Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties encountered in their computation. To address these problems, we define Bayes factor functions (BFF) directly from common test statistics. BFFs depend on a single non-centrality parameter that can be expressed as a function of standardized effect sizes, and plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies. Such summaries eliminate the need for arbitrary P-value thresholds to define ``statistical significance.'' BFFs are available in closed form and can be computed easily from z, t, chi-squared, and F statistics.
翻译:Bayes系数代表了相竞科学假设为数据所分配的概率比。Bayes系数的缺点在于它们依赖于以前界定无效和替代假设的规格以及计算过程中遇到的困难。为了解决这些问题,我们直接从共同的测试统计中界定Bayes系数函数。BFF值依赖于单一的非中央参数,该参数可以表示为标准化效应大小的函数,BFFs图段与影响大小的图段提供了可以很容易地在各种研究中加以汇总的假设测试信息摘要。这些摘要消除了任意的P值阈值来界定“统计意义”的必要性。BFF值以封闭的形式提供,可以很容易地从z、t、chisquared和F统计数据中计算。