Introduction1
Racial residential segregation is a longstanding problem that has plagued the United States for roughly a century. Although leading measures suggest a gradual decline since the 1970s, our 2021 national study revealed surprising increases in observed levels of racial residential segregation in recent decades and examined the harmful correlates and racial disparities associated with it based on a range of life outcomes, including educational attainment, life expectancy, and wealth accumulation.
To accompany that study, we created an interactive mapping tool that provided data and demographics for the entire country, from the neighborhood (census tract) to the metropolitan region, over five decades for every major measure of racial residential segregation commonly relied upon by social scientists. In our report and analysis, however, we introduced and used a bespoke and more intuitive measure segregation, based in part on a recently developed formula, to help readers and users understand the dynamics and patterns we observed.
In this report, a follow up to that study, we compare each of the major measures of racial residential segregation featured on our interactive mapping tool and which are described in our Technical Appendix. This supplemental report shows how the level of segregation indicated by each of these major measures of segregation has changed over time, and compares the results. We use the longest possible time scale to view these changes based upon available data.2
Our goal is to illustrate the behavioral differences and similarities between these different measures, and, hopefully, to provide important or interesting insights on the nature and dynamics of racial residential segregation in the United States generally. This effort should help us better understand how these measures work and what they tell us, in addition to revealing broader insights about the dynamics of segregation in the United States.
To the best of our knowledge, no one has presented a summary description of the directional changes for each of the most common measures over time. Most studies of racial residential segregation select and then focus on a specific measure, usually to the exclusion of others.3 Other studies have focused on mathematical and conceptual differences or other technical aspects of the measures while paying less attention to the output differences.4 This report fills a crucial gap in knowledge by showing now only how these measures indicate changes in levels of segregation over time, but compares those changes directionally and in terms of magnitude, and thereby yields new insights into what these measures tell us about the nature of racial residential segregation.
In particular, we will present and describe changes to national levels of segregation as measured by the Dissimilarity Index, the Exposure Index, the Isolation Index, the Entropy Score, the Diversity Index, the Mutual Information Index, the Multigroup Entropy Index, and the Divergence Index. (For the formulas for each of these measures, please consult our Technical Appendix.) The Location Quotient is included in our mapping tool, but not possible to calculate at the national level, so it is not part of our presentation and analysis here. In addition to our descriptive presentation, we also calculated and present the correlational statistics between these measures, followed by a few concluding observations.
Why Measure Segregation?
Before we review the changes to the major measures of segregation, it is worth taking a moment to explain why we use measures of segregation. After all, we can see segregation visually through maps that show where members of different racial groups live.
For this reason, many presentations of segregation focus on comparing demographic or compositional differences. For example, a recent report on inter-district school segregation simply compared demographic differences by race to indicate segregation.5 Specifically, it compared the percentage of students of color in one district to that percentage in an adjacent district, and labeled districts with the largest difference between them the most “segregated.”6
Or, alternatively, it is not uncommon to see reports display changes in the percentage of a particular racial group, such as a decline in the percentage white or increase in a particular racial group, such as Black or Latino, into a neighborhood, school or community, and conclude that these changes reflect a decrease in segregation or an increase in integration.7
There are several problems with these approaches. Although dot-maps and other compositional maps and change maps may be visually striking and representationally clear, they don’t actually tell us the precise level of segregation that exists. It would be like trying to guess the air temperature by stepping outdoors. Precision requires measurement.
Relatedly, demographic differences are difficult to scale and compare. If we want to know whether one community is more segregated than another, we cannot tell by looking at a demographic compositional map or a change map or table. Depending on the context, the direction of change or magnitude of the differences may look like more segregation, but it might actually be less. Or it may look like less segregation, but prove to be more.
To appreciate this problem, imagine two communities. One community is heavily white, say 90 percent white, and the other is heavily non-white, say only 30 percent white. Within the first community, you may have a neighborhood that is 95 percent white and another that is 85 percent white, a difference of 10 percent points. The second community is only 30 percent white, but may have a neighborhood that is 25 percent white and another that is 35 percent white. Both communities have a 10 percent white gap between their neighborhoods, but that doesn’t actually mean they are equally segregated. The second community, in particular, could be either more or less integrated than the first, depending upon the distribution of white and non-white people, and the proportions of non-white groups relative to each other.
To address this problem, some segregation scholars have devised “typologies” that purport to characterize different degrees or types of segregation. One example of such a typology is a 6-type framework that separates neighborhoods based upon the relative proportions of different groups.8 For example, under this methodology, a “Type I” neighborhood is one where a “charter” racial group is more than 80 percent of the population, whereas a “Type II” neighborhood is one where that group is 50-80 percent of the population. In contrast, Type III, IV, V, and IV neighborhoods are all those in which non-charter (minority or formerly minority) groups are a numerical majority, but in different configurations or combinations. Such typologies can helpfully distinguish between meaningfully different situations, but can quickly become complicated and difficult to interpret or hard to apply or compare in many real-world applications.9
But another problem with compositional changes is that the change in the overall proportion of a single racial group or even a cluster of groups cannot tell you if segregation has increased or decreased in fact. At most, it is highly suggestive. Segregation is the distribution or spatial arrangement of people. One group can increase or decrease, but if those changes are accompanied by changes to where members of that group live, then the latter fact may be more important than the former. Consider an example that illustrates this idea.
Imagine a city is a so-called “majority-minority” city, where most residents are people of color, although there are a significant number of white residents. Suppose that many heavily non-white neighborhoods experience a decline in the percentage of white residents over the next few years. Ostensibly, that could indicate an increase in segregation, since there are proportionally fewer white people than there were before. However, if the city-wide proportions of white residents declined more than the white declines in those particular neighborhoods, then the opposite inference might be warranted: that segregation actually decreased because the remaining white population is more integrated as a whole.
To see this point more clearly, consider the opposition situation: demographic and compositional proportions stay exactly the same over the next few years. Does that mean that there has been no change in the level of segregation? Not necessarily. If members of the different racial groups move into opposite-race neighborhoods, there can be no proportional changes whatsoever and yet also decreases (or increases) in segregation. What matters is not the relative proportions, but the distribution of proportions. The more geographic units you are analyzing, the better you can get a handle on distributions, but simple compositional statistics, or changes in those statistics, is not enough to indicate the degree, level or change in segregation alone. This is why segregation indices are generally important. They provide a single statistic that is comparable over time and between regions or jurisdictions.10 The remainder of this essay reviews those major measures of segregation and compares what they tell us.
Major Measures of Segregation
There are many possible measures of segregation.11 We only analyze the major measures, meaning the measures that are most widely used in segregation studies, and which are featured in our project and described in our Technical Appendix.
1. The Dissimilarity Index
As noted in our Technical Appendix, the Index of Dissimilarity is probably the most widely used measure of segregation. It measures “evenness” or the relative spatial distribution of racial populations, and is scaled either between 0 and 1 or 0 and 100. A value of 0 indicates complete integration, and a value of 100 indicates complete segregation. Values in between those extremes indicate the percentage of either racial group that would have to move to a different-race neighborhood for a larger geography to become fully integrated.
Figure 1 below shows the Black-nonBlack dissimilarity score from 1890 to 2020 for the entire country.12 The data point markers indicate the measured level of Black-nonBlack segregation for each decennial census in that period. The reference ranges on the right hand side reflect the general consensus characterizing those values.
Figure 1
Descriptively, the Black-nonBlack Dissimilarity Index rose every decade from 1890 until 1960, where it leveled out until 1970, after which it began a slow decline that continues to the present. National segregation levels, as measured by the Dissimilarity Index, peaked in 1960 and 1970 at an extraordinarily high level of racial residential segregation. This measure would indicate that nearly 80 percent of either Black or nonBlack families would have to move to a different race neighborhood to achieve complete integration.
Contrary to the presumption that racial residential segregation was a product of slavery or the Reconstruction Era, what this index clearly indicates is that Black-nonBlack racial residential segregation was speedily constructed in the first half of the twentieth century, with the largest and fastest increase occurring between 1920 and 1930, as the first wave of the Great Migration was well underway, and then consolidated and expanded in the decades that followed. We have been living with the consequences of this development ever since. Racial residential segregation in 2020 was higher than at any point since before 1920.
The largest decrease in segregation between census periods, according to this measure, was between 1970 (the year the federal Fair Housing Act of 1968 went into effect) and 1980, a decline of 6.0 points, followed by declines at the same rate between 1980 and 1990, and by interval decreases of 3.0, then 5.0, and most recently 4.0 (as indicated by the figures between the markers in that period) between 2010 and 2020. This indicates gradual, but slowing improvement. The rate of change is slowing even though the score is falling.
Perhaps most importantly, however, a Black-nonBlack dissimilarity score of 55.0 indicates a country that is significantly segregated. Although falling into the “moderate” range, it still indicates that most Black or nonBlack Americans would need to move to a different neighborhood to achieve integration. Figure 1 not only reminds us that segregation today is still higher than it was in 1890, 1900 or 1910, but that it is objectively pronounced.
Figure 2, below, displays the changes in Asian-white and Hispanic-white dissimilarity from 1980 to 2020.
Figure 2
Our presentation for Asian and Hispanic segregation begins in 1980, because that is when the census began collecting ethnic and racial data for these groups separately. As shown in Figure 2, both Asian-white and Hispanic-white residential segregation, as indicated by the Dissimilarity Index, rose significantly from 1980 to 1990, especially for the latter, which increased by more than 6 points. This is important because it may help explain why other, more holistic, multi-group measures of segregation show increases during this period even as Black-white segregation declined.
The good news, however, according to Figure 2, is that both Asian-white and Hispanic-white segregation has slowed or attenuated since 1990.The bad news is that both levels of segregation remain in the moderately high range, and persist in that range.They are almost as high (51.4 and 51.7, respectively) as Black-white dissimilarity (55.0). That suggests a convergence among the three forms of segregation, as measured by dissimilarity.
Figure 3, below, completes our presentation of the Dissimilarity Index by indicating changes in the measured levels of racial residential segregation according to this index for Black-Asian, Black-Hispanic, and Hispanic-Asian from 1980 to 2020.
Figure 3
These three forms of racial residential segregation show strikingly different (and similar) behavior. The Black-Asian and Black-Hispanic patterns of segregation follow similar trajectories, starting at a fairly high level (and virtually identical values) in both 1980 and 1990, followed by gradual declines. By 2020, Black-Asian segregation has fallen by nearly 9 points, although remains nearly a full point higher than Black-nonBlack segregation, suggesting that Black Americans are more segregated from Asians than from white people in the present moment. And Black-Hispanic segregation also remains moderately-high, and probably higher than many people would presume, at nearly 53. Again, this indicates that most members of either group would have to move into the other group’s neighborhood to become fully “integrated.”
By contrast, however, Figure 3 shows that Hispanic-Asian segregation, according to this measure, has consistently fluctuated within a narrow 2.2 point range from 1980 to 2020 during the five decades shown, slightly rising and falling over that period. Hispanic-Asian segregation falls clearly within the moderate range, and the lowest observed levels of national segregation we see.
Overall, the Dissimilarity Index shows a country that remains racially separate, with majorities of each group needing to move into different race neighborhoods to become integrated. It also shows progress in recent decades, but stalling out at a moderately high level for all groups, while many of the values are converging to a similar moderately-high level.
2. The Exposure Index
The so-called Exposure Index is one of the isolation indices, as described in our Technical Appendix. Simply put, it captures the neighborhood composition of the average or median member of a particular racial group. Figure 4, below, displays the Black-white Exposure Index values from 1940 to 2020. This indicates the percentage of white people residing in the neighborhood of the typical Black American (34 percent, as of 2020).
In many ways, this is a superior representation of segregation as it captures the ordinary case, which can be obscured by progress for a relative smaller share of the population or some neighborhoods, where such progress would appear in the Dissimilarity Index score as falling values, even as the ordinary person of that race’s neighborhood composition remains roughly the same.
Figure 4
Descriptively, the Black-white Exposure Index indicates a precipitous decline in the presence of white neighbors residing in the typical Black American’s neighborhood, especially from 1940 to 1980, with a gradual increase from 1980 to 1990, and again from 2000 to 2010, followed by a slight decline from 2010 to 2020. This shows that the typical or average Black American has far fewer white neighbors than the white proportion of the American population would suggest, suggesting a significant degree of Black-white racial residential segregation keeping people apart.
Notably, the Black-white Exposure Index behaves quite differently than the Black-white Dissimilarity Index shown in Figure 1. Several of these differences are worth noting. First, the most segregated point in time occurs in 1980 rather than in 1970. In 1980, the typical Black neighborhood had just 31 percent white residents, a tick lower than in 1970, although the Dissimilarity Index indicates massive improvement toward greater integration in that time period.
Secondly, although there is a steady increase in segregation as captured by this instrument from 1940 to 1980, improvement since then has not been continuous. In 2020, the Black-white Exposure Index actually fell (worsened) although dissimilarity continued its gradual decline (improvement).
Third, the greatest improvement occurred between 1980 and 1990, whereas the Black-white Dissimilarity Index shows the greatest improvement from 1970 to 1980, as just noted.
Reading this chart, it indicates that Black-white segregation is measurably worse as of 2020 than it was in 1950, and is basically as bad as it was in 1960.
When we compile the figures for all of the exposure values to get a panoramic view of the typical person of a particular race, we can see more clearly how different neighborhood environments are for white and Black Americans.13 The typical white neighborhood is 69% white, 9% black, 12% Hispanic, and 6% Asian in 2020; in contrast, the typical Black neighborhood is 41% black, 34% white, 17% Hispanic, and 6% Asian. The only common proportion are Asian neighbors. White Americans live in neighborhoods that are radically compositionally different by race than typical Black Americans.
We have also calculated Asian-white and Hispanic-white exposure scores, shown in Figure 5 below.
Figure 5
As shown in Figure 5, the exposure of Asian and Hispanic Americans to white Americans has precipitously declined from 1980 to 2020, a contrast from the dissimilarity indices of the same, since those scores rose and then fell during this period. In 1980, the typical Asian-American lived in a neighborhood that was 65 percent white, compared to only 44 percent white in 2020. Similarly, the typical Hispanic-American lived in a neighborhood that was 56 percent white in 1980, compared to just 39 percent white in 2020.
Although the isolation scores could simply reflect the declining number of white Americans as a proportion of the population, we should note that whites are still about 58 percent of the American population. This suggests increasing segregation for both groups, especially from whites.
The growth in both the Hispanic and Asian populations in the United States may be contributing to these changes. We have seen both of these racial groups grow significantly in recent decades.14 If Asian-Americans and Hispanic-Americans disproportionately live in Asian and Hispanic communities, respectively, then an increase in population relative to the entire population would result in greater racial isolation and reduced exposure to members of other racial groups due to segregation. That is what Figures 5 and 6 seem to indicate.
3. The Isolation Index
The Isolation Index is part of the Exposure Index, since it is the “exposure” of members of a racial group to members of the same group, but it is differently named (presumably because it would be strange to denote same-race contact as “exposure”). Figure 6 below indicates the changes in white, Hispanic and Asian isolation from 1980 to 2020 in the United States.
Figure 6
Figure 6 suggests several interesting trends. First, we see that white isolation has declined steadily between 1980 and 2020, from a score of 82.9 to 66.5. This indicates that the typical white American now “only” lives in a neighborhood that is about 70 percent white, compared to living in an 83 percent white neighborhood as of 1980. Since the proportion of white population has declined from 80 percent to 57.8 percent between 1980 and 2020, this is not surprising. The decline in white isolation matches the changing demographics of the country, although the Isolation Index score is still higher, indicating that whites tend to be more segregated on average than their proportion of the population would suggest.
And, given the growth in Hispanic and Asian populations, it is not surprising that they have seen a corresponding increase in segregation for these groups in the same period. Hispanic isolation has risen from 28.5 in 1980 to 38.2 in 2020. This level of isolation outstrips the proportion of the Hispanic population, again suggesting significant segregation.
Asian isolation has also consistently risen in this period, but at a slower pace, from 12.4 in 1980 to 17.4 as of 2020, while the Asian (alone) population increased from 3.7 million people (1.5 percent of the population) in 1980 to 19.9 million (6.1 percent) in 2020.
The good news, according to this measure, is that Black isolation continues to decline, from 37.4 in 1980 to 30.3 in 2020. This means that the typical Black American resides in a neighborhood that is only 30.3 percent Black in 2020, suggesting a greater diversity of neighbors. On the other hand, since Black Americans are just 12.1 percent of the population (as of 2020), this shows that Black isolation, on a relative basis, is the highest among the four racial groups shown here.
Figure 7, below, shows each racial group's Isolation Index score against their proportion of the population at the same decennial census. This figure shows a relationship between population proportions and isolation scores, but also shows some important differences.
Figure 7
Figure 7 vividly displays the difference between the observed level of isolation (segregation/concentration) of each racial group and their relative proportion of the US population. If people tend to cluster together, because of discrimination, port-of-entry effect, or compositional preferences, we might expect that groups that are a larger percentage of the population to have higher isolation scores. That’s what this data indicates. Thus, the white population, still a majority of the US, will tend to have the highest isolation scores.
But a group is only segregated, according to this measure, if that racial group's isolation score is higher than its proportion of the overall population. As Figure 7 suggests, although white Americans have higher Isolation scores, the differences between the relative proportion of the population and isolation scores are actually larger for non-whites.
Whites are 57.8 percent of the population, but have an Isolation Index score of 66.5, meaning that the typical white person lives in a neighborhood that is only two-thirds white, only slightly more than their share of the population — a difference of only 9 points.
The difference between the share of the population and the isolation score is 11.3 for Asians, 19.5 for Hispanics, and 18.2 for Black Americans. This suggests that Hispanics are the most concentrated, and, in a sense, segregated from other races according to the Isolation Index, followed by Black Americans.
This tells a different story than the Exposure Index. Especially since the group-white exposure scores suggest that Black Americans, not Hispanics, are the most segregated group from whites.
But, as this analysis shows, it is difficult to disentangle these measures of segregation from the relative proportions of the population. This is a reason why multi-group measures may be superior.
4. Entropy Score and Diversity Index
Although sometimes used as a proxy for segregation, the Entropy Score and Diversity Index are not measures of segregation per se (again, see our Technical Appendix). Rather, they are measures of diversity. The Entropy Score indicates how diverse a place is, given a predetermined number of groups (i.e. six racial groups).15 And the Diversity Index predicts same or different group neighbors based upon existing patterns.16 Unsurprisingly, they produce very similar results, directionally and in terms of magnitude, as shown in Figure 8 below.
Figure 8
According to Figure 8, the Entropy Score for the United States has steadily risen between 1980 and 2020, reflecting the country’s increasing diversity, especially the growth of Asian and Hispanic populations. The Entropy Score rose from 0.468 in 1980 to 0.637 in 2020, with steady increases of about 6 points in between each decennial census from 1990 to 2020.
The Diversity Index similarly shows a nearly identical trajectory and pattern, with steady increases between intervals from 1990 to 2020, with the largest increase occurring between 1990 and 2000, from 0.422 to 0.509.
Since these are not measures of “segregation,” they simply tell us about the potential for segregation more than showing segregation itself. But it is notable that measured levels of “diversity” do not match, track or tightly correspond to the observed changes in levels of segregation according to any of the measures of segregation we have examined so far. This suggests that the measures of “segregation” examined so far are revealing dynamics or phenomena beyond changes in diversity.
Diversity is necessary for segregation to arise, but it does not necessarily result in segregation. Depending on the arrangement of living patterns and people, diversity can result in integration instead. A place could be diverse and integrated or diverse and segregated. Thus, we need measures of segregation, not simply diversity, to tell us which situation we inhabit.
6. The Mutual Information Index
An important multi-group segregation index is known as the Mutual Information Index, or Theil’s M.17 Some researchers believe this is represents an improvement on measuring segregation for a variety of technical reasons,18 although it has disadvantages as well (such as it is hard to interpret because it is not scaled between zero and one).19 One of its principal advantages is that it can represent segregation for multiple racial groups simultaneously.
We have calculated this index for the entire country from 1980 to 2020, as shown below in Figure 9.
Figure 9
As you can see, the Mutual Information Index shows that segregation increased substantially between 1980 and 2000, but has gradually declined since, but still remains higher than 1990. None of the measures examined so far show this pattern in this particular time frame, as you can see by comparing figures and shape.
7. The Multigroup Entropy Index
The Multigroup Entropy Index, also known as Theil’s H is another sophisticated and interesting measure of segregation.20 The Entropy Index is a preferred measure of segregation by other social scientists.21 Some versions of it control for diversity (it can be just Theil’s M divided by the group entropy score).22 And it allows users to decompose into smaller geographies.
According to this measure, the United States has experienced continuous and precipitous decline in racial residential segregation from 1980 to 2020, from 0.443 to 0.284, as shown in figure 10 below. This decline is steeper than indicated by any other measure examined so far, although the largest declines occurred between 1980 and 1990 and between 2010 and 2020 (5.0 points in both cases).
Figure 10
Multigroup Entropy thus presents one of the more hopeful stories of segregation in the United States, if credited.
8. Divergence Index
The Divergence Index, on the other hand, tells a very different tale. We prominently featured the divergence index in our main project, essay and analysis. Figure 11, below, indicates the divergence index scores from 1980 to 2020.
Figure 11
This chart contains the population-weighted average of the Divergence Index for the nation. Like the Entropy Index, the Divergence Index looks at all racial groups simultaneously and then compares a larger geography to a smaller geography to see how much they “diverge” from each other, with higher scores indicating more segregation.23
If we assume that this can be done over time (meaning that changes to the Divergence Index score over time are meaningful comparable, and not scrambled or overly warped by changes in underlying diversity), then the Divergence Index suggests a decrease in segregation between 1980 and 1990, followed by increases from 1990 to 2000 and 2000 to 2010 (peaking in 2010), but followed by another substantial decrease in 2020, to a point somewhere in the middle of the observed range. This is the basis for our main finding that segregation has increased nationwide since 1990.
Once again, this measure appears to behave, at least directionally, quite differently from the other measures, with a “down-up-down” pattern.
Correlations Analysis of the Divergence Index
As can be seen visually, each of these measures seems to tell us different stories about the dynamics of segregation. But to move beyond visual impressions, we have conducted a correlational analysis. In particular, we probe the behavior of the Divergence Index in relation to the aforementioned measures. The higher the correlation, the more strongly they move together.
Prior research suggests that segregation measures are highly correlated with each other,24 but, as we can see here, they are nonetheless behaviorally quite different, especially in terms of direction, amplitudes and magnitudes.
Table 1: Correlations between the Divergence Index and Measures of Diversity, 1980-2020
| Year | Divergence (Entropy) | Divergence (Diversity) |
| 1980 | 0.711 | 0.709 |
| 1990 | 0.700 | 0.631 |
| 2000 | 0.682 | 0.555 |
| 2010 | 0.680 | 0.496 |
| 2020 | 0.651 | 0.462 |
Table 1 shows the relationship between the Divergence Index and our two “diversity” measures. It suggests an initially high correlation that consistently declines over time. This is consistent with our observation, above, that the Divergence Index appears to denote or indicate measured levels of segregation that are directionally different from growing diversity. This would seem to undercut (although not fully rebut) critiques that changes in divergence are based upon changes in diversity.
Table 2: Correlations between the Divergence Index and the Dissimilarity Index, 1980-2020
Table 2 shows the correlations between the Divergence Index and different dissimilarity scores from 1980 to 2020. What is fascinating is how different the correlations and their respective ranges are depending upon the dyad examined. Asian-white dissimilarity has the weakest correlation with divergence, whereas Black-Hispanic strangely has the strongest. The ranges are also starkly different, falling between 0.306 to 0.377 for Asian-white dissimilarity to 0.554 to 0.706 for Black-Hispanic, a more than 20 point difference. The Hispanic-white Dissimilarity Index also has the widest correlational range with the Divergence Index, from 0.459 to 0.624. To us, this suggests that these indices are measuring different dynamics, or partly different dynamics, rather than the same phenomena.
Table 3: Correlations between the Divergence Index and the Isolation Index, 1980-2020
The Isolation Index correlation scores with the Divergence Index reinforce this observation, especially when we see that white isolation is negatively correlated with the Divergence Index. The only Isolation Index score that is highly correlated with the Divergence Index is Black Isolation, and it is positively correlated, while the others are either negative or weakly correlated.
Table 4: Correlations between the Divergence Index and the Black Exposure Index, 1980-2020
Table 4 shows the correlations between the Divergence Index and the exposure indices. Once again, the correlations here are strange. Not only are the correlations all negative, but the ranges are starkly different. The Black-white Exposure Index is strongly correlated, but in a negative direction. The other two exposure indices shown here, are very weakly correlated.
Table 5: Correlations between the Divergence Index and the white Exposure Index, 1980-2020
Table 5 shows the correlations between the Divergence Index and white exposure indices. Once again, there are no strong correlations, although white-Black exposure is consistently correlated at the moderate range. The other white exposure measures are very weakly correlated.
Table 6: Correlations between the Divergence Index and the Asian Exposure Index, 1980-2020
Table 7: Correlations between the Divergence Index and the Hispanic Exposure Index, 1980-2020
Tables 6 and 7 present statistical correlations between the Divergence Index and Asian and Hispanic exposure indices, respectively. As is the case with the other measures, we see no strong correlations, and oddly different levels, depending upon the application. In the case of Asian exposure, the strongest correlations are with Asian-Black exposure. In the case of Hispanic, it is Hispanic-white, although in a negative direction.
Overall, the Divergence Index does not appear to be strongly and consistently correlated in a positive direction with any of the traditional measures of segregation, although it is strongly correlated with at least one application, Black Isolation. That is not true of the other multi-group measures.
Table 8: Correlations between the Divergence Index and Theil’s H and M indices, 1980-2020
| Year | Divergence - Theil's H | Divergence - Theil's M |
| 1980 | 0.850 | 0.995 |
| 1990 | 0.836 | 0.994 |
| 2000 | 0.871 | 0.994 |
| 2010 | 0.893 | 0.992 |
| 2020 | 0.927 | 0.992 |
Rounding out our analysis, as shown in Table 8, the Divergence Index is clearly correlated with both “entropy” indices, the Multigroup Entropy Index (Theil’s H) and the Mutual Information Index (Theil’s M), although much more strongly correlated with the latter. Although Thiel’s M is highly correlated with Divergence, the patterns we saw above are quite different.
Summary Observations
This review of the different measures of racial residential segregation suggests significant differences as well as striking similarities.
1. Different Measures Measure Different Things
Each of the measures appears to behave quite differently from each other measure. Although prior research has established strong correlations between traditional measures of segregation, as we can see, observationally, they all suggest different directions, magnitudes and amplitudes in terms of measured levels of segregation. This has profound implications for researchers studying this phenomenon: the selection of measures will significantly affect your conclusions.
In addition to presenting these differences for the first time, we have also extended the correlational analysis to the Divergence Index. None of the traditional measures or specific applications of these measures appear to be strongly correlated with the Divergence Index. The strongest correlation with the Divergence Index was Black-white exposure, but that was a negative correlation. Among the multi group measures, there are stark differences in their degree of correlation, especially over time, although Thiel’s M is highly correlated with it.
Altogether, this suggests that segregation truly is a multi-faceted phenomena, and that each measure is measuring something different, a different aspect to that phenomena. Importantly, it also suggests, although not necessarily conclusively, that the Divergence Index is not a byproduct of changing diversity, or else we would expect a higher correlation with measures of diversity.
2. Most Segregated Group?
Each of these measures tells us something different about the most segregated racial group. According to the Dissimilarity Index, Black Americans seem to be the most segregated, with the highest scores for Black-white and Black-Asian dissimilarity. Similarly, the Exposure Index suggests that Black Americans are the most segregated. But Hispanics have the highest Isolation scores relative to their proportion of the population. Again, different measures suggest different conclusions.
3. Peak Segregation?
According to the Dissimilarity Index, segregation seems to peak in 1970 for Black and white Americans (see Figure 1) and 1990 for Asian and Hispanic Americans (we lack data prior to 1980 for the latter two groups). But according to the Exposure Index, segregation seems to peak in 1980. Although our data starts in 1980 for the Mutual Information Index and Multigroup Entropy Index, the former peaks in 2000 while the latter peaks in 1980. According to the Divergence Index, however, segregation rises after 1990 and seems to peak in 2010 (although our data only starts in 1980). Remarkably, each measure indicates different dates for peak segregation.
4. Decreasing or Increasing Segregation?
Each of the measures also tells a different story about whether segregation is increasing or decreasing.
Asian and Hispanic Isolation have increased in the period reviewed (1980 to 2020), while only Asian-white segregation did for the Dissimilarity Index. Black-white exposure also increased. The Divergence Index and the Mutual Information Index show significant increases, followed by declines, in this period. Looking at the period as a whole, all other measures show an overall decrease in segregation in this period, although there have been oscillations.
5. Growing Diversity
Each of the measures seems to be telling us something different about the foregoing. There is one constant, however. Regardless of the measure, we see a clearly diverse country becoming more so. We can see that in terms of overall population trends but also in the diversity indices, which have steadily risen in our review periods.
This diversity is, from our perspective, a welcome development, but it also creates more potential for segregation, and may be slowing or stalling the goal of a more integrated America. Only time (and further study) will tell.
- 1The authors have many people to thank, beginning with Arthur Gailes, Phuong Tseng, Chih-Wei Hsu, Joseph Ahrenholtz, Ipso Cantong, Peter Matingly, Karina French, Abby Steckel, Zoya Gheisar, Varun Fuloria and Shahan Shahid Nawaz.
- 2There is limited data for some racial groups before 1990. For example, the census only began separately collecting Hispanic data in 1980. “History: 1980 Overview,” United States Census Bureau, accessed July 18, 2024, https://www.census.gov/history/www/through_the_decades/overview/1980.html (“A question on Spanish or Hispanic origin or descent was added to the 100-percent questions for the first time; in 1970 this question was asked of only 5 percent of the population.”)
- 3 See e.g. Jessica Trounstine, “Segregation and Inequality in Public Goods,” American Journal of Political Science 60, no. 3 (2016): 709-725, https://doi.org/10.7910/DVN/4LZXTY. Insert examples. At most, they supplement their main measure with another. See Richard Sander, Yana A. Kucheva, and Jonathan M. Zasloff, Moving Toward Integration: The Past and Future of Fair Housing (Cambridge, MA: Harvard University Press, 2018).
- 4Sean F. Reardon and David O’Sullivan, “Measures of Spatial Segregation,” Sociological Methodology 34, no. 1 (2004): 121-162, https://doi.org/10.1111/j.0081-1750.2004.00150.x.
- 5Zahava Stadler and Jordan Abbott, Crossing the Line: Segregation and Resource Inequality Between America's School Districts (New America: February 2024), newamerica.org/education-policy/crossing-the-line-report/.
- 6Stadler and Abbott, Crossing the Line, 13, Figure 5.
- 7Or vice versa. See e.g. Tony Roshan Samara, Race, Inequality, and the Resegregation of the Bay Area (Oakland, CA: Urban Habitat, 2016), 10, 11, map 5, map 6, https://urbanhabitat.org/resource/race-inequality-and-the-resegregation-of-the-bay-area/; Alex Schafran, The Road to Resegregation: Northern California and the Failure of Politics (Oakland: University of California Press, 2018), 47.
- 8Christopher D. Lloyd, Ian Shuttleworth, and David W. Wong, eds., Social-Spatial Segregation: Concepts, Processes and Outcomes (Bristol, UK: Policy Press, 2014), 20, Figure 2.1. This approach was based upon Ron Johnston, Michael Poulsen, and James Forrest, “Ethnic and Racial Segregation in U.S. Metropolitan Areas, 1980-2000: The Dimensions of Segregation Revisited,” Urban Affairs Review 42, no. 4 (2007): 479-504, https://doi.org/10.1177/1078087406292701.
- 9In the development of our Racial Residential Segregation in the Bay Area 5-part series, we experimented with a 7 part-typology, one iterations of which was as follows: Type A: extremely white, Type B: heavily white, Type C: predominantly white, heavier Asian, Type D: diverse, plurality white or Asian, Type E: predominantly hispanic, Type F: predominantly/ Asian, and Type G: Diverse & Integrated. We ran the numbers and tried to sort neighborhoods into configurations of categories such as this, but found them to be overly complicated, confusing, incomplete, and ultimately, unhelpful. We settled on just dividing the Divergence Index into three groups based upon index score thresholds, and then, for our national study, we created a bespoke measure that relied heavily on the Divergence Index.
To be specific, in our Bay Area study, we divided the Divergence Scores for all tracts into those below 0.1075 and above 0.215, and a third grouping those tracts that fell between those two values. We used a slightly modified approach to this for the 3 extremely rural Bay Area counties. This is all explained in footnote 14. Stephen Menendian and Samir Gambhir, “Racial Segregation in the San Francisco Bay Area, Part 1,” Othering and Belonging Institute, October 30, 2018, https://belonging.berkeley.edu/racial-segregation-san-francisco-bay-area-part-1#footnoteref14_qdf7ic8. For our national study, we define the categories here: “FAQ: The Roots of Structural Racism Project,” Othering and Belonging Institute, July 13, 2021, https://belonging.berkeley.edu/faq-roots-structural-racism#indexcalc. - 10For more on this, see Lloyd, Shuttleworth, and Wong, Social-Spatial Segregation, 16-31.
- 11There are also many interesting “bespoke” measures that are proposed or being proposed regularly. See e.g. Trevon Logan and John Parman, “The National Rise in Residential Segregation” (working paper, National Bureau of Economic Research, Cambridge, MA, 2015), https://www.nber.org/papers/w20934 (introducing the idea of “neighborhood-based segregation” based upon publicly released census records). Some time ago, we tried to create a spreadsheet to catalog them, and realized that there were too many to reasonably organize and compare. See e.g. Ron Johnston, Michael Poulsen, and James Forrest, "Ethnic and Racial Segregation in U.S. Metropolitan Areas, 1980-2000: The Dimensions of Segregation Revisited," Urban Affairs Review 42, no. 4 (2007): 479-504, https://doi.org/10.1177/1078087406292701. See Table 1 for a list of 20 indices as a starting point.
- 12john a. powell, Samuel L. Myers, and Susan T. Gooden, “Introduction to the Issue,” Russell Sage Foundation Journal of the Social Sciences 7, no. 1 (2021): 1-17, https://doi.org/10.7758/RSF.2021.7.1.01; Edward L. Glaeser and Jacob L. Vigdor, Racial Segregation in the 2000 Census: Promising News (Washington, DC: Brookings, 2001), https://www.brookings.edu/wp-content/uploads/2016/06/glaeser.pdf. Note: There are sometimes differences in national figures depending on whether the dissimilarity scores are population weighted or not.
- 13John R. Logan and Brian J. Stults, Metropolitan Segregation: No Breakthrough in Sight (Providence, RI: Diversity and Disparities Project, Brown University, 2021), 3-4, https://s4.ad.brown.edu/Projects/Diversity/Data/Report/report08122021.pdf.
- 14The Asian population increased from 1.5% of the US population in 1980 to 6.1% of the US population in 2020. The Hispanic population increased from 6,4% to 18.7% within the same time period.
- 15Mixed Metro (website), accessed August 22, 2024, https://mixedmetro.com/ (you can select any city in any state in the country, and it will give you the diversity score).
- 16For prominent applications, see: “Diversity Index,” USA Today, October 2014, accessed June 11, 2024, https://www.gannett-cdn.com/experiments/usatoday/2014/10/diversity-index-mobile/index.html; Dylan Lukes and Christopher Cleveland, “The Lingering Legacy of Redlining on School
Funding, Diversity, and Performance” (working paper, Annenberg Institute, Brown University, Providence, RI, 2021), https://www.edworkingpapers.com/sites/default/files/ai21-363.pdf; Soumya Karlamangla, “Five Census Findings You May Have Missed,” New York Times, August 17, 2021, https://www.nytimes.com/2021/08/17/us/ca-census-findings.html. - 17Henry Theil and Anthony J. Finizza, “A note on the measurement of racial integration of schools by means of informational concepts,” Journal of Mathematical Sociology 1, no. 2 (1971) 187-193, https://doi.org/10.1080/0022250X.1971.9989795; “mutualinf: Computation and Decomposition of the Mutual Information Index,” Comprehensive R Archive Network, accessed August 19, 2024, https://cran.r-project.org/web/packages/mutualinf/index.html; Ricardo Mora and Javier Ruiz-Castillo, “Entropy-Based Segregation Indices,” Sociological Methodology 41, no. 1 (2011): 159-194, https://doi.org/10.1111/j.1467-9531.2011.01237.x.
- 18Ricardo Mora, “Implementing the Mutual Information Index in Stata” (presentation, Universidad Carlos III de Madrid, October 2013), https://www.stata.com/meeting/spain13/abstracts/materials/sp13_mora.pdf.
- 19Benjamin Elbers, “A Method for Studying Differences in Segregation Across Time and Space,” Sociological Methods & Research 52, no. 1 (2023): 5-42, https://doi.org/10.1177/0049124121986204.
- 20John Iceland, “The Multigroup Entropy Index (Also Known as Theil’s H or the Information Theory Index),” U.S. Census Bureau, December 2004, https://www2.census.gov/programs-surveys/demo/about/housing-patterns/multigroup_entropy.pdf.
- 21Sean F. Reardon and Glenn Firebaugh, “Measures of Multigroup Segregation,” Sociological Methodology 32, no. 1 (2002): 33-67, https://doi.org/10.1111/1467-9531.00110. See also, Michael J. White, “The Measurement of Spatial Segregation,” American Journal of Sociology 88, no. 5 (1983): 1008–18, http://www.jstor.com/stable/2779449; Mary J. Fischer, “The Relative Importance of Income and Race in Determining Residential Outcomes in U.S. Urban Areas 1970-2000,” Urban Affairs Review 38, no. 5 (2003): 669–96, https://doi.org/10.1177/1078087403038005003.
- 22Benjamin Elbers, “Trends in U.S. Residential Racial Segregation, 1990 to 2020,” Socius 7 (2021): https://doi.org/10.1177/23780231211053982; Benjamin Elbers, “Entropy-Based Segregation Indices,” segregation, accessed June 13, 2024, https://elbersb.github.io/segregation/.
- 23Elizabeth Roberto, “The Divergence Index: A Decomposable Measure of Segregation and Inequality,” February 20, 2024, https://arxiv.org/abs/1508.01167; Jackelyn Hwang, Elizabeth Roberto, and Jacob Rugh, “Residential Segregation in the Twenty-First Century and the Role of Housing Policy,” in How Public Policy Impacts Racial Inequality, ed. Josh Grimm and Jaime Loke (Baton Rouge: Louisiana State University Press, 2019), 28-55.
- 24Douglas S. Massey and Nancy A. Denton, “The Dimensions of Residential Segregation,” Social Forces 67, no. 2 (1988): 281–315, 302, Table 3, https://doi.org/10.1093/sf/67.2.281.
