Description
Power analysis: effect size, significance level, power, test type, design-adjusted sample size computation with attrition corrections.
A study with too few participants cannot detect a real effect: it is underpowered. A study with too many wastes resources and detects trivial effects as statistically significant. Power analysis finds the minimum sample size that can detect your target effect with acceptable certainty. FIVE INPUTS: 1. EFFECT SIZE (d): standardized difference between groups. Cohen's d = (mean1 minus mean2) / pooled_sd. Small=0.2, Medium=0.5, Large=0.8. 2. SIGNIFICANCE LEVEL (alpha): probability of false positive. Default 0.05. Lower alpha (0.01) requires larger sample. 3. POWER (1-beta): probability of detecting a true effect. Default 0.80. 0.90 for confirmatory studies. 4. TEST TYPE: one-tailed (direction known) or two-tailed (direction unknown). Two-tailed requires about 25% larger sample. 5. DESIGN: independent groups (A/B test), paired (pre/post), or repeated measures. Paired uses smaller samples. COMPUTATION — Two-sample t-test: n = 2 x ((Z_(alpha/2) + Z_beta) / d)^2 Where Z_(alpha/2)=1.96 (alpha=0.05 two-tailed), Z_beta=0.84 (power=0.80). For d=0.5: n = 2 x ((1.96 + 0.84) / 0.5)^2 = 2 x (5.6)^2 = 63 per group. REAL-WORLD ADJUSTMENTS: - Attrition: planned_n / (1 minus drop_out_rate). If 20% drop out, n = 63 / 0.8 = 79 per group. - Clustering: design effect = 1 + (cluster_size - 1) x ICC. - Minimum detectable effect: given fixed sample (N=100, alpha=0.05, power=0.80), d = 2 x (1.96+0.84)/sqrt(100) = 0.40. OUTPUT: Input table (five parameters), computed sample size per group, adjusted sample, MDE, power curve plot data.
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