Interval estimation procedures for true scores of a test composed of polytomous items: An application of the multinomial error model.

Abstract

When a person takes alternative forms of the same test across replications of the testing procedure, the test taker's observed scores on the alternative forms are rarely identical. In educational and psychological measurement, inconsistencies in a test taker's scores that are irrelevant to the construct being measured are attributed to errors of measurement. Typically, errors of measurement are summarized as the standard deviation of a test taker's observed scores over replication of the same testing procedure. Assuming that errors of measurement follow a multinomial distribution (i.e., multinomial error model), the main goal of this study was to propose two interval estimation procedures, which are referred to as the score-like and Perks procedures, for true scores of a test with polytomous items. The performance of the score-like and Perks procedures was compared with that of two normal approximation procedures under the multinomial error model and a procedure based on item response theory (IRT) through simulation. In general, the score-like and Perks procedures outperformed the other three procedures when data were generated under the multinomial error theory framework and showed reasonable results when data were generated under the IRT framework. (PsycInfo Database Record (c) 2021 APA, all rights reserved).