Binary coefficients: A theoretical and empirical study

Binary coefficients can be assigned to several categories on the basis of algebraic and conceptual properties. The phi coefficient of association is related algebraically to the chi-square statistic for 2-by-2 contingency tables, and use of this coefficient in cluster analysis permits the objective, nonarbitrary partitioning of objects among groups on the basis of previously selected levels of significant, positive association. Similarity, matching, and distance coefficients possess neither conceptual nor operational statistical meaning for many geological data sets. The weighted pair group method and flexible clustering strategy may give an overly conservative partitioning of objects among groups. Clustering by the unweighted pair group method, using the phi coefficient, is recommended for the analysis of biostratigraphic and paleoecologic presence—absence data.