An Empirical Examination of the Behavior of Selected Measures of Tree and Partition Similarity in Relation to the Investigation of the Sampling Stability of Aid

A comparison has been made between various measures of similarity of tree and partition structures in an empirical, operational context. The particular context is an examination on empirical data (National child development study) of the sampling stability of AID. (Sonquist & Morgan (1964), Fielding & Shepard (1973), Fielding (1977)), a programmed technique for the preliminary analysis of survey data, which produces output in the form of a labelled, binary, hierarchical tree. sures of similarity of (final) partitions include many of those compared by Arabie & Boorman (1973) and two developed by Frank (1976). In addition, four measures of tree similarity are produced by the combination of two methods of labelling the nodes and two methods of comparing the associated similarity matrices produced. The measures are compared, using multidimensional scaling methods, over samples of a given size drawn from a large "master" sample. They are also examined on the basis of two criteria developed in terms of the relation of the measures to sample size. Two measures are chosen to form the basis for the comparison of different criteria for AID, the problems involved in this will be discussed.