Dear Allstat
Thanks to all of those who replied to my question regarding the above. A
summary of the responses is as follows:
1. If you have the raw data then you can use the complex samples module
within spss which should calculate this for you
2. The Mantel-Haenszel test is a common approach.
3. I believe you can use the existing formula for comparing the difference
between two populations when the samples are random, making a few
alterations to take into account the design effect due to the
stratification.
4. If you can produce C.I.s you presumably can also produce a standard error
for the estimates. What is wrong with using these to construct a 'z' test?
5. I would ask the question: Do the proportions vary a lot across the
strata? If so, what use is a comparison of the overall population
proportions, particularly if the sampling fractions vary in the two
populations?
In general, an analysis of proportions can be carried out as a
generalized linear model in several packages (Genstat, S-Plus, Stata)
and these packages would allow you to weight the proportions by both the
stratum sizes and the sampling weights. This would allow you to fit a
model with terms for population and stratum, and understand the
structure of the variation before you calculate weighted summaries.
6. Use the SVY commands in STATA. This can deal with variable sampling
fractions as well as stratification: all you need is a variable in the
data file that identifies the design weight and a variable that
indicates stratum.
I think a bit of further reading is required from myself!
Many thanks,
Stephen
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