Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
0.22
Power Analysis:
Our main specification will regress the outcome in question (see above) on the gender of participant i controlling for age, nationality, education, round and session fixed effects. Standard errors will be clustered at the group level.
We will conduct all regressions using the entire sample as well as the subsample of the last 5 periods only where we observe more “mature” behaviour in this environment.
As there are no prior studies with effect sizes on which to base our choice of sample size we proceeded as follows. We conducted sessions with 60 participants in total of the treatment with heterogeneous task value. In these sessions we detected an effect size of around -0.22 (coefficient on the female dummy) for our main specification and our first outcome (average number of unilateral links). We calculate the sample size needed to detect this effect size using a simple t-test (80% power at significance level of 0.05) and then augment it to give us enough power for our other main outcomes as well as to do subsample analysis.
Taken together these considerations lead us to adopt a sample size of 150 participants per treatment.