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.
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.
Note: Excel cannot perform a one-sample t-test.
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.
Statisticians consider differences between group means to be an unstandardized effect size because these values indicate the strength of the relationship using values that retain the natural units of the dependent variable. Cohen’s d is the corresponding standardized effect size and it’s appropriate to report in some cases. Effect sizes help you understand how important the findings are in a practical sense. To learn more about unstandardized and standardized effect sizes, read my post about Effect Sizes in Statistics.
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! This test is also known as the independent samples t-test. Click the link to learn more about its hypotheses, assumptions, and interpretation.
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.
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.
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.
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! Learn about the T Distribution.
If you want to learn more about how t-tests work, read my post 1-sample, 2-sample, and Paired t-Tests.
If you’re learning about hypothesis testing and like the approach I use in my blog, check out my Hypothesis Testing book! You can find it at Amazon and other retailers.