The difficulty of test items that measure more than one ability

Abstract

Many test items require more than one ability to obtain a correct response. This article proposes a multidimensional index of item difficulty that can be used with items of this type. The proposed index describes multidimensional item difficulty as the direction in the multidimensional space in which the item provides the most information and the distance in that direction to the most informative point. The multidimensional difficulty is derived for a particular item response theory model and an example of its application is given using the ACT Mathematics Usage Test.