We have a population of approximately 4000 people we want to do some research on, to see the effects on mean cost of an intervention. We know this population is extremely skewed at the moment - mean is approximately 80k but the top 10% is approximately 300K.
If we are only interested in mean cost does the central limit theorem mean that we don't have to over-sample for high cost cases?
Thanks Sergei I'm going to work through this and think about it
Grainne
Have you considered fitting a skewed distribution such as Log-normal or Weibull? Do contact me if you require a collaborator.
Grainne -
You ask about an "...over-sample for high cost cases." Does that mean that you have auxiliary/regressor data that will tell you 'ahead of time' which ones will be the high cost cases, or at least indicate which ones are likely to be those high cost cases? If so, as Neelam noted, at a minimum, you can do much better with stratified random sampling. See a survey statistics book such as Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
If you have just minimal enough such information to form some rough categories by size, you can stratify, perhaps even with a certainty stratum included. If it is a bit better, and you can say you have a size measure, you might try selection probability proportional to size (PPS) sampling, and the attendant estimation methodology. Or you could try model-based estimation if you have good regressor data, or model-assisted design-based methods.
Cheers - Jim
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