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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.
Christopher Winship (Wed,) studied this question.