Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a null hypothesis. This paper presents a modal logic of short-run frequentist confirmation developed by leveraging the duality between hypothesis testing and statistical estimation. It is shown that a hypothesis is confirmable if and only if it satisfies the topological condition of having nonempty interior. Consequently, two-sided hypotheses are not statistically confirmable owing to defects in their topological structure. Equivalence hypotheses are, by contrast, confirmable.

翻译：零假设统计检验是各学科进行统计分析的主导框架。关于证据是否以及在何种情况下可被视为对零假设具有证实作用，学界仍存在广泛争议。本文通过利用假设检验与统计估计之间的对偶性，构建了一种短期频率主义证实的模态逻辑。研究证明：一个假设可被证实的充要条件是其满足具有非空内部的拓扑条件。因此，由于拓扑结构缺陷，双侧假设不具备统计可证实性。相比之下，等价性假设则具有可证实性。