Ordinal Measures of Association

Abstract Ordinally invariant, i.e., rank, measures of association for bivariate populations are discussed, with emphasis on the probabilistic and operational interpretations of their population values. The three measures considered at length are the quadrant measure, Kendall's tau, and Spearman's rho. Relationships between these measures are discussed, as are connections between these measures and certain measures of association for cross classifications. Sampling theory is surveyed with special attention to the motivation for sample values of the measures. The historical development of ordinal measures of association is outlined. * This research was supported in part by the Statistics Branch, Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the United States Government. A large part of the work leading to this paper was done at the Department of Statistics, University of California, Berkeley. I would like to thank the following persons for their suggestions and criticisms: R. Féron (University of Paris), M. Fréchet (University of Paris), C. Gini (University of Rome), H. D. Griffin (Lincoln, Nebraska), W. Hoeffding (University of North Carolina), H. S. Konijn (University of Sydney), H. Messinger (University of California), J. R. Rosenblatt (National Bureau of Standards), T. Salvemini (University of Rome), I. R. Savage (University of Minnesota), A. Stuart (London School of Economics and Political Science), R. M. Sundrum (University of Rangoon). Notes * This research was supported in part by the Statistics Branch, Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the United States Government. A large part of the work leading to this paper was done at the Department of Statistics, University of California, Berkeley. I would like to thank the following persons for their suggestions and criticisms: R. Féron (University of Paris), M. Fréchet (University of Paris), C. Gini (University of Rome), H. D. Griffin (Lincoln, Nebraska), W. Hoeffding (University of North Carolina), H. S. Konijn (University of Sydney), H. Messinger (University of California), J. R. Rosenblatt (National Bureau of Standards), T. Salvemini (University of Rome), I. R. Savage (University of Minnesota), A. Stuart (London School of Economics and Political Science), R. M. Sundrum (University of Rangoon).