Sample size (or number of clusters) by treatment arms
We anticipate collecting a total of approximately 250 observations across each of our four treatment conditions for a total of 1,000 observations. Briefly, we base this on the following ex-ante power calculation + logic: Because an interesting and possible outcome in our study is that different incentives do not induce significant treatment effect, we want sufficient statistical power to trust null results. Therefore, our goal is to collect enough data so that we can detect reasonably small effects (Cohen's D of ~ .3) at alpha=.01 and power =.8. Assuming equal variance across treatment, this implies we need approximately 262 participants per treatment (to make all pair-wise comparisons).