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The 'Right' Extension of Type-I Error to Data-Dependent Levels
[Submitted on 27 May 2026] · 2026-05-28 · via stat updates on arXiv.org

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Abstract:The literature on hypothesis testing with data-dependent and post-hoc significance levels relies on a particular extension of the Type-I error to data-dependent levels. Existing arguments for this extension are heuristic, and primarily motivated by a resulting connection to the E-value. Our main contribution is to argue that the extension is 'right', by showing that it emerges from three axioms: it is the only extension that nests classical Type-I error validity for data-independent levels, preserves classical validity for data-dependent levels and is monotone in the strength of the rejection claim. We subsequently apply this result to support the common definition of the E-value, by showing that it arises as the 'right' notion of validity for the numerical representation of a generalized hypothesis test that may reject at different data-driven significance levels.

Submission history

From: Nick Koning [view email]
[v1] Wed, 27 May 2026 12:59:29 UTC (14 KB)