Jahn et al. (1947) [201] First appearance (as far as I can tell) of index of dissimilarity as a measure of segregation (among other things, discusses need to standardise measure by dividing by the maximum possible). Other criteria, and discussion of desirable properties of such measures. A minor comment in Hornseth (1947) [189].
Williams (1948) [386] Discussion of Jahn et al. (1947) [201] and properties of segregation indices.
Duncan and Duncan (1955) [116] Methodological review of various segregation indices; mathematical properties, relationships, requirements, relationship to the `segregation curve'. Index of dissimilarity emerges with fairly good marks overall.
Cortese et al. (1976) [86]
Shows how the mean of segregation $\Delta$ depends on the margins.
Suggests standardised measure instead. The hypergeometric distribution
of $\Delta$ under a random allocation model, and a binomial
approximation of the mean (nothing for the variance). [How about a
significance test based on the same idea -- distribution of test
statistic?]. Notes on the interpretation of $\Delta$ as a minimum
proportion of required moves, corresponding proportion when considering
exchanges.
Taeuber and Taeuber (1976) [361]
Comment to and criticism of
Cortese et al. (1976) [86], addressing each
of their objections to $\Delta$. Distinction between statistical and
substantive significance (as in
Masey (1978) [261]). Notes that
possible bounds for $\Delta$ may be constrained if only integer-values
solutions (as in the real world) are allowed. In a reply,
Cohen et al. (1976)
[83] defend the use of a standardised $\Delta$ for
comparisons.
Winship (1977) [388] Comparing even distribution and random allocation as baselines for analysis of segregation; effects on segregation indices, in particular the mean of the index of dissimilarity under random allocation (depends on the margins). Proposes adjusting index by subtracting mean. [A nice paper.] In a comment,
Falk et al. (1978) [128] Claims the both the binomial and the normal approximation to the mean of the index are fairly inaccurate. In his reply, Winship (1978) [389] declares that he has changed his mind, and argues that the index (or an adjustment of it) is inappropriate because it violates some of the criteria formulated in economic literature for measures of inequality.
Massey (1978) [261]
A nice comment to
Cortese et al. (1976) [86]. Points out that the standardised
$\Delta$ confuses statistical and substantive significance of
observed difference from random allocation. Discussion of standardised
measure as a possible test statistic (although distribution is unknown).
Examples on a census tract level (typically $N_{i}\approx 4000$,
variances of $\Delta$ computed using the jackknife): in such data
any subtantively interesting differences are significant. In reply,
Cortese et al. (1978) [85]
maintain [unconvincingly] that they regard the
standardised measure the better way of producing a measure comparable
across populations. [The definition of `segregation' for such
comparisons seems unclear.]
Kestenbaum (1980) [222] Simulations of the mean and variance of index of dissimilarity under various marginal distributions.
Merschrod (1981) [271] Proposes $\Delta$ as
a measure of (economic) inequality, partly because of its easy
interpretability in terms of transfers and because it can (unlike the
Gini coefficient) be used for time series data. Shows how results for
aggregated data can be used to obtain an interval containing the value
of the index at the individual level.
Sakoda (1981) [323]
Index of dissimilarity generalized to a $R\times C$ (rather than
$2\times C$) table. [Equal to $\Delta$ for an independence model in a
tw-way table, divided by its maximum given fixed row totals.]
Morgan and Norbury (1981) [276] Same index as in Sakoda (1981) [323], but a better paper. Also discusses the mean of the index under random allocation model.
Massey (1981) [262]
Relationship between social class (C) and ethnic segregation (area [A]
by Race [R]). Compares class-specific indices
of dissimilarity [scaled $\Delta$ for model (AC,RC), when full three-way
table is available] (`direct standardisation') and an 'indirectly
standardised measure' computed when only the two-way margins are
available [ID for the two-way table R$\times$A when expected values are
obtained from the same model as above and collapsed]. Notes that the
former [partitioned $\Delta$] provides more information than the latter
[one number].
James and Taeuber (1985) [202]
Review of measures of segregation (plus some new ones), including
$\Delta$. Proposes criteria, adapted from theory of inequality
(e.g. [Schwartz and Winship 1979]), that measures should satisfy.
Comparison of measures w.r.t. these and in an empirical example of
racial segregation in schools.
White (1986) [384] A nice review of segregation (and diversity) measures. Empirical comparisons.
Inman and Bradley (1981) [200]
Mean and variance of $\Delta$ for $2\times C$ tables, when the `model'
is the observed distribution of one of the rows (i.e. the standard
$\Deltan$ segregation measure). Distribution under a random allocation
model, both exact (difficult to compute) and (multivariate normal)
approximations. Thus provides results
Cortese et al. (1976)
[86]
could not give.