The procedure of M.L. Stocking and F.M. Lord (1983) for computing equating coefficients for tests having dichotomously scored items is extended to the case of graded response items. A system of equations for obtaining the equating coefficients under the graded response model is derived. (SLD)

Examined whether the item response theory (IRT) true-score equating method is more adversely affected by the presence of multidimensionality than two conventional equating methods, linear and equipercentile equating. Results of two simulation studies suggest that the IRT method performs as well as the conventional methods when the correlation…

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…

Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equi-percentile equating property. True score…

The use of educational tests in practical situations often requires that tests that are built to different content and/or statistical specifications be statistically linked. When equating methods are applied to tests that differ in content, difficulty, and/or reliability, the resulting scores cannot be used interchangeably. This study examined…

It is a widely held belief that an anchor test used in equating should be a miniature version (or "minitest") of the tests to be equated; that is, the anchor test should be proportionally representative of the two tests in content and statistical characteristics. This paper examines the scientific foundation of this belief, especially…

Consistent behavior is a desirable characteristic that common items are expected to have when administered to different groups. Findings from the literature have established that items do not always behave in consistent ways; item indices and IRT item parameter estimates of the same items differ when obtained from different administrations.…

The logic and uses of test equating are discussed, including three methods of test equating. The focus is on the conceptual underpinnings of each test equating method, rather than on the mathematics of the procedures. Additional consideration is given to the assumptions of each method and its respective strengths and weaknesses. A commonly…

This paper addresses the sample invariant properties of four equating methods (Tucker and Levine linear equating, equipercentile equating through an anchor test, and three-parameter item response theory equating). Data from several national administrations of the Scholastic Aptitude Test served as the source of data for the study. Equating results…

A new and unified approach to test equating is described that is based on log-linear models for smoothing score distributions and on the kernel method of nonparametric density estimation. The new method contains both linear and standard equipercentile methods as special cases and can handle several important equating data collection designs. An…

Section Pre-Equating (SPE) is a method used to equate test forms that consist of multiple separately timed sections. SPE does not require examinees to take two complete forms of the test. Instead, all of the old form and one or two sections of the new form are administered to each examinee, and missing data techniques are employed to estimate the…

To explore the appropriateness of the Rasch model for the vertical equating of a multi-level, multi-form achievement test series, both the Rasch model and the traditional Thurstone procedures were applied to the Listening Comprehension subtest scores of the Stanford Achievement Test. Two adjacent levels of these tests were administered in 1981 to…

The Los Angeles Unified School District has been concerned over the excess testing of elementary school pupils, particularly those who are in special programs. When the Board of Education decided to have yearly testing of pupil progress using a locally developed criterion-referenced test, the intention was to replace a previously used…

Procedures used to compare the results from item response theory as well as more traditional equating methods were described and critically analyzed. The implications of the comparison of equipercentile, linear, one-parameter (Rasch), and three-parameter methods for equating twelve forms of each of the five tests of General Educational Development…

Seven papers on technical and practical issues in equating are presented. Problems related to the use of conventional and item response theory equating methods, using pre- and post-smoothing to increase equipercentile equating's precision, and linear equating models for common-item nonequivalent-population design are discussed. (SLD)