Model-free evaluation of equating and scaling

Standardized tests are equated and scaled in order that scores on different tests can be compared. If one test yields higher expected scaled scores than another, the scale is biased against those who take the latter test. The amount of bias, defined as the difference between expected values, depends on ability. This paper presents two methods for estimating this relationship and the bias in the scale, using a predictor as the measure of ability. The resulting evaluation is absolute in the sense that the scale is judged according to its own properties and not by comparison with an arbitrarily designated criterion scale. Moreover, there is no need to assume a particular theoretical model to be correct. An application of the methods showed that the Rasch model is not suitable for vertical equating of multiple-choice tests