Conditional Standard Error of Measurement as an Estimand of Individual Score Precision: Remarks on Pfadt et al. from an Operator-Theoretic Perspective.

Abstract

This commentary supports Pfadt et al.'s (2026, Psychometrika, 2026, 1-35. https://doi.org/10.1017/psy.2026.10081) recommendation that individual score interpretation should rely on conditional standard errors of measurement rather than a single unconditional standard error. I argue, however, that this recommendation requires a sharper test-theoretic formulation. Conditional precision is not merely a computational refinement of the standard error of measurement; it is a different estimand, defined by the information structure relative to which score precision is interpreted. Using an operator-theoretic formulation of classical test theory, I treat the true score as a conditional expectation, the error score as a projection residual, and the standard error of measurement as the norm of that residual. From this perspective, conditional standard errors localize residual variation with respect to observed scores, score bands, persons, trait levels, or measurement contexts. This formulation clarifies why assumptions associated with particular estimation procedures should not be attributed to classical test theory itself, and why practices such as pooling sparse score groups change the estimand. The commentary concludes that responsible individual score interpretation requires identifying the relevant conditional-precision estimand before selecting an estimator or software procedure.