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arXiv · 2605.24995

Information-Theoretic Reliability is Robust to Analytic Choice: A 24-Specification Multiverse on Public Cognitive Test-Retest Data

Maria Westrin
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Abstract

Background. The reliability paradox describes the empirical observation that cognitive tasks producing robust group-level effects often yield poor between-individual reliability. Existing approaches rely predominantly on the intraclass correlation coefficient (ICC), which captures only linear, second-moment dependence between test and retest. Methods. We introduce a normalized, information-theoretic complement to ICC, NLR{\Delta}, defined as the difference between empirically estimated mutual information and the analytic Gaussian baseline implied by the test-retest correlation. We pair NLR{\Delta} with ICC(2,1), bias-corrected and accelerated (BCa) bootstrap intervals, Benjamini-Hochberg false discovery rate (FDR) control, and a 24-cell multiverse over the KSG nearest-neighbour parameter, correlation method, and minimum-sample threshold. The full pipeline is governed by pre-specified claim contracts, content-addressed provenance, and SHA-256-verified raw data ingestion, and is released as the MixMind Reliability Framework. Results. Across 50 estimable primary measures from the Flanker, Stroop, Stop-Signal, Go/No-Go, and Posner task families, the median NLR{\Delta} is -0.138 nats, with interquartile range [-0.257, -0.034]. Zero of 50 primary measures exceed the headline rule. The companion ICC(2,1) analysis recovers the classical reliability paradox pattern, and the 24-specification multiverse yields 0 of 1,200 estimable cells passing the headline rule. Conclusions. On these two public datasets, replacing or augmenting ICC with an information-theoretic reliability measure does not rescue cognitive tasks from the reliability paradox. The robust null is invariant to the analytic choices examined here. We release the full pipeline, raw-data hashes, and contracts to enable exact replication and extension to other datasets and tasks.

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Maria Westrin. 2026-05-24. Information-Theoretic Reliability is Robust to Analytic Choice: A 24-Specification Multiverse on Public Cognitive Test-Retest Data. https://arxiv.org/abs/2605.24995

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