Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations are based on estimates from Chapman et al. (2024), which our experimental design closely follows in both task structure and outcome measures. The study reports mean values and standard deviations for risk aversion (ρ) and loss aversion (λ) across both representative and student samples. Using these values, we conducted two-sample t-tests in STATA assuming a significance level of 5% and 80% power, targeting a moderate effect size of Cohen’s d = 0.5.
Across tasks, the Minimum Detectable Effect Sizes (MDES) are as follows:
Main Sample – Lottery Equivalent Tasks:
Risk Aversion (ρ): Mean = 0.88, SD = 0.39 → MDES = 0.20 (≈ 22.6% of control mean)
Loss Aversion (λ): Mean = 1.18, SD = 0.98 → MDES = 0.49 (≈ 41.5%)
Main Sample – Certainty Equivalent Tasks:
Risk Aversion (ρ): Mean = 1.09, SD = 0.29 → MDES = 0.15 (≈ 13.9%)
Loss Aversion (λ): Mean = 2.16, SD = 1.27 → MDES = 0.63 (≈ 29.2%)
Student Sample – Lottery Equivalent Tasks:
Risk Aversion (ρ): Mean = 1.05, SD = 0.30 → MDES = 0.15 (≈ 14.3%)
Loss Aversion (λ): Mean = 1.30, SD = 0.69 → MDES = 0.35 (≈ 26.9%)
Student Sample – Certainty Equivalent Tasks:
Risk Aversion (ρ): Mean = 1.06, SD = 0.30 → MDES = 0.15 (≈ 14.2%)
Loss Aversion (λ): Mean = 2.26, SD = 0.86 → MDES = 0.43 (≈ 19.0%)
These MDES values indicate the smallest change in parameters (in original units and as a percentage of the control group mean) that the study is adequately powered to detect under standard assumptions. All calculations were made using power twomeans in STATA. Clustering is not a major concern given the random assignment at the individual level within sessions.
Reference: Chapman, J., Snowberg, E., Wang, S.W., & Camerer, C. (2024). Looming large or seeming small? Attitudes towards losses in a representative sample. Review of Economic Studies, p.rdae093.