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Logically-consistent hypothesis testing and the hexagon of oppositions

Stern, Julio Michael and Izbicki, Rafael and Esteves, Luis Gustavo and Stern, Rafael Bassi (2017) Logically-consistent hypothesis testing and the hexagon of oppositions. [Preprint]

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Abstract

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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Stern, Julio Michael0000-0003-2720-3871
Izbicki, Rafael
Esteves, Luis Gustavo
Stern, Rafael Bassi
Additional Information: Preprint version
Keywords: Statistical hypothesis tests, hexagon of oppositions, logical consistency, agnostic hypothesis tests, probabilistic and alethic modalities.
Subjects: General Issues > Scientific Metaphysics
General Issues > Causation
General Issues > Confirmation/Induction
General Issues > Decision Theory
General Issues > Evidence
General Issues > Explanation
Specific Sciences > Probability/Statistics
Depositing User: Prof. Julio Michael Stern
Date Deposited: 01 Apr 2023 22:10
Last Modified: 01 Apr 2023 22:10
Item ID: 21929
Journal or Publication Title: Logic Journal of the IGPL
Official URL: http://doi.org/10.1093/jigpal/jzx024
DOI or Unique Handle: https://doi.org/10.1093/jigpal/jzx024
Subjects: General Issues > Scientific Metaphysics
General Issues > Causation
General Issues > Confirmation/Induction
General Issues > Decision Theory
General Issues > Evidence
General Issues > Explanation
Specific Sciences > Probability/Statistics
Date: 2017
Page Range: pp. 741-757
Volume: 25
Number: 5
ISSN: 1367-0751
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21929

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