Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations assume two-sided tests, a significance level of α = 0.05, and power of 80%. Randomization is at the individual level, and no clustering adjustment is required. Under equal allocation across the four experimental groups, the main treatment effects are estimated by pooling two groups versus two groups within the 2 × 2 factorial design.
Main outcome 1: Survival belief bias
The outcome is measured in probability units (0–1). We assume a standard deviation of approximately 0.23. The minimum detectable effect size for the main effect of the survival literacy treatment is 0.0285 (2.85 percentage points), which requires approximately 511 observations per experimental cell (total N ≈ 2,044). The minimum detectable effect for the financial literacy treatment is 0.057 (5.7 percentage points), requiring approximately 128 observations per cell (total N ≈ 512).
The assumed effect sizes are guided by prior evidence on subjective survival expectations and their responsiveness to information. In particular, Hurwitz, Mitchell, and Sade (2022, Journal of Economic Behavior & Organization) show that longevity beliefs can be meaningfully updated in response to informational interventions.
Main outcome 2: Risky asset share
The outcome is defined as the fraction of a hypothetical endowment allocated to a risky asset (ranging from 0 to 1). We assume a standard deviation of 0.25, consistent with the dispersion observed in survey and experimental data. The minimum detectable effect size for the main treatment effects is 0.03 (3 percentage points), which requires approximately 545 observations per experimental cell (total N ≈ 2,180). Larger effects of 0.05 (5 percentage points) would be detectable with approximately 196 observations per cell (total N ≈ 784).
The assumed effect sizes are informed by prior experimental evidence. In particular, Billari, Favero, and Saita (2023, Journal of Banking & Finance) document increases in equity exposure of approximately 3 percentage points following interventions combining financial and demographic information. The assumed range of 3–5 percentage points reflects conservative benchmarks based on this literature.
Interaction effects in the 2 × 2 design require substantially larger samples and are therefore treated as exploratory. For example, detecting an interaction effect of 0.0285 in survival belief bias would require more than 2,000 observations per experimental cell (total N > 8,000).
The planned sample size of approximately 3,600 individuals provides sufficient power to detect main effects for both primary outcomes within the range of effect sizes considered.