thanks to Nick Cox and Roger Newson for their responses to my question about
robust tests of dependent proportions. Nick gave several references I'll
look up. Roger thinks I wouldn't do to bad with paired t-tests as they are:
"a special case of the Huber variance for clustered data (where the clusters
are the pairs of responses and the observations are the individual
responses)". I wonder if you have a refernce for this I could cite?
I don't think there is any need for a reference, as the point is so
trivial. If you are estimating the difference between 2 population
proportions from 2 different sample proportions on the same sample, then
you are estimating the mean of Z=X-Y, where X and Y are Bernoulli
variables. You are therefore simply estimating the population mean Z from
the sample mean Z. The large sample theory applies, courtesy of the central
limit theorem for ordinary sample means, whether Z is normal (as with the
usual 2-sample t-test) or a discrete distribution with possible values -1,
0 and 1 (as here).
