st: Aggregated Weighted Summary Statistics Using Probability Weights

[Lindsay Newman <lrshorr@gmail.com>]

I am using survey data with probability weights.  I want to compute
various summary statistics, including the mean and standard deviation,
of the data at an aggregated level.  In particular, I want to use
individual responses to certain questions to calculate the country
year weighted mean and standard deviation of the response.  For
instance, if 200 individuals responded to a particular question, what
is the weighted average response for that country year?  What is the
weighted standard deviation of the responses for that country year?

When I sort by country year and use the following code:

(1) by countryyear: summarize (response variable) [aw=weight variable]

I get different results for the standard deviations than when I either run:

(2) summarize (response variable) if countryyear ==x [aw=weight variable]

or when I calculate the standard deviation manually using:

(3)  di sqrt(e(N) * el(e(V_srs),1,1))


When I analyze the responses for just one country year (i.e. deleting
all but responses from a single country year) using:

(4) svy: mean (response variable) estat sd,

the standard deviations match 2 and 3 but not 1.  Why is this?

Thank you.
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