thoroughly researched your subject.  

3. Objectives  

Once the background and gaps in the research topic have been established, authors must now state the aims of the research clearly. Hypotheses should be mentioned here. This section further helps readers understand what your study’s specific goals are.  

4. Research design and methodology  

Here, authors should clearly describe the methods they intend to use to achieve their proposed objectives. Important components of this section include the population and sample size, data collection and analysis methods and duration, statistical analysis software, measures to avoid bias (randomization, blinding), etc.  

5. Ethical considerations  

This refers to the protection of participants’ rights, such as the right to privacy, right to confidentiality, etc. Researchers need to obtain informed consent and institutional review approval by the required authorities and mention this clearly for transparency.  

6. Budget/funding  

Researchers should prepare their budget and include all expected expenditures. An additional allowance for contingencies such as delays should also be factored in.  

7. Appendices  

This section typically includes information that supports the research proposal and may include informed consent forms, questionnaires, participant information, measurement tools, etc.  

8. Citations  

Important Tips for Writing a Research Proposal  

Writing a research proposal begins much before the actual task of writing. Planning the research proposal structure and content is an important stage, which if done efficiently, can help you seamlessly transition into the writing stage. 3,5  

The Planning Stage  

• Manage your time efficiently. Plan to have the draft version ready at least two weeks before your deadline and the final version at least two to three days before the deadline.
• What is the primary objective of your research?  
• Will your research address any existing gap?  
• What is the impact of your proposed research?  
• Do people outside your field find your research applicable in other areas?  
• If your research is unsuccessful, would there still be other useful research outcomes?  

  The Writing Stage  

• Create an outline with main section headings that are typically used.  
• Focus only on writing and getting your points across without worrying about the format of the research proposal , grammar, punctuation, etc. These can be fixed during the subsequent passes. Add details to each section heading you created in the beginning.   
• Ensure your sentences are concise and use plain language. A research proposal usually contains about 2,000 to 4,000 words or four to seven pages.  
• Don’t use too many technical terms and abbreviations assuming that the readers would know them. Define the abbreviations and technical terms.  
• Ensure that the entire content is readable. Avoid using long paragraphs because they affect the continuity in reading. Break them into shorter paragraphs and introduce some white space for readability.  
• Focus on only the major research issues and cite sources accordingly. Don’t include generic information or their sources in the literature review.  
• Proofread your final document to ensure there are no grammatical errors so readers can enjoy a seamless, uninterrupted read.  
• Use academic, scholarly language because it brings formality into a document.  
• Ensure that your title is created using the keywords in the document and is neither too long and specific nor too short and general.  
• Cite all sources appropriately to avoid plagiarism.  
• Make sure that you follow guidelines, if provided. This includes rules as simple as using a specific font or a hyphen or en dash between numerical ranges.  
• Ensure that you’ve answered all questions requested by the evaluating authority.  

Key Takeaways   

Here’s a summary of the main points about research proposals discussed in the previous sections:  

• A research proposal is a document that outlines the details of a proposed study and is created by researchers to submit to evaluators who could be research institutions, universities, faculty, etc.  
• Research proposals are usually about 2,000-4,000 words long, but this depends on the evaluating authority’s guidelines.  
• A good research proposal ensures that you’ve done your background research and assessed the feasibility of the research.  
• Research proposals have the following main sections—introduction, literature review, objectives, methodology, ethical considerations, and budget.  

Frequently Asked Questions  

Q1. How is a research proposal evaluated?  

A1. In general, most evaluators, including universities, broadly use the following criteria to evaluate research proposals . 6  

• Significance —Does the research address any important subject or issue, which may or may not be specific to the evaluator or university?  
• Content and design —Is the proposed methodology appropriate to answer the research question? Are the objectives clear and well aligned with the proposed methodology?  
• Sample size and selection —Is the target population or cohort size clearly mentioned? Is the sampling process used to select participants randomized, appropriate, and free of bias?  
• Timing —Are the proposed data collection dates mentioned clearly? Is the project feasible given the specified resources and timeline?  
• Data management and dissemination —Who will have access to the data? What is the plan for data analysis?  

Q2. What is the difference between the Introduction and Literature Review sections in a research proposal ?  

A2. The Introduction or Background section in a research proposal sets the context of the study by describing the current scenario of the subject and identifying the gaps and need for the research. A Literature Review, on the other hand, provides references to all prior relevant literature to help corroborate the gaps identified and the research need.  

Q3. How long should a research proposal be?  

A3. Research proposal lengths vary with the evaluating authority like universities or committees and also the subject. Here’s a table that lists the typical research proposal lengths for a few universities.  

Q4. What are the common mistakes to avoid in a research proposal ?  

A4. Here are a few common mistakes that you must avoid while writing a research proposal . 7  

• No clear objectives: Objectives should be clear, specific, and measurable for the easy understanding among readers.  
• Incomplete or unconvincing background research: Background research usually includes a review of the current scenario of the particular industry and also a review of the previous literature on the subject. This helps readers understand your reasons for undertaking this research because you identified gaps in the existing research.  
• Overlooking project feasibility: The project scope and estimates should be realistic considering the resources and time available.   
• Neglecting the impact and significance of the study: In a research proposal , readers and evaluators look for the implications or significance of your research and how it contributes to the existing research. This information should always be included.  
• Unstructured format of a research proposal : A well-structured document gives confidence to evaluators that you have read the guidelines carefully and are well organized in your approach, consequently affirming that you will be able to undertake the research as mentioned in your proposal.  
• Ineffective writing style: The language used should be formal and grammatically correct. If required, editors could be consulted, including AI-based tools such as Paperpal , to refine the research proposal structure and language.  

Thus, a research proposal is an essential document that can help you promote your research and secure funds and grants for conducting your research. Consequently, it should be well written in clear language and include all essential details to convince the evaluators of your ability to conduct the research as proposed.  

This article has described all the important components of a research proposal and has also provided tips to improve your writing style. We hope all these tips will help you write a well-structured research proposal to ensure receipt of grants or any other purpose.  

References  

• Sudheesh K, Duggappa DR, Nethra SS. How to write a research proposal? Indian J Anaesth. 2016;60(9):631-634. Accessed July 15, 2024. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5037942/  
• Writing research proposals. Harvard College Office of Undergraduate Research and Fellowships. Harvard University. Accessed July 14, 2024. https://uraf.harvard.edu/apply-opportunities/app-components/essays/research-proposals  
• What is a research proposal? Plus how to write one. Indeed website. Accessed July 17, 2024. https://www.indeed.com/career-advice/career-development/research-proposal  
• Research proposal template. University of Rochester Medical Center. Accessed July 16, 2024. https://www.urmc.rochester.edu/MediaLibraries/URMCMedia/pediatrics/research/documents/Research-proposal-Template.pdf  
• Tips for successful proposal writing. Johns Hopkins University. Accessed July 17, 2024. https://research.jhu.edu/wp-content/uploads/2018/09/Tips-for-Successful-Proposal-Writing.pdf  
• Formal review of research proposals. Cornell University. Accessed July 18, 2024. https://irp.dpb.cornell.edu/surveys/survey-assessment-review-group/research-proposals  
• 7 Mistakes you must avoid in your research proposal. Aveksana (via LinkedIn). Accessed July 17, 2024. https://www.linkedin.com/pulse/7-mistakes-you-must-avoid-your-research-proposal-aveksana-cmtwf/  

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Get accurate academic translations, rewriting support, grammar checks, vocabulary suggestions, and generative AI assistance that delivers human precision at machine speed. Try for free or upgrade to Paperpal Prime starting at US$19 a month to access premium features, including consistency, plagiarism, and 30+ submission readiness checks to help you succeed.  

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Journal articles are the academic's stock in trade, t he basic means of communicating research findings to an audience of one’s peers. That holds true across the disciplinary spectrum, so no matter where you land as a concentrator, you can expect to rely on them heavily. 

Regardless of the discipline, moreover,  journal articles perform an important knowledge-updating function .

Textbooks and handbooks and manuals will have a secondary function for chemists and physicists and biologists, of course. But in the sciences, articles are the standard and  preferred publication form. 

In the social sciences and humanities , where knowledge develops a little less rapidly or is driven less by issues of time-sensitivity , journal articles and books are more often used together.

Not all important and influential ideas warrant book-length studies, and some inquiry is just better suited to the size and scope and concentrated discussion that the article format offers.

Journal articles sometimes just present the most  appropriate  solution for communicating findings or making a convincing argument.  A 20-page article may perfectly fit a researcher's needs.  Sustaining that argument for 200 pages might be unnecessary -- or impossible.

The quality of a research article and the legitimacy of its findings are verified by other scholars, prior to publication, through a rigorous evaluation method called peer-review . This seal of approval by other scholars doesn't mean that an article is the best, or truest, or last word on a topic. If that were the case, research on lots of things would cease. Peer review simply means other experts believe the methods, the evidence, the conclusions of an article have met important standards of legitimacy, reliability, and intellectual honesty.

Searching the journal literature is part of being a responsible researcher at any level: professor, grad student, concentrator, first-year. Knowing why academic articles matter will help you make good decisions about what you find -- and what you choose to rely on in your work.

Think of journal articles as the way you tap into the ongoing scholarly conversation , as a way of testing the currency of  a finding, analysis, or argumentative position, and a way of bolstering the authority (or plausibility) of explanations you'll offer in the papers and projects you'll complete at Harvard. 

• Next: Subject Databases: Organizing Research Conversations >>

Except where otherwise noted, this work is subject to a Creative Commons Attribution 4.0 International License , which allows anyone to share and adapt our material as long as proper attribution is given. For details and exceptions, see the Harvard Library Copyright Policy ©2021 Presidents and Fellows of Harvard College.

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What Research Says About Being a Stay-at-Home Parent

Ask people what they think about  stay-at-home moms  (SAHMs) and stay-at-home parents in general, and you'll likely get a variety of answers. Some might say they've got it easy, or that life at home with the kids would be boring. Some might think they're lazy or not contributing much to society. Others contend that stay-at-home parents are making the best decision of their lives and that they're making a noble, worthwhile sacrifice to stay home and nurture their kids day in and day out.

If you're contemplating whether or not to be a stay-at-home parent, what matters most is what works best for your family. So, first and foremost, consider your personal beliefs, priorities, finances, and lifestyle. However, there is also a wealth of research on the subject that you can consult when making your decision. The findings on life as a stay-at-home parent may surprise you.

Brianna Gilmartin

Pros and Cons of Staying at Home

There are, of course, many personal reasons for or against staying home with your kids. Benefits may include more opportunities for quality time with your children and having more direction over their learning and development. You may not want to miss a minute of their childhoods. You also might not trust others to care for your little loves. Drawbacks include the big hit to your family's income and the trajectory of your career as well as the big change to your lifestyle.

While there is no right or wrong answer, this research may help inform your choice. Remember that each of these benefits and drawbacks may or may not apply to you. There are many different factors, such as budget, lifestyle, priorities, social support, relationship status, spousal involvement, and your kids' specific needs, to consider before making your final decision.

Evidence-Based Benefits of Being a Stay-At-Home-Parent

There are many reasons that parents choose to stay at home with their children. Studies have shown that many people think this is the best option for kids when financially plausible. According to a Pew Research Center study, about 18% of American parents stayed home with their children in 2021.

According to Pew Research Center's Social and Demographic Trends, 60% of Americans say a child is better off with at least one parent at home. While 35% of responders said that kids are just as well off with both parents working outside the home.

Benefits for Children of Stay-at-Home-Parents

A 2014 study found that the benefits of having a parent at home extend beyond the early years of a child's life. The study measured the educational performance of 68,000 children. Researchers found an increase in school performance to high school-aged children. However, the biggest educational impact was on kids ages 6 and 7.

Most  homeschooled students  also have an at-home parent instructing them. A compilation of studies provided by the National Home Education Research Institute supports the benefits of a parent at home for educational reasons. Some research has found homeschoolers generally score 15 to 30 percentile points above public school students on standardized tests and achieve above-average scores on the ACT and SATs.

Regardless of whether parents stay home or work outside the home, research shows that parent involvement in schools makes a difference in children's academic performance and how long they stay in school.  Some kids with learning differences and/or special needs may do better in a school (vs. homeschooling) to access any required services .

Decreased Stress and Aggression in Kids

Some studies link childcare with increased behavioral problems and suggest that being at home with your children offers benefits to their development compared with them being in  being in childcare  full-time.  This may be reassuring news for stay-at-home parents knee-deep in diapers and temper tantrums.

Studies have found that children who spend a large amount of their day in daycare experience high stress levels, particularly at times of transition, like drop-off and pick-up.

Subsequent studies also showed higher levels of stress in children in childcare settings compared with those who are cared for at home. But that doesn't mean you have to keep your children with you every minute until they're ready to go to school. Look for a nanny or babysitting co-op that allows your kids to play with others while giving you some time alone.

Greater Control of Children's Upbringing

The ability to directly protect, spend time with, and nurture their children each day is often cited as a primary benefit of not working outside the home. Studies show that some parents stay home specifically to have greater first-hand control over the influences their child is exposed to. Others simply see it as their duty to be the one who provides daily care to their little ones.

More Parents Want to Stay Home

According to the Pew Research Center, more people are becoming stay-at-home parents—and 60% of Americans believe that choice is best for children. The number of stay-at-home parents jumped from a low of 23% in 1999 to 29% in less than 15 years. However, today's rates don't match those of the 1970s and earlier when around 50% of women (and very few men) were stay-at-home parents.

While the number of men taking on this role is far lower than that of women (around 210,000 compared with over 5.2 million), the rate of men becoming stay-at-home dads is on an upswing, too. Between 2010 and 2014, the prevalence of men choosing to stay home increased by 37%.

Downsides of Being a Stay-at-Home Parent

Regardless of the increasing numbers and some important benefits, a decision to quit your job to become a stay-at-home parent shouldn't be made out of guilt or peer pressure. While there are many great reasons to be a stay-at-home parent, it's not necessarily right or beneficial (or financially plausible) for everyone. For some families, the drawbacks significantly outweigh any positives.

Some People Miss Working

Research shows that many stay-at-home parents miss working outside the home and think about  going back to work  someday.  It can be tough to leave behind the tangible rewards and results of a job, especially one you enjoyed and were good at.

If you stay home when your kids are little but plan to return to the workforce, you can take some steps to bridge that employment gap, such as taking classes, earning licenses or certificates that enhance your resume, or even taking a part-time job.  You might also consider at-home business opportunities as well as  remote jobs  that let you stay home while also earning money and reclaiming some of what you missed about your career.

Costs to Your Career and Wallet

The decision to stay at home with your kids means giving up income. Research shows that stay-at-home parents must contend with lost wages now and decreased wages when returning to work. This "wage penalty" often amounts to 40% less in earned income over time.

There is also a big hit to the stay-at-home parent's career trajectory. Some parents can regain their previous work roles upon reentering the workforce, while others struggle to get a foothold professionally after taking time off.

The direct impact on your family's finances will depend on your personal earning potential, skills, and career choices—as well as the income of your partner if you have one. However, studies show that mothers who reenter work after having children experience between a 5% and 10% pay gap compared with their childless peers. This is in addition to the gender pay gap.

Adverse Impacts on Physical and Mental Health

Studies show that stay-at-home parents experience poorer physical and mental health compared with parents who work outside the home. Effects include higher rates of mental health conditions, such as depression and anxiety, as well as higher rates of chronic illness. A 2012 Gallup poll surveyed 60,000 women including women with no children, working moms, and stay-at-home moms who were or were not looking for work, and found more negative feelings among SAHMs. There are likely several reasons for this, including experiencing more parental and financial stress. Working parents tend to have access to more robust health insurance plans than stay-at-home parents. They also tend to benefit from greater self-worth, personal control over their life, economic security, and more dynamic socio-economic support.

However, it's worth noting that significant research shows that whether they work outside the home or not, parents generally are less happy than their childless counterparts.  Of course, the joy you get from parenting (and staying home with the kids) is likely to be highly individual.

More Social Isolation

A 2015 study found that many moms are spending lots of time with their kids, more so than in years past. Researchers believe this extra kid-focus results in a higher potential for social isolation. Interestingly, the research found no scientifically proven difference in outcomes for the children with this additional parental attention.

Some stay-at-home parents may feel isolated or undervalued by what some call the " mommy wars, " which pit parents against each other. This social dynamic can create perceived judgments or pressures that leave some stay-at-home parents feeling like they're not respected as worthy members of society. On the flip side, some working parents may feel criticized for not spending as much time with their children. Both groups can end up feeling socially isolated.

A 2021 study found that around a third of all parents experience loneliness. That's why it's so important for all parents (whether they stay at home or work outside the home) to find the right balance of social activities, exercise, sleep, hobbies, and self-care. Additionally, it's helpful to make the most of your family time, including  creating gadget-free zones  and planning fun activities you can all enjoy.

It's also key to take care of your own emotional well-being and let your children spend some time away from you. Whether it's a date night with your spouse or scheduling a day off so you can have some alone time, you're not going to shortchange your child because you didn't spend every minute with them. Giving yourself parenting breaks and opportunities to socialize is important for your well-being, particularly during times of stress.

Parenthood and well-being: A decade in review .  J Marriage Fam .

Stay at home moms and dads account for about 1-in-5 U.S. parents . Pew Research Center. 

After decades of decline, a rise in stay-at-home mothers . Pew Research Center. 

Home with mom: The effects of stay-at-home parents on children’s long-run educational outcomes .  J Labor Econ. 

National Home Education Research Institute.  Research facts on homeschooling .

Effect of parental involvement on children’s academic achievement in chile .  Front Psychol.  

School performance among children and adolescents during COVID-19 pandemic: A systematic review .  Children (Basel) .

The NICHD study of early child care and youth development . U.S. Department of Health and Human Services. 

Toddlers’ stress during transition to childcare .  European Early Childhood Education Research Journal .

Examining change in cortisol patterns during the 10-week transition to a new child-care setting .  Child Dev .

7 key findings about stay-at-home moms . Pew Research Center. 

The mother's perspective: Factors considered when choosing to enter a stay-at-home father and working mother relationship .  Am J Mens Health .

The relationships between mothers' work pathways and physical and mental health .  J Health Soc Behav .

The motherhood penalty at midlife: Long-term effects of children on women's careers .  J Marriage Fam .

Parents' work schedules and time spent with children .  Community Work Fam .

Gallup.  Stay-at-home moms report more depression, sadness, anger .

Parenthood and happiness: Effects of work-family reconciliation policies in 22 OECD countries .  AJS .

Does the amount of time mothers spend with children or adolescents matter? .  J Marriage Fam.

Experiencing loneliness in parenthood: A scoping review .  Perspect Public Health .

  First things first: Parent psychological flexibility and self-compassion during COVID-19.   Behav Anal Pract .

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What we know about unauthorized immigrants living in the U.S.

The unauthorized immigrant population in the United States grew to 11.0 million in 2022, according to new Pew Research Center estimates based on the 2022 American Community Survey, the most recent year available. The increase from 10.5 million in 2021 reversed a long-term downward trend from 2007 to 2019. This is the first sustained increase in the unauthorized immigrant population since the period from 2005 to 2007.

However, the number of unauthorized immigrants living in the U.S. in 2022 was still below the peak of 12.2 million in 2007.

Pew Research Center conducted this research to understand changes in the unauthorized immigrant population in the United States. The Center has published estimates of the U.S. unauthorized immigrant population for more than two decades. The estimates presented in this research for 2022 are the Center’s latest.

Center estimates of the unauthorized immigrant population use a “residual method.” It is similar to methods used by the U.S. Department of Homeland Security’s Office of Immigration Statistics and nongovernmental organizations, including the Center for Migration Studies and the Migration Policy Institute . Those organizations’ estimates are generally consistent with ours. Our estimates also align with official U.S. data sources, including birth records, school enrollment figures and tax data, as well as Mexican censuses and surveys.

Our residual method includes these steps:

• Estimate the total number of immigrants living in the country in a particular year using data from U.S. censuses and government surveys such as the American Community Survey and the Current Population Survey.
• Estimate the number of immigrants living in the U.S. legally using official counts of immigrant and refugee admissions together with other demographic data (for example, death and out-migration rates).
• Subtract our estimate of lawful immigrants from our estimate of the total immigrant population. This provides an initial estimate of the unauthorized immigrant population.

Our final estimate of the U.S. unauthorized immigrant population, as well as estimates for lawful immigrants, includes an upward adjustment. We do this because censuses and surveys tend to miss some people . Undercounts for immigrants, especially unauthorized immigrants, tend to be higher than for other groups. (Our 1990 estimate comes from work by Robert Warren and John Robert Warren .)

The term “unauthorized immigrant” reflects many academic researchers’ and policy analysts’ standard and customary usage. The U.S. Department of Homeland Security’s Office of Immigration Statistics also generally uses it. The term means the same thing as “undocumented immigrants,” “illegal immigrants” and “illegal aliens.”

For more details on how we produced our estimates, read the Methodology section of our November 2018 report on unauthorized immigrants.

The unauthorized immigrant population includes any immigrants not in the following groups:

• Immigrants admitted for lawful residence (i.e., green card admissions)
• People admitted formally as refugees
• People granted asylum
• Former unauthorized immigrants granted legal residence under the 1985 Immigration Reform and Control Act
• Immigrants admitted in categories 1-4 who have become naturalized U.S. citizens
• Individuals admitted as lawful temporary residents under specific visa categories, such as those for foreign students, guest workers and intracompany transfers.

Read the Methodology section of our November 2018 report on unauthorized immigrants for more details.

Pew Research Center’s estimate of unauthorized immigrants as of July 2022 includes more than 3 million immigrants who have temporary protection from deportation and permission to be in the United States. Some also have permission to work in the country. These immigrants account for almost 30% of our national estimate of 11.0 million unauthorized immigrants for 2022.

Although these immigrants have permission to be in the country, they could be subject to deportation if government policy changes. Other organizations and the federal government also include these immigrants in their estimates of the U.S. unauthorized immigrant population.

Unauthorized immigrants can receive temporary permission to be in the U.S. through the following:

Asylum applicants

Individuals who have applied for asylum and are awaiting a ruling are not legal residents but cannot be deported. There are two types of asylum claims, defensive and affirmative .

Defensive asylum applications are generally filed by individuals facing deportation or removal from the U.S. These are processed by the Department of Justice’s Executive Office for Immigration Review (EOIR). As of July 2022, there were about 915,000 individuals with applications pending.

Affirmative asylum claims are made by people who are not in the process of being deported or removed. These claims are handled by the Department of Homeland Security’s U.S. Citizenship and Immigration Services (USCIS). In mid-2022, about 720,000 individuals were awaiting decisions on more than 500,000 applications for affirmative asylum.

Temporary Protected Status (TPS)

As of July 2022, there were about 650,000 unauthorized immigrants with Temporary Protected Status . This status provides protection from removal or deportation to individuals who cannot safely return to their country because of civil unrest, violence or natural disaster.

Deferred Action for Childhood Arrivals (DACA)

Deferred Action for Childhood Arrivals (DACA) offers protection from deportation to individuals who were brought to the U.S. as children before 2007. In July 2022, there were about 595,000 active DACA beneficiaries , largely immigrants from Mexico.

Applicants for other visas

Many immigrants in the U.S. apply for visas to gain lawful immigrant status. In some cases, individuals awaiting decisions on these applications can remain in the country.

T and U visas are for victims of trafficking and certain criminal activities, including domestic violence, sexual assault, hate crimes and involuntary servitude. In mid-2022, the backlog for these visas reached 300,000. The individuals in this backlog are considered part of the unauthorized immigrant population.

These new estimates do not reflect events since mid-2022. The U.S. unauthorized immigrant population has likely grown over the past two years, based on several alternative data sources. For example, encounters with migrants at U.S. borders reached record levels throughout 2022-23 , and the number of applicants waiting for decisions on asylum claims increased by about 1 million by the end of 2023.

In addition, through December 2023, about 500,000 new immigrants were paroled into the country through two federal programs – the Cuban, Haitian, Nicaraguan and Venezuelan ( CHNV ) program and Uniting for Ukraine ( U4U ). Groups like these have traditionally been considered part of the unauthorized immigrant population, but almost none of them appear in the 2022 estimates.

While these new arrivals probably increased the U.S. unauthorized immigrant population, it remains to be seen how much. New arrivals can’t simply be added to the existing estimate because some unauthorized immigrants leave the country every year, some die and some gain lawful status. (For details, read “What has happened with unauthorized migration since July 2022?”)

The Pew Research Center estimates presented here use the 2022 American Community Survey (ACS). The 2022 ACS provides data for July 1, 2022. We cannot make estimates for 2023 or later until new ACS data is released.

About 1.5 million immigrants have received protection from deportation since 2022, according to a Pew Research Center review of federal immigration data. However, it is not appropriate to derive a new estimate of the unauthorized immigrant population by adding these 1.5 million immigrants to the estimate of 11.0 unauthorized immigrants in 2022. This would be inaccurate because the unauthorized immigrant population changes for many reasons, including outmigration from the U.S., deaths and transitions to lawful immigration statuses.

In addition, this approach would double-count some immigrants because an individual can be included in multiple immigration programs. The exact number of people who are double-counted is unknown.

Here are the main groups of unauthorized immigrants with protection from deportation and how the numbers have changed in the past two years:

Asylum applicants. Immigrants who have applied for asylum but whose cases have not been resolved are included in our estimate of the unauthorized immigrant population because they have not been admitted as permanent residents. The number with pending cases has grown substantially since July 2022. Most immigrants in these backlogs are in the United States.

The backlog of affirmative asylum cases (i.e., cases adjudicated by the Department of Homeland Security’s U.S. Citizenship and Immigration Services) increased from about 500,000 as of June 30, 2022, to more than 1.1 million at the end of 2023. Since each case can include more than one person, we estimate that these additional cases added 870,000 immigrants to the backlog at the end of 2023. Most of these people are new arrivals to the U.S.

During this period, the backlog for defensive asylum (i.e., cases adjudicated by the Department of Justice Executive Office for Immigration Review ) grew by about 120,000 people, from about 900,000 to 1 million people.

CHNV parolees. A new program allows people living in Cuba, Haiti, Nicaragua and Venezuela to apply to enter the U.S. as parolees . Since these migrants are not admitted for permanent U.S. residence, they would be included in our estimate of the unauthorized immigrant population under current definitions.

The program began full operation in January 2023. By the end of 2023, about 320,000 new immigrants had entered the country under CHNV parole.

Uniting for Ukraine (U4U) . Created in April 2022, this program allows Ukrainian citizens and their families to live in the U.S. on a temporary basis under certain conditions. More than 170,000 Ukrainians had been admitted on a two-year parole as of December 2023.

Because these immigrants do not have permanent residence, they would be considered unauthorized immigrants based on current definitions. Virtually all U4U parolees came to the U.S. after July 2022 and are not part of the 2022 unauthorized immigrant population estimate.

Victims of human trafficking and other crimes. T and U visas are available for victims of certain crimes who assist law enforcement in pursuing the criminals. The backlogs for these visas increased by about 50,000 people since July 2022 .

Temporary Protected Status (TPS) . TPS allows migrants to live and work in the U.S.and avoid deportation because their home countries are unsafe due to war, natural disasters or other crises. Some people with TPS have been in the U.S. for more than 20 years.

The population of immigrants eligible for or receiving TPS recently increased to about 1.2 million. Most of these people were already in the country as of July 2022, so they do not contribute to growth in the unauthorized immigrant population. Further, many newer additions to the TPS population are counted in other groups.

Deferred Action for Childhood Arrivals (DACA). DACA allows unauthorized immigrants who were brought to the U.S. before their 16th birthday and who were in the U.S. on June 15, 2012, to live and work in the country. Initially, about 700,000 individuals received benefits under DACA.

Since then, the number of DACA recipients has dropped steadily as some have acquired permanent status and others have left the country or otherwise not renewed their status. At the end of 2023, about 530,000 people had DACA status. These individuals are in our unauthorized immigrant population estimates for 2022.

In addition to these groups with protection from deportation, there are other indicators of overall growth:

Encounters at U.S. borders. U.S. immigration authorities encounter a large and growing number of migrants at the border. While many migrants are detained and denied entry into the U.S., some are allowed to remain in the U.S. temporarily. Most who are allowed to stay are included in other groups and do not represent additional unauthorized immigrants.

Immigrants in the Current Population Survey (CPS) . This government survey provides data on the total U.S. population as well as immigrants, both from the monthly CPS and the Annual Social and Economic Supplement (ASEC) every March. CPS data on the immigrant population shows substantial growth since 2022, beyond what can be accounted for by lawful immigration.

Here are key findings about how the U.S. unauthorized immigrant population changed recently:

• The number of unauthorized immigrants from Mexico dropped to 4.0 million in 2022 from a peak of 6.9 million in 2007. Mexico has long been , and remains, the most common country of birth for unauthorized immigrants.
• From 2019 to 2022, the unauthorized immigrant population from nearly every region of the world grew. The Caribbean, South America, Asia, Europe and sub-Saharan Africa all saw increases.
• The unauthorized immigrant population grew in six states from 2019 to 2022 – Florida, Maryland, Massachusetts, New Jersey, New York and Texas. Only California saw a decrease.
• About 8.3 million U.S. workers in 2022 were unauthorized immigrants, an increase from 7.4 million in 2019. The 2022 number is essentially the same as previous highs in 2008 and 2011.

Composition of the U.S. immigrant population

Immigrants made up 14.3% of the nation’s population in 2022. That share was slightly higher than in the previous five years but below the record high of 14.8% in 1890.

As of 2022, unauthorized immigrants represented 3.3% of the total U.S. population and 23% of the foreign-born population. These shares were lower than the peak values in 2007 but slightly higher than in 2019.

Meanwhile, the lawful immigrant population grew steadily from 24.1 million in 2000 to 36.9 million in 2022. The growth was driven by a rapid increase in the number of naturalized citizens, from 10.7 million to 23.4 million. The number of lawful permanent residents dropped slightly, from 11.9 million to 11.5 million. As a result, in 2022, 49% of all immigrants in the country were naturalized U.S. citizens.

Who lives with unauthorized immigrants?

Unauthorized immigrants live in 6.3 million households that include more than 22 million people. These households represent 4.8% of the 130 million U.S. households.

Here are some facts about these households in 2022:

• In 86% of these households, either the householder or their spouse is an unauthorized immigrant.
• Almost 70% of these households are considered “mixed status,” meaning that they also contain lawful immigrants or U.S.-born residents.
• In only about 5% of these households, the unauthorized immigrants are not related to the householder or spouse. In these cases, they are probably employees or roommates.

Of the 22 million people in households with an unauthorized immigrant, 11 million are U.S. born or lawful immigrants. They include:

• 1.3 million U.S.-born adults who are children of unauthorized immigrants. (We cannot estimate the total number of U.S.-born adult children of unauthorized immigrants because available data sources only identify those who still live with their unauthorized immigrant parents.)
• 1.4 million other U.S.-born adults and 3.0 million lawful immigrant adults.

About 4.4 million U.S.-born children under 18 live with an unauthorized immigrant parent. They account for about 84% of all minor children living with their unauthorized immigrant parent. Altogether, about 850,000 children under 18 are unauthorized immigrants in 2022.

The share of households that include an unauthorized immigrant varies across states. In Maine, Mississippi, Montana and West Virginia, fewer than 1% of households include an unauthorized immigrant. Nevada (9%) has the highest share, followed by California, New Jersey and Texas (8% each).

What countries do unauthorized immigrants come from?

The origin countries for unauthorized immigrants have changed since the population peaked in 2007. Here are some highlights of those changes:

The 4.0 million unauthorized immigrants from Mexico living in the U.S. in 2022 was the lowest number since the 1990s. And in 2022, Mexico accounted for 37% of the nation’s unauthorized immigrants, by far the smallest share on record .

The decrease in unauthorized immigrants from Mexico reflects several factors:

• A broader decline in migration from Mexico to the U.S.;
• Some Mexican immigrants returning to Mexico; and
• Expanded opportunities for lawful immigration from Mexico and other countries, especially for temporary agricultural workers.

The rest of the world

The total number of unauthorized immigrants in the U.S. from countries other than Mexico grew rapidly between 2019 and 2022, from 5.8 million to 6.9 million.

The number of unauthorized immigrants from almost every world region increased. The largest increases were from the Caribbean (300,000) and Europe and Canada (275,000). One exception was Central America, which had led in growth until 2019 but saw no change after that.

After Mexico, the countries with the largest unauthorized immigrant populations in the U.S. in 2022 were:

• El Salvador (750,000)
• India (725,000)
• Guatemala (675,000)
• Honduras (525,000)

The Northern Triangle

Three Central American countries – El Salvador, Honduras and Guatemala – together represented 1.9 million unauthorized immigrants in the U.S. in 2022, or about 18% of the total. The unauthorized immigrant population from the Northern Triangle grew by about 50% between 2007 and 2019 but did not increase significantly after that.

Other origin countries

In 2022, Venezuela was the country of birth for 270,000 U.S. unauthorized immigrants. This population had seen particularly fast growth, from 55,000 in 2007 to 130,000 in 2017. It is poised to grow significantly in the future as new methods of entry to the U.S. are now available to Venezuelans.

Other countries with large numbers of unauthorized immigrants have also seen increases in recent years. Brazil, Canada, Colombia, Ecuador, India, and countries making up the former Soviet Union all experienced growth from 2019 to 2022.

However, other countries with significant unauthorized immigrant populations showed no change, notably China, the Dominican Republic and the Philippines.

Detailed table:   Unauthorized immigrant population by region and selected country of birth (and margins of error), 1990-2022  (Excel)

Which states do unauthorized immigrants call home?

Most U.S. states’ unauthorized immigrant populations stayed steady from 2019 to 2022. However, six states showed significant growth:

• Florida (+400,000)
• Texas (+85,000)
• New York (+70,000)
• New Jersey (+55,000)
• Massachusetts (+50,000)
• Maryland (+40,000)

California (-120,000) is the only state whose unauthorized immigrant population decreased.

States with the most unauthorized immigrants

The six states with the largest unauthorized immigrant populations in 2022 were:

• California (1.8 million)
• Texas (1.6 million)
• Florida (1.2 million)
• New York (650,000)
• New Jersey (475,000)
• Illinois (400,000)

These states have consistently had the most unauthorized immigrants since at least 1980. However, in 2007, California had 1.2 million more unauthorized immigrants than Texas. Today, with the declining number in California, it has only about 150,000 more. The unauthorized immigrant population has also become considerably less geographically concentrated over time. In 2022, the top six states were home to 56% of the nation’s unauthorized immigrants, down from 80% in 1990.

Detailed table:   Unauthorized immigrant population for states (and margins of error), 1990-2022  (Excel)

Detailed table:   Unauthorized immigrants and characteristics for states, 2022  (Excel)

Unauthorized immigrants in the labor force

The number of unauthorized immigrants in the U.S. workforce grew from 7.4 million in 2019 to 8.3 million in 2022. The 2022 number equals previous highs in 2008 and 2011.

Unauthorized immigrants represent about 4.8% of the U.S. workforce in 2022. This was below the peak of 5.4% in 2007.

Since 2003, unauthorized immigrants have made up 4.4% to 5.4% of all U.S. workers, a relatively narrow range.

The share of the U.S. workforce made up by unauthorized immigrants is higher than their 3.3% share of the total U.S. population. That’s because the unauthorized immigrant population includes relatively few children or elderly adults, groups that tend not to be in the labor force.

Detailed table:   Unauthorized immigrants in the labor force for states, 2022  (Excel)

The share of unauthorized immigrants in the workforce varied across states in 2022. Nevada (9%), Texas (8%), Florida (8%), New Jersey (7%), California (7%) and Maryland (7%) had the highest shares, while fewer than 1% of workers in Maine, Montana, Vermont and West Virginia were unauthorized immigrants.

Note: This is an update of a post originally published Nov. 16, 2023.

• Immigrant Populations
• Immigration Issues
• Unauthorized Immigration

Jeffrey S. Passel is a senior demographer at Pew Research Center .

Jens Manuel Krogstad is a senior writer and editor at Pew Research Center .

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

Cultural issues and the 2024 election, latinos’ views on the migrant situation at the u.s.-mexico border, u.s. christians more likely than ‘nones’ to say situation at the border is a crisis, how americans view the situation at the u.s.-mexico border, its causes and consequences, most popular.

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ABOUT PEW RESEARCH CENTER  Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of  The Pew Charitable Trusts .

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Jack L. Treynor Papers Open for Research

August 1, 2024.

The Jack L. Treynor papers are now open for research as part of the Economists’ Papers Archive.  These important manuscripts were acquired in collaboration between the Rubenstein Library and the Center for the History of Political Economy. Treynor made significant contributions to the field of financial analysis his academic peers recognized his having “changed the direction of the profession.” Demonstrating his innovative spirit, Treynor also registered a patent in 2004 for a “Method for maintaining an absolute risk level for an investment portfolio.” Please enjoy this recent acquisition.  

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