Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We assess statistical power using two-sided tests with α = 0.05 and the conventional 80% power target. With R = 2,500 respondents, J = 7 tasks, and K = 2 profiles, the raw number of profile evaluations is nraw = R x J x K = 35,000. To account for within-respondent clustering, we apply a design-effect correction with cluster size m = J x K = 14 and an intra-cluster correlation of ρ = 0.05, giving DE = 1 + (m − 1)ρ = 1.65 and an effective sample size of neff = nraw/DE ≈ 21,212. The minimum detectable effect at 80% power is MDE = (z1−α/2 + z1−β ) SE. For the eight conjoint attributes, the minimum detectable AMCE ranges from approximately 1.9 percentage points (two-level attributes) to 3.0 percentage points (five-level attributes such as residence). These MDEs lie below the 3–8 pp AMCEs typically reported in the candidate-locality literature, so the main-effect
tests (H1–H3) are well powered.