A general delta method is described for computing the standard error (SE) of a chain of linear equations. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. Computer simulations demonstrate the method. (SLD)

The effects of different degrees of smoothing on results of equipercentile equating in random groups design using a postsmoothing method based on cubic splines were investigated, and a computer-based procedure was introduced for selecting a desirable degree of smoothing. Results suggest that no particular degree of smoothing was always optimal.…

The equating of results from the PC-BILOG computer program to an underlying metric was studied through simulation when a two-parameter item response theory model was used. Results are discussed in terms of the identification problem and implications for test equating. (SLD)

A numerical approach for computing standard errors (SEs) of a linear equating is described in which first partial derivatives of equating functions needed to compute SEs are derived numerically. Numerical and analytical approaches are compared using the Tucker equating method. SEs derived numerically are found indistinguishable from SEs derived…

In applying I. I. Bejar's method for detecting the dimensionality of achievement tests, researchers should be cautious in interpreting the slope of the principal axis. Other information from the data is needed in conjunction with Bejar's method of addressing item dimensionality. (SLD)

An equating design in which two groups of examinees from slightly different populations are administered a different test form with a subset of common items is widely used. This paper presents standard errors and a simulation that verifies the equation for large samples for an equipercentile equating procedure for this design. (Author/BS)

This study compared the performance of the LOGIST and BILOG computer programs on item response theory (IRT) based scaling and equating for the Test of English as a Foreign Language (TOEFL) using real and simulated data and two calibration structures. Applications of IRT for the TOEFL program are based on the three-parameter logistic (3PL) model.…

Large sample standard errors of linear equating for the single-group design are derived without making the normality assumption. Two general methods based on the delta method of M. Kendall and A. Stuart (1977) are described. One method uses the exact partial derivatives, and the other uses numerical derivatives. Simulation using the beta-binomial…

Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…

Empirical evidence is presented of the relative efficiency of two potential linkage plans to be used when equivalent test forms are being administered. Equating is a process by which scores on one form of a test are converted to scores on another form of the same test. A Monte Carlo study was conducted to examine equating stability and statistical…