Excel can perform various statistical analyses, including t-tests. It is an excellent option because nearly everyone can access Excel. This post is a great introduction to performing and interpreting t-tests even if Excel isn’t your primary statistical software package.

In this post, I provide step-by-step instructions for using Excel to perform t-tests. Importantly, I also show you how to select the correct form of t-test, choose the right options, and interpret the results. I also include links to additional resources I’ve written, which present clear explanations of relevant t-test concepts that you won’t find in Excel’s documentation. And, I use an example dataset for us to work through and interpret together!

T-tests are hypothesis tests that assess the means of one or two groups. Hypothesis tests use sample data to infer properties of entire populations. To be able to use a t-test, you need to obtain a random sample from your target populations. Depending on the t-test and how you configure it, the test can determine whether:

- Two group means are different.
- Paired means are different.
- One mean is different from a target value.

For more information about the types of t-tests you can use, read my post about 1-sample, 2-sample, and Paired t-Tests.

## Install the Data Analysis ToolPak in Excel

The Data Analysis ToolPak must be installed on your copy of Excel to perform t-tests. To determine whether you have this ToolPak installed, click *Data* in Excel’s menu across the top and look for *Data Analysis* in the *Analyze* section. If you don’t see Data Analysis, you need to install it. Don’t worry. It’s free!

To install Excel’s Analysis Tookpak, click the *File* tab on the top-left and then click *Options* on the bottom-left. Then, click *Add-Ins*. On the *Manage* drop-down list, choose *Excel Add-ins,* and click *Go*. On the popup that appears, check *Analysis ToolPak* and click *OK*.

After you enable it, click *Data Analysis* in the Data menu to display the analyses you can perform. Among other options, the popup presents three types of t-test, which we’ll cover next.

## Two-Sample t-Tests in Excel

Two-sample t-tests compare the means of precisely two groups—no more and no less! Typically, you perform this test to determine whether two population means are different. For example, do students who learn using Method A have a different mean score than those who learn using Method B? This form of the test uses independent samples. In other words, each group contains a unique set of people or items.

The standard form tests the following hypotheses:

- Null: The two population means are equal.
- Alternative: The two population means are not equal.

If the p-value is less than your significance level (e.g., 0.05), you can reject the null hypothesis. The difference between the two means is statistically significant. Your sample provides strong enough evidence to conclude that the two population means are different.

For more information about the null and alternative hypotheses and other hypothesis testing terms, see my Hypothesis Testing Overview.

Also, learn about the difference between descriptive statistics and inferential statistics.

## t-Tests for Equal and Unequal Variances

You’ll notice that Excel has two forms of the two-sample t-test. One that assumes equal variances and the other that assumes unequal variances. Variances and the closely related standard deviation are measures of variability. All t-tests assume you obtained data from normally distributed populations. However, the conventional t-test also assumes the standard deviations/variances for both groups are equal. Another form of the test, known as Welch’s t-test, does not assume equal variances.

As an aside, thanks to the central limit theorem, you can safely use t-tests to analyze nonnormal data when have ~20 or more observations per group.

### Which One to Use?

Advice for using either the equal or unequal variances form of the 2-sample t-test varies because this issue is more complicated than it first appears. Some analysts advise using an F-test to determine whether the variances are unequal. And, Excel does offer the F-test Two-Sample for Variances. However, using additional tests always increases the probability of both false positives and false negatives (a.k.a, Type I and Type II errors).

Additionally, if you have a large sample size, the f-test has more statistical power. This condition can cause the test to identify an inconsequential difference as being statistically significant. That’s the difference between practical significance and statistical significance. Conversely, small sample sizes can fail to detect a substantial difference between variances.

When you have an equal, or nearly equal, number of observations in both groups and a moderate sample size, t-tests are robust to differences between variances. If you find one group has twice the variance of another group, it might be time to worry! However, you don’t need to worry about smaller differences.

Other analysts suggest always using the form of the t-test that assumes unequal variances. If you use this approach when the variances are equal, you lose a trivial amount of statistical power, but you’ll be better off when the variances are not equal.

If you have unequal variances *and* unequal samples sizes, it’s vital to use the unequal variances version of the 2-sample t-test!

## Step-by-Step Instructions for Running the Two-Sample t-Test in Excel

Let’s conduct a two-sample t-test! Our hypothetical scenario is that we are comparing scores from two teaching methods. We drew two random samples of students. One sample comprises students who learned using Method A while the other sample learned using Method B. These samples contain entirely different students. Now, we want to determine whether the two means are different. Download the CSV file that contains all data for both t-test examples in this post: t-TestExamples.

To perform a 2-sample t-test in Excel, arrange your data in two columns, as shown below.

Let’s assume that the variances are equal and use the Assuming Equal Variances version. If we had chosen the unequal variances form of the test, the steps and interpretation are the same—only the calculations change.

- In Excel, click
*Data Analysis*on the Data tab. - From the Data Analysis popup, choose
*t-Test: Two-Sample Assuming Equal Variances*. - Under
*Input*, select the ranges for both*Variable 1*and*Variable 2*. - In
*Hypothesized Mean Difference*, you’ll typically enter zero. This value is the null hypothesis value, which represents no effect. In this case, a mean difference of zero represents no difference between the two methods, which is no effect. - Check the
*Labels*checkbox if you have meaningful variables labels in row 1. This option helps make the output easier to interpret. Ensure that you include the label row in step #3. - Excel uses a default Alpha value of 0.05, which is usually a good value. Alpha is the significance level. Change this value only when you have a specific reason for doing so.
- Click OK.

For the example data, your popup should look like the image below:

After Excel creates the output, I autofit the width of column A to display all text in it.

## Interpreting the Two-Sample t-Test Results

The output indicates that mean for Method A is 71.50362 and for Method B it is 84.74241. Looking in the Variances row, we can see that they are not exactly equal, but they are close enough to assume equal variances. The p-value is the most important statistic. If you want to learn about the other statistics, you can read my posts about the t Stat (i.e., the t-value), df (degrees of freedom), and the t Critical values.

If the p-value is less than your significance level, the difference between means is statistically significant. Excel provides p-values for both one-tailed and two-tailed t-tests.

One-tailed t-tests can detect differences between means in only one direction. For example, a one-tailed test might determine only whether Method B is greater than Method A. Two-tailed tests can detect differences in either direction—greater than or less than. There are additional drawbacks for using one-tailed tests—so I’ll stick with the standard two-tailed results. To learn more, read my post about one-tailed and two-tailed tests.

For our results, we’ll use P(T<=t) two-tail, which is the p-value for the two-tailed form of the t-test. Because our p-value (0.000336) is less than the standard significance level of 0.05, we can reject the null hypothesis. Our sample data support the hypothesis that the population means are different. Specifically, Method B’s mean is greater than Method A’s mean.

## Paired t-Tests in Excel

Paired t-tests assess paired observations, which are often two measurements on the same person or item. Statisticians call these dependent samples. Suppose you gather a random sample of people. You give them all a pretest, administer a treatment, and then perform a posttest. Each subject has a pretest and posttest score. Or, perhaps you have a sample of wood boards, and you paint half of each board with one paint and the other half with different paint. Then, you measure the paint durability for both types of paint on all the boards. Each board has two paint durability scores.

In both cases, you can use a paired t-test to determine whether the difference between the means of the two sets of scores is statistically significant.

Unlike independent t-tests, paired t-tests use the same people or items in both groups. One way to determine whether a paired t-test is appropriate for your data is if each row in the dataset corresponds to one person or item. For our pretest/posttest example, we measure each subject before and after the experiment and placed the measurements for an individual on one row.

**Related post**: Independent and Dependent Samples

## Step-by-Step Instructions for Running the Paired t-Test in Excel

For this example, imagine that we have a training program, and we need to determine whether the difference between the mean pretest score and the mean posttest score is significantly different.

To perform a paired t-test in Excel, arrange your data into two columns so that each row represents one person or item, as shown below. Note that the analysis does not use the subject’s ID number.

- In Excel, click
*Data Analysis*on the Data tab. - From the Data Analysis popup, choose
*t-Test: Paired Two Sample for Means*. - Under
*Input*, select the ranges for both*Variable 1*and*Variable 2*. - In
*Hypothesized Mean Difference*, you’ll typically enter zero. This value is the null hypothesis value, which represents no effect. In this case, a mean difference of zero represents no difference between the two methods, which is no effect. - Check the
*Labels*checkbox if you have meaningful variables labels in row 1. This option helps make the output easier to interpret. Ensure that you include the label row in step #3. - Excel uses a default Alpha value of 0.05, which is usually a good value. Alpha is the significance level. Change this value only when you have a specific reason for doing so.
- Click OK.

For the example data, your popup should look like the image below:

## Interpreting Excel’s Paired t-Test Results

The output indicates that mean for the Pretest is 97.06223 and for the Posttest it is 107.8346.

If the p-value is less than your significance level, the difference between means is statistically significant. Again, Excel provides p-values for both one-tailed and two-tailed t-tests—and we’ll stick with the two-tailed result. For information about the other statistics, click the links in the 2-sample t-test section.

For our results, we’ll use P(T<=t) two-tail, which is the p-value for the two-tailed form of the t-test. Because our p-value (0.002221) is less than the standard significance level of 0.05, we can reject the null hypothesis. Our sample data support the hypothesis that the population means are different. Specifically, the Posttest mean is greater than the Pretest mean.

## What Excel’s t-Tests Do Not Include

As nice as it is to be able to perform t-tests in Excel, it leaves out some essential features. Notably, Excel cannot create confidence intervals. The means in these analyses are the point estimates for the population means. However, thanks to random error, the sample means never precisely equal the population mean. There is a margin of error around the estimates. Confidence intervals use a margin of error to calculate a range of values that is likely to contain the actual population mean for each group. Learn more about confidence intervals.

Excel also doesn’t calculate the estimated difference between the means. The difference between the means is the effect size for the analysis—an important value to know. By using a formula in Excel, you can easily calculate the difference between means. However, it would be nice to have a confidence interval for this difference too. For more information, read my post about using confidence intervals to assess differences between means.

Finally, Excel, strangely, does not provide a one-sample t-test! In some cases, you might have a single sample of data and need to determine whether it is different from a target value. For example, you might measure the strength of a product and use a one-sample t-test to determine whether it is significantly different from an important strength value.

t-Tests can compare up to two groups. If you have three or more groups, you’ll need to use ANOVA. For more information, see my posts about how to do one-way ANOVA in Excel and how to do two-way ANOVA in Excel!

If you’re learning about hypothesis testing and like the approach I use in my blog, check out my eBook!

Stacey says

Hi Jim!!!!

Thank you for the easy to understand explanation. I have used the t-test before but never truly understood it or when to use it the way I do now!

Jim Frost says

Hi Stacey, thanks for writing! I’m so glad to hear that this post was helpful!

Valodia says

Hi Jim. This is an excellent explanation. Thank you so much.

I was wondering if there is a way to calculate the standard deviation from the information that results from the excel output?

Thanks.

Valodia

Jim Frost says

Hi Valodia,

Yes, you can! The standard deviation is just the square root of the variance. So, all you need to do is look for variance in the output and take the square root of it to find the standard deviation. For example, if you look in Excel’s output for the 2-sample t-test, you’ll see variances for each group and the pooled variance. Take the square root of those variances to find the standard deviation for each group and the pooled standard deviation, which is for all the data.

I hope that helps!

Aniket says

Thanks for your comments Jim!! I ended up doing a 3 way ANOVA. I thought to share my results with you. Might interest you. Worked like a charm!!

Jim Frost says

Hi Aniket,

I’m so glad it worked like a charm!! I had to remove the output because it was so long. But, that’s great!

Jeyasushma Veeriah says

Hi Jim, I am a newbie in discovering the wonders of Excel in calculations. I am in a dilemma now. I have this questionnaire with 4 dimensions – so lets say for Dimension A, I have 7 questions, Dimension B (11 questions), Dimension C (10 questions) and Dimension D (7 questions). Now I would like to see the relationship between gender and dimension as a whole. Now, my questions are (1) How do I group the 7 questions in Dimension A as one variable? (2) How do I group all the questions in the 4 dimensions as 1 variable? Thank you Jim.

Aniket says

Holy heck Jim no one has ever replied to me on any other stats message board. Thanks.

I want to pick your brain a little bit more. Below will be the structure of the data. Such data will be collected for 4 weeks at two temperature each. Can i do a one factor anova for one week data and compare if the formulations are different? At the end of the study I will take each formulation at different weeks and do another anova to check how formulations behave over time. Is there a simpler way?

Week0

F1 F2 F3 F4 F5 F6 F7 F8

Outcome-Repeat1 x x x x x x x x

Outcome-Repeat2 x x x x x x x x

Outcome-Repeat3 x x x x x x x x

Jim Frost says

Hi Aniket,

You’re very welcome!

I don’t see why you couldn’t do it that way. However, you’re throwing away valuable information by not including the week 0 (i.e. pretest) information. That would be my concern. If you have that data, you might as well use it in a repeated measures design.

If you go the route of a one-way ANOVA at week one, that would tell if the formulations have different group means at that point. However, that test will have less power than the repeated measures design including the pretest scores.

So, can it be done? Yes. It’s a simpler model too. But, you lose some statistical power. My upcoming post is about independent and dependent groups, which gets into repeated measures designs and the issues involved.

Aniket says

Hi Jim!! Big Fan. I have the following problem. Would like to know what you think

I am screening different liquid formulations for a drug. There are 8 unique formulations studied at two different temperatures. The aim is to identify which formulation is best with respect to stability. I was planning to do an ANOVA for the 8 different formulations to see if the formulations are different from each other and then do a pairwise t test at the two temperatures as it is essentially the same sample at two different temperatures. Is this a good approach?

Jim Frost says

Hi Aniket,

It sounds like you need to perform a repeated measures ANOVA, which is an extension of the paired t test. You’d include Formulation, Temperature, and Time in your model. You’d be particularly interested in the interactions between Formulation*Time (does the relationship between formulation and your DV depend on time). If that term is significant, then you know the formulations behave differently over time. Also, you could include temperature in that interaction. Three-way interactions are rare in analyses, but your model might call for it. It would answer the question whether the relationship between Formulation and the DV depends on both time and temperature.

Additionally, you can perform post hoc analyses on these interactions terms so you can control the familywise error rate for all these comparison. You don’t get that benefit if you use a series of paired t-tests.

I hope that helps!

Anum says

how we will tell that mean of one variable is greater than the other variable in two tailed t test

Jim Frost says

Hi Anum,

There are two ways. One is just to look at the two mean values. The output should display the mean for each group. That’s the easiest way. For example, if the mean of group 1 is greater than group two, and the results are significant, then you know that the mean 1 is significantly larger than mean 2. You can also look at the t-values and then link that to critical areas and how that relates to your hypothesis test.

But, I’d just look at the group means!

Natalia K says

Hi Jim. Could you please clarify if t-test can be used if data have a number of outliers, i.e. distributions are heavily skewed?

Many thanks

Jim Frost says

Hi Natalia,

T-tests are not recommended when you have outliers that skew the distributions. A few values can dramatically change your results. Consider using a nonparametric test instead. I talk about this in my post about parametric vs. nonparametric tests. It’s under one of the benefits of using nonparametric tests.

Geeta Pradeep says

Hello Jim,

I am trying to assess the impact of an intervention in a sample of 30 participants pre and post intervention using a set of clinical outcome measures sample before and after the intervention.

As the intervention was applied at different times for each participant, I have collected different number of pre and post intervention outcome measures.

To clarify: I have 2 pre-intervention outcome measures and only one post intervention measures for participant X while I have 3 pre-intervention and post intervention measures for participant Y.

What is the best way to do a paired sample T test in such a case?

For some participants, there is no corresponding post-intervention outcome recorded as the prescriber did not request for the clinical test.

Do I just choose the last recorded pre and post intervention values or do I calculate an average of pre and post intervention measures for each participant? If I am to calculate the average, then how do I account for a single or no outcome value?

I’d appreciate your advice on this.

Thank you

Geeta

Geeta Pradeep says

Hi Jim,

Your website has been a heaven sent for me! My knowledge of statistics is rudimentary and I cannot thank you enough for the simple way in which you explain concepts.

I am currently writing up my thesis and I had a question about selection of variables in a paired sample t-test. My research looks at the impact ( if any) of having a pharmacist involved in the care of people with type 2 diabetes and I have clinical parameters measured pre and post intervention. I also have a control group who have been exposed to usual care.

My question is – does it matter in what order I choose my sample variable when I do the paired t-test ( using XLSTAT). I have added pre-intervention means as variable 1 and post-intervention as variable 2.

Would the values change if I conduct the test choosing post intervention as variable 1 and pre as variable 2?

Apologies in advance if this is a silly question but I just want to be sure I am on the right path here.

Once again, many thanks.

Cheers

Geeta

Iqra says

Thnks jim

Iqra says

Hey sidra .you find the answer yet or not.i thnk tour student of b.ed i am also looking for ths answer

Jim Frost says

Hi, I answered Sidra’s question in the comments. You might need to scroll down.

Sidra says

Thank you Jim. your answer was really helpful.

Sidra says

Hi jim

i am a new student of statistics. I really need to solve question. Can you give me any idea which test will be suitable for this research. “A researcher conducted a research that majority of the people who died during pandemic bought a new phone during last year.If his assumption is correct which statistical test should be appropriate “

Jim Frost says

Hi Sidra,

It sounds like you need to perform a two proportions test. You need to determine whether the proportion of pandemic deaths is different between the group that bought a new phone within a year versions those who did not. Caution: For these data, you wouldn’t be proving that buying phones caused pandemic deaths. Instead, you’d be showing a correlation (not causation) between them.

In my new ebook about hypothesis testing, I cover proportions tests in great detail.

Brandi C Sturgis says

I am conducting a quantitative research study. The hypothesis is does Variable 1 (intervention) impact Variable 2 (posttest scores). I have a control group and an experimental group and pretest and posttest scores for all participants. I have entered all scores as 1 data set in excel and from my understanding should use the paired mean t-test? But then how do I compare the groups? For example how do I find the mean for the experimental group separately from the control group? Or the separate standard deviations? When reporting results would I use the one p-value calculated for the total group for the null hypothesis testing?

Jim Frost says

Hi Brandi,

Based on what you write, it sounds like you’ll need to use repeated measures ANOVA rather than a t-test. You have pre-test and post-test scores and you have two experimental groups. That’s four groupings based on two independent variables, time and experimental group. T-tests can’t analyze that type of design.

To answer your question about whether the mean difference between pre-test and post-test scores depend on group assignment, you’ll need to include an interaction term for time*group in your repeated measures ANOVA model.

Camryn Froerer says

Hi Jim,

I am attempting to run a t-Test comparing time to complete a task where the pre- and post array data each have 70 days. However, in the post data there are days when the task didn’t occur. Is the correct way to represent this within the array to include a 0 in each of the lines, or to leave it blank?

I have run it each way and in this instance the p-value becomes >0.05 if the 0’s are included for time measures, but become significant if the 0’s aren’t included. However, I want to represent the data correctly regardless of the resulting significance.

Thank you for your help.

Jim Frost says

Hi Camryn,

I’m assuming you’re using a pair t-test with a pre and post test time for each subject. In this case, if a subject doesn’t complete both the pre and post test, you need to exclude that subject from the analysis. You definitely don’t want to enter a zero for missing data because the analysis will interpret that as a time of zero.

I hope that helps. Best of of luck with your analysis!

Kevin says

Hi Jim! Your explanation helped me a lot to understand how a t-Test works! I have one question about multiple t-Tests. If I conducted a t-Test (4 groups 1,2,3,4 and tested 1&4 / 2&3) and ANOVA for all 4 together does this count as multiple Testing? Therefore a Bonferroni correction is needed?

Thanks a lot!

Kevin

Jim Frost says

Hi Kevin, yes, that definitely does count as multiple testing. You shouldn’t be using t-tests for that. Instead, conduct the ANOVA and then use a post hoc test. Click that link to read an article I wrote about them. Bonferroni is a type of post hoc test and that would be an acceptable one to use. However, I don’t usually recommend that particular test because it’s known to be more conservative (less statistical power) than other post hoc tests.

Jim Hardman says

Hi Jim (Great name btw!). I have a question about the one tailed P-Value that Excel reports. It specifically says “P[T <= t]" which if interpreted literally would be P[ T <= – 1.652] if the t test statistic were -1.652, and if there were, say, 13 df, then P[T <= -1.652] would be equal to 0.061235 (rounded off to the 5th decimal place). If, on the other hand, the t test statistic had been +1.652, then P[T <= 1.652] = 0.93877 (rounded off to the 5th decimal place), BUT Excel would still report, "P[T <= t"] as 0.061235. So my question is this: even though Excel prints "P[T <= t] one tailed", it's really calculating the left-hand tail probability if the test statistic is a negative number, and the right-hand tail probability if the test statistic is a positive number? Do I have that correct? Thanks (for the life of me I could not find the answer to this question out there on the "interwebs"!)

Jim Frost says

Hi Jim! Yes, it is indeed a great name!

Those labels in Excel are wonky. My take is that they’re missing symbols for absolute values. I noticed this weirdness before but your comment prompted me to think it through for both one- and two-tailed cases. T are t-values in the t-distribution while t is from your sample.

For both one-tailed tests and two-tailed tests, I believe it should be: P(|T| ≥ |t|).

This indicates the probability of obtaining absolute t-values at least as extreme as the absolute value of the t-value your study obtained. That covers all the cases I think for both positive and negative sample t-values and one-tailed tests in either direction. Excel would include “one-tailed” or “two-tailed” after that label because that tells you whether that probability is distributed between two tails or just one tail.

–The other Jim

Maja says

Hey Jim,

I would like to know if you happen to know which formula Excel are using when calculating the t-value in the unequal variance t-test?

So sorry for my “danglish” 🙂

Lauren Zeglio says

Hi Jim,

Super helpful, i need to create a box plot from my P value, how would i go about doing this.

Thanks

Jim Frost says

Hi Lauren, I don’t understand what you mean by creating a box plot from a p-value. I do have a post that explains box plots. Perhaps that will help. If that post doesn’t answer your question, please comment in the boxplot post and provide more details about what you want to do exactly. Thanks!

Mike H says

Hi Jim. Thank you for the work you are doing here. I read this article to help me better explain how to decide which excel tool to use when for a t-test. It helped much! I was disappointed to learn that excel doesn’t do one sample t-tests… but maybe we have a ray of hope? I read another article you wrote about one or two or paired t-tests (first link in this article) and there you wrote “Here’s a secret! Paired t-tests and 1-sample t-tests are the same hypothesis test incognito!”

So, a question – can one, using excel’s paired t-test function, put sample data in the first column and the null hypothesis value, repeatedly, in the second column and “trick” excel into running a one sample t-test using the paired t-test function?

Jim Frost says

Hi Mike,

That’s a great question. If you enter your 1-sample data in one column and then enter all zeroes in the other column, that

shoulddo the trick. I haven’t tested that to know for sure but will try it when I can. I suppose there’s a chance that Excel might choke on that.If that approach works, entering all zeroes for one column will test the hypothesis of whether your data are significantly different from zero. Entering a different value from zero should test whether your data are different from that value. For example, if you wanted to determine whether your data were significantly different from a mean of 5, you’d enter all 5s in the 2nd column.

As you’ve noted from the other post, paired t-tests simply subtract one observation from another for each subject/item and then performs a 1-sample t-test using those paired differences.

Penn Gao says

Thank you, Jim!

Your explanation is very clear and it helps me a lot.

Marty Shudak says

Jim, I know you are an expert with Minitab. I recently learned that the test of two proportions have two ways to calculate the z score depending upon whether you indicate it use a pooled or separate estimate of p. Can you explain how I would decide that as the differences in results can be substantial. Also, I’m not sure which one is used in Excel.

Mommy Bloggers Phil (@MommyBloggersPh) says

A rather technical post but I’m sure this will be helpful for those mastering Excel.

Jim Frost says

Hi Phil,

I do provide the step-by-step instructions for how to do this in Excel. However, I hope to have accomplished other goals in the process. For instance, there are several t-test to choose from–which one is appropriate. And, how to choose the correct p-value to use? What’s the correct interpretation? There’s also links to other resources of mine the explain the various other statistics you’ll see in the output. And, importantly, what can’t Excel do? Excel doesn’t elaborate on all of that. Hopefully, that information is useful to readers!

Ramesh Chandra Das says

Nice Explanation!!!!!!!!!!!

Muruhura Nickson says

yess… it was so helpful.. thank you