Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
A sample size analysis assuming an alpha of 0.05 and a power of 80% indicated that we need a sample size of at least 252 participants per treatment in order to detect the smallest effect size* found in the scenario of a previous lab experiment, closest to our current parameters, with a Wilcoxon Mann Whitney test.
* Mean investments in ECU in previous experiment No Insurance versus Mandatory Insurance:
2711.9 (sd 4102.4) versus 1793.4 (sd 3976.8): effect size 27% -> sample size needed 252
* Mean investments in ECU in previous experiment Mandatory Insurance versus Premium Discount:
1793.4 (sd 3976.8) versus 3550 (sd4560.1): effect size 41% -> sample size needed 78