Paired T-Test Examples

Statistics · Axiom Academy

EXAMPLE Paired T-Test Examples Three complete worked examples demonstrating paired t-test procedures for dependent samples Example 1: Weight Loss Program Effectiveness Problem: A nutritionist wants to test if a weight loss program is effective. 8 participants were weighed before and after the 12-week program. Test at α = 0.05 if the program reduces weight. Excellent work! You've completed three comprehensive paired t-test examples. Here's what we learned: Paired Data Structure: Paired t-tests are used when observations come in natural pairs (before/after, matched subjects, same subject under different conditions). We always compute differences first. Hypothesis Testing Steps: Always start by setting up hypotheses about μ d (the mean difference), then compute statistics on the differences, calculate the test statistic, and compare to critical values. Test Statistic Formula: The paired t-test uses t = (d̄ - μ d ) / (s d / √n) with df = n - 1, where n is the number of pairs (not individual observations). Interpreting Results: When |t| > t critical or when p-value < α, we reject H₀ and conclude there is significant evidence of a difference between the paired measurements. One-tailed vs Two-tailed: Use a one-tailed test when you have a specific direction in mind (increase or decrease), and a two-tailed test when you're looking for any difference.

This is the written version of the interactive lesson above. See the full Statistics course.