Some Statistical Problems Arising from the Use of the Information Statistic in Numerical Classification

Abstract

The aim of classification is to group together individuals that are in some sense similar. It is, therefore, a useful technique only if it is suspected that the individuals under consideration belong to different natural groupings. All of the methods of classification currently adopted are designed to isolate these groupings; but in order to obtain a sensible interpretation of the results from any of these methods, it is necessary to construct a test to decide at what level further sub-division of the groups becomes meaningless. One method which has been widely applied in ecology involves the use of the information statistic, AI. This statistic may be considered as the logarithm of the reciprocal of the likelihood ratio statistic for testing the homogeneity of two samples with unspecified parameters: hence for large samples, 2AIis approximately distributed as x2 with p degrees of freedom (df) (p being the number of attributes). Its small sample properties, however, have not been fully investigated and caution is needed if conclusions are to be drawn from the use of the statistic when only a few individuals are involved.