Power Analysis AI Prompt

Conduct a power analysis to determine the sample size needed for my study.

Study design: {{design}}
Primary statistical test: {{test}}
Effect size: {{effect_size_estimate}} and its source (prior study, meta-analysis, minimum clinically/practically important difference)
Desired power: 0.80 (conventional minimum) or {{desired_power}}
Alpha level: 0.05 (two-tailed) or {{alpha}}

1. Choose the effect size input correctly:

   Priority order for effect size estimation:
   a. Minimum effect size of practical/clinical importance: 'What is the smallest effect that would matter for practice or policy?' Use this if you have domain knowledge.
   b. Meta-analytic estimate: if a meta-analysis of similar studies exists, use its pooled effect size.
   c. Well-powered prior study: a single prior study estimate is noisy; treat it with caution and consider using a smaller estimate.
   d. Cohen's benchmarks (d = 0.2/0.5/0.8): use only as a last resort — these are not field-specific and lead to widely varying conclusions.

   Common mistake: using an effect size from a small pilot study. Small studies overestimate effect sizes (winner's curse). If using a pilot estimate, shrink it by 50%.

2. Run the power analysis:
   - Calculate required N for power = 0.80 and power = 0.90
   - Calculate the minimum detectable effect size at the available N
   - For the recommended design, account for: attrition (inflate N by expected dropout rate), multiple testing (if testing multiple outcomes), clustering (design effect for clustered samples)

3. Sensitivity analysis:
   - Show how required N changes if the true effect size is 50%, 75%, 100%, and 125% of the assumed effect size
   - This illustrates how sensitive the study is to assumptions about effect size

4. Present the power analysis transparently:
   Report: assumed effect size and its source, alpha level, desired power, calculated N, attrition adjustment, final recommended N. State the software/package used.

5. What to do if the required N is not feasible:
   - Use a larger alpha (0.10) only if pre-specified and justified
   - Accept lower power (0.70) only for preliminary studies
   - Narrow the target population to increase homogeneity (reduces within-group variance, increases power)
   - Use a within-subjects design (more efficient than between-subjects)
   - Use a more sensitive primary outcome
   - Abandon and redesign if power cannot exceed 0.50 — an underpowered study is usually not worth running

Return: power analysis results at multiple power levels, sensitivity analysis table, sample size recommendation with attrition adjustment, and methods text.