Approximating Scale Score Standard Error of Measurement From the Raw Score Standard Error

Abstract

Conditional estimates of the standard error of measurement (SEM) are necessary for conveying precision at a given score level. The reported metric for score level SEMs is almost always the raw score scale; however, test interpretation typically centers on derived scores. A further hindrance for utilizing the reported error information is the nonlinear relation between raw scores and derived scores. To overcome these limitations, 2 relatively simple methods for estimating the conditional SEM for nonlinearly derived score scales are proposed. Empirical applications of these methods indicate the derived score level SEM, like its raw score counterpart, varies across the score scales. However, unlike the raw score scale SEMs, the variation displayed in derived score units tends to be erratic. The irregularity appears to be a consequence of integer conversions. The 2 proposed procedures produced fairly consistent estimates that tended to peak near the high end of the scale and reach a minimum in the middle of the raw score scale.