Paired T-Test

Statistics · Axiom Academy

Understanding when and how to compare paired measurements using the paired t-test 1. When to Use a Paired T-Test The paired t-test is appropriate when you have two related measurements and want to test whether their mean difference is significantly different from zero. Before-and-After Studies: Measuring the same subjects before and after a treatment (e.g., blood pressure before and after medication) Matched Pairs: Pairing subjects based on similar characteristics (e.g., twins, siblings, or matched controls) Repeated Measures: Two measurements under different conditions on the same subject (e.g., left hand vs. right hand grip strength) The first step in a paired t-test is to calculate the difference for each pair. This reduces our two-sample problem into a one-sample problem. d i = difference for the i-th pair x 1i = first measurement (e.g., "before") x 2i = second measurement (e.g., "after") Once we have the differences, we calculate the test statistic using the mean difference and the standard deviation of the differences . t = test statistic for the paired t-test d̄ = mean of the differences (d-bar) s d = standard deviation of the differences This formula tells us how many standard errors the mean difference is from zero. A larger absolute value of t provides stronger evidence against the null hypothesis (that the mean difference is zero). The degrees of freedom for a paired t-test is based on the number of pairs , not the total number of measurements.

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