This week's Economist reported [paid subscription only] on a new academic study on black/white integration (or segregation) in US cities. The study, conducted by John Pawasarat and Lois Quinn of the University of Wisconsin-Milwaukee, attempts to challenge prevailing definitions of integration and to overturn the conventional wisdom that their hometown of Milwaukee is one of the most racially segregated cities in the country. The good news, according to their report, is that Milwaukee is no longer the 98th most integrated of the 100 largest American cities, it is in the middle of the pack at 43. The bad news is that they accomplished this legerdemain simply by devising a thoroughly bogus measure of integration. The worse news is that neither the Economist, nor the Milwaukee Journal-Sentinel, which dedicated a three-part series to the study, even commented on the fundamental mathematical silliness in Pawasarat and Quinn's definitions.
There are many legitimate questions to ask about integration/segregation that have nothing to do with mathematics. It is true that many black people in large cities live in predominantly black neighborhoods, and that many white people live in mostly white communities. Some cities (like Houston) have far more black people (25%) than other cities (like El Paso, 3%). There are historical factors that explain racial patterns of residence, and in many cases institutionalized discrimination played a role. It is also the case that many people voluntarily gravitate to live among those of similar backgrounds. And just as many black people choose to live where there are other black people, so too are there clusters of Polish Americans, electrical engineers and gay people, for example. The interesting questions are not which city is the most integrated (however that's defined) but whether people can exercise their right to live where they can afford, and whether everyone has real opportunities for upward mobility; or are people prevented from attaining their goals on the basis of their race?
For now, let's focus on the Milwaukee study's flawed definitions, which won't add much value to anybody's understanding of trends in segregation and integration.
The researchers define integration by looking at each city block (using 2000 Census data). A block is defined to be black/white integrated if at least 20% of its residents are black and at least 20% of its residents are white. The study does acknowledge that this has the limitation of ignoring the fact that many people are neither white nor black while others are mixed race (a big limitation). So a block that is 21% black and 79% white is considered "integrated", but a block that is 12% black and 22% Asian and 66% white is not considered "integrated". The study then counts the percentage of people who live on "integrated" blocks, the higher the better, and ranks the cities accordingly. Their most "integrated" of the 50 largest cities is Virginia Beach, VA where 19.5% of the population is black and 41.1% of the residents live on "integrated" blocks. The least "integrated" of the 50 largest cities is Albuquerque, where 3.2% of the population is black and only 0.3% of the residents live on "integrated" blocks.
But their math really falls apart when you consider that they require 20% of a block to be black in order for the block to be considered integrated. But blacks are only 13% of the US population. This means that in what most people would think of as a perfectly integrated and colorblind society -- where race is almost invisible and people would be evenly distributed everywhere -- every block would be 13% black and by the Milwaukee definition, no block anywhere in the country could be "integrated"! Looking at it another way, the only way for a block to be "integrated", is to have at least 50% more blacks than it would if all races were evenly distributed. The most integrated society under this definition (with the maximum number of people living in "integrated" blocks), would have 65% of the population living in blocks that were 20% black, and 35% of the population living in blocks that had no black people at all (the calculation is left as an exercise to the reader).
This methodology looks even more absurd when it is applied to cities that have even smaller black populations. Salt Lake City is derided for being the 99th least "integrated" of the 100 largest metropolitan areas, as only 0.1% of the residents live on "integrated" blocks. But only 1.3% of the population is black, which means that a block can be "integrated" only if its proportion of black people is 15 times that of the metro area as a whole, and to maximize "integration" without busing in a lot of (reluctant, I would imagine) black people, the city would have to put 6.5% of its residents in blocks that were 20% black, with the other 93.5% of the population living on white-only blocks. I doubt that this would fit many people's intuitive notion of "integration". On the other hand, a city that has a small black community, and where race is not an obstacle to housing, would probably show a very low number of blocks that were 20% black.
I don't claim to know the extent to which Milwaukee is an integrated or a segregated city. All I can say is that this particular method for measuring integration is inherently absurd and unhelpful. (A more sensible measure of integration, I think, would be based on a weighted average of "sum of squares of differences" between a theoretical evenly distributed population and the actual population, and it would also take into account the ethnic variety that goes beyond black and white). And the NAACP, for its own reasons, didn't think much of the study either.
And this story illustrates yet another shortcoming of the cult that equates diversity with skin color -- even when dealing with the subject of race. While the Milwaukee Journal-Sentinel has been sensitive to hire reporters of diverse ethnic backgrounds (Click here and scroll through the "Getting to know us" section), they didn't see fit to also diversify by educational background. If they had, they might have had someone on board who knew the tiny amount of algebra it took to see through the integration study's specious methodology.
P.S. I've come to expect this sort of sloppy innumeracy from an American daily newspaper, but the Economist has no excuse.
Posted by Stefan Sharkansky at January 28, 2003 07:21 AM