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 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
