Simultaneous equating of multiple forms

Abstract

When test forms are calibrated separately, item response theory parameters are not comparable because they are expressed on different measurement scales. The equating process converts the item parameter estimates to a common scale and provides comparable test scores. Various statistical methods have been proposed to perform equating between two test forms. However, many testing programs use several forms of a test and require the comparability of the scores of each form. To this end, Haberman (ETS Res Rep Ser 2009(2):i–9, 2009) developed a regression procedure that generalizes the mean-geometric mean method to the case of multiple test forms. A generalization to multiple test forms of the mean-mean, the Haebara, and the Stocking-Lord methods was proposed in Battauz (Psychometrika 82:610–636, 2017b). In this paper, the methods proposed in the literature to equate multiple test forms are reviewed, and an application of these methods to data collected for the Trends in International Mathematics and Science Study will be presented.