Standard errors of measurement, confidence intervals, and the distribution of error for the observed score curve

Abstract

This paper reviews the basic literature on the suggested applications of the standard error of measurement (SEM), and points out that there are discrepancies in its suggested application. In the process of determining the efficacy and appropriateness of each of the proposals, a formula to determine the distribution of error for the observed score curve is derived. The final recommendation, which is congruent with Cronbach, Gleser, Nanda & Rajaratnam's (1972) recommendations, is to not use the SEM to create confidence intervals around the observed score: The predicted true score and the standard error of the prediction are better suited (non-biased and more efficient) for the task of estimating a confidence interval which will contain an individual's true score. Finally, the distribution of future observed scores around the expected true score is derived.