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st: Comparing multiple sample proportions to population proportions


From   Zoe Hyde <junk@hobbes.kittybutler.org>
To   statalist@hsphsun2.harvard.edu
Subject   st: Comparing multiple sample proportions to population proportions
Date   Thu, 15 Sep 2011 15:54:03 +0800

Hi Everyone,

I know that I can compare a sample proportion to a population proportion
with either a one-sample Z test or a binomial probability test.

e.g., to see if the proportion of drug use in my sample is different to
the proportion in the population (16.2%):


prtest drug_use == 0.162
OR
bitest drug_use == 0.162


However, I'm wondering what I should do when I have multiple categories.

For example, let's say I have a variable that records smoking status:


tab smoke

      smoke |      Freq.     Percent        Cum.
------------+-----------------------------------
    Current |         11       22.00       22.00
  Ex-smoker |         12       24.00       46.00
      Never |         27       54.00      100.00
------------+-----------------------------------
      Total |         50      100.00


I would like to compare these proportions against proprtions
for the general population, but it seems wrong to do three tests 
(sort of like doing a bunch of Mann Whitney U tests without first 
seeing if a Kruskal-Wallis is significant):


bitesti 50 0.22 0.172
bitesti 50 0.24 0.285
bitesti 50 0.54 0.543


So, I'm wondering what I should do?  What would be the correct way to
see if smoking status in my sample is different from the general
population?


Thanks,

Zoe.
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