Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We aim for a power of 0.8 and an alpha of 0.05.
We have 20 rounds per cluster (group), so this is 20 observations on market level per cluster.
The main outcome variable of interest is welfare, measured as the sum of payoffs of all traders. Relative to the intial endowments, welfare can increase up to 200 ECU or can decrease up to 200 ECU, depending on the number and kinds of trades made.
Suppose welfare is uniformly distributed in [0,80], i.e., between 0% and 40% of maximum gains. This implies an SD of about 25.
We assume the intracluster correlation to be 0.5. In a previous experiment (Corgnet, DeSantis and Porter (2020)) it was lower than that, sometimes it is higher, so this is our best guess.
Under these conditions, how many clusters per treatment would we need if we want to be able to detect a treatment difference of 25?
According to Stata, we need 9 clusters per treatment, but we will make it 10 to be sure. The command:
power twomeans 0 25, m1(20) m2(20) sd(25) rho(0.5) cluster