ABSTRACT This article examines the evidence contained in t statistics that are marginally significant in 5% tests. The bases for evaluating evidence are likelihood ratios and integrated likelihood ratios, computed under a variety of assumptions regarding the alternative hypotheses in null hypothesis significance tests. Likelihood ratios and integrated likelihood ratios provide a useful measure of the evidence in favor of competing hypotheses because they can be interpreted as representing the ratio of the probabilities that each hypothesis assigns to observed data. When they are either very large or very small, they suggest that one hypothesis is much better than the other in predicting observed data. If they are close to 1.0, then both hypotheses provide approximately equally valid explanations for observed data. I find that p-values that are close to 0.05 (i.e., that are “marginally significant”) correspond to integrated likelihood ratios that are bounded by approximately 7 in two-sided tests, and by approximately 4 in one-sided tests. The modest magnitude of integrated likelihood ratios corresponding to p-values close to 0.05 clearly suggests that higher standards of evidence are needed to support claims of novel discoveries and new effects.

中文翻译：

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来自边际显着 t 统计量的证据

摘要 本文检查了 t 统计量中包含的证据，这些证据在 5% 的检验中具有边际意义。评估证据的基础是似然比和综合似然比，它们是在关于零假设显着性检验中的替代假设的各种假设下计算的。似然比和综合似然比为支持竞争假设的证据提供了有用的度量，因为它们可以被解释为代表每个假设分配给观察数据的概率的比率。当它们非常大或非常小时，它们表明一个假设在预测观察到的数据方面比另一个好得多。如果它们接近 1.0，则两个假设都为观察到的数据提供了大致相同的有效解释。我发现接近 0.05 的 p 值（即“边际显着”）对应于综合似然比，在双边检验中以大约 7 为界，在单方检验中以大约 4 为界。与接近 0.05 的 p 值对应的综合似然比的适度幅度清楚地表明需要更高标准的证据来支持新发现和新效果的主张。