Multiple hypothesis testing, an important quantitative tool to report the results of scientific inquiries, frequently leads to contradictory conclusions. For instance, in an analysis of variance (ANOVA) setting, the same dataset can lead one to …

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be …

This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results …

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are …

Many authors have argued that, when performing simultaneous statistical test procedures, one should seek for solutions that lead to decisions that are consistent and, consequently, easier to communicate to practitioners of statistical methods. In …

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