Divergence versus decisionP‐values: A distinction worth making in theory and keeping in practice: Or, how divergenceP‐values measure evidence even when decisionP‐values do not
本文区分了两种P值定义：分歧P值衡量数据与模型的兼容性，决策P值用于决策规则；论证了分歧P值在衡量证据时优于决策P值，并建议在教学中明确区分。
Abstract There are two distinct definitions of “ P ‐value” for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was expected under the model, such as a sum of squares or a deviance statistic. A P ‐value is then the ordinal location of the measure in a reference distribution computed from the model and the data, and is treated as a unit‐scaled index of compatibility between the data and the model. In the other definition, a P ‐value is a random variable on the unit interval whose realizations can be compared to a cutoff α to generate a decision rule with known error rates under the model and specific alternatives. It is commonly assumed that realizations of such decision P ‐values always correspond to divergence P ‐values. But this need not be so: Decision P ‐values can violate intuitive single‐sample coherence criteria where divergence P ‐values do not. It is thus argued that divergence and decision P ‐values should be carefully distinguished in teaching, and that divergence P ‐values are the relevant choice when the analysis goal is to summarize evidence rather than implement a decision rule.