st: An allowance for clustering should only increase SE's?

 From "CDSC - Nichols, Tom" To "'statalist@hsphsun2.harvard.edu'" Subject st: An allowance for clustering should only increase SE's? Date Wed, 13 Apr 2005 11:42:10 +0100

```Dear statalist,

I have survey data of patients clustered within a sample of hospitals.

If I use:
svyset [pweight=weight], psu(hospital) clear
svymean outcome

this sometimes gives me a SE less than if I had ignored the clustering in
the sample:
svyset [pweight=weight], clear
svymean outcome

I suppose this is because there is rather less variation between cluster
means than within clusters.
But shouldn't an allowance for clustering in the sample increase the SE, not
reduce it?

I understand the formula for the sampling variance from a cluster sample is
var(C) = var(R)*[1+(N-1)*rho]
where var(C) is the variance from the cluster sample of equal size clusters,
var(R) is the variance from a simple random sample of the same size,
N is the size of a cluster, and
rho is the intracluster correlation which must be between 0 and 1.
So var(C) must be greater than var(R).

For some outcomes using the psu( ) option increases the SE and for others
(as mentioned above) it decreases the SE.
The average change for all the outcomes is probably a small increase.
Should I use the psu( ) option only if it increases SE's?
Or should I always use the psu( ) option and just accept that this will
sometimes decrease SE's?

Any advice would be much appreciated.

Tom

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