True score equating by Fixed b's scaling: A flexible and stable equating alternative

Abstract

Six methods of equating The Test of English as a Foreign Language (TOEFL) test scores were evaluated in terms of scale stability. True score item response theory (IRT) equating based on "Fixed b’s" scaling, the current TOEFL operational scaling and equating procedure, was found to produce the least discrepant results when compared to two IRT models (b parameter estimated, a and c parameters fixed; all three parameters reestimated), and to three conventional equating methods (Tucker, Levine, and equipercentile). The results for Fixed b’s scaling were limited by an inadequately fit item; but if such items can be identified prior to calibration, or if pretested data are observed to produce reliable estimates of total group data, then true score IRT equating based on scaling by fixing the b parameters of a set of pretested items may be a very acceptable option.