When is a paired t-test appropriate?

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Two related measurements from the same subjects or from matched pairs call for a paired t-test. You look at the difference within each pair and test whether the average difference is zero. This approach leverages the pairing to remove individual variability, giving a more precise inference about the change or effect. You compute the difference for each pair, then perform a one-sample t-test on these differences (t = mean difference divided by the standard deviation of differences divided by the square root of the number of pairs). It’s especially appropriate for before–after studies, repeated measures, or matched subjects like twins.

If the samples were unrelated, you’d use an independent-samples t-test. If you’re testing a single sample against a known value, you’d use a one-sample t-test. If comparing more than two groups, you’d use ANOVA. These scenarios don’t involve paired measurements, so a paired t-test isn’t the right choice.