A Method for Describing Quantitatively the Correspondence of Geographical Distributions1

T HE subject to be considered in this paper is the development of a logically sound and easily applied method by means of which one may quantitatively describe and map, for an area, the manner in which the continuous variations within one class of phenomena correspond to the variations within another class. Nothing is more fundamental in geographical research than the recognition and description of similarities and differences in cultural and physical behavior from place to place. Although this concept of spatial association is central to the science of geography, the techniques presently employed to recognize and describe such relationships are often somewhat less than rigorous. A recent monograph clearly states the problem and the need for methods to solve it: It seems clear that geographic investigation is concerned with discovering and describing areal variations in the occurrence of phenomena on the earth's surface, and also with the search for other areally associated factors that may help to explain the observed distributions. all such cases, questions are bound to arise as to the degree of association that exists between two (or more) phenomena. Areal association is indicated when a variation from place to place in the occurrence of one variable is accompanied by a similar place-to-place variation in the occurrence of another. geographic research, areal associations in the occurrence of related phenomena (such as wheat yields and rainfall) have often been discovered by comparing maps of the distributions of those phenomena; and the resulting generalizations have, usually taken a form such as, In this region, there is a tendency for wheat yields to decrease as rain-