Effect Size for Two Groups

Statistics · Axiom Academy

LESSON Effect Size for Two Groups Understanding Cohen's d and the practical significance of group differences 1. Cohen's d: Standardized Mean Difference Cohen's d is the most common effect size measure for comparing two group means. It expresses the difference between groups in standard deviation units, making the effect size interpretable regardless of the original measurement scale. x̄₁ and x̄₂ are the means of groups 1 and 2 s pooled is the pooled standard deviation that accounts for variability in both groups The pooled standard deviation is calculated as: where n₁ and n₂ are the sample sizes of each group. 2. Interpreting Effect Sizes: Cohen's Benchmarks Jacob Cohen proposed conventional benchmarks for interpreting effect sizes in behavioral science research. These provide a rough guide for understanding the magnitude of an effect: 3. Why Effect Sizes Matter Beyond p-values P-values tell us whether an effect is statistically significant, but they don't tell us if it's practically important. Consider these scenarios: Scenario A: Large sample (n = 10,000 per group) Mean difference: 0.5 points on a 100-point scale p-value: p < 0.001 (highly significant!) Cohen's d: 0.05 (trivial effect) Scenario B: Moderate sample (n = 50 per group) Mean difference: 12 points on a 100-point scale p-value: p = 0.08 (not significant) Cohen's d: 0.7 (medium-to-large effect)

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