Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We perform a simulation-based, between-subject ANOVA power analysis in order to estimate the minimum sample sized needed to minimise the probability of incurring a Type II error. Our a priori calculation uses Caldwell and Läkens’ Superpower R package, whose algorithm relies on 10,000 Monte Carlo data set simulations with attributes specified by the researcher. We have defined the input parameters, mu = [2,1,4.5,2.5,5.5,4.5] {Each mean corresponds to the following condition, respectively: Control with Peer Effects, Control, Altruism Narrative with Peer Effects, Altruism Narrative, Self-Interest Narrative with Peer Effects, Self-Interest Narrative.} and sigma = 2.89$, based on a linear approximation of Metzger and Günther's (2019) experimental mean and standard deviation whose design is similar to ours. We adapt these numbers to our hypotheses. With a power score of 100 for the narrative factor, 100 for the peer effects factor, and 81.4 for the interaction between these two factors, a sample size of n = 250 per experimental condition suffices to reach the recommended power level (Cohen, 1988), when alpha = 0.05. Cohen’s f estimates of 0.5, 0.23 and 0.08 (respectively) coincide with benchmark big, medium and small effect sizes (0.4, 0.25, 0.1).