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This study applied a method of generating task hierarchies (ordering theory) to seven Piagetian tasks. Thirty subjects were individually administered three concrete operational and four formal operational tasks. Analysis of the response patterns on the dichotomously scored tasks revealed the following findings. First, the Piagetian theory that success on concrete operational tasks is a necessary prerequisite to success on formal operational tasks was confirmed. Second, the seven tasks were closely interrelated with an array of prerequisite relations more complex than a simple linear hierarchy. The methodology utilized appears to have value for defining nonlinear lines of implication among behavioral science phenomena.The purpose of this study was to explicate ordering theory, a measurement model which identifies necessary and sufficient performance conditions between test items or tasks, by analyzing seven Piagetian tasks. Ordering theory is an extension of Guttman (1944Guttman ( , 1950 scaling procedures in that it identifies nonlinear as well as linear hierarchies among items or tasks. Scalogram analysis is used to order a group of items or tasks into a linear hierarchy and to evaluate whether or not the hierarchy is unidimensional and cumulatively hierarchical. The degree to which a group of items or tasks is judged to be unidimensional and cumulative is determined by the extent to

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