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Abstract:
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The notion of p-value is fundamental in statistics. However, it is often misinterpreted, misused or miscommunicated. In this article, we propose a general and rigorous definition of p-value that fulfills the two expected characteristics of it. The proposal incorporates all existing definitions of p-value available, and justifies their interpretations. The paper further presents a concrete approach to formulate and calculate p-values based on confidence distribution. It has two main advantages. First, it is applicable for a wide range of hypothesis testing problems, including the conventional one- and two-sided tests, tests with interval-type null, intersection-union tests, multivariate tests and so on. Second, it can naturally lead to a coherent interpretation of p-value as the strength of evidence in support of the null hypothesis, as well as a meaningful measure of degree of such support. Numerical examples are used to illustrate the wide applicability and computational feasibility of our approach. We show that our proposal is a safe and universally effective and can be applied broadly, without further consideration of the form/size of the null space.
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