If I have a national survey data that used stratified random sample design, and the proportion of each stratum (e.g., state) sampled is not identical to the proportion of the population (e.g., proportions of the actual state populations) [I am assuming that the stratification was not done based on the proportion of the actual state population, but based on something else. i.e., strata were not states], do I need to use a weight to account for disproportionate selection if I want to make comparisons between states?

I would appreciate if you could provide a good reference for that as well.

Thank you in advance for your help!

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#### Best Answer

A stratified design effectively means that separate surveys are designed within each stratum – units selected within one stratum are independent of all selections within other strata. Estimates of total are made within each stratum, and then combined to come up with the estimate of total across the population:

$$ hat{Y} = sum_{text{strata}}hat{Y}_{text{stratum}}\ = sum_{text{strata}}sum_{text{units}}y_iw_i $$

The design weight for a unit in the survey should only weight the unit within the stratum that the unit belongs to. There is no need to modify design weights, assuming you have them.

I recommend reading Model Assisted Survey Sampling (Sarndel, Swenson, Wretman) or Practical Sampling Techniques (K Som)

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