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 | |||||||||||||||
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| 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 |
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| 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: | 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 |
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| Date: | 2017 | |||||||||||||||
| Page Range: | pp. 741-757 | |||||||||||||||
| Volume: | 25 | |||||||||||||||
| Number: | 5 | |||||||||||||||
| ISSN: | 1367-0751 | |||||||||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21929 |
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