Comparing Groups Summary

Statistics · Axiom Academy

Let's review the key methods for comparing two groups using statistical inference. Research Questions: Does treatment A differ from treatment B? Is there a difference between men and women? Two Numerical Variables: Compare means using t-tests (independent or paired) Two Categorical Variables: Compare proportions using z-tests Goal: Determine if observed differences are statistically significant or due to chance Independent Samples: Two separate groups with no natural pairing (e.g., control vs treatment, males vs females) Paired Samples: Each observation in one group is matched with one in the other (e.g., before/after, twins, matched pairs) Key Question: "Are the same subjects measured twice?" If yes, use paired design Why It Matters: Paired designs control for individual variation and are more powerful Two-Sample t-Test (Independent Samples) Purpose: Compare means of two independent groups Pooled t-test: Assumes equal population variances ( σ₁² = σ₂² ); uses pooled standard error Welch's t-test: Does NOT assume equal variances; adjusts degrees of freedom (more conservative, generally preferred) Degrees of Freedom: Pooled: n₁ + n₂ - 2 ; Welch's: complex formula (calculated by software) Purpose: Compare means of matched pairs or repeated measures Method: Calculate differences for each pair, then perform one-sample t-test on differences Test Statistic: where d̄ is mean difference Degrees of Freedom: n - 1 where n is number of pairs

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