A comparison of five methods for estimating the standard error of measurement at specific score levels

Abstract

The Standards for Educational and Psychological Testing (1985) recommended that test publishers provide multiple estimates of the standard error of measurement-one estimate for each of a number of widely spaced score levels. The presumption is that the standard error varies across score levels, and that the interpretation of test scores should take into account the estimate applicable to the specific level of the examinee. This study compared five methods of estimating conditional standard errors. All five of the methods yielded a maximum value close to the middle of the score scale, with a sharp decline occurring near the extremes of the scale. These trends probably characterize the raw score standard error of most standardized achievement and ability tests. Other types of tests, constructed using alternative principles, might well exhibit different trends, however. Two methods of estimation were recommended: an approach based on polynomial smoothing of point estimates suggested by Thorndike (1951) for specific score levels and a modification proposed by Keats (1957) for the error variance derived under the binomial error model of Lord (1955).