Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
This study does not have treatment and control arms. Instead, the main contrasts of interest are gender-based differences (men vs. women) in expression outcomes and in influence on requests. Therefore, we report the Minimum Detectable Effect Sizes (MDEs) for two-sample comparisons (men vs. women) under standard power assumptions (α = 0.05, power = 0.80). With N = 60–120 participants (balanced by gender), the MDE is approximately 0.5–0.7 SD for standardized continuous outcomes (e.g., tone score), and 23–36 percentage points for binary outcomes (e.g., refusal indicator). With repeated measures (5 rounds/participant) and assuming an intra-class correlation of 0.2, the effective sample size is reduced, leading to MDEs of 0.7–1.0 SD and 30–45 percentage points, respectively.