We offer methods to create an accurate graph for comparing confidence intervals for two proportions. The firstmethod involves using weighted sum contrasts when fitting logistic regression with a binary explanatory variable. Since it iscomplicated to estimate standard errors of the logit function, the second method is thus based on applying a delta method tothe logit function of the proportions to get their individual estimated standard errors and shrink them to get their comparisonstandard

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... s. The two methods give an accurate approximation of confidence intervals for comparing proportions that isconsistent with the p-values near 0.05 provided by logistic regression.