Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
The main hypothesis that we will test is whether, after round 31, orange workers in metagroup one are less likely to educate than orange workers in metagroup two. We will restrict this analysis to medium and high ability workers, since low ability should in theory never educate. We will use a regression analysis where the outcome variable is whether a worker educates in each period. We will explain it with a dummy indicating whether the round is after round 31, this dummy interacted with a dummy indicating whether the megagroup is the first or the second one, and subject fixed effects.
We performed a power analysis after running the first two sessions. We could not perform it before since our priors regarding the underlying data generating process were too noisy. To perform the power analysis, we bootstrap the sample from the first two sessions to reach 320 subjects. We then randomly assign them to one of the two metagroups and perform the regression described above. We run 10000 simulations and store the (on average null) treatment effects for each regression. We use these data to estimate that with 320 subjects we have 80% power to detect an effect of 0.112 percentage points at the 5% level. In other words, if orange workers in the naive pool are 0.112 pp less likely to educate than orange workers in the bayesian pool, we have an 80% chance to capture a significant effect.
- Employers: Before runnuing the main test, the first hypothesis that we will test is whether employers who can choose between two graduated workers are indeed more likely to hire the yellow worker than the orange worker. This test is essential for the rest of the analysis. We expect to easily reject the test that on average employers hire yellow workers half of the time.
- Employers: We will study whether employers become more bayesian or naive over time.
- Emplyoers: We will explore whether employers' naiveté is correlated with their answers in a post-experimental survey.
- Workers: We will also study whether yellow workers choose differently depending on the megagroup that they are placed in, as predicted by the theory.
- Workers: We will also explore whether workers' decisions is correlated with their answers in a post-experimental survey.