A Revaluation of Indexes of Residential Segregation

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New criteria for indexes of residential segregation are developed. It is argued that a pattern of random segregation rather than complete desegregation should be used as a baseline for measuring segregation. It is shown that any index whose relationship to one baseline is independent of the proportion black in a city, necessarily has a dependent relationship with respect to the other baseline. The index of dissimilarity is adjusted to serve as a measure of deviation from random segregation. Eta-square, which was shown by Duncan and Duncan to depend on the proportion black, is shown to be independent of the proportion black when random segregation is used as a baseline. It is argued that segregation should be measured from a situation of complete desegregation when its effects are of concern, but that it should be measured from random segregation when its causes are being analyzed. Over the years, sociologists have been continually interested in residential segregation. Much of this interest has been in the segregation of blacks from whites. Recently such inquiries have increased as sociologists have realized that residential segregation is the basis for other sorts of discrimination. In particular, residential segregation is the basis for much discrimination in both education and employment (Pettigrew). From the years 1947 to 1955 a series of articles appeared in the literature, mostly in the American Sociological Review, concerned with developing various indexes of residential segregation. The standard dogma during this period was that there were many different indexes, each of which was appropriate for different theoretical reasons. The actual consequences of these articles were, however, quite the opposite. The outcome has been an overwhelming tendency to look at residential segregation from one perspective-that of the segregation curve and its deviation from complete desegregation-and the summary of this deviation in terms of the index of dissimilarity. The purpose of the paper is to show that there are at least two different perspectives from which residential segregation can be examined. Segregation can be measured as it deviates from a situation of complete desegregation or in terms of a situation in which there is random segregation in the city. The indexes that have been developed and those that will be examined in this paper assume that the segregation data are in a very specific form. It is assumed that the data are either the number of people or households that are black and that are white for either census tracts or blocks of a given city. In this paper it will be assumed that the data are renorted in terms of households per block.