Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Using the results of the Probabilistic Reasoning subset (main reference for the system 1 bias questions) in Stanovich, West and Toplak (2016) as the outcome of control group (mean 11.2, SD 3.6), with power = 0.8, alpha=0.05 (adjusting for multiple testing), MDE is 5.163 (=a 46% increase)
Stanovich, K. E., West, R. F., & Toplak, M. E. (2016). The rationality quotient: Toward a test of rational thinking. MIT Press.