T-Test Explained: Independent Samples, Paired Samples, Interpretation

A t-test checks whether the difference between two group means, or between one group mean and a reference value, is statistically significant. It comes in one-sample, independent samples, and paired samples forms. Check normality and equality of variances first, then judge the result from the t statistic and its p-value.

What Is a T-Test?

A t-test uses the t distribution to judge whether a difference in means is larger than chance would comfortably explain. With three or more groups, repeated t-tests accumulate error, so analysis of variance (ANOVA) is used instead.

What Types of T-Tests Are There?

There are three types, depending on what is compared and how the samples are structured.

Type	What is compared	Example
One-sample t-test	One group mean vs. a reference value	Is our class average different from the national average
Independent samples t-test	Means of two separate groups	Treatment group vs. control group
Paired samples t-test	Pre and post means for the same cases	Before treatment vs. after treatment

How Do You Run a T-Test?

Check the assumptions, run the test, then interpret the result.

Step 1: Check Assumptions

Confirm the normality of the dependent variable, and for independent samples check equality of variances with Levene's test. If normality is badly violated, consider a nonparametric test (Mann-Whitney U, Wilcoxon).

Step 2: Run the Test and Interpret

Compute the t statistic, degrees of freedom, and p-value. If p falls below the threshold (usually .05), the difference in means is interpreted as statistically significant.

Step 3: Report Effect Size

Significance alone says nothing about how large the difference is, so report an effect size such as Cohen's d alongside it.

What Are the Assumptions of a T-Test?

Normality must hold, and for independent samples so must equality of variances. When variances are unequal, use Welch's t-test, and when normality is badly violated, use a nonparametric alternative.

What If You Have Three or More Groups?

With three or more groups, do not repeat t-tests — use analysis of variance (ANOVA). Repeated t-tests inflate the Type I error rate, meaning you start calling differences significant when they are not.

Summary

A t-test tests a difference in means between two groups, or against a reference value. Check normality and equality of variances, and report the p-value together with an effect size. For three or more groups go to ANOVA, and to estimate effects on a continuous outcome go to regression analysis.