-squared measures developed specifically for multilevel contexts are susceptible to upward bias, both analytically via expectation algebra and empirically via simulation; and (c) provide and evaluate a set of adjustments that correct for this bias. We ultimately show that the proposed adjustments do, in fact, yield less bias than the unadjusted versions of measures and discuss factors affecting the discrepancy between adjusted and unadjusted versions, as well as the differential impact such factors have across different measures. We also discuss software with which researchers can compute adjusted measures and illustrate their computation with an empirical example. (PsycInfo Database Record (c) 2026 APA, all rights reserved).
Guo et al. (2026) studied this question.