What you see is not what you get: Observed scale score comparisons misestimate true group differences.

Abstract

Social sciences of all kinds are interested in latent variables, their measurement, and how they differ between groups. The present study argues the importance of analyzing mean differences between groups using the latent variable approach. Using an open-access repository of widely applied personality questionnaires (N = 999,033), we evaluate the extent to which the commonly used observed sum score is susceptible to measurement error. Our findings show that Cohen's d values based on the observed variance significantly misestimate the true group difference (based on just the factor score variance) in 33 of the 70 studied cases, and by an average of 25.0% (or 0.048 standard deviations). There was no meaningful relationship between the effect size discrepancy and scale reliability as measured by McDonald's ω. We discuss the implications of these results and outline concrete steps that applied researchers can take to improve their analyses.