Optimal Method for Realizing Two-Sided Inferences About a Linear Combination of Two Proportions

In order to reach the inference about a linear combination of two independent binomial proportions, various procedures exist (Wald's classic method, the exact, approximate, or maximized score methods, and the Newcombe-Zou method). This article defines and evaluates 25 different methods of inference, and selects the ones with the best behavior. In general terms, the optimal method is the classic Wald method applied to the data to which z ² _α/2/4 successes and z ² _α/2/4 failures are added (≈1 if α = 5%) if no sample proportion has a value of 0 or 1 (otherwise the added increase may be different).

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