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arXiv · 2610.03006

Psychometric Tests: Quantifying the Consequences of Low Reliability and Improving Reliability Estimation

Rose Baker
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Abstract

We introduce a set of consequence-based measures that quantify the misclassification arising from imperfect reliability in multi-item psychometric scales. Particular attention is given to the probability of individuals in extreme latent-trait percentiles being correctly identified from their observed scores. These cost functions provide a principled and interpretable way to characterise how inadequate reliability distorts classification and reduces the informational value of test scores. We also examine methodological issues in estimating reliability under common-factor models, with emphasis on McDonald's omega and the construction of accurate confidence intervals. To address the computational burden of model fitting, especially in small samples, we derive a modified version of Cronbach's alpha that closely approximates omega when the common-factor model holds. This estimator has comparable sampling variability to omega while requiring no parameter estimation, offering a practical and computationally efficient alternative. y

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Rose Baker. 2026-10-02. Psychometric Tests: Quantifying the Consequences of Low Reliability and Improving Reliability Estimation. https://arxiv.org/abs/2610.03006

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