Hail the impossible: p-values, evidence, and likelihood.
Hail the impossible: p-values, evidence, and likelihood.
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为不可能的事情欢呼：p 值、证据和可能性。
DOI：
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发表时间：
2011
影响因子：
2.1
通讯作者：
T. Johansson
中科院分区：
文献类型：
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作者：
T. Johansson
基于p值的显著性检验是心理学研究和教学中的标准。通常情况下，研究文章和教科书提出并使用p作为反对零假设的统计证据的度量（费舍尔解释），尽管使用的概念和工具基于完全不同的p作为控制长期决策错误的工具（奈曼-皮尔逊解释）。使用p作为证据的度量有四个主要问题，这些问题在心理学领域经常被忽视。首先，p在零假设下是均匀分布的，因此永远不能表明零假设的证据。第二，p仅以零假设为条件，因此不适合量化证据，因为证据总是相对的，即相对于另一个假设支持或反对一个假设。第三，p表示获得证据的概率（假设为空），而不是证据的强度。第四，p取决于未观察到的数据和主观意图，因此，在给定证据解释的情况下，这意味着观察到的数据的证据强度取决于没有发生的事情和主观意图。总之，使用费雪意义上的p作为统计证据的度量，无论是在统计上还是在概念上都是有问题的，而奈曼-皮尔逊解释根本不是关于证据的。相比之下，似然比逃脱了上述问题，并建议作为一种工具，心理学家代表所获得的数据相对于两个假设传达的统计证据。
Significance testing based on p-values is standard in psychological research and teaching. Typically, research articles and textbooks present and use p as a measure of statistical evidence against the null hypothesis (the Fisherian interpretation), although using concepts and tools based on a completely different usage of p as a tool for controlling long-term decision errors (the Neyman-Pearson interpretation). There are four major problems with using p as a measure of evidence and these problems are often overlooked in the domain of psychology. First, p is uniformly distributed under the null hypothesis and can therefore never indicate evidence for the null. Second, p is conditioned solely on the null hypothesis and is therefore unsuited to quantify evidence, because evidence is always relative in the sense of being evidence for or against a hypothesis relative to another hypothesis. Third, p designates probability of obtaining evidence (given the null), rather than strength of evidence. Fourth, p depends on unobserved data and subjective intentions and therefore implies, given the evidential interpretation, that the evidential strength of observed data depends on things that did not happen and subjective intentions. In sum, using p in the Fisherian sense as a measure of statistical evidence is deeply problematic, both statistically and conceptually, while the Neyman-Pearson interpretation is not about evidence at all. In contrast, the likelihood ratio escapes the above problems and is recommended as a tool for psychologists to represent the statistical evidence conveyed by obtained data relative to two hypotheses.