THE BIOLOGICAL SIGNIFICANCE OF CERTAIN DIFFERENCES BETWEEN THE VALUES OF THE CORRELATION COEFFICIENT, CORRELATION RATIO, AND CONTINGENCY COEFFICIENT

Abstract

Because of the great complexity of biological, social, and economic phenomena, and because of the various (and often illogical) ways in which measurements are made and data recorded by workers who are not trained in mathematical reasoning, it has been necessary to deduce a large number of biometric formulae in an effort to secure methods for dealing with all kinds of frequency distributions and frequency surfaces. In comprehensive investigations it often becomes necessary to consider in a comparative way the values of constants determined by different methods, or based on data of different nature or origin. An essential to the drawing of sound biological conclusions from such comparisons is a full understanding of the limitations of applicability of the various formulae. Since all of the biometric equations in their theoretical development rest on antecedent assumptions, these must be borne in mind in the interpretation of the constants in terms of which the results of specific investigations are expressed. This is especially important when various constants (for example correlation coefficients, correlation ratios, and contingency coefficients) based on different kinds of data are compared. The purpose of the present paper is to discuss the biological significance of the differences between the measures of interrelationship afforded by the correlation coefficient, correlation ratio, and contingency coefficient when applied to certain botanical data, and to indicate the reasons for the differences in the magnitudes of these coefficients, with a view to emphasizing the importance of morphological considerations in the selection of the specific method to be applied in any particular case.