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Subject:

Sample Weights

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Date:

Thu, 13 May 1999 10:21:20 +0100 ()

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 Dear Allstat I have a query regarding the sample weighting scheme when units at the first stage of a two stage sampling scheme are sampled with probability proportional to size. The data I am analysing comes from a study where hospitals are sampled from the set all district general hospitals in the UK with probability in proportion to their catchment population. Then in each of the sampled hospitals a number of patients are sampled at random. I have read in text that if say the patient population for all district general hospitals is N and the catchment population for sampled hospital i is Ni and b hospitals are selected in total, then the probability of selection for hospital i (assuming the hospitals are selected with replacement) is pi = bNi/N I cannot however believe this to be correct, since there is the chance that pi > 1 if Ni is large enough in comparison to N. I make the probability of hospital i being selected pi = 1-(1-Ni/N)^b which is 1- the probability of hospital i not being selected. Can anyone clarify this ? The next question is how do I weight each of the patients selected in hospital i ? If there are ni patients selected in hospital i, then I think that the probability of any individual patient selected in hospital i is p1i = pi*ni/Ni Again can anyone clarify this and possibly be able to provide some useful references. Many Thanks Trevor Mole Department of Medical Statistics and Evaluation Imperial College School of Medicine Hammersmith Hospital London ---------------------- trevor mole [log in to unmask] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%