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Re: st: pweight question

From   Stas Kolenikov <>
Subject   Re: st: pweight question
Date   Thu, 29 Apr 2010 22:23:32 -0500

On Thu, Apr 29, 2010 at 7:31 PM, Randall Lewis <> wrote:
> Should I really think about pweights as stratified sampling (i.e., is this how people generally think about them)? Or should I think of them as 1/f(i) where f(i) is the probability of drawing that individual from the population? You seem to have described it in the former way, rather than the latter. Or does it matter? (I'm pretty sure it should matter for some estimators--like if you were trying to compute the median of an RV, x, and had stratified sampled 100 observations according to each percentile, your estimate of the median would have a much different S.E. than if you had just sampled individuals randomly, via simple random sampling.

I always think of probability weights as the inverse selection
probabilities, as in Horvitz-Thompson estimator. Stratified sampling
is one special case that might generate differential weights, but (a)
it is not necessary that stratified sampling produces differential
weights (example: proportional allocation), (b) different
probabilities of selection might come from other sources, typically in
multistage sampling (e.g. when your measure of size needs corrections
in PPS sampling), (c) the weights given in the publicly released files
will have post-stratification and non-response adjustments on top of
the inverse probability of selection weights.

In your hypothetical example of deeply stratified sampling, the
variance is not estimable if you take one unit from each stratum.
Think of 100 of independent samples of size 1; you cannot estimate any
variances from any of these samples. But if you took say 10 units from
each decile, then yes, that would give you more accurate estimate of
pretty much anything related to the distribution of that variable.

Stas Kolenikov, also found at
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