This paper investigates four methods of linear equating under the common item nonequivalent groups design. Three of the methods are well known: Tucker, Angoff-Levine, and Congeneric-Levine. A fourth method is presented as a variant of the Congeneric-Levine method. Using simulation data generated from the three-parameter logistic IRT model we…

A series of resampling studies investigated the accuracy of equating by four different methods in a random groups equating design with samples of 400, 200, 100, and 50 test takers taking each form. Six pairs of forms were constructed. Each pair was constructed by assigning items from an existing test taken by 9,000 or more test takers. The…

Operational testing programs employing item response theory (IRT) applications benefit from of the property of item parameter invariance whereby item parameter estimates obtained from one sample can be applied to other samples (when the underlying assumptions are satisfied). In theory, this feature allows for applications such as computer-adaptive…

The primary objective of this study was to find the smallest sample size for which equating based on a random groups design could be expected to result in less overall equating error than had no equating been conducted. Mean, linear, and equipercentile equating methods were considered. Some of the analyses presented in this paper assumed that the…