Ecological Correlations and the Behavior of Individuals.

AN INDIVIDUAL CORRELATION is a correlation in which the statistical object or thing described is indivisible. The correlation between color and illiteracy for persons in the United States, shown later in Table I, is an individual correlation, because the kind of thing described is an indivisible unit, a person. In an individual correlation the variables are descriptive properties of individuals, such as height, income, eye color, or race, and not descriptive statistical constants such as rates or means. In an ecological correlation the statistical object is a group of persons. The correlation between the percentage of the population which is Negro and the percentage of the population which is illiterate for the 48 states, shown later as Figure 2, is an ecological correlation. The thing described is the population of a state, and not a single individual. The variables are percentages, descriptive properties of groups, and not descriptive properties of individuals. Ecological correlations are used in an impressive number of quantitative sociological studies, some of which by now have attained the status of classics: Cowles’ ‘‘Statistical Study of Climate in Relation to Pulmonary Tuberculosis’’; Gosnell’s ‘‘Analysis of the 1932 Presidential Vote in Chicago,’’ Factorial and Correlational Analysis of the 1934 Vote in Chicago,’’ and the more elaborate factor analysis in Machine Politics; Ogburn’s ‘‘How women vote,’’ ‘‘Measurement of the Factors in the Presidential Election of 1928,’’ ‘‘Factors in the Variation of Crime Among Cities,’’ and Groves and Ogburn’s correlation analyses in American Marriage and Family Relationships; Ross’ study of school attendance in Texas; Shaw’s Delinquency Areas study of the correlates of delinquency, as well as The more recent analyses in Juvenile Delinquency in Urban Areas; Thompson’s ‘‘Some Factors Influencing the Ratios of Children to Women in American Cities, 1930’’; Whelpton’s study of the correlates of birth rates, in ‘‘Geographic and Economic Differentials in Fertility;’’ and White’s ‘‘The Relation of Felonies to Environmental Factors in Indianapolis.’’ Although these studies and scores like them depend upon ecological correlations, it is not because their authors are interested in correlations between the properties of areas as such. Even out-and-out ecologists, in studying delinquency, for example, rely primarily upon data describing individuals, not areas. In each study which uses ecological correlations, the obvious purpose is to discover something about the behavior of individuals. Ecological correlations are used simply because correlations between the properties of individuals are not available. In each instance, however, the substitution is made tacitly rather than explicitly. The purpose of this paper is to clarify the ecological correlation problem by stating, mathematically, the exact relation between ecological and individual correlations, and by showing the bearing of that relation upon the practice of using ecological correlations as substitutes for individual correlations.