Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Analyzing self-set wages, I will compare wages levels in T1 to wages in T2. Based on a two-sided Wilcoxon-Mann-Whitney test, an error probability of 0.05, and a power of 0.80, we require about 160 participants per treatment to detect an effect of Cohen’s d of 0.32. For the proportion of people choosing the maximum wage, an effect of 14.6 percentage points will be detectable with 160 participants.
For effort, I will compare effort provision in T1 + T2 to effort levels in T3 (1 GBP fixed wage) and T4 (2 GBP fixed wage). According to the literature, this effect should be rather large (approximately d=0.5). Based on a two-sided Wilcoxon-Mann-Whitney test, an error probability of 0.05, and a power of 0.80, we require about 80 participants per treatment to detect an effect of Cohen’s d of 0.36 (compared to T1 + T2). Between T3 and T4, the minimum detectable effect size is d=0.46 with 80 participants per treatment.