Testing for differences in chain equating

Abstract

The comparability of the scores obtained in different forms of a test is certainly an essential requirement. This paper proposes a statistical test for the detection of noncomparable scores based on item response theory (IRT) methods. When the IRT model is fit separately for different forms of a test, the item parameter estimates are expressed on different measurement scales. The first step to obtain comparable scores is to convert the item parameters to a common metric using two constants, called equating coefficients. The equating coefficients can be estimated for two forms with common items, or derived through a chain of forms. The proposal of this paper is a statistical test to verify whether the scale conversions provided by the equating coefficients are as expected when the assumptions of the model are satisfied, hence leading to comparable scores. The method is illustrated through simulation studies and a real‐data example.