Conditional Standard Errors of Measurement for Composite Scores Using IRT

Abstract

Composite scores are often formed from test scores on educational achievement test batteries to provide a single index of achievement over two or more content areas or two or more item types on that test. Composite scores are subject to measurement error, and as with scores on individual tests, the amount of error variability typically depends on the individual's score level. A procedure is presented for estimating conditional standard errors of measurement and reliability for composite scores. Item response theory (IRT) models are used as the psychometric foundation for developing the procedure. First, a general procedure is described, followed by specific applications for estimating conditional standard errors of measurement of the ACT Assessment composite and a weighted summed score on a mathematics test. General issues in estimating conditional standard errors of measurement for composite scores are discussed.