Fundamental Measurement

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Abstract
Additive conjoint measurement is one of a number of theories allowing interval measurement of psychological and social attributes. If certain axioms are satisfied, the theory proves the existence of certain representations of the data. While clearly of great value theoretically, additive conjoint methods have rarely been used in education (with the exception of Rasch models). The measurement theory is algebraic and deals with deterministic (perfectly reliable) data. The lack of a commonly agreed upon method for determining model fit in the presence of error has limited its use. This paper reviews methods for assessing fit to an additive conjoint model, outlines another method for assessing fit, and reports an application of the method to a problem in educational testing. Multiple-choice test items were systematically varied along two dimensions (language difficulty and semantic similarity of response options) and the effects on item difficulty assessed. Some theoretical and practical implications of the study are discussed.