Mixed measures: different definitions of racially diverse neighborhoods compared

Abstract

Focusing on neighborhoods that researchers consider particularly diverse, this paper assesses the ways scholars have characterized neighborhood racial diversity in the United States. Social scientists use a variety of methods to define and measure highly racially diverse places, resulting in a single label being used to capture very different aspects of a census tract’s racial demography. We examine the criteria used to classify neighborhood racial diversity to bring perspective on the logic behind various approaches. We then group the range of schemas into several broad types from which we choose a representative four. These form the basis for a series of empirical comparisons using U.S. Census data to reveal the contexts where the taxonomies produce similar outcomes and those where they do not. The analysis goes on to consider the implications stemming from the choices social scientists make when they opt for one approach over another.

“If mix is the dominant situation, methods are needed that identify rather than obscure it”

(Ron Johnston et al., 2010, p. 697).

Introduction

The United States has become more racially diverse in the last few decades. This has occurred at many scales, including neighborhoods, and scholars researching these environs have devised what Maria Krysan has called a “dizzying array” of different approaches to characterize mix (Sin & Krysan, 2015, p. 5; Krysan et al., 2017, p. 2). The analysis reported here centers on a subset of the neighborhood diversity literature: that is, the ways scholars have characterized and classified neighborhoods as highly racially diverse. We do not detail the methods used in each and every study. We do, though, synthesize a large and growing literature by unpacking several widely cited approaches and engaging in a comparative analysis of some of the most common taxonomies that social scientists have used to define the most racially diverse neighborhoods – the places where the extent of neighborhood racial diversity is distinctive – and then subject those choices to empirical tests of comparison.

We are motivated to do this because different approaches produce very different results. Suppose someone was interested in identifying the most racially diverse neighborhoods in Boston and that, for sake of argument, the researcher used, as many do, census tracts to stand in for neighborhoods. Emily Walton and Mae Hardebeck (2016) devised a method that produces just two neighborhoods in Boston that they called “multiethnic”. Relaxing their restriction that such racially mixed places must maintain their diversity over two decades to be included, then 33 tracts met their standard in 2010. This tally is similar to one derived from the schema developed by Steven Holloway et al. (2012), whose approach yielded 31 “highly racially diverse” neighborhoods in 2010. These totals, however, fall short of the 43 neighborhoods that met the “mixed minority enclaves” derived from Michael Poulsen’s (Poulsen et al., 2001) framework and they constitute just 36% of the 85 found using Ingrid Gould Ellen (1998)’s definition of a “multiethnic” neighborhood. Furthermore, the discrepancies do not end with counts by metropolitan area. For example, in Boston, of the 33 tracts identified by Walton and Hardebeck’s method and the 31 by Holloway et al.’s scheme, only 12 are common to both.

Perhaps the problem is Boston. The Los Angeles metropolitan area is more racially diverse than Boston so it follows that we might find more congruence among these schemas in LA’s greater metropolitan area. Not so fast. For 2010, Walton and Hardebeck’s method yields 102 tracts, Holloway et al.’s identifies 70, Poulsen et al.’s produces 423, while Ellen’s generates just 48. In this context, the larger count is almost 10 times that of the lower one. Additionally, Ellen’s method applied to Boston produced the largest number of neighborhoods whereas for Los Angeles Poulson et al.’s detected, by far, the most. In LA, however, there is a greater correspondence between Walton and Hardebeck’s method and that of Holloway et al.: the schemas identify 52 tracts common to both.

How do we make sense of all this and how should scholars proceed? We organize our answers in two stages. We first outline the thinking behind the main methods and distill the many approaches into four types. We then draw one representative schema from each of these types, analyzing these exemplars with the goal of identifying the ways (literally and practically) these four methods overlap. Are there, for instance, particular places in which they are congruent in their identification of racially diverse neighborhoods? Working through the logic of each helps researchers understand which one might be better suited for a certain type of investigation. We conclude with set of practical recommendations for researchers.

The anatomies of highly racially diverse neighborhoods

Understandings of what constitutes “racial diversity” in the United States have evolved (see Sin & Krysan, 2015 for a review). For decades these had mostly centered on Black-White divides in all walks of life. Times have changed as the racial and ethnic makeup of the United States has changed. To give a sense of this, Barrett Lee’s (1985) analysis of racially mixed neighborhoods focused exclusively on Black-White neighborhood combinations. He built his argument, in part, on previous research (by Bradburn et al., 1971) on White neighborhoods that were at least “nominally integrated (i.e., that had two or more Black families)” (p. 346).

Largely driven by immigration, over the last several decades the United States has become far more racially diverse. This is most noticeable in the largest metropolitan areas where the majority of immigrants settle. Since the 1950s, the predominant flows of migrants to the United States have switched from being mainly European to coming from Mexico, Central America, and the Caribbean and Asian countries such as China, India, and the Philippines. With the first and second generations together constituting about one quarter of the United States population, the racial makeup of the United States has changed considerably. These alterations manifest themselves at both the national level as well as state, metropolitan, and neighborhood spatial scales Wright et al., 2014). Because the United States is very different demographically than 40 years ago, researchers have invented new language and techniques to characterize the wider range of neighborhoods now observed in the 21st century (Clark et al., 2015).

That said, the issue of how to classify urban neighborhoods by race today resembles some of the challenges of the past. We recognize but set aside for the moment critical issues with how the US Census Bureau (and all data-gathering infrastructures, more generally) problematically classifies race and ethnicity and how it changes over time. For this paper, the question of how to identify racially diverse neighborhoods pivots on the basic issue of thresholds. The simplest is an absolute number approach (see Logan & Zhang, 2010, 1082–3 for a brief synopsis) wherein a fixed numerical threshold is used to establish the meaningful presence of a group or groups. While some studies in the past have used this technique (e.g., Alba et al., 1995), the varying population sizes of census tracts limit any widespread application of such an approach.

To avoid the problems of absolute counts, scholars interested in the racial diversity of metropolitan landscapes have turned increasingly to ordinal classification schemes based on relative presence criteria. These studies divide into four broad types:

• those that use a referent (most commonly a city, county, metropolitan area, a group of metropolitan areas, or the country as a whole) to gauge relative neighborhood racial diversity (e.g., Bellman et al. 2018; Logan & Zhang, 2010; Maly, 2000; Smith, 1998);

• those that use a method that classifies the racial diversity in any place without a referent based instead on pre-determined group-percentage thresholds (e.g., Ellen, 1998; Friedman, 2008);

• those that use a method that classifies the racial diversity in any place without a referent based instead on standardized entropy scores (e.g., Farrell & Lee, 2018; Holloway et al., 2012; Lee & Hughes, 2015);

• and variants of this third type that use a global standard to open up research possibilities for international comparative urban analysis (e.g., Poulsen et al., 2001).

We now examine each of these in turn

Threshold approaches that use a referent

Michael Maly’s (2000) Neighborhood Diversity Index serves as an example of a technique that uses a metropolitan referent. He compared the proportions of each of four racial groups in a census tract to the share those same racial groups had in the city a whole. Thus, when the local proportion matched the city-wide share the index would be zero. He then used this tract score to rank neighborhoods as “integrated”, “moderately integrated” or “segregated”. In a sense, Maly’s approach incorporates the idea that race and space are mutually constitutive (Delaney, 2002): i.e., how demographic integration is experienced varies by geographic context (Sin & Krysan, 2015). The problem with this approach is that a neighborhood in one metropolitan area might be classed differently from another neighborhood with precisely the same racial make-up in a different metropolitan area.

Building in part on Maly’s early work and inspired also by Saskia Sassen’s conceptualization and analysis of Global Cities (1991), Logan and Zhang (2010) coined the term “global neighborhoods” (see also Zhang & Logan, 2016). They used this to describe the new racial and ethnic diversity in certain parts of the United States experiencing the increasing presence of Latinx and Asian populations where long-standing Black-White neighborhood dynamics have been modified by more complex racial demographics. The term “global neighborhood”, then, is generic and Logan and Zhang develop a scheme that generates 15 different neighborhood types based on the mix of four racialized groups (whites, Blacks, Latinx, and Asians). The fifteen neighborhood types represent all the possible combinations of the four groups (i.e., White (W), Black (B), Asian (A), Latinx (L); WB, WL, WA, BL, BA, LA; WBL; WBA; LBA, WLA; and WBLA). (Native Americans were not considered.) While our focus in this essay falls on the most diverse–WBLA – because this article has been influential, the logic by which they arrive at this scheme is worthwhile explaining in some detail.

Logan and Zhang (2010) decided that the disadvantages of schemes based on entropy outweighed their strengths. The entropy index summarizes the relative presence of racialized groups in a tract or alternative spatial unit. The index is at its minimum if only one group is present. It reaches its maximum when every group is present in the same shares. With four groups, White, Black, Asian, and Latinx, the most diverse neighborhood is the one that is made up of 25% from each group. For them, this was an “unreachable standard” because the four groups vary considerably in their overall shares of the population. They added another criticism, pointing out that, except in the rarest cases (e.g., parts of Los Angeles, San Francisco, and New York), a neighborhood that has a 25% Asian share represents an unusually high level of Asian concentration relative to the national share (of 5.5% in 2010). In contrast, a neighborhood where the White share was 25% stood as an example of considerable relative under-representation (Logan & Zhang, 2010, p. 1083).

Logan and Zhang (2010) “global neighborhood” study involved 24 metropolitan areas and used as the referent the percentage of each group in the overall population of the combined 24 metropolises in each of 1980, 1990, and 2000). The reference points thus shifted each decade to accommodate the fact that population shares altered over the study period. Having next settled on a minimum group presence criterion, they arrived at their 15 neighborhood types. The average composition of their most racially diverse neighborhood type (WBLA), the one that interests us, was:

in 1980: 59.2% W, 15.0% B, 18.5% L, and 6.8% A;

in 1990; 54.8% W, 13.2% B, 21.9% L, and 9.7% A;

in 2000; 47.9% W, 13.1% B, 26.7% L, and 11.9% A.

Classification schemes that use a referent are not without their challenges. Scholars who use a local referent, say the metropolitan area shares of groups to determine over or under representation in that metropolitan area’s census tracts, are tied to that frame of reference. What you find in Pittsburgh, for example, will differ considerably from, say, San Francisco. A highly diverse neighborhood relative to the Pittsburgh referent may well not qualify as highly diverse in a metropolitan context like San Francisco because the underlying referent is much less racially diverse. The results stemming from such analysis will tend to be unique to each particular place. Inter-metropolitan comparative analyses using a local, metropolitan scale, referent are difficult, if not impossible.

Logan and Zhang (2010) thus charted a way around this issue. Their analysis of neighborhood racial anatomy used the pooled proportions of the four principal racialized groups from the set of 24 metropolitan areas in their study set. Further, they dynamized the method: the reference points shifted each decade to recognize and account for the changing shares of the different racialized groups over time. This expansive frame of reference obviates many of the problems that accompany a more circumscribed reference point but does not eliminate them entirely. Comparing neighborhood composition among places outside the group of 24 metropolitan areas requires the construction of a new taxonomy as would a related analysis that involved neighborhood composition analysis between one of the 24 selected metropolitan areas and one outside that set. The term, then, that Logan and Zhang coin – “global neighborhoods” – is a little misleading. Their neighborhood categorizations are not global but nor are they local; they’re in between.

As this essay attempts a comparative analysis across all large US metropolitan areas, adapting Logan and Zhang’s method directly presents some steep challenges. We note, however, that the average composition of Logan and Zhang’s most diverse “global neighborhoods” involving a minimum share of close to 10% for any group (for 1990 and 2000) surfaces in other schemes. And we are not the first group of scholars to make and apply this observation. Walton and Hardebeck (2016) framework, for example, requires diverse neighborhoods to have the presence of the four largest racialized groups (Whites, Latinos, Blacks and Asians), all greater than 10% of the tract population. They include the additional criterion of survivorship: that is, these tracts must have sustained these standards for three consecutive censuses. They call these places “consistently multiethnic”.

Thresholds based on pre-determined shares

Walton and Hardebeck’s approach is not the only one that set specific percentage thresholds. Ingrid Gould Ellen’s (1998) definition of a “multiethnic neighborhood” requires the presence of three groups in a tract, two of which must be White and Black. This latter criterion acknowledges the history of urban residential racial segregation in the United States and much of the basis on which neighborhood racial diversity research builds. It also references the fact that racial diversity is no longer binary but tri-racial or multiracial. For Ellen, “multiethnic neighborhoods” must be at least 40% White, at least 10% Black, and must include at least 10% of some other racialized group. Others adopt the same definition of a multiethnic neighborhood in their research (e.g., Crowder et al., 2012; Fasenfest et al., 2004; Friedman, 2008). This approach joins Logan and Zhang’s in the sense that both require a meaningful presence of Blacks, thereby recognizing their historical legacies of subordination and attendant spatial segregation. It departs from Logan and Zhang’s approach (as well as other scholars) in that this perspective on neighborhood multiethnicity requires a significant presence of whites, and thus accents their mixing with other racialized groups.

Thresholds based on entropy

Definitions of demographic racial diversity have come to require the meaningful (Holloway et al., 2012) or substantial presence of more than two different racial groups in a spatial unit (White, 1986). It follows that not all assessments of highly diverse neighborhoods trend toward the presence of four different groups. Lee et al. (2013) and Farrell and Lee (2018) developed a straightforward approach to racial diversity. The authors define no-majority census-identified places as areas where no racialized group makes up more than half of the population (see also Bellman et al. 2018). Focusing on five ethno-racial categories (White, Black, Latinx, Asian, and other [comprising people claiming “some other race”, native peoples and multiracials]), their study applied a “majority rule” to all census places by decade, yielding 6 classes of place: no majority; White majority, Black majority, and so on. They additionally measured the diversity of each no-majority/group majority status place using the entropy index (White, 1986), a common measure of tract compositional diversity.

While sociologists have furnished most of the research on neighborhood racial diversity, other social scientists, notably geographers, have also devised taxonomies. Holloway et al. (2012) introduced their notion of “highly diverse” census tracts to the literature in a study of the racial fragmentation of United States metropolitan areas between 1990 and 2010. Their schema relates to Ellen’s in that to be highly diverse a neighborhood requires the meaningful presence of at least three different racialized groups. It differs most notably from her ideas in that it does not center attention on whites or blacks. In fact, they do not require any group (White, Black or some other) to be meaningfully present for a place to be “highly diverse”.

Their intent was to create a classification system that would allow scholars to categorize a broad range of census tracts on the basis of racial composition with an explicit accent on racial diversity. They opted for a classification scheme based on a-priori logic, rather than an empirical scheme tuned to racial distributions in a particular metropolitan context. The goal was to generate tracts (or other spatial units) with three levels of diversity, subdivided by the dominant racial group, that could be mapped. They used entropy, scaled to range between 0 and 1, to measure tract diversity (cf. Sandoval, 2011; Walker, 2018; White, 1986). “Low diversity” tracts were those where (a) one of the racial groups comprised at least 80% of the tract population, or (b) the scaled entropy index was less than or equal to 0.3707. This value is based on two criteria. One, this is the maximum scaled entropy that can be reached in a tract where one of six groups (whites, Blacks, Latinx, Asians, Native Americans, and people claiming some other race) constitutes 85% of the population – i.e., each of the other five groups constitutes exactly 3% of the population. Two, scaled entropy can be less than .3707 even when no group constitutes 80% of the population – for example, if Group A = 65%, Group B = 35% and the other Groups = 0%, scaled entropy = 0.36. So, for the 65/35 tract, even though Group A does not dominate at the 80% level, the absence of any other group renders the tract as low diversity in this scheme.

On the other end of spectrum, “High Diversity” tracts were those that had a scaled entropy greater than or equal to .7414 and no group constituted more than 45% of the tract’s population. The 45% rule ensures that no group constitutes an absolute majority (cf. Farrell & Lee, 2018). When the 45% threshold is combined with the .7414 entropy threshold, a tract’s top two groups can have a combined percentage of no more than 80% of the tract population, which ensures that “High Diversity” tracts must have a substantial presence of other groups.¹ Moderate diversity tracts were all those in-between.

Global thresholds

Holloway and colleagues were explicitly interested in the spatial dynamics of (changes) in mixed neighborhoods in the United States. In contrast, another team of geographers, Poulsen et al. (2001), devised a method of tract classification for racial groups intending to analyze new dimensions of neighborhood racial mix not only within but also between different countries (specifically the UK and Anglo settler countries). Their schema identified six general types of neighborhood, which spanned from what they variously named “isolated host communities” or “White citadels” to “polarized enclaves” and “ghettos”. In the middle of this range, they identify two types of mixed neighborhood: “assimilation-pluralism enclaves” and “mixed minority enclaves”.

For our purposes, the second of these two types is likely to be the most racially diverse so we focus on it. For mixed minority enclaves, whites must be less than 30% of the tract’s population; in addition, no one nonwhite group can exceed 66.6% of the remainder (i.e., the largest share a nonwhite group can be in a mixed-minority enclave is 66.6% of 70% or 46.2%). Put differently, to qualify, 70% or more of a tract’s population must be nonwhite, but no one nonwhite group can be more than twice the size of any individual group or the total nonwhite groups combined. “These are areas of high relative minority group mixture (typically with each of two minority groups comprising more than 20% of the population) …” (Ron Johnston et al., 2006, p. 320). This approach has provided these scholars with a powerful lens through which to compare both old and new urban racial neighborhood processes within and between national systems.

Distillation

It should be apparent by now that the literature does indeed offer a “dizzying” assortment of methods from which scholars can choose to address the growing racial diversity of places in the US and beyond. The remainder of the paper undertakes a deeper and more systematic comparative analysis of similarities and differences among the methods in their assessments of the extent, stability, and location of highly diverse residential spaces in the US. Comparisons of every single one would be a lengthy undertaking and unnecessary, given the similarities between subgroups of methods. Accordingly, we distill the methods to consider four representative schemas for use in subsequent comparative analysis. We are guided in our choices by the influence of each technique as captured by its citation rate.

1. The most cited method that uses a quasi-local referent was introduced by Logan and Zhang (2010). Google Scholar reports 238 citations at the time of writing. To avoid the problems of Logan and Zhang’s dynamic thresholds and their 24 metropolitan area place specificity, we substitute Walton and Hardebeck’s more straight-forward schema for Logan and Zhang’s semi-local referent approach. Much like Logan and Zhang (2010) 2000 thresholds, their schema requires that Blacks, Whites, Asians and Latinos exceed 10% of the population to reach the standard of “highly diverse”. Thus, Walton and Hardebeck’s method resembles Logan and Zhang’s in guaranteeing the substantial presence of four groups in highly diverse tracts. We will also relax their temporal criterion during most of our comparative analyses.

2. We also assess Ellen’s approach (Ellen, 1998), as it has been adopted by other researchers (e.g., Crowder et al., 2012; Friedman, 2008). At the time of writing, according to Google Scholar that 1998 paper that introduced the paper had been cited over 80 times. Her related book that uses the same methods (Ellen, 2000) close to 500 times.

3. We deploy Holloway et al.’s (2012) approach to represent other entropy-based schemas (e.g., Farrell & Lee, 2018). This paper had 123 citations at the time of writing.

4. Finally, we include Poulsen et al.’s (2001) schema as this team has published some two dozen papers based on this approach and stands out as it’s designed for international comparative analysis. The suite of articles this team has published using this method has been cited well over 1000 times.

Some differences among the approaches are immediately apparent. Unlike the two schemes devised by Geographers, the Ellen, and Walton and Hardebeck schemas require that a tract have minimum of 10% Black. Both methods also require a minimum presence of whites: ≥40% for Ellen and ≥10% for Walton and Hardebeck. Intentionally or not, these scholars reference the long-standing disciplinary interest in Black-White neighborhood co-presence (or lack thereof)(Sin & Krysan, 2015). Whereas Ellen, and Walton and Hardebeck require the presence of whites, Holloway et al. and Poulsen et al. allow for the absence of whites in highly diverse tracts. Holloway et al.’s research on highly diverse spaces grew from testing the following hypothesis: if you are part of a mixed-race union, where in a city would you live? (Ellis et al., 2012; Holloway et al., 2005;Wright et al., 2013). The expectation was that mixed-race couples, the majority of which are a white-nonwhite mix, would be more likely to be found in racially diverse neighborhoods. Holloway et al. were attentive to the race of partners, but their analyses included the possibility that the mixed spaces in which they might live need not have a meaningful presence of whites.

Poulsen et al.’s schema has very different origins and was explicitly designed for the international comparative analysis of neighborhood racial and ethnic composition of cities in the UK and Anglo settler countries. The authors were expressly interested in methods that superseded single-number indices to better account for the increasingly complex racialized landscapes of many major metropolitan areas in societies with histories of immigration. Within that broad objective was a particular interest in those neighborhoods where whites were relatively absent. Most profoundly, the classifications of Poulsen et al. and Ellen do not overlap at all as Ellen requires a tract minimum of 40% White while Poulsen et al.’s definition stipulates a maximum of 30% White for a tract to be a “mixed-minority enclave”.

The schemas differ along other axes. Walton and Hardebeck, like Logan and Zhang, are only interested in the four largest racialized groups in the United States whereas the other techniques allow for the inclusion of people who self-identify as Native American. Holloway et al. (like Farrell & Lee, 2018) are explicit that highly diverse means no majority (cf. Sandoval, 2011). Poulsen et al.’s definition falls in line with that thinking too. In contrast, both Ellen’s and Walton and Hardebeck’s classification methods permit the possibility that diverse tracts could contain a majority group.

These similarities and differences are summarized in Table 1. This table suggests that the four methods might pair off with Ellen, and Walton and Hardebeck forming one group (minimum Black requirement and allowing for majority White) and Poulsen et al. and Holloway et al. forming the other pair (no majority and no specific parameters for other groups). The remainder of the article drives at these and other aspects of these approaches in increasingly greater detail. After describing the data used, we start with some basic counts and measure the diversity of “multiethnic” neighborhoods, which begins to expose the effects of group maxima and minima criteria that each method employs differently. Another means of comparison explores the congruences among the four approaches. As many scholars are interested in temporally stable neighborhood diversity, and Walton and Hardebeck used stability as a criterion, we then use their definition of survivorship (defined as tracts that must have remained highly racially diverse for three consecutive censuses) to compare the four methods. The analysis culminates by focusing on the metropolitan dimension of this research. Global, multiethnic, multiracial neighborhoods – call them what you will – have emerged in large metropolitan areas. We complete the analysis by exploring how each schema plays out in these settings.

Table 1.

The basic characteristics of the four representative approaches.

	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
Minimum Black	10%			10%
Minimum White	40%			10%
Minimum Asian				10%
Minimum Latinx				10%
Maximum White	80%	45%	30%	70%
No Majority		Yes	Yes
Includes Native Americans	Yes	Yes	Yes

Analysis

Data

We follow the convention of much neighborhood racial demography research (and the specific research that attempts to identify highly diverse neighborhoods) and treat census tracts of residence as approximate neighborhoods of residence. (While census tracts are the spatial unit of interest, none of the approaches reviewed here require analysis be at that specific scale.) Census tracts comprise populations that range in size but a large majority fall between 2000 and 8000 people and resolve around a median of about 4,000. For this analysis, we use publicly available data at www.mixedmetro.com. These data, drawn from the 1990, 2000, and 2010 United States censuses and harmonized to the 2000 census tract boundaries, yield a national count of 65,444 total census tracts for each of the three years. As the U.S. Census changes how it measures race from decade to decade, these data are also matched to the six racialized groups defined in the 1990 Census (White, Black, Latinx, Asian, Native American, and some other race) through the fusion of the Hawaiian/Pacific Islander group into the Asian category and the union of the group “American Indian and Alaska Native” into a single “Native American” category. Following convention in most studies of race and ethnicity, we treat Latinx populations as a racialized group. As the 2000 Census was the first to allow respondents to claim more than one race, these data meld mixed-race individuals into the set of single-race categories as of 1990.² We set aside from analysis any tract with a population less than 50. We use the county-based 1999 Office of Management and Budget (OMB) metropolitan statistical area (MSA) designations to create subsets of tracts that are “metropolitan”.³ Our use of a single set of data minimizes any variation between published studies that derives from changing census tract and metropolitan area boundaries and changing definition and number of racial groups. We apply the criteria from each of the four representative studies to the single data set as faithfully as possible. Finally, because large metropolitan areas are where the main demographic changes of the last few decades are most evident, part of our analysis focuses on the 53 metropolitan areas that had populations in excess of 1 million people in 2000.

Basic counts and compositional diversity

We start with simple counts: how many highly mixed-race neighborhoods did these approaches find. Table 2 shows that Ellen’s method consistently produced the largest counts followed by Poulsen et al. then Walton and Hardebeck and Holloway et al. To put these counts in a different light, 1803 tracts (Ellen in 1990) represented about 2.7% of all census tracts in the United States; the 197 that Holloway et al.’s method recorded represents about 0.3% of all tracts.

Table 2.

The tally of highly racially diverse census tracts.

Year	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
1990	1803	197	1262	462
2000	2899	878	2043	923
2010	4299	998	2838	1407

We expect that methods that include tracts with a racial majority will have lower average entropy scores than those methods that have a non-majority criterion. That is borne out in Table 3, which reports on the mean scaled entropy of the tracts listed in Table 2. These two tables in conversation reveal that more restrictive definitions of “highly diverse” produce not only lower tallies of tracts that meet those standards but also tracts that have greater compositional diversity (larger average scaled-entropy scores). A joint consideration of these tables also results in the observation that as the numbers of highly diverse tracts increased from 1990 to 2000, so too did their compositional diversity. This particular tendency captured by each technique, however, subsided in the 2000s.

Table 3.

The mean scaled entropy of highly racially diverse census tracts.

Year	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
1990	0.594	0.769	0.602	0.713
2000	0.633	0.785	0.654	0.756
2010	0.626	0.774	0.651	0.74

Digging deeper into compositional diversity, by definition Holloway et al. and Poulsen et al. do not allow for a majority, while the other two schemas allow for a racial majority. For these, what does this look like in terms of the likelihood and racial composition of a majority population? Table 4 provides one perspective. Ellen’s specific interest in neighborhoods that have population minima for whites (≥40%) and Blacks (≥10%) produces situations where over two thirds of the census tracts are White majority. None of these tracts would be multiracial spaces using either Poulsen et al.’s or Holloway et al.’s criteria. In fact, Holloway et al. would classify these tracts as “moderately diverse, White dominated”. Over 25% of Walton and Hardebeck’s tracts had majority groups; as Table 4 shows, most, but not all, were majority White. One quarter of all tracts that are at least 10% White, Black, Asian, and Latinx register a majority in each of the three census years studied. Reading the table across we also see that the numbers of tracts that were mixed but had nonwhite majorities were increasing in number and, in the case of the Latinx group, increasing in share as well.

Table 4.

The share of highly diverse census tracts with a racial majority: Walton/Hardebeck and Ellen compared.

Walton and Hardebeck	1990	2000	2010
Majority	Groups ≥ 50%	Groups ≥ 50%	Groups ≥ 50%
White	106	192	252
Black	7	11	19
Asian	5	7	12
Latinx	15	28	70
Total	133 (28.79%)	238 (25.79%)	353 (25.09%)
Ellen	1990	2000	2010
Majority	Groups ≥ 50%	Groups ≥ 50%	Groups ≥ 50%
White	1293	2003	2899
Black	0	0	0
Asian	0	0	0
Latinx	0	0	0
Total	1293 (71.71%)	2003 (69.09%)	2899 (67.43%)

Congruences

Table 5 reports on the pairwise congruence of the four schemas. As already mentioned, because of conflicting criteria, Ellen’s (minimum 40% White) and Poulsen et al.’s (maximum of < 30% White) do not overlap. Ellen’s method and that of Holloway et al. produced few tracts in common: about 7% in 1990 and 13% in 2010. The taxonomies with largest degree of congruence are Holloway et al.’s and Walton and Hardebeck’s: almost 81% tract commonality in 1990, which declined in 2000 to 60% but rose again in 2010 to 71.8%. Overall, Table 5 makes clear that the four different conceptualizations of multiethnic/highly racially diverse tracts often identify different places: of the 18 cells in the matrix, just four exceed 50% congruence. Not surprisingly, when we consider overlaps among three schemas at the same time, congruence declines further (see Table 6).

Table 5.

Two-way congruencies (% = percent of scheme with lower count).

	Ellen; Holloway et al.	Ellen; Poulsen et al.	Ellen; Walton and Hardebeck	Holloway et al.; Poulsen et al.	Walton and Hardebeck; Holloway et al.	Walton and Hardebeck; Poulsen et al.
1990	14 (7.1%)	0	207 (44.8%)	115 (58.4%)	159 (80.7%)	175 (37.9%)
2000	120 (13.7%)	0	364 (39.4%)	376 (42.8%)	528 (60.1%)	335 (36.3%)
2010	131 (13.1%)	0	551 (39.2%)	469 (47%)	717 (71.8%)	493 (35%)

Table 6.

Three-way congruences (% = percent of scheme with lower count).

	Ellen; Walton and Hardebeck; Holloway et al.	Walton and Hardebeck; Poulsen et al. Holloway et al.
1990	11 (5.6%)	102 (51.8%)
2000	82 (9.3%)	250 (28.5%)
2010	100 (10%)	335 (33.6%)

Change over time

All four methods reveal that the number of highly diverse tracts increased between 1990 and 2010. All four show that the rate of growth was larger in the 1990s than in the 2000s (Table 7). Ellen and Poulsen et al. registered similar rates of change for both decades. Holloway et al. detected the largest gains in the 1990s and fewest in the 2000s. (This large percentage change is explored in detail elsewhere: Wright et al. (2018).)

Table 7.

Percent change in highly racially diverse census tracts.

	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
1990	-	-	-	-
2000	61%	346%	62%	100%
2010	48%	14%	39%	52%

While introducing the variety of methods scholars adopt to study highly racially diverse neighborhoods, we noted that Walton and Hardebeck included not just compositional criteria but also a temporal criterion: that is, tracts had to maintain their diversity over three census periods. Much of our comparative assessment relaxes this restriction but we reintroduce it here to drive at an important question: how common is stable demographic integration? (e.g., Bader & Warkentien, 2016; Ellen et al., 2012; Wright et al., 2018; Talen, 2010). Table 8 shows the count (and percentage) of highly racially diverse tracts in 1990 surviving until 2000 and 2010. Poulsen et al.’s method yields the greatest stability across 10 and 20 years; Ellen’s the least. Three approaches have 20-year survivorships ranging between 22% and 38%, which suggests considerable instability and a process of racial succession for highly racially diverse tracts. Poulsen et al.’s approach is the exception.

Table 8.

Survivorship.

	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
1990	1803	197	1262	462
2000	733 (41%)	104 (53%)	943 (75%)	266 (58%)
2010	398 (22%)	59 (30%)	738 (58%)	176 (38%)

Metropolitan dimensions

The increasing racial diversity of the United States finds particular expression in the country’s metropolitan areas. Does the 10% minimum Black requirement (Ellen; Walton and Hardebeck) affect where highly diverse census tracts are located by metropolitan area? Tables 9 and 10 begin to answer to this and related questions by reporting on the tallies of highly diverse census tracts by large U.S. metropolitan areas. Our discussion of the evolution of interest in multi-racial neighborhoods references the immigration-driven growth of Latinx and Asian/Asian American populations. Even though immigrants are settling outside traditional metropolitan gateways in greater numbers, most of them still make their homes in large metropolitan areas (Ellis et al., 2014). Therefore, not surprisingly, highly racially diverse census tracts are also found disproportionately in such environs (Wright et al., 2018). The 53 metropolitan areas with populations greater than 1 million in 2000 accounted for 58 percent of the total US population in that year. As Table 9 shows their share of highly racially diverse census was far higher for all four methods, but especially for Walton and Hardebeck, Holloway et al., and Poulsen et al. This table also shows that three of the four methods found modest metropolitan deconcentration of highly diverse tracts between 1990 and 2010. Poulsen et al.’s method, however, moved in the opposite direction, revealing an increasing share of these types of tracts in the largest U.S. metropolitan areas. As their approach requires a racially diverse tract to be at least 70% nonwhite, this suggests that tracts with the largest nonwhite shares are increasingly concentrated in large metropolitan areas.

Table 9.

Share of highly racially diverse census tracts in the 53 largest MSAs.

	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
1990	78.3%	95.4%	83.2%	95.9%
2000	72.6%	91.8%	84.8%	92.7%
2010	67.0%	90.3%	85.3%	90.9%

Table 10.

Counts of highly diverse census tracts for the largest 53 metropolitan areas.

		Ellen			Holloway et al.			Poulsen et al.			Walton and Hardebeck
MSA	Total Tracts (2000)	1990	2000	2010	1990	2000	2010	1990	2000	2010	1990	2000	2010
New York	5054	276	316	312	35	201	195	361	579	686	84	143	218
Los Angeles	3333	150	108	48	35	99	70	291	394	423	88	104	102
Chicago	2040	60	94	147	3	15	12	32	42	74	13	22	33
Philadelphia	1565	36	85	162	3	11	18	17	43	80	5	17	28
Detroit	1561	13	32	73	0	4	1	1	5	11	0	0	2
San Francisco	1449	101	85	64	37	142	145	97	185	272	96	144	178
Boston	1221	35	50	85	7	28	31	11	24	43	8	22	33
Washington DC	1030	80	135	153	4	50	81	9	42	91	18	70	139
Houston	873	134	109	104	3	49	41	35	99	150	36	68	76
Cleveland	870	11	42	79	0	1	1	0	0	4	0	1	2
Seattle	769	16	76	89	1	17	51	6	10	10	0	29	85
Minneapolis	742	12	42	82	5	27	39	3	25	34	0	19	29
Pittsburgh	699	0	2	2	0	0	0	0	0	0	0	0	0
Dallas	688	66	110	110	1	16	25	13	37	70	4	30	54
Phoenix	675	12	12	18	0	1	8	10	5	8	0	0	1
Atlanta	658	7	47	87	2	10	17	41	12	47	3	21	31
Baltimore	622	2	14	59	0	0	0	0	0	4	0	0	7
Miami	618	53	64	87	0	4	2	17	36	56	0	0	3
Denver	612	12	40	53	0	0	4	5	11	15	0	3	5
San Diego	596	37	34	27	22	26	13	41	49	45	37	36	32
Tampa	542	17	51	84	0	0	1	1	2	13	0	1	7
St. Louis	524	1	3	16	0	0	0	0	0	0	0	0	1
Kansas City	489	11	15	38	1	3	2	1	1	11	0	1	2
Portland	484	1	10	20	0	0	1	1	0	0	0	1	6
Cincinnati	477	1	3	12	0	0	0	0	0	0	0	0	1
Milwaukee	454	6	15	20	1	1	2	0	5	5	1	2	1
Sacramento	393	49	59	53	22	63	65	14	35	48	43	80	89
New Orleans	390	10	14	37	0	0	0	2	1	9	0	0	0
Columbus	368	0	2	12	0	0	0	0	0	0	0	0	0
Norfolk	362	3	18	40	0	0	0	0	0	0	0	0	2
Fort Worth	351	27	60	60	0	5	14	4	11	39	0	16	23
Indianapolis	339	1	8	32	0	0	0	0	0	2	0	0	1
Oklahoma City	329	14	20	42	0	7	3	1	1	0	1	2	2
Orlando	324	17	44	65	0	4	4	0	3	11	0	2	4
Las Vegas	320	17	49	52	0	1	17	1	5	17	0	5	36
San Antonio	314	27	20	12	0	0	1	6	10	17	0	0	2
Charlotte	300	1	19	45	0	0	2	0	3	15	0	0	2
Buffalo	297	7	14	22	0	0	4	1	2	4	0	0	2
Hartford	288	13	28	36	0	0	4	6	8	16	0	1	11
Salt Lake City	282	0	1	1	1	1	1	0	0	0	0	0	0
Memphis	272	0	3	9	0	1	0	0	1	1	0	2	1
Rochester	266	12	12	12	0	2	2	7	16	29	0	0	0
West Palm Beach	265	13	30	55	0	0	0	2	4	11	0	0	0
Greensboro	263	0	20	41	0	0	5	0	2	12	0	0	5
Providence	258	6	16	20	5	12	10	7	11	12	6	5	3
Austin	255	35	19	23	0	1	5	6	12	10	0	5	8
Grand Rapids	255	1	5	23	0	0	0	0	0	2	0	0	0
Richmond	252	1	10	22	0	0	0	0	0	4	0	1	2
Nashville	247	1	14	41	0	2	1	0	0	1	0	1	2
Louisville	241	1	2	8	0	0	1	0	0	0	0	1	2
Raleigh	210	2	16	47	0	2	2	0	1	9	0	1	3
Tucson	198	3	4	2	0	0	0	0	0	0	0	0	0
Jacksonville	197	0	5	38	0	0	0	0	0	0	0	0	3

Between 1990 and 2010, almost all large metropolitan areas experienced an increase in the number of highly diverse census tracts. This is evident no matter which lens we use (Table 10). But the relationship between metropolitan area size and the count of highly diverse tracts are imperfectly correlated. For example, in 2010, the correlation (not shown) of highly diverse tracts and total tracts ranged from 0.73 for Walton and Hardebeck to 0.91 for Poulsen et al. New York is the largest MSA and each approach recorded the largest count in 2010 for this metropolitan area. With fewer total tracts, San Francisco recorded a high count as did San Diego.

We have established that the four schemas tally diverse tracts differently with Holloway et al. identifying the fewest and Ellen’s identifying the most. This observation is generally supported when we inspect individual metropolitan areas; but not in every case. Some places, e.g., San Diego, produced very similar tallies. In other metropolitan areas, Miami for example, the different approaches yielded very different counts. The notable exception is Ellen’s method. For example, while all the other approaches registered robust increases in racially diverse tracts in San Francisco, Ellen’s technique noted a 36% decline. A related comment applies to measurement in Chicago and Detroit: Chicago and Detroit have relatively few highly mixed neighborhoods–this is evident with all the approaches except, again, using Ellen’s schema. Ellen’s method also departs from others when we look at Los Angeles. Her method cataloged a large decrease over this 20-year period whereas the other three methods showed that either highly diverse tracts are on the rise or are stable. It works differently because her method has different requirements, centered on Black-White presence. Thus, Ellen’s technique identified highly racially diverse tracts in many southern metropolitan areas, such as New Orleans, Memphis, Nashville, Jacksonville, and Norfolk. The others located zero or few such tracts in those places.

With some notable exceptions (e.g., New York), northeastern and midwestern metropolitan areas register relatively few highly diverse neighborhoods in the 1990–2010 period. Most of these metropolitan areas have Black population shares well above 10% and much smaller shares of population from other nonwhite groups. These metropolitan areas typically have high levels of Black-White segregation and were identified by Massey et al. (1993) as “hypersegregated” using 1990 census data . In many of these places – for example, Baltimore, Cleveland, Detroit, Indianapolis, Milwaukee, and St Louis – the numbers of highly diverse tracts captured by methods other than Ellen’s is zero or close to zero. Only Ellen’s method consistently registers the presence of small numbers of highly diverse tracts in these places. This pattern is not restricted to metropolitan areas with high black population shares. A third (18/53) of the metropolitan areas had less than 10% black in 2010 and these are typically in the west, including such places as Salt Lake City, Portland, and Tucson registering less than 4%. As in the hypersegregated, high-percentage black metropolitan areas of the northeast and Midwest, many of these places had few highly diverse tracts no matter the method, but Ellen’s method generally registers more than the others.

To explore the relationships among the four methods a little further, Table 11 displays three sets of correlation matrices, one for each decade, for the metropolitan area data displayed in Table 10.

Table 11.

Correlations among the four schemas for the 53 largest metropolitan areas: a) 1990, b) 2000, and c) 2010.

	Ellen	Holloway et al.	Poulsen et al.	Walton and Hardebeck
a)
Ellen	-
Holloway et al.	0.76	-
Poulsen et al.	0.88	0.81	-
Walton and Hardebeck	0.83	0.97	0.83	-
b)
Ellen	-
Holloway et al.	0.83	-
Poulsen et al.	0.83	0.91	-
Walton and Hardebeck	0.79	0.96	0.83	-
c)
Ellen	-
Holloway et al.	0.69	-
Poulsen et al.	0.69	0.87	-
Walton and Hardebeck	0.70	0.98	0.84	-

These tables reinforce the results of some of the previous analysis while adding some more nuance. There are three main findings. First, the counts of highly racially diverse tracts found in the large metropolitan areas of the United States revealed by Walton and Hardebeck’s and Holloway et al.’s methods are highly correlated in every decade. Second, when it comes to these counts by metropolitan area, Ellen’s technique produces some very different counts from the other methods; this observation is most evident in 2010 but holds across the three time periods. Third, Poulsen et al.’s taxonomy occupies a sort of shifting middle ground. It’s in between the others in terms of the correlation coefficients and shifting in the sense that correlation between this schema and Ellen drops from 0.88 in 1990 to 0.69 in 2010.

Discussion and conclusions

Few people would disagree that the neighborhood is a cardinal aspect of urban society. Neighborhood differentiation is evident in almost all urban contexts–across space and time (Sampson, 2019) and the racialization of different groups of people both produces and is produced by space (Delaney, 2002). The issue of neighborhood racial concentration and attendant inequalities require continuing and robust attention. Neighborhoods with diverse racial populations are also important, but for different reasons. Racial residential isolation produces disparities in almost all walks of life from school outcomes to wealth to employment to interactions with the police and judiciary. Racially diverse neighborhoods therefore stand in contrast to ones dominated numerically by one racialized group or another. We know they are growing in number but we also need to know how these spaces come about, how stable they are, the nature of their racial diversity, and how other categories such as age, housing tenure, poverty, nativity, and income may intersect with race. But answering these questions with confidence requires that the foundations of such analyses themselves are positioned clearly.

The findings reported here show how different neighborhood classification schemes aimed at identifying the most demographically integrated census tracts (Molotch, 1972) can produce very different outcomes. In one sense, then, this essay is a cautionary tale. Scholars wanting to study neighborhood racial diversity face a dilemma. They can devise a schema of their own tailored to helping answer a particular problem or they use one of several methods that other social scientists have developed. If they choose the latter route, the literature offers a wide range of ways that scholars have measured compositional racial diversity to classify census tracts, with each yielding a different tally of neighborhoods for a metropolitan area or more generally. Our analysis makes no claims about the superiority of one technique or about the deficiencies of another but rather points out that the overlap among these methods can, in some instances, be surprisingly slim. It follows that researchers interested in questions of neighborhood diversity in the context of growing national diversity should choose the means by which they classify such places with great care.

The analysis unfolded in four phases: by making basic counts, by identifying the overlaps, through looking at change over time, and by examining a few metropolitan dimensions. Ingrid Gould Ellen’s technique was the most generous in the sense that her schema identified the largest number of “multi-ethnic” neighborhoods in all periods examined. The method developed by Steven Holloway and coauthors identified the fewest highly racially diverse tracts. The analysis revealed that the more restrictive definitions that yielded the fewest counts (Holloway et al. and Walton and Hardebeck) also produced tallies of neighborhoods with the highest levels of average compositional racial diversity (as captured by scaled entropy). Both methods require a racial “balance” or the meaningful presence of multiple groups to qualify as highly diverse and were thus the most congruent. Congruencies among the four approaches, however, ranged from as high as 81% to zero, depending on decade. More specifically, there was zero overlap between the scheme developed by Ellen and the one that Poulsen et al. fashioned. Poulsen et al.’s definition is potentially capturing a different phenomenon than the other three because it requires highly racially diverse tracts to be at least 70% nonwhite and has no minimum percentage required for whites. Poulsen et al.’s method thus identifies tracts with predominantly minority race groups rather than tracts where there is more of a “balance” of different races. For scholars interested in those places that are mixed and where whites are a minority, even absent, Poulsen et al.’s method is a good choice. It is worth noting, however, that this method orients the definition of highly diverse racial spaces to a disproportionate nonwhite presence rather than requiring a racial “balance” of all groups, including whites.⁴ In instances where researchers place a premium on such “balance” the methods of Holloway et al. or Walton and Hardebeck would be a better choice. In other research contexts where mixing with Whites constitutes an analytical centerpiece, Ellen’s method might rise to the fore.

Broad agreement did occur in some areas. All four methods found that the rate of growth in highly racially diverse census tracts slowed in the 2000s compared to the 1990s. All four approaches also identified low levels of survival of diverse tracts. Understanding the causes of this (in)stability should be of considerable academic and policy interest because of its implications for the ways in which increased diversity is accommodated in residential environments. Much more research is needed in this area and the research reported here suggests that scholars may productively examine this phenomenon using any one of these methods of classification. Wright et al. (2018) provides one such example.

All four schemas showed that highly racially diverse tracts are heavily concentrated in the largest United States metropolitan places. Ellen’s technique, however, recorded the lowest large-metropolitan share, a difference that grew between 1990 and 2010. Shifting scale to specific metropolitan areas further separated Ellen’s approach from the others. In Washington DC for example, – a place with a long history of Black-White segregation but with a recent history of considerable Latinx and Asian immigration, the four approaches all found high rates of growth in the count of racially diverse tracts. But for other metropolitan areas, Ellen’s method departed from the others, producing not only different counts but also different directions of change: finding large increases in the tally of multiethnic tracts where the other schemas found no such trend. Ellen’s method also generated seemingly counter-intuitive outcomes, such as the declining number of highly racially diverse tracts in Los Angeles between 1990 and 2010. That said, scholars wanting to examine how Blacks play into neighborhood diversity in the US, should consider using Ellen’s method given its requirement for a substantial Black presence. Walton and Hardebeck’s scheme is also a possibility here for while their method emphasizes “balance”, it also requires the presence of Blacks for a neighborhood to attain their threshold for diversity. We thus agree with Sin and Krysan (2015, p. 7) when they say that “future studies need to be more explicit in clarifying which ethnoracial group is sharing a residential space with whom and, importantly, spelling out the implications of these decisions.”

This essay provides both a set of cautions as well as a set of guidelines that can help scholars make choices that best fit their needs. For example, the approaches devised by both Poulsen et al. and Holloway et al. were designed with cartography in mind (Johnston et al., 2009). Both teams have produced insightful maps of urban residential diversity and segregation in their publications. Holloway et al. have gone further and used their schema to produce an online interactive web-based atlas of the entire United States (www.mixedmetro.com) that users can use to examine neighborhood change between 1990 and 2010 and to examine the intersections of racialized space with other variables such as nativity and poverty.

While this research systematically addressed some similarities and differences among four representative techniques, several questions still remain. For example, how does using a local referent to gauge racial diversity differ from one that uses one based on a broader frame such as a group of metropolitan areas, or a state or a national referent? Logan and Zhang (2010), for example, used a percentage threshold for a racial group that changes each decade in accordance with shifts in the racial composition of a referent set of metropolitan areas. They argued against the usage of entropy and claim that this index, while useful for single region studies, which sets the standard for maximum diversity to be the coequal presence of each group, is unattainable and does not account for local distribution/presence of racial groups. Thus, the entropy index might be most useful at local scales and focused studies but might be less effective at capturing trends at a national scale. That said, Walton and Hardebeck’s threshold for highly racially diverse, which by requiring at least 10% population shares for four groups generates entropy scores near the top of the observed range of this measure, comes very close to what Logan and Zhang had in mind for their 24 metropolitan area analysis.

We also want to also note the irony that while these representative schemas are deeply interested in mixed-race places none easily accommodate mixed-race people. All four schemes discussed here make no mention of mixed-race people or devise ways to account for them explicitly. Scholars, however, could use any of the taxonomies to test hypotheses about diverse residential neighborhood contexts and mixed-race people. The fact remains that mixed-race bodies are not discussed enough in conversations about mixed-race places. This observation leads to another point. There are limits to what we can recommend, how prescriptive we can be, based on the empirical work we share in this essay. Researchers must supplement our findings by reflecting on the conceptual, theoretical, rationale for what is best for their project. For example, insisting on including a measure of the percent Black in a multi-ethnic/racial neighborhood, that Blacks have been uniquely racialized and discriminated against in the United States, risks obscuring the emergence of highly racially diverse neighborhood spaces driven by the increasing presence of Asians and Latinos in places in the American West such as Los Angeles, San Diego, and San Francisco.

This leads to our final comment. Much of the interest in neighborhood racial diversity derives from the demographic shifts that have taken place since the 1970s. First- and second-generation immigrants account for a quarter of the United States population and many of these people claim either a Latinx or Asian identity (National Academies of Sciences, Engineering and Medicine & Committee on Population, 2016). And the Latinx and Asian segments of the United States population are on the rise. With births accounting for the lion’s share of United States Latinx population growth (Pew Hispanic Center, 2011) and immigration from Asia now exceeding that of Latinx populations, the future of the United States population in terms of race is increased diversity largely driven by the growth of these groups. One of the main research questions attends to how these shifts are shaping residential outcomes, including the emergence of more demographically diverse neighborhood spaces (Clark et al., 2015). How we think about and measure that diversity matters. We hope that the discussion and the findings reported here offer a few more guidelines for those choices than have been available to date.