Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Unit of measurement: the fraction of trips ending in crowded areas at the individual user level. For a type I error probability of alpha = 0.05 and a power of 1- k = 0.8, and N =1,000 per treatment arm, the standardized minimum detectable effect size is 0.126 standard deviations. The standard deviation of out outcome variable is highest when half of the users always parks in a crowded area and the other half never, in which case s.d. = 0.5. In this most extreme case, the minimum detectable effect size (MDE) would be a change in parking in disorderly areas of 6.3 percentage points (=0.5x0.126). If only half of the selected individuals takes up treatment (that is: completes at least one trip in the experimental period), the MDE would increase to 8.9 percentage points. Increasing the power to 1-k =0.9 increases the MDE to 7.3 percentage points. In the experimental area, the benchmark percentage of parking in crowded area’s is over 40%.