The denominator chooses the estimand: A target-population true-score framework for standardized mean differences.

Abstract

The standardized mean difference (SMD) is a workhorse effect-size index across psychology, education, and the behavioral sciences, but its denominator embeds estimand-level commitments-about reliability, sample heterogeneity, and the reference scale on which the effect is interpreted-that are rarely made explicit. We treat the choice of SMD denominator as an estimand-level choice (Lundberg et al., 2021) and develop the latent true-score and target-population-anchored geometric SMD (LTG-SMD): an SMD in which the denominator is the geometric mean of group-specific true-score standard deviations in an explicitly chosen target reference population. An algebraic decomposition relates LTG-SMD to Hedges's g through two transparent factors-a reliability factor and a study-to-target factor-that show exactly when conventional SMDs converge with LTG-SMD and when they diverge. We develop plug-in estimation with both analytic delta-method confidence intervals and bias-corrected nonparametric bootstrap intervals, evaluate finite-sample properties across 1,152 simulation conditions, and illustrate the framework in three empirical settings spanning a high-reliability educational trial with a holdout reference, a moderate-reliability brief personality scale with an external reference, and a 23-site Many Labs 2 replication using a cross-site reference. The framework has direct implications for meta-analysis and multisite research: Anchoring effects to a common target reference separates one important source of denominator-driven heterogeneity from substantive heterogeneity, though it does not address all sources of measurement or design heterogeneity. LTG-SMD is offered as a complementary estimand, not a universal replacement for conventional SMDs. (PsycInfo Database Record (c) 2026 APA, all rights reserved).