Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
This study incorporates two separate experiments: the first comparing Pre-Project Decision with Post-Project Uncertainty groups, and the second assessing Positive Outcome versus Negative Outcome groups. Each experiment independently employs a two-tailed t-test to compare outcome variables between the groups. The sample size calculation, based on a medium effect size (Cohen's d of 0.5), an alpha error (significance level) of 0.05, and a desired power of 0.95, estimates the need for approximately 105 participants per group. This leads to a total of about 210 participants for each experiment, and 420 participants for both experiments combined.
However, beyond the primary comparison using t-tests, the study also intends to examine the interactions of individual characteristics with the treatment effects. This additional analysis necessitates a larger sample size to maintain statistical power and precision. The calculation for this aspect of the study, which considers the complexity and variability introduced by examining interactions, results in a total sample size of 520 participants. This increased sample size ensures that the study is adequately powered not only for the main effects analysis but also for the exploration of these interaction effects, thereby enhancing the comprehensiveness and depth of the research findings.