# Test for comparing "mean of means"

I have a treatment and a control group. Both groups consist of several teams, each with several individuals. When I want to compare the performance between the groups, I could run a t-test or Wilcoxon ranksum test on the individual values within both groups, and that's fine.

1) However, because those teams are very different in size, the "mean of means" looks more like what I get in parametric regressions later. With "mean of mean" I refer to first taking the mean of individual values within the team, then take the mean of team means within the group. Denote by $t$ team, $i$ individual within the group, then $$\text{mean of means}=1/T\sum_{t=1}^{T} (1/n_t \sum_{i=1}^{n_{t}} x_{it}).$$ The question is: are there tests that allow me to test the hypothesis that the two "mean of means" are equal?

2) If not, how would you compute the standard deviation of the mean of means? Clearly, just using the SD of the team means wastes information. In wikipedia I came across pooled standard deviations, which seem to be suitable in this context. Would it be valid to construct standard errors based on these pooled SDs and use them for the hypothesis test?

Thank you very much!

• Thank you! You are right, fixed effects (for team) wouldn't do work since then I couldn't estimate the treatment effect (every team either receives treatment or not). Just to be clear: you propose a linear regression $y_i= b_1*treatment_{it}+constant+e_{it}$ with random effects on team level and a t-test for b_1? And intuitively, what this does is take out the group specific effect, right? Commented Apr 30, 2013 at 15:18