Common items with inconsistent b-parameter estimates may have a serious impact on item response theory (IRT)--based equating results. To find a better way to deal with the outlier common items with inconsistent b-parameters, the current study investigated the comparability of 10 variations of four IRT-based equating methods (i.e., concurrent…

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.…

A computer simulation study was conducted to investigate the amount of uncertainty added to National Assessment of Educational Progress estimates by equating error under three different equating methods and while varying a number of factors that might affect accuracy of equating. Data from past NAEP administrations were used to guide the…

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 attempt was made to determine which item response theory (IRT) equating method results in the least amount of equating error or "scale drift" when equating scores across one or more test forms. An internal anchor test design was employed with five different test forms, each consisting of 30 items, 10 in common with the base test and 5…

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

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.…

This study examined how four commonly used test equating procedures (linear, equipercentile, Rasch Model, and three-parameter) would respond to situations in which the properties or the two tests being equated were different. Data for two tests plus an external anchor test were generated from a three parameter model in which mean test differences…

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…

In item response theory (IRT), preequating depends upon item parameter estimate invariance. Three separate simulations, all using the unidimensional three-parameter logistic item response model, were conducted to study the impact of the following variables on preequating: (1) mean differences in ability; (2) multidimensionality in the data; and…