Directed Graph Representations of Association Structures: A Systematic Approach

Methods for analyzing structures of psychological associations in a systematic way are developed. A framework is developed which shows relations among the methods. First, a directed graph representation and a cluster analysis procedure are considered for a particular application for which the data was obtained in a controlled association test. Second, the directed graph and the cluster analysis serve as a basis for developing two methods for statistical hypothesis testing. These hypothesis-testing methods are used for comparing association structures between two populations. Finally, a framework showing the relation among these four methods is used for developing a different system of methods for a free association test. These methods are applied to data obtained from association tests. A questionnaire on the living conditions of local residents in urban areas was administered to obtain this data. The aim of the questionnaire is to provide macroscopic views for decisionmaking on improvement needed for the urban environment. Several diagrams showing the association structures are given, and the significance of this family of methods is discussed.