Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis testing by means of the Bayes factor provides one avenue to do so, requiring the specification of prior distributions for parameters. The most popular analysis approach views the comparison of proportions from a contingency table perspective, assigning prior distributions directly to the two proportions. Another, less popular approach views the problem from a logistic regression perspective, assigning prior distributions to logit transformed parameters. Reanalyzing 39 null results from the New England Journal of Medicine with both approaches, we find that they can lead to markedly different conclusions, especially when the observed proportions are at the extremes (i.e., very low or very high). We explain these stark differences and provide recommendations for researchers interested in testing the equality of two proportions and users of Bayes factors more generally.

翻译：测试两种比例的平等是科学的一个常见程序,特别是在医学和公共卫生方面。在这些领域,重要的是能够量化缺乏治疗效果的证据。用贝叶斯系数进行的巴伊西亚假设测试提供了一种途径,要求具体说明先前的参数分布。最受欢迎的分析方法从应急表的角度看待比例的比较,将先前的分布直接分配给两种比例。另一个较不受欢迎的方法从后勤回归的角度来看待问题,将先前的分布分配分配分配用于对日志变化参数。用这两种方法重新分析《新英格兰医学杂志》的39个无效结果,我们发现它们可以得出明显不同的结论,特别是在观察到的比例处于极端(即非常低或非常高)的情况下。我们解释这些明显差异,并向有兴趣测试基斯因素的两种比例和使用者的更普遍程度平等的研究人员提出建议。