Inference Procedures for Ordering Theory

Given observations on a set of n dichotomously scored test items representing certain skills or tasks, ordering theory attempts to identify a hierarchical organization among the n items. Using this basic framework, a directed graph representation for the empirically obtained hierarchy is discussed along with several assumptions that are necessary from a substantive point of view to justify the analysis that ordering theory provides. Furthermore, a permutation test procedure is introduced that allows a formal comparison of a postulated hierarchy among the n items to the hierarchy elicited from the available data set.