Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
For continuous outcomes, we rely on Johnson and Mislin’s (2011) Meta-Study on trust game behavior. They find that, across 161 independent trust games, the share of tokens sent by the first-mover was 0.5 with a standard deviation of 0.12. Based on these fig-ures, we perform our power calculation for our first primary outcome, overall efficienty as measured by first-mover choices. Comparing first movers between treatments G-G (80 observations) and G-A (80 observations), our minimal detectable effect size is 5 percent of initial endowment. Comparing first movers between treatments G-A (80 ob-servations) and G-A_signal (110 observations) yields a minimal detectable effect size of 5 percent of the initial endowment.
For our second set of primary outcomes, the dependent variable is binary (e.g., 1=signaling Armenian ethnicity, 0 else). Assuming that in treatment G-A_signal 30 percent of second-movers reveal their Armenian identity, the minimal detectable effect size for comparing second-mover’s signals between G-A_signal and A-A_signal is 19 percentage points.