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I'm dealing with a random sample and I have a question about its poststratification weights. Let's assume that:

  • this is a random sample of addresses, but post-stratification weights have been calculated (using Census estimates) because the sample doesn't match the target population with respect to some important variables.
  • there are no major non-response problems.

Should the post-stratification weights be used:

  1. as probability weights (for example using [pweight] in Stata or Lumley's survey package in R) when estimating variance, SE, etc... OR
  2. should they simply be used to re-adjust the sample (changing the distribution but not the total sample size) which can then be analysed with random sample variance estimation procedures?

I'd opt for the first option (probability weights, but I may be wrong). Most discussions I find are about clustered samples or more generally samples that were not designed as random in the first place. Other discussions show how post-stratification weights are combined with other types of weights (e.g., to correct for missing data) to produce the final probability weights, but they don't discuss post-stratification in itself. In a survey with good response rates, I see post-stratification as a way to correct non-response bias when this is not very clearly driven by some characteristics and to make the population representative at the same time, two things which are I think often fairly hard to distinguish in some surveys. In other words even when they are just issued as just post-stratification weights and no major non-response problem is mentioned they should be used as probability weights when estimating standard errors etc....

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As probability weights.

The weights don't tell you anything about the precision of the observations, so if you use them as other sorts of weights you will get (in general) the wrong standard errors.

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