Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Main outcome is the investment frequency, which in equilibrium ranges from 0, 2, 4,6 and 8 firms across the 5 treatments. This implies an nominal equilibrium (predicted) effect size of 2. The standard deviation in average investment across 8-subject groups in an earlier related study by Cason, Stranlund and de Vries (2023, JAERE) ranged between 0.5 and 0.6 across treatments. We assume a standard deviation of 1.0 to be conservative, leading to a normalized effect size of 2.0 across pairwise adjacent treatments.
These assumptions lead to a required sample size of 6 sessions per treatment for one-tailed tests that can detect treatment differences in the main investment outcome at 90 percent power with 0.05 significance, for both t-tests and nonparametric Wilcoxon-Mann-Whitney tests (G*Power 3.1.9.4). One-tailed tests are justified due to theoretically-based directional hypotheses of investment levels across treatments. Variance may be elevated due to the lack of price controls in the baseline treatment; additional groups may be scheduled for this treatment if preliminary data indicate variance that is greater than what is assumed here.