Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Baysian method was used, and simulations based on a population model were employed to examine the effect of a sample size of 6000. The model was coded in the R package lavaan (v. 0.6-18). The simulations were conducted using a structural equation model where the two overarching cultural dimensions were modeled as latent variables with the same ten indicators. Factor loadings were determined based on previous research. The outcome measure was the self-reported probability of accepting notifications about critical peak events [0–100%]. The outcome was predicted by the latent cultural dimensions, a health index, and income, separately for the 12 different groups (information treatments 4 × 3 countries). Regression coefficients between -0.05 and 0.25 were used to distinguish effects between the groups. The simulation used standardized values with n=500 per group. A total of 20 independent samples were drawn from the population model and analyzed separately.
The analysis of the simulated datasets was conducted using blavaan (v. 0.5-5). The same equation structure as in the simulation was used, but assumptions were altered to allow for more degrees of freedom, and diffuse priors were employed to make the analysis more conservative. The latent cultural variables were loaded onto only five indicators each, and the covariance between them was set to 0. Prior values for factor loadings were taken from previous research. Default values were used for the variances, Γ (3,3). Priors for the regressions were diffuse, normally distributed, and centered around 0. For each analysis, 5000 samples were drawn across three independent Hamiltonian Monte Carlo chains.
Across the 20 analyses, the majority of parameter estimates yielded similar results within the highest posterior density interval (95%). The effect sizes that, in fewer than 80% of cases, had consistent result interpretations (direction, magnitude, crossing zero) were only those with population effects of 0.05 and 0. Population effects within this range may therefore be challenging to distinguish between groups in the actual dataset.