Beta-binomial meta-analysis of individual differences based on sample means and standard deviations: Studying reliability of sum scores of binary items.

Abstract

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).