Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Assumptions:
- Power (1-ß): 0,80
- Type I error rate: 0,05
- Delta: 0.4 percentage points (4.4% - 4%)
- Equally Sized Groups (low and high uncertainty treatments)
- Standard deviation: 2 percentage points
Outcome Variable:
Percentage of revenue used for large investment projects.
Stata Code:
power twomeans 4 4.4, power(0.8) sd(2)
Based on our assumptions above, we expect to detect a treatment effect of 20 percent of a standard deviation (0.4/2), i.e., we expect to detect a potential decrease in the percentage of revenue invested between the low and high uncertainty treatments.
This requires a sample size of around 1000 respondents (400 - low uncertainty group; 400 - high uncertainty group; 200 - Control Mean Group).