确认零假设：关于等价性检验与确认的拓扑结构评述
Confirming the Null: Remarks on Equivalence Testing and the Topology of Confirmation
AI总结：
本文利用假设检验与估计的对偶性，提出短程频率主义确认的模态逻辑，证明假设可确认当且仅当拓扑内部非空，从而说明双侧假设不可确认而等价性假设可确认。
摘要：
零假设显著性检验是各科学领域进行统计分析的主导框架。关于证据在何种情况下可以被视为对零假设具有确认性，学界仍存在相当大的争论。本文提出了一种短程频率主义确认的模态逻辑，该逻辑通过利用假设检验与统计估计之间的对偶性而构建。研究表明，一个假设是可确认的，当且仅当它满足具有非空内部的拓扑条件。因此，双侧假设因其拓扑结构缺陷而在统计上不可确认。相比之下，等价性假设是可确认的。
英文摘要：
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.
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