An Alternative Approach for IRT Observed-Score Equating of Number-Correct Scores

Abstract

An alternative approach for item response theory observed-score equating is described. The number- correct score distributions needed in equating are found by numerical integration over the theoretical or empiri cal distributions of examinees' traits. The item response theory true-score equating method and the observed- score equating method described by Lord, in which the number-correct score distributions are summed over a sample of trait estimates, are compared in a real test example. In a computer simulation, the observed-score equating methods based on numerical integration and summation were compared using data generated from standard normal and skewed populations. The method based on numerical integration was found to be less biased, especially at the two ends of the score distribu tion. This method can be implemented without the need to estimate trait level for individual examinees, and it is less computationally intensive than the method based on summation.