Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Outcome: claimed own share of the team's work, in percentage points (0 to 100). Randomisation is at the individual level, blocked on work site, so there is no clustering; the calculation allows for site fixed effects absorbing an assumed 15 percent of the variance and, for the pooled estimate, an assumed within-person correlation across waves of 0.5. Assuming 90 percent response at Survey 1 falling five percentage points per wave (83 per arm at Survey 1, 64 at Survey 5), the minimum detectable effect for a two-sided 5 percent test with 80 percent power is about 0.40 standard deviations at Survey 1 and about 0.32 standard deviations pooled over the five waves. The standard deviation of claimed share is not known before fielding; if it lies between 15 and 20 percentage points, the Survey 1 figure corresponds to roughly 6 to 8 percentage points of claimed share and the pooled figure to roughly 5 to 6 points, against a control-arm mean likely to be near 20 to 25 percent in teams of four to five. The closest prior study (Schroeder, Caruso and Epley 2016, Experiment 3) found an effect of about 0.27 standard deviations on the same contrast; power against an effect of that size is about 0.47 at Survey 1 and about 0.66 pooled.