Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The planned sample size is 1,280 individual participants, with approximately 160 participants in each of the eight experimental cells. The outcome variables are measured as probability estimates on a 0–100 scale, so the unit of the minimum detectable effect is percentage points on this scale.
Assuming 80% power, a two-sided 5% significance level, no clustering, equal cell sizes, and an outcome standard deviation of 20 points, the minimum detectable effect for a simple comparison between two equally sized experimental cells is approximately 0.31 standard deviations, or 6.2 percentage points.
Because the main estimands involve interaction effects, the relevant minimum detectable effects are larger. Under the same assumptions, the approximate minimum detectable effect for the 2 × 2 candidate-gender-by-evaluator interaction within one information condition is approximately 0.44 standard deviations, or 8.8 percentage points. The approximate minimum detectable effect for the full information-by-candidate-gender-by-evaluator interaction is approximately 0.63 standard deviations, or 12.6 percentage points. These calculations are benchmarks; realized power will depend on observed outcome variance, realized cell balance, and the final analysis specification.