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arXiv · 2007.05857

Measurement error and reliability from a different perspective: Reliability of decision functions and the sum score

Lourens Waldorp·Maarten Marsman·Denny Borsboom
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Abstract

We propose an alternative framework for measurement error that allows us to determine reliability at the level of the decision, such as the decision to pass or fail. This framework makes it possible to answer the question which properties of a decision function are relevant to make decisions. The mechanism is relatively simple for dichotomous items: The response to any item has probability $\tfrac{1}{2}(1-ρ)$, with $ρ\in [-1,1]$, to be different from the original response. We show that this framework satisfies the classical axioms (those of Lord and Novick) and can therefore be considered as being aligned with classical test theory. We also show some relations to modern test theory and its connections to graphs. We then connect the idea of reliability at the level of the decision to the idea of how many of the (two-response) items are required to be flipped to change the decision; this is referred to as stability. Finally, we argue that from this perspective the best decision function (with respect to a set of properties including stability) is a weighted sum score with threshold value.

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Lourens Waldorp, Maarten Marsman, Denny Borsboom. 2026-08-17. Measurement error and reliability from a different perspective: Reliability of decision functions and the sum score. https://arxiv.org/abs/2007.05857

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