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 two measurements on the same person or item. 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.

## 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!

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