Phattrawan Tongkumchum, Rattikan Saelim, Nifatamah Makaje, and Aniruth Phon-On

pp. 235 - 241

Abstract

We offer methods to create an accurate graph for comparing confidence intervals for two proportions. The first
method involves using weighted sum contrasts when fitting logistic regression with a binary explanatory variable. Since it is
complicated to estimate standard errors of the logit function, the second method is thus based on applying a delta method to
the logit function of the proportions to get their individual estimated standard errors and shrink them to get their comparison
standard errors. The two methods give an accurate approximation of confidence intervals for comparing proportions that is
consistent with the p-values near 0.05 provided by logistic regression.