Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study targets 1,200 participants, each contributing four avatar-level observations, for a total of 4,800 participant–avatar observations. The main power calculation is based on the primary avatar-level specification with participant fixed effects, story fixed effects, and order fixed effects, and with standard errors clustered at the participant level.
In the absence of pilot data, the calculation relies on standard design assumptions. Specifically, we assume balanced treatment assignment, 80% power, a 5% two-sided significance level, a within-participant correlation of 0.4 to account for repeated observations within individuals, and an outcome standard deviation of 0.25 for primary outcomes measured on a 0–1 scale. Under these assumptions, the minimum detectable effect for the main avatar-level treatment effects is approximately 0.12 standard deviations, corresponding to about 0.03 points on the 0–1 scale, or roughly 3 percentage points.