Abstract: Motivated by Freeman-Tukey statistical test, a new equating criterion under item response theory, known as square root criterion (SQRcrit), is proposed. The new method has some features, such as the probabilities for correct response and error response appear simultaneously in the formula and they could not be replaced each other. It is easy to generalize from dichotomous version to polytomous version. It could be regarded as one of weighted versions of Haebara equating criterion. In term of the recovery of estimating the equating coefficients and based on Wilcoxon sign-rank test, the findings of Monte Carlo study show an interesting phenomenon that if the equating approaches are proper relates to the accuracy of the estimation of the item parameters (AEIP) and to the domain of the equating coefficient A, but not to the domain of B. When the AEIP is higher, the new equating criterion is proper for 0.9≤A≤1.3. And when the AEIP is lower, the new equating criterion is proper for 1≤A≤2.

Key words: item response theory, test equating criterion, equating coefficient