Cluster analysis of title overlap in twenty-one library collections in western New York

Abstract

Title overlap of 21 libraries in western New York, was described by the Jaccard similarity coefficient. The coefficient has two features appropriate for describing overlap : it is self-normalizing and avoids mutual lack of ownership as a basis for similarity . The matrix of 210 coefficients was submitted t o 4 methods of cluster analysis : single linkage, complete linkage, average linkage and Ward's. Cophenetic correlation coefficients for single, complete, and average linkage, 0.55, 0.69, and 0.74, respectively, suggested that the average linkage was best. Ward's was judged poorest on the basis of visual inspection. Two clusters fran the average linkage method, with 8 and 12 libraries each, were prominent. A third contained only 1 library. The one-dimensional solution to ultidimensional scaling (MDS) tended to confirm the clusters. Two variables were hypothesized to account for the two large clusters : circulation and total volumes. Both were significantly associated with the clusters, but analysis of covariance showed that when total volmes were treated as the covariate, circulation was not significant. Hence neither variable was considered explanatory. Principle contribution to overlap analysis was (1) use of the Jaccard coefficient, (2) the attempt t o validate overlap clusters using MDS, and (3) an effort to explain clusters by other variables.