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Coherent Hypothesis Testing

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Fossaluza, Victor [1] ; Izbicki, Rafael [2] ; da Silva, Gustavo Miranda [1] ; Esteves, Luis Gustavo [1]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Univ Sao Paulo, Dept Stat, Rua Matao, 1010 Cidade Univ, BR-05508020 Sao Paulo - Brazil
[2] Univ Fed Sao Carlos, Dept Stat, Sao Carlos, SP - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: AMERICAN STATISTICIAN; v. 71, n. 3, p. 242-248, 2017.
Citações Web of Science: 1

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 reject the equality of two means, say (1) = (2), but at the same time to not reject the hypothesis that mu(1) = mu(2) = 0. These two conclusions violate the coherence principle introduced by Gabriel in 1969, and lead to results that are difficult to communicate, and, many times, embarrassing for practitioners of statistical methods. Although this situation is common in the daily life of statisticians, it is usually not discussed in courses of statistics. In this work, we enrich the teaching and discussion of this important topic by investigating through a few examples whether several standard test procedures are coherent or not. We also discuss the relationship between coherent tests and measures of support. Finally, we show how a Bayesian decision-theoretical framework can be used to build coherent tests. These approaches to coherence enlighten when such property is appealing in multiple testing and provide means of obtaining it. (AU)

Processo FAPESP: 14/25302-2 - Uma abordagem flexível para a estimação de uma densidade condicional em problemas com alta dimensionalidade
Beneficiário:Rafael Izbicki
Linha de fomento: Auxílio à Pesquisa - Regular
Processo FAPESP: 09/03385-5 - Classes de testes de hipóteses
Beneficiário:Rafael Izbicki
Linha de fomento: Bolsas no Brasil - Mestrado