Erroneous Generalization - Exploring Random Error Variance in Reliability Generalizations of Psychological Measurements

Reliability Generalization (RG) studies frequently interpret meta-analytic heterogeneity in score reliability as evidence of differences in an instrument’s measurement quality across administrations. However, such interpretations ignore the fact that, under Classical Test Theory (CTT), score reliability depends on two parameters: true score variance and error score variance. True score variance refers to the actual variation in the trait we aim to measure, while error score variance refers to non-systematic variation arising in the observed, manifest variable. If the error score variance remains constant, variations in true score variance can result in heterogeneity in reliability coefficients. While this argument is not new, we argue that current approaches to addressing this issue in the RG-literature are insufficient. Instead, we propose enriching an RG study with Boot-Err: Explicitly modelling the error score variance using bootstrapping and meta-analytic techniques. Through a comprehensive simulation scheme, we demonstrate that score reliability can vary while the measuring quality remains unaffected. The simulation also illustrates how explicitly modelling error score variances may improve inferences concerning random measurement error and under which conditions such enhancements occur. Furthermore, using openly available direct replication data, we show how explicitly modelling error score variance allows for an assessment to what extent measurement quality can be described as identical across administration sites.