st: clustered SE smaller than

["Robert G. LaChausse" <rlachaus@csusb.edu>]

Hi- I'm very new to using Stata and certainly no statistician.

I have a clustered RCT with treatment and control conditions where 
subjects are clustered in 22 school sites. Subjects provided pretest 
and posttest scores. The level of random assignment was at the school 
(site) level.  I'm using  Stata to obtain robust standard errors for 
an ITT analysis. I am attempting to predict a posttest score 
(continuous measure) from the group variable (treatment or control; 
binary) controlling for the pretest score.

I ran the analysis without considering  the clusters (.regress 
posttestscore pretestscore Group) and then again using  .regress 
posttestscore pretest score Group, vce(cluster site).  I wanted to 
see for myself the differences in SE's.

My understanding is that the robust SE should be larger than the 
regular OLS SE. I found that the robust SE were actually a little 
smaller (ie .17 regular SE and .14 robust SE). The cluster sizes 
range from 13 to 321. There are 22 clusters. The only thing I can 
think of is that the ICC is negative but don't know why. There aren't 
any outliers making one site different from another.  Is it possible 
to run the .regress posttestscore pretest score Group, vce(cluster 
site) using a random effects approach so that the ICC are all 
positive? Would that change the interpretation of the ITT analysis? 
What would be the command?
Thanks, RGL




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