Conditional Standard Error of Measurement in Prediction

Abstract

Previous methods for estimating the conditional standard error of measurement (CSEM) at specific score or ability levels are critically discussed, and a brief summary of prior empirical results is given. A new method is developed that avoids theoretical problems inherent in some prior methods, is easy to implement, and estimates not only a quantity analogous to the CSEM at each score but also the conditional standard error of prediction (CSEP) at each score and the conditional true score standard deviation (CTSSD) at each score, The new method differs from previous methods in that previous methods have concentrated on attempting to estimate error variance conditional on a fixed value of true score, whereas the new method considers the variance of observed scores conditional on a fixed value of an observed parallel measurement and decomposes these conditional observed score variances into true and error parts. The new method and several older methods are applied to a variety of tests, and representative results are graphically displayed. The CSEM‐Iike estimates produced by the new method are called conditional standard error of measurement in prediction (CSEMP) estimates and are similar to those produced by older methods, but the CSEP estimates produced by the new method offer an alternative interpretation of the accuracy of a test at different scores. Finally, evidence is presented that shows that previous methods can produce dissimilar results and that the shape of the score distribution may influence the way in which the CSEM varies across the score scale.