Group-Size Bias in the Measurement of Residential Sorting

In this paper, we revisit a common issue with popular indices used for measuring residential sorting, that is, the extent to which a sub-group of the population is spatially distributed (sorted or segregated) differently from the remainder of the population. Specifically, we show that three common measures of residential sorting (namely, the Index of Segregation, the Index of Isolation and the Entropy Index of Segregation) are affected by group size, that is, the expected values of the indices are positive rather than zero under random sorting, and the size of this positive bias is related to group size. This is an important issue because it is common to compare sorting indices across groups of rather different sizes, both cross-sectionally and over time. Using New Zealand data, we demonstrate group-size impact on bias in measures of residential sorting by means of four methods: (1) plotting the relationship between group size and each residential sorting measure; (2) randomly allocating individuals across the area units, calculating the resulting residential sorting measures, and regressing these on group size; (3) showing that normalised/systematic indices of sorting are also related to group size; and (4) calculating the measurement bias for each index and plotting them against group size. Our empirical illustration uses microdata on the self-reported ethnicity of individuals (with multiple responses possible) from the New Zealand Census of Population and Dwellings (1991-2013) for the Auckland region, selected due to its high ethnic diversity. Our results demonstrate that the Entropy Index of Systematic Segregation measure of residential sorting is the measure that is the least affected by group size variation. As a result, we strongly recommend using this index of sorting as a preferred measure.