Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Given the sample size, it is possible to identify an effect of receiving access to the game (independent of the sub-treatments) of 0.114 standard deviations (s) on continuous variables and 5.7 percentage points on discrete variables.
When only the 500 participants in each sub-treatment group are compared with the control group, the MDEs are 0.154s on continuous variables and 7.6 percentage points on proportions. Likewise, the MDE of the additional effects of both sub-treatments is 0.177s on continuous variables and 8.8 percentage points on proportions.