Dennis,
I am not sure about this, but here goes anyway. Since the decision making process is based on Type I error (Critical Point and p-value), and since Type I error is under the assumption that the Null Hypothesis is true, then the "pooled" formula is appropriate. However, when one is doing Power calculations, then one would not use the "pooled" formula (similar to using a non-central t with continuous data).
Howard Kaplon
-----Original Message-----
From: dennis roberts [mailto:[EMAIL PROTECTED]]
Sent: Thursday, November 15, 2001 8:30 AM
To: [EMAIL PROTECTED]
Subject: diff in proportions
in the moore and mccabe book (IPS), in the section on testing for
differences in population proportions, when it comes to doing a 'z' test
for significance, they argue for (and say this is commonly done) that the
standard error for the difference in proportions formula should be a POOLED
one ... since if one is testing the null of equal proportions, then that
means your null is assuming that the p*q combinations are the SAME for both
populations thus, this is a case of pooling sample variances to estimate a
single common population variance
but since this is just a null ... and we have no way of knowing if the null
is true (not that we can in any case) ... i don't see any logical
progression that would then lead one to also assume that the p*q
combinations are the same in the two populations ... hence, i don't see why
the pooled variance version of the standard error of a difference in
proportions formula would be the recommended way to go
in their discussion of differences in means ... they present FIRST the NON
pooled version of the standard error and that is there preferred way to
build CIs and do t tests ... though they also bring in later the pooled
version as a later topic (and of course if we KNEW that populations had the
same variances, then the pooled version would be useful)
it seems to me that this same logic should hold in the case of differences
in proportions
comments?
==============================================================
dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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