Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Minimum detectable effect size for primary outcomes (accounting for sample design and clustering)
For the first hypothesis, we are adopting a within-person design. With a within-person (paired) comparison with N = 1,200, two-sided α = 0.05, and 80% power, the minimum detectable effect in SD of the difference scores (Cohen’s d_z) is: 0.08 of a standard deviation.
For the second hypothesis, where we compare observations across samples, we would be comparing the mean of participants' WTP gap for a ton of CO2 across the first and fourth, and second and fourth treatment arms. Assuming that we get 125 observations in the first two, each, and 700 in the latter, an alpha of 0.05, a power of 80%, and a two-sided test, we can detect effect sizes of 0.27 of a standard deviation. We will also perform a comparison using both institutional asset owner and asset manager samples combined, resulting in 250 and 700 observations and a minimum detectable effect size of 0.21 standard deviations. Since these minimum effect sizes are large, we might need to collect additional responses from institutional asset owners and firm management.