An Approach to Scoring and Equating Tests With Binary Items: Piloting With Large-Scale Assessments.

This article describes an approach to test scoring, referred to as (-scoring), for tests with dichotomously scored items. The -scoring uses information from item response theory (IRT) calibration to facilitate computations and interpretations in the context of large-scale assessments. The -score is computed from the examinee's response vector, which is weighted by the expected difficulties (not "easiness") of the test items. The expected difficulty of each item is obtained as an analytic function of its IRT parameters. The -scores are independent of the sample of test-takers as they are based on expected item difficulties. It is shown that the -scale performs a good bit better than the IRT logit scale by criteria of scale intervalness. To equate -scales, it is sufficient to rescale the item parameters, thus avoiding tedious and error-prone procedures of mapping test characteristic curves under the method of IRT true score equating, which is often used in the practice of large-scale testing. The proposed -scaling proved promising under its current piloting with large-scale assessments and the hope is that it can efficiently complement IRT procedures in the practice of large-scale testing in the field of education and psychology.