title: More reliable inference for the dissimilarity index of segregation.
abstract: The most widely used measure of segregation is the so-called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce adjustments to the index, based on an underlying statistical model. We specify the assignment problem in a very general way, with differences in conditional assignment probabilities underlying the resulting segregation. From this, we derive a likelihood ratio test for the presence of any systematic segregation, and bias adjustments to the dissimilarity index. We further develop the asymptotic distribution theory for testing hypotheses concerning the magnitude of the segregation index and show that the use of bootstrap methods can improve the size and power properties of test procedures considerably. We illustrate these methods by comparing dissimilarity indices across school districts in England to measure social segregation.
authors: Institute of Education, University of London 20 Bedford Way London WC1H 0AL UK.
authors: Rebecca
authors: R
authors: Allen
authors: CMPO Department of Economics, University of Bristol 8 Woodland Road Bristol BS8 1TN UK.
authors: Simon
authors: S
authors: Burgess
authors: Department of Economics McGill University 855 Rue Sherbrooke Ouest Montreal Quebec H3A 2T7 Canada; AMSE-GREQAM Centre de la vieille Charité 2 rue de la Charité13002 Marseille France.
authors: Russell
authors: R
authors: Davidson
authors: CMPO Department of Economics, University of Bristol 8 Woodland Road Bristol BS8 1TN UK.
authors: Frank
authors: F
authors: Windmeijer
keywords: Bootstrap methods; Dissimilarity index; Hypothesis testing; Segregation