Evaluating the Effects of Differences in Group Abilities on the Tucker and the Levine Observed-Score Methods for Common-Item Nonequivalent Groups Equating

The most critical feature of a common-item nonequivalent groups equating design is that the average score difference between the new and old groups can be accurately decomposed into a group ability difference and a form difficulty difference. Two widely used observed-score linear equating methods, the Tucker and the Levine observed-score methods, have different statistical assumptions when decomposing the score difference. Variation in the decomposition of group ability and form difficulty differences can affect the equating results. This study confirmed previous findings in the literature that when form and group differences are small, both equating methods produce similar results. When the group ability difference is large, however, the Levine observed-score method produces more accurate equating results than the Tucker method. The results indicated that the Levine observed-score method not only decomposes form and group differences more accurately, but also yields smaller unweighted absolute equating differences and average weighted root mean square differences. This study showed that the Levine observed-score method is also robust to the form difference. i