A Comparison of Two Procedures for Computing IRT Equating Coefficients

Abstract

In order to equate tests under Item Response Theory (IRT), one must obtain the slope and intercept coefficients of the appropriate linear transformation. This article compares two methods for computing such equating coefficients–Loyd and Hoover (1980) and Stocking and Lord (1983). The former is based upon summary statistics of the test calibrations; the latter is based upon matching test characteristic curves by minimizing a quadratic loss function. Three types of equating situations: horizontal, vertical, and that inherent in IRT parameter recovery studies–were investigated. The results showed that the two computing procedures generally yielded similar equating coefficients in all three situations. In addition, two sets of SAT data were equated via the two procedures, and little difference in the obtained results was observed. Overall, the results suggest that the Loyd and Hoover procedure usually yields acceptable equating coefficients. The Stocking and Lord procedure improves upon the Loyd and Hoover values and appears to be less sensitive to atypical test characteristics. When the user has reason to suspect that the test calibrations may be associated with data sets that are typically troublesome to calibrate, the Stocking and Lord procedure is to be preferred.