How to obtain standard error of mean from SVY: MEAN

[Maisha Huq]

Hello,

The question: Is it true that calculating the square root of the variance-covariance matrix after using (i) svy: mean, and (ii) matrix V= e(V) provides the standard error of the mean (SEM) not the standard deviation? I think my question has to do just as much with the statistics of if the square root of the variance-covariance matrix=SEM, I also wanted to know from you all if STATA's matrix V = e(V) in fact provides the square of the SEM or something else. I appreciate your time and help! Thank you so much

For context:

The dataset: I'm using two sample clustered (non-longitudinal) survey data.

 foreach v of varlist married school_v2 electricity fridge {
        svy: mean `v', over(source) 
        matrix means =  e(b)
        matrix list means
        svmat means
        rename means* `v'_means*
        
        replace `v'_means1 = (`v'_means1)*100
        replace `v'_means2 = (`v'_means2)*100
        replace `v'_means3 = (`v'_means3)*100
        replace `v'_means4 = (`v'_means4)*100
        replace `v'_means5 = (`v'_means5)*100
        replace `v'_means6 = (`v'_means6)*100
        
        matrix V = e(V)           // <- gets the variance-covariance matrix
        matrix Var = vecdiag(V)     // <- gets the diagonal elements
        svmat Var
        rename Var* `v'_SE*
        replace `v'_SE1 = (sqrt(`v'_SE1))*100 .  // <- the Standard error of means 
        replace `v'_SE2 = (sqrt(`v'_SE2))*100
        replace `v'_SE3 = (sqrt(`v'_SE3))*100
        replace `v'_SE4 = (sqrt(`v'_SE4))*100
        replace `v'_SE5 = (sqrt(`v'_SE5))*100
        replace `v'_SE6 = (sqrt(`v'_SE6))*100    
        
        matrix N = e(N)

Here are some results to compare. Is the SEMs from the SVY means if source==1 step so different from the tabstat if source==1 step
simply because I wasn't actually accounting for survey correlations when I used tabstat or something else?

[Clyde Schechter]

To put it precisely, after using -svy: mean-, the square roots of the diagonal elements of e(V) are, indeed, the standard errors of the estimated means.

More generally, after Stata regression commands, e(V) contains the estimated sampling covariance matrix of the estimates produced. The square roots of the diagonal elements will be the standard errors of the estimates in e(b). This is, in fact, the definition of standard error.

This is very different from what you are seeing in the -tabstat- commands. With -tabstat- you are not accounting for the survey design. If you ran -mean- without the -svy- prefix, you would see that the results for mean and semean are the same as you get from -tabstat-.

[Maisha Huq]

That answers my question! Thank you so much, Clyde