证明随机测试形式的信度按斯皮尔曼-布朗公式的比率趋近于 1,且与项目池的维度无关。

IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Psychometrika Pub Date : 2024-09-01 Epub Date: 2024-03-12 DOI:10.1007/s11336-024-09956-7
Jules L Ellis, Klaas Sijtsma
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引用次数: 0

摘要

研究表明,基于随机抽样项目和不相关误差的任何真分模型的心理测验信度,在假定一些一般规律性条件的情况下,随着测验长度的增加,信度收敛到无穷大,概率为 1。斯皮尔曼-布朗(Spearman-Brown)公式给出了渐近收敛率,为此不需要项目是平行的,或潜在单维的,甚至是有限维的。用 2 参数逻辑项目反应理论模型模拟的结果表明,短多维测验的信度可能是正偏的,也就是说,在这种情况下应用斯皮尔曼-布朗公式会导致对加长测验的信度预测过高。然而,简短测验的设计者一般都会设计只测量一种属性的简短测验,因此偏差问题可能与实际意义不大。对于 2 参数逻辑模型下的单维度简短测验,信度几乎是无偏的,这意味着在这些实用性更强的情况下,应用斯皮尔曼-布朗公式可以得出近似无偏的预测结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Proof of Reliability Convergence to 1 at Rate of Spearman-Brown Formula for Random Test Forms and Irrespective of Item Pool Dimensionality.

Proof of Reliability Convergence to 1 at Rate of Spearman-Brown Formula for Random Test Forms and Irrespective of Item Pool Dimensionality.

It is shown that the psychometric test reliability, based on any true-score model with randomly sampled items and uncorrelated errors, converges to 1 as the test length goes to infinity, with probability 1, assuming some general regularity conditions. The asymptotic rate of convergence is given by the Spearman-Brown formula, and for this it is not needed that the items are parallel, or latent unidimensional, or even finite dimensional. Simulations with the 2-parameter logistic item response theory model reveal that the reliability of short multidimensional tests can be positively biased, meaning that applying the Spearman-Brown formula in these cases would lead to overprediction of the reliability that results from lengthening a test. However, test constructors of short tests generally aim for short tests that measure just one attribute, so that the bias problem may have little practical relevance. For short unidimensional tests under the 2-parameter logistic model reliability is almost unbiased, meaning that application of the Spearman-Brown formula in these cases of greater practical utility leads to predictions that are approximately unbiased.

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来源期刊
Psychometrika
Psychometrika 数学-数学跨学科应用
CiteScore
4.40
自引率
10.00%
发文量
72
审稿时长
>12 weeks
期刊介绍: The journal Psychometrika is devoted to the advancement of theory and methodology for behavioral data in psychology, education and the social and behavioral sciences generally. Its coverage is offered in two sections: Theory and Methods (T& M), and Application Reviews and Case Studies (ARCS). T&M articles present original research and reviews on the development of quantitative models, statistical methods, and mathematical techniques for evaluating data from psychology, the social and behavioral sciences and related fields. Application Reviews can be integrative, drawing together disparate methodologies for applications, or comparative and evaluative, discussing advantages and disadvantages of one or more methodologies in applications. Case Studies highlight methodology that deepens understanding of substantive phenomena through more informative data analysis, or more elegant data description.
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