ETS and the ETS logo are registered trademarks of Educational Testing Service (ETS). AbstractKernel equating (KE) is a new approach to observed-score equating and is described in detail in von Davier, Holland, and Thayer (2004b). Over the past months, several evaluation studies of KE have been designed and carried out. In this part of the overall evaluation study, we compared the KE method with other equating methods using real data from the program of Praxis Series:Professional Assessments for Beginning Teachers®. The goal of this study was to check how closely the KE results agree with the results from other observed-score equating methods in different operational settings. The equating designs involved include an equivalent-groups (EG) design and two nonequivalent groups with anchor test (NEAT) designs with different sample sizes and different characteristics. We compared KE with the equating methods that were used operationally. The results showed that the differences between KE and the traditional equating methods are very small in the EG design, especially in the linear case. In the two NEAT designs, the KE version of poststratification equating with optimal bandwidths produced close results to its analogue, frequency estimation equipercentile equating, except at the lower score range. The KE linear method yielded very similar results to the Tucker method.

Some previous research results imply that women tend to perform better, relative to men, on constructed‐response (CR) tests than on multiple‐choice (MC) tests in the same subjects. An analysis of data from several tests used in the licensing of beginning teachers supported this hypothesis, to varying degrees, in most of the tests investigated. The hypothesis was strongly supported in Praxis™ Principles of Learning and Teaching tests for secondary school teachers and in subject‐knowledge tests for social studies teachers, science teachers, and middle school mathematics teachers. Evidence for the hypothesis was weak in subject‐knowledge tests for middle school English teachers and for secondary school mathematics teachers. Subject‐knowledge tests for secondary school English teachers did not show the hypothesized relationship. The analysis was based on plots showing the cumulative percentages of men and women attaining each possible score on the MC and CR tests.

This study examined population invariance of equating functions over subgroups defined by ethnicity on a teacher certification test. Investigating subgroup equating invariance was important because the total group who took this test consists of two subgroups (i.e., Hispanic and non‐Hispanic) and the Hispanic group is a distinctively more able group as compared to the non‐Hispanic group on the construct being measured. The study used data collected during the 2003 and 2004 administration of a teacher certification test. The chained equipercentile and linear equating methods were used to derive the equating functions. The root expected square difference was used to compare equating functions derived using the total group with equating functions derived using either the Hispanic or non‐Hispanic groups. Findings suggested lack of subgroup invariance in equatings for the first test form (Form X). Also, the Hispanic group equating was less invariant as compared to the non‐Hispanic group equating. The second form of the test (Form Y) showed more subgroup invariance in equating. This difference may partly be attributed to the fact that Form Y had a much bigger sample size as compared to Form X and the difference in equating functions observed in Form X for the total group and the two subgroups may be due to sampling variability. Implications of these results on actual pass/fail rates are also presented and discussed.