This state-of-the-art review describes the genesis, structure, methods, applications, limitations and goals of the ordering analytic approach to hierarchical analysis, with specific reference to its relevance and use in educational, psychology and behavioral sciences. Hierarchy is defined as an "ordering" of objects such that the…

Presented is a method, derived from ordering theory, for the multidimensional scaling of dichotomous item data. The method is said to be related to the methodological multivariate extension of I. Guttman's scalogram analysis developed by C. Coombs and his students. An example is used to compare the data analytic results of the ordering theoretic…

Some of the ramifications of the linear order assumption underlying much of measurement theory are discussed. Ordering theory is then described as an alternative deterministic measurement model that does not make the linear order assumption. (Author/RC)

Refined item digraph analysis (RIDA) is a way of studying diagnostic and prescriptive testing. It permits assessment of a test item's diagnostic value by examining the extent to which the item has properties of ideal items. RIDA is illustrated with the Orange Juice Test, which assesses the proportionality concept. (TJH)

With the ordering-theoretic method of item hierarchy construction any array of bivalued item data can be analyzed to determine the item hierarchy structure. (Authors)

Using ordering theory, a boolean algebraic measurement model in which item response patterns are viewed as atoms in a boolean algebra with as many generators as there are items being considered, a hierarchy-generative procedure is developed. This procedure relates to the determination of prerequisite relationships between pairs of items. An…

Authors describe a measurement technique which processes item data so as to indicate logical relationships among items. (HB)

One hundred eighty one sets of black twins and 223 sets of white twins provided responses to four 12-item subtests of the Raven's Progressive Matrices Test, Standard Version. The children were in elementary school and their item response patterns were analyzed with the use of revised ordering-theoretic methods to search for best-fitting…

The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…

In Piaget's developmental psychology the fourth and highest stage of human cognitive development is that of formal operations. The research on formal thought instruments is outlined. This study was designed to construct and validate paper-and-pencil instruments which could be used to select students capable of abstract conceptualization,…