I need help determining the minimum sample size for a randomized controlled experiment. The treatment (1 Factor, 3 Levels) will be administered to different households clustered within 5 routes. There are at least two dependent variables: the proportion of households with citations (citation is a binary 0/1 measure) and number of citations per household. I am having trouble identifying a formula that can compare the three means/proportions and provide a breakdown of the number of observations needed per treatment and control groups. My goal is to be able to identify which treatment is most effective. Any help is much appreciated!
Violations(i,t) = Treatment1 + Treatment2 + Treatment3 + Controls
The number of violations for household i, period t is a function of which treatment the household received plus other fixed effects/controls such as median income, population density, etc.