Graphing and measuring segregation (Detroit and Atlanta)

There have been a few attempts to measure segregation in American cities, although the most cited attempts have shortcomings with their methodology.

A common one is looking at what percentage of a metro area's population would have to move for all census tracts to have an ethnic distribution equal to the metro area average. This tends to give an advantage to cities that are dominated by a single rate (whites, with the exception of a few border cities).

For example, in a city that is 90% white and 10% black, and fully segregated with all the whites living in all white census tracts and all the blacks living in all black census tracts, 90% of the 10% blacks would have to move, and 10% of the 90% whites would have to move, so that 0.9*10+0.1*90 = 18% of the metro area would have to move.

A city that is 50% white and 50% black with half the city that is 25% white/75% black and the other half that is 75% white/25% black would have to have to have a quarter of the population of each half move, so 25% of the metro area.

Although the half white, half black metro area is still relatively segregated, I think most would agree it is still much less segregated than the 90% white, 10% black city.

I think a better way to measure segregation is to compare the census tract composition where the average member of a certain group lives to the metro area average.

Detroit is considered one of the most black-white segregated cities, and Atlanta is one of the least black-white segregated among large cities with large black populations.

Here are the 2010 Stats

Detroit MSA:

Black population: 983,367
% Black: 22.65
% Non-Hispanic White: 68.18
% Other: 9.17
Census tract composition for the average black person
72.09% black
21.82% white
6.09% other

Atlanta MSA:

Black population: 1,618,633
% Black: 31.58
% Non-Hispanic White: 52.06
% Other: 16.36
Census tract composition for the average black person
68.63% black
17.24% white
14.13% other

Now there's a bunch of different indexes you could come up with based on this, so feel free to use this data to come up with your own indexes. My index will be to take to average of how many times too many blacks and how many times too few whites there are.

For example, the average census tract blacks of the Detroit MSA live in has 3.18x more blacks than the MSA average, and 3.12x fewer whites than the MSA average. The average of these two is 3.15. So a completely unsegregated metro area would have a value of 1, a segregated one would have a very high number (technically could be infinity).

So using my segregation index
Detroit: 3.15
Atlanta: 2.60

It's also nice to see the data graphically. For maps, there's several good ones.

http://www.socialexplorer.com/89AACD3A4F1E4E1/explore
http://projects.nytimes.com/census/2010/map
http://www.washingtonpost.com/wp-srv/special/nation/census/2010/
http://www.urbanresearchmaps.org/comparinator/pluralitymap.htm

However, I haven't really seen attempts to graph this, so I decided to do so.

So this shows the % of MSA blacks by black % +/- 2% at the census tract level.

For example, 23.5% of Metro Detroit blacks live in census tracts that are 96-100% black. About 8.5% of Metro Atlanta blacks live in census tracts that are 36-40% black.

The vertical line shows the MSA average, so if metro area was highly integrated, the curves would peak there. Instead, they peak at the far right end, as far to the right as possible for Detroit, and only slightly better for Atlanta. But you can see that a bigger chunk of Atlanta's black population lives in more integrated census tracts.

Alright, but how are these integrated? Are the non-blacks all Hispanic or other minorities, or is there a chance of blacks in these cities having white neighbours too? Atlanta does have more Hispanics than Detroit...

However, it still looks like Detroit is less integrated, although both cities are highly segregated.