Power Analysis and Sample Size AI Prompt

Conduct a power analysis and determine the required sample size for this study.

Study design: {{study_design}}
Statistical test: {{test}}
Effect size: {{effect_size}} (or provide: expected means/proportions and standard deviation to compute it)
Significance level: alpha = {{alpha}} (default 0.05)
Desired power: 1 - beta = {{power}} (default 0.80; use 0.90 for high-stakes studies)

1. Effect size calculation:
   If raw parameters are given rather than a standardized effect size:

   Cohen's d (for means): d = (mu_1 - mu_2) / pooled_SD
   - Small: d = 0.2, Medium: d = 0.5, Large: d = 0.8

   Cohen's h (for proportions): h = 2 arcsin(sqrt(p1)) - 2 arcsin(sqrt(p2))
   - Small: h = 0.2, Medium: h = 0.5, Large: h = 0.8

   Cohen's f (for ANOVA): f = sigma_between / sigma_within
   - Small: f = 0.10, Medium: f = 0.25, Large: f = 0.40

   Pearson r (for correlation):
   - Small: r = 0.10, Medium: r = 0.30, Large: r = 0.50

2. Sample size formula per test:

   Two-sample t-test:
   n per group = 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)

   One-sample t-test:
   n = ((z_alpha/2 + z_beta) / d)^2

   Chi-square test of two proportions:
   n per group = (z_alpha/2 sqrt(2 p_bar (1-p_bar)) + z_beta sqrt(p1(1-p1) + p2(1-p2)))^2 / (p1-p2)^2
   where p_bar = (p1 + p2) / 2

   Calculate the required n for the stated parameters.

3. Power curve:
   Show how power changes as n increases from n/2 to 3n.
   Identify where additional subjects yield diminishing returns (power > 0.95).

4. Sensitivity analysis:
   - Required n if effect size is 25% smaller than expected
   - Required n at power = 0.90 vs 0.80
   - Required n at alpha = 0.01 vs 0.05

5. Practical considerations:
   - Add 10-20% to account for dropouts or missing data
   - For clustered designs: multiply by the design effect (DEFF = 1 + (m-1) x ICC, where m is cluster size)
   - Is the required n feasible given the study constraints?

Return: standardized effect size, required n with formula, power curve description, sensitivity table, and feasibility assessment.