发表机构
School of Business, University of Salford（索尔福德大学商学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于后果的度量来量化心理测量量表低可靠性导致的错误分类，并改进可靠性估计，包括修正Cronbach's alpha以逼近omega，提供计算高效的替代方案。
AI 中文摘要
我们引入了一组基于后果的度量，用于量化多项目心理测量量表因不完美可靠性而产生的错误分类。特别关注的是，处于极端潜在特质百分位数的个体能否根据其观测分数被正确识别的概率。这些成本函数提供了一种有原则且可解释的方式，来描述不充分的可靠性如何扭曲分类并降低测试分数的信息价值。我们还考察了在共同因子模型下估计可靠性的方法论问题，重点放在McDonald's omega以及准确置信区间的构建上。为了解决模型拟合的计算负担，尤其是在小样本中，我们推导了Cronbach's alpha的一个修正版本，当共同因子模型成立时，该版本能紧密逼近omega。该估计器具有与omega相当的抽样变异性，同时无需参数估计，提供了一种实用且计算高效的替代方案。
英文摘要
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
Comments13 pages, 4 figures, 3 tables
