A theoretical and conceptual framework for true-score equating using a simple-structure multidimensional item response theory (SS-MIRT) model is developed. A true-score equating method, referred to as the SS-MIRT true-score equating (SMT) procedure, also is developed. SS-MIRT has several advantages over other complex multidimensional item response…

Smoothing is designed to yield smoother equating results that can reduce random equating error without introducing very much systematic error. The main objective of this study is to propose a new statistic and to compare its performance to the performance of the Akaike information criterion and likelihood ratio chi-square difference statistics in…

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

Test equating might be affected by including in the equating analyses examinees who have taken the test previously. This study evaluated the effect of including such repeaters on Medical College Admission Test (MCAT) equating using a population invariance approach. Three-parameter logistic (3-PL) item response theory (IRT) true score and…

This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

This article uses simulation to compare two test equating methods under the common-item nonequivalent groups design: the frequency estimation method and the chained equipercentile method. An item response theory model is used to define the true equating criterion, simulate group differences, and generate response data. Three linear equating…

The concept of invariance in equating and linking is traced from the 1950s to the present. A number of research studies that examined population invariance are reviewed. Theory and research suggest that linkings other than equatings are population dependent. Theory also indicates that equatings are population dependent, although when test forms…

An analytic procedure for smoothing in equipercentile equating using cubic smoothing splines is described and illustrated. The effectiveness of the procedure is judged by comparing the results from smoothed equipercentile equating with those from other equating methods using multiple cross-validations for a variety of sample sizes. (Author/JKS)

An alternative approach for item response theory observed-score equating is described. Number-correct score distributions are integrated over theoretical or empirical distributions of examinees' estimated trait levels. Comparisons with alternative methods are made. The method can be implemented without the need to estimate trait level for…

Two traditional equating schemes and seven item response theory equating schemes were compared. Data used came from the 1978 equating project of the Iowa Tests of Educational Development. The study entailed both the equating of forms of similar difficulty and the equating of levels of differing difficulty. (Arthor/RL)

A quadratic curve test equating method for equating different test forms under a random-groups data collection design is proposed that equates the first three central moments of the test forms. When applied to real test data, the method performs as well as other equating methods. Procedures from implementing the test are described. (SLD)

Articles on equating test forms in this issue are reviewed and discussed. The results of these papers collectively indicate that matching on the anchor test does not result in more accurate equating. Implications for research are discussed. (SLD)

Discusses some practical issues in linking educational assessments, focusing on the importance of clarity of purpose when assessments are linked. Also stresses the importance of the design used to collect data for linking. Uses linking studies from a variety of situations to illustrate these points. (SLD)

Item response models can be applied in many test equating situations by making strong statistical assumptions. Thus, studying the robustness of the models to violations of the assumptions and investigating model-data fit are essential in all item response theory (IRT) equating applications (M. Kolen and R. Brennan, 1995). Previous studies dealing…

Compared bootstrap standard errors of five item response theory (IRT) equating methods for the common-item nonequivalent groups design using test results for 1,493 and 1,793 examinees taking a professional certification test. Results suggest that standard errors of equating less than 0.1 standard deviation units could be obtained with any of the…