Individual differences are studied with a multitude of test instruments. Meta-analysis of tests is useful to understand whether individual differences in certain populations can be detected with the help of a class of tests. A method for the quantitative meta-analytical evaluation of test instruments with dichotomous items is introduced. The method assumes beta-binomially distributed test scores, an assumption that has been demonstrated to be plausible in many settings. With this assumption, the method only requires sample means and standard deviations of sum scores (or equivalently means and standard deviations of percent-correct scores), in contrast to methods that use estimates of reliability for a similar purpose. Two parameters are estimated for each sample: mean difficulty and an overdispersion parameter which can be interpreted as the test's ability to detect individual differences. The proposed bivariate meta-analytical approach (random or fixed effects) pools the two parameters simultaneously and allows to perform meta-regression. The bivariate pooling yields a between-sample correlation of mean difficulty parameters and overdispersion parameters. As a side product, reliability estimates are obtained which can be employed to disattenuate correlation coefficients for insufficient reliability when no other estimates are available. A worked example illustrates the method and R code is provided. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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基于样本平均值和标准差的个体差异的β二项式荟萃分析：研究二元项目总分的可靠性。


使用多种测试仪器研究个体差异。测试的荟萃分析有助于了解是否可以借助一类测试来检测某些人群的个体差异。介绍了一种对二分项测试仪器进行定量荟萃分析评价的方法。该方法假设测试分数呈贝塔二项式分布，这一假设已被证明在许多情况下是合理的。在此假设下，该方法仅需要总分的样本平均值和标准差（或等效的正确百分比分数的平均值和标准差），这与出于类似目的而使用可靠性估计的方法不同。为每个样本估计两个参数：平均难度和过度离散参数，该参数可以解释为测试检测个体差异的能力。所提出的双变量元分析方法（随机或固定效应）同时汇集两个参数并允许执行元回归。双变量池化产生平均难度参数和过度离散参数的样本间相关性。作为副产品，获得了可靠性估计，当没有其他估计可用时，可以使用该可靠性估计来消除可靠性不足的相关系数。一个工作示例说明了该方法并提供了 R 代码。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。