Entropy in the hierarchical cluster analysis of hospitals

A new technique integrating concepts from cluster analysis and information theory was applied to the classification of Michigan hospitals. First, a number of cost-related variables that describe the hospitals and their surroundings were used in a cluster analysis to produce a hierarchy of classifications. Then for each classification, the within-group entropy was computed for each group of hospitals and averaged over the classification. Finally, this average entropy was used as an aid to judgment in deciding which of the many classifications in the hierarchy yields the most reasonable groupings of hospitals.