Methods of digraph representation and cluster analysis for analyzing free association

A method for constructing two measures of association between a pair of words that distribute over a sequence is developed. The association measures are used for digraph representation and cluster analysis. In particular, study of a measure for cluster analysis leads to a new algorithm for hierarchical agglomerative clustering. The digraph representation and the cluster analysis are applied to data of free (psychological) association obtained from a questionnaire survey on the living environment of local residents. The two association measures are interpreted as estimates of probabilistic parameters. Hence, methods of hypothesis testing are developed for showing differences of structures of the free associations between two different populations. The results of the analysis of the association data are summarized into figures of digraphs and clusters that show structures of free associations of groups of people