Equating Methods and Sampling Designs

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Abstract
The equating methods used and sampling designs employed by the empirical studies in this special issue are described in this introductory article. This theoretical article sets the stage for the empirical articles that follow by introducing the methods and designs and by relieving subsequent authors of the need to spend much time describing either the methods or sampling designs. Four requisites for equating are listed and the invariance of equating functions requisite is identified as the focus of this special issue. Descriptions are given of the Tucker linear equating method, the Levine equally reliable and unequally reliable linear equating methods, the chained equipercentile equation method, the frequency estimation equipercentile and linear equating methods, and the 3PL item response theory true-score equating method. All these methods employ data collected within an anchor test design. The description of each method focuses on assumptions made by that method, may include some basic mathematical expressions associated with the method, and details procedural aspects of the method. Similarities and differences among methods are also discussed. Three types of sampling designs are described: representative sampling, new-form matched sampling (old-form sample to new-form sample), and reference or target matched sampling (old and new samples to a reference population). Some of the practical mechanics of matching are discussed.