The Discriminating Power of Items That Measure More Than One Dimension

Determining a correct response to many test items frequently requires more than one ability. This paper describes the characteristics of items of this type by proposing generalizations of the item response theory concepts of discrimination and information. The conceptual framework for these statistics is presented, and the formulas for the statistics are derived for the multidimensional extension of the two-parameter logistic model. Use of the statistics is demonstrated for a form of the ACT Mathematics Usage Test. Index terms: item discrimination, item information, item response theory, multidimensional item response theory. Statistical measures of item discrimination are computed for several reasons. The traditional measures, usually the point-biserial or biserial correlations between item scores and total scores, ar