EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1973, 33, 291-300. BART (in press) and Airasian and Bart (1971) introduced tree theory as an alternative measurement model with a boolean algebraic framework. Subsequent to those two statements tree theory was relabelled by Bart and Airasian so that the theory would more closely mirror its algebraic framework. Ordering theory has as its primary intent either the testing of hypothesized hierarchies among items or the determination of hierarchies among items. In ordering theory, response patterns for bivalued items are viewed as atoms in a boolean algebra with as many generators as there are items being considered. An ordering (formerly termed a tree) is the union of the obtained atoms and indicates the logical relationships among the items.Ordering theory shares with classical models the item response matrix, but does not use summation across subject rows to express in the form of the correct responses of a subject his standing on the trait measured. This is the first departure of ordering theory from older models of measurement. These models invariably assume that the trait measured is linearly ordered and can be measured with a simple additive model-e.g., a summative score (Gulliksen,

A general logical model of properties of suppressor variables is proposed. Consistent exploration of possible manifestations of suppressor variables within this theoretical framework accounts for extant classifications of suppressor variables into the classical, net, and cooperative categories and suggests existence of new subcategories, not detected previously. The discussed model leads to consistent identification and classification of suppressor variables and facilitates computer simulation. A GENERAL LOGICAL MODEL OF SUPPRESSOR VARIABLESof one element and a criterion variable (Y) XI Diagrammatically, the variables and elements represent a suppressor model; however, a special formula for the coefficient of correlation must be used to demonstrate its properties. In this formula, the correlation rxy is computed aswhere n; equals the number of elements unique to X, n, the number of elements unique to Y, and n c the number of elements common to both variables. For example,These correlations represent the prediction model which contains a suppressor variable. However, the necessity to use a special formula to discuss its assumptions limits its utility. The purpose of this paper is to elaborate and generalize the McNemar model. Also, consistent unfolding of the new model was attempted to demonstrate its ability to account for extant categories of suppressor variables and to indicate whether existence of alternate or additional classification categories is a theoretical possibility.Since Horst (1941) introduced the concept of the suppressor variable, this "quasiparadoxical curiosity" (to use Cohen & Cohen's, 1975, term) has received sustained attention (Darlington, 1968;Dayton, 1972;Lubin, 1957). In its classical rendering, a suppressor variable has a zero correlation with the criterion, but nevertheless contributes to the predictive validity of a test battery. The current definition of a suppressor variable is that it is a variable which increases regression weights and, thus, increases the predictive validity of other variables in a regression equation (Conger, 1974, pp. 36-37).Classification of suppressor variables into several categories was a logical outcome of the increase in generality of the suppressor variable concept. Conger (1974) identified three kinds of suppressor variables: traditional, negative, and reciprocal. Cohen and Cohen (1975, pp. 84-91) named the same categories classical, net, and cooperative. Succinctly defined, If the [predictor variable] in question has a zero (in practice very small) correlation with the [criterion variable], thesituation is oneof classical suppression. If itsbetaweight is of opposite signfrom its [correlation withthe criterion], it is serving as a net suppressor. If its beta weight exceeds its correlation with the criterion and is of the same sign, cooperative suppression is indicated. (Cohen & Cohen, 1975, p. 91) The same authors also call attention to the fact that a beta coefficient, which falls outside the limits defined by the correlation of its correspond...

No abstract

A method for the multidimensional scaling of dichotomous item data is presented which is derived from ordering theory. This method is related to the methodological multivariate extension of Guttman's scalogram analysis developed by Coombs and his students. An example is provided and comparison is provided between the data analytic results of the ordering theoretic method and those of the method of Coombs and his students for their conjunctive model. Some relationships of this method to conventional psychometric data analytic procedures are discussed.ORDERING theory has been introduced as an alternative model of measurement that makes rich use of boolean algebraic procedures and that serves as an extension of Guttman's scalogram analysis. A qualifying property of data analysis from an ordering-theoretic perspective is that the item response matrix is used not to generate summative scores or square correlation matrices but rather to generate square matrices indicating frequencies of certain item response patterns. For example, Bart and Krus (1973) discussed the use of a square matrix, which indicates the frequencies of (0, 1)

Negative coefficients of reliability, sometimes returned by the standard formulae for estimation of the internal-consistency reliability, are neither theoretically nor numerically correct. Alternate strategies for test development in this special case are suggested.