Equating; Frequency Estimation Equipercentile

This paper studies whether equating results can be improved if the variable that accounts for all systematic differences between equating populations is identified and used as an anchor in anchor test design or as a variable on which to match equating samples. The sample invariant properties of four anchor test equating methods (Tucker and Levine equally reliable linear models, chained equipercentile, and frequency estimation equipercentile models) were examined under representative, matched-on-equating-test, and matched-on-selection-variable conditions. The selection variable, the variable along which subpopulations differ, was also used as an anchor for the four equating methods and compared to equatings in which the equating test served as the anchor. All equatings were performed with real Scholastic Aptitude Test (SAT) populations or simulated populations. Accuracy criteria were equivalent-group