Plausible measurement analogies to some psychometric models of test performance

Abstract

Psychometricians hypothesize that cognitive abilities such as reading, writing and spelling are measurable. However, they prefer to model item response probabilities than to study the internal structure of cognitive attributes. The theory of conjoint measurement, via its unique capacity to detect the quantitative structure of non-extensive attributes, can be used for the latter purpose. It is shown that conjoint systems analogous to the numerical composition rules advanced by the Rasch, many facet Rasch and two-parameter logistic models can be formulated using well-established axioms, representation theorems and proofs. Examples using empirical and synthetic data are presented. It was concluded that the lack of descriptive, behavioural theory remains the biggest obstacle to the scientific measurement of cognitive abilities.

Evaluating the Equal-Interval Hypothesis with Test Score Scales

“…These models are not necessary and merely introduce additional notational and theoretically complexity. In this way, as in several others, my presentation is more along the lines of Kyngdon (2011). …”

“…Errors could be made in the ordering. When trying to order items on the Lexile scale, for example, Kyngdon (2011) ran into a potential mis-ordering. He found such the error to be relatively minor since the overlap between the two items was within measurement error and reversing the ordering resolved the problem.…”

“…His analyses, however, are rather cursory (for instance, he only looks at a single instance of double cancellation compared to the complete approach in the original work), so I don't think much is added to the understanding of the original data. 4 Kyngdon (2011) builds upon this work by applying the methodology to a dataset far closer to the types seen in large-scale educational assessments than that used by Karabatsos (2001) and also by suggesting a philosophical stance that is more likely to be embraced by practictioners. To contrast the philosophies, let us begin with Karabatsos's description of his work:…”

“…Indeed, my description of the approach is general enough to allow it. Karabatsos (2001) and Kyngdon (2011) both used these checks in small matrices (3 × 3 for the former and 3 × 4 for the latter), so such an observation would not have made much difference. On the one hand, if only a single check of single cancellation needed to be performed, this would be much more efficient.…”

“…In this dissertation, I build upon the ideas of Karabatsos (2001) and Kyngdon (2011) in extending a method for evaluating whether a collection of dichotomously scored test item responses can bear the weight of an interval scale. My methodological extensions are two-fold.…”