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**Agnostic tests can control the type I and type II errors simultaneously.**
*(English)*
Zbl 1445.62009

Summary: Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null hypothesis \((H_0)\) cannot reasonably be interpreted as its acceptance. We propose that this dilemma can be overcome by using agnostic hypothesis tests, since they can control the type I and II errors simultaneously. In order to make this idea operational, we show how to obtain agnostic hypothesis in typical models. For instance, we show how to build (unbiased) uniformly most powerful agnostic tests and how to obtain agnostic tests from standard \(p\)-values. Also, we present conditions such that the above tests can be made logically coherent. Finally, we present examples of consistent agnostic hypothesis tests.

### MSC:

62A01 | Foundations and philosophical topics in statistics |

62F03 | Parametric hypothesis testing |

62C25 | Compound decision problems in statistical decision theory |

### Keywords:

hypothesis test; uniformly most powerful tests; logical consistency; three-decision problem### Software:

BayesFactor
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\textit{V. Coscrato} et al., Braz. J. Probab. Stat. 34, No. 2, 230--250 (2020; Zbl 1445.62009)

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