Coherent Hypothesis Testing

Fossaluza, Victor; Izbicki, Rafael; Silva, Gustavo Miranda da; Esteves, Luís Gustavo

doi:10.1080/00031305.2016.1237893

Cited by 9 publications

(9 citation statements)

References 16 publications

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“…If a logically coherent test accepts B, then it also accepts A. This property is called monotonocity [1,[35][36][37]. One might also impose that Pg, such that if a logically coherent hypothesis test accepts Pg(B), then it should also accept Pg(A).…”

Section: Definition 7 (Agnostic Test Based On a Region Estimator) Tmentioning

confidence: 99%

Pragmatic Hypotheses in the Evolution of Science

Esteves

Izbicki

Stern

et al. 2019

Entropy

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This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

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Section: Definition 7 (Agnostic Test Based On a Region Estimator) Tmentioning

confidence: 99%

Pragmatic Hypotheses in the Evolution of Science

Esteves

Izbicki

Stern

et al. 2019

Entropy

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“…that at least some rules taking decisions d = N are admissible-we shall also require that α A + α B < 1. A proof is given in Appendix A; for related discussions of restricting loss functions for admissibility and coherence see Fossaluza et al (2017) and Schervish (1996). For prior work featuring losses for this 'three-decision problem' see for example Duncan (1965).…”

Section: Loss Functions For Hypothesis and Significance Testsmentioning

confidence: 99%

“…A proof is given in Appendix A; for related discussions of restricting loss functions for admissibility and coherence see Fossaluza et al . () and Schervish (). For prior work featuring losses for this ‘three‐decision problem’ see for example Duncan ().…”

Section: Introductionmentioning

confidence: 99%

Knowing the Signs: A Direct and Generalizable Motivation of Two-Sided Tests

Rice

Bonnett

Krakauer

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Many well‐known problems with two‐sided p‐values are due to their use in hypothesis tests, with ‘reject–accept’ conclusions about point null hypotheses. We present an alternative motivation for p‐value‐based tests, viewing them as assessments of only the sign of an underlying parameter, where we can conclude that the parameter is positive or negative, or simply say nothing either way. Our approach is decision theoretic, but—unusually—we consider the whole set of possible utility functions available. Doing this we show how, in a specific sense, close analogues of familiar one‐ and two‐sided tests are always the optimal decision. We argue that this simplicity could aid non‐experts’ understanding and use of tests—and help them to think critically about whether or not tests are appropriate tools for answering their questions of interest. Several extensions are also considered, showing that the simple idea of determining the signs of parameters yields a rich framework for inference.

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“…In such a situation, one expects that the rejection of B would imply the rejection of A. However, this property does not apply to standard tests, such as the ones based on the p-value or the Bayes factor (Schervish, 1996;Lavine and Schervish, 1999;Fossaluza et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Logically-consistent hypothesis testing and the hexagon of oppositions

Stern

Izbicki²,

Esteves

et al. 2017

Logic Journal of the IGPL

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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 logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations.

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Coherent Hypothesis Testing

Cited by 9 publications

References 16 publications

Pragmatic Hypotheses in the Evolution of Science

Pragmatic Hypotheses in the Evolution of Science

Knowing the Signs: A Direct and Generalizable Motivation of Two-Sided Tests

Logically-consistent hypothesis testing and the hexagon of oppositions

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