Noninformative Bayesian $P$-values for testing marginal homogeneity in $2 \times 2$ contingency tables

Author:

Chen Lee-Shen,Yang Ming-Chung

Abstract

This article considers the problem of testing marginal homogeneity in $2 \times 2$ contingency tables under the multinomial sampling scheme. From the frequentist perspective, McNemar's exact $p$-value ($p_{_{\textsl ME}}$) is the most commonly used $p$-value in practice, but it can be conservative for small to moderate sample sizes. On the other hand, from the Bayesian perspective, one can construct Bayesian $p$-values by using the proper prior and posterior distributions, which are called the prior predictive $p$-value ($p_{prior}$) and the posterior predictive $p$-value ($p_{post}$), respectively. Another Bayesian $p$-value is called the partial posterior predictive $p$-value ($p_{ppost}$), first proposed by [2], which can avoid the double use of the data that occurs in $p_{post}$. For the preceding problem, we derive $p_{prior}$, $p_{post}$, and $p_{ppost}$ based on the noninformative uniform prior. Under the criterion of uniformity in the frequentist sense, comparisons among $p_{prior}$, $p_{_{{\textsl ME}}}$, $p_{post}$ and $p_{ppost}$ are given. Numerical results show that $p_{ppost}$ has the best performance for small to moderately large sample sizes.

Publisher

Tamkang Journal of Mathematics

Subject

Applied Mathematics,General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Powerful Test of Two Proportions by Assuming a Registered Prior Density;Communications in Statistics - Simulation and Computation;2016-06-02

2. Improving and extending the McNemar test using the Bayesian method;Statistics in Medicine;2016-01-18

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