Well, I went digging through the documentation and came across two things that might affect this. The first is that the standard error of the mean is the square root of the variance. Note that this is different to the square root of the variance divided by n, which is what I think you were expecting. The second thing is how the variance is estimated. The default is a Taylor series expansion, and it looks like the formulas do involve various values for n by cluster. However, later on when the documentation talks about degrees of freedom it says:
Taylor Series Variance Estimation
For the Taylor series method, PROC SURVEYMEANS calculates the degrees of freedom for the t test as the number of clusters minus the number of strata. If there are no clusters, then the degrees of freedom equals the number of observations minus the number of strata. If the design is not stratified, then the degrees of freedom equals the number of PSUs minus one.
To me, that says that the divisor when calculating the variance is the number of clusters minus the number of strata. If not stratified, then it is the number of primary sampling units minus one. There is nothing about the sample size within clusters entering into this calculation. So to match up the t test calculation to the variance calculation, I would expect you would have to use the same logic. I am really willing to believe I might be in error on this, but based on your example, that is what it looks like is happening.
SteveDenham
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