Confirming the Null: Remarks on Equivalence Testing and the Topology of Confirmation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913362901729280 |
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| author | Dale, Reid |
| author_facet | Dale, Reid |
| contents | Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a null hypothesis. This paper presents a modal logic of short-run frequentist confirmation developed by leveraging the duality between hypothesis testing and statistical estimation.
It is shown that a hypothesis is confirmable if and only if it satisfies the topological condition of having nonempty interior. Consequently, two-sided hypotheses are not statistically confirmable owing to defects in their topological structure. Equivalence hypotheses are, by contrast, confirmable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confirming the Null: Remarks on Equivalence Testing and the Topology of Confirmation Dale, Reid Statistics Theory Logic Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a null hypothesis. This paper presents a modal logic of short-run frequentist confirmation developed by leveraging the duality between hypothesis testing and statistical estimation. It is shown that a hypothesis is confirmable if and only if it satisfies the topological condition of having nonempty interior. Consequently, two-sided hypotheses are not statistically confirmable owing to defects in their topological structure. Equivalence hypotheses are, by contrast, confirmable. |
| title | Confirming the Null: Remarks on Equivalence Testing and the Topology of Confirmation |
| topic | Statistics Theory Logic |
| url | https://arxiv.org/abs/2405.16331 |