# Minimum Sample Size For Clustered Data Randomized Experiment

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!

Model Details

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.

• Minimum sample size will depend on exact model specification (and the model itself). I would recommend adding that to your Q.
– 1muflon1
Oct 14, 2020 at 14:26
• Thanks. I tried to provide more details. Please let me know if anything else would be helpful. Oct 14, 2020 at 14:30
• I think it is still little bit too ambiguous. For example, in OLS, and this also holds in FE panel regression, as rule of thumb you should have about 25-30 observations per independent regressors (textbook authors differ). However, if you just say I want to add "controls" and just name few and leave others as etc. there is no way for people knowing how many independent regressors will be in your regression. Unless the above mentioned rule of thumb already solved your issue, you should post exact model specification. Also at this site you can typeset equations the same way as in LaTex
– 1muflon1
Oct 14, 2020 at 14:34
• There are also additional data requirement depending whether you anticipate that autocorrelation/heteroskedasticity could be a problem as in panel regressions one way to conveniently solve for those is to use clustered standard errors but those require as a rule of thumb at least $\approx$ 40 clusters (see Mostly Harmless Econometrics) there is of course always bootstrapping but you might prefer clustering if possible.
– 1muflon1
Oct 14, 2020 at 14:39