Has school segregation gone down since MLK?

I received this very useful email from Ken Hirsch:

I looked into the basis for the statement I read on Marginal Revolution that "American schools are more segregated by race and class today than they were on the day Martin Luther King, Jr. was killed". The source that was given did not actually have statistics going back to the 1960s, but the author of the report, Gary Orfield, pointed me to an earlier report, "Brown at 50: King's Dream or Plessy's Nightmare" (http://tinyurl.com/BrownAt50), which did contain a time series for one measurement, "Percent of Black Students at Majority White Schools".  There's a graph of this statistic for Southern black children on the cover of the report which I am attaching to this email.

This statistic is quite problematic. Most starkly, in "majority minority" states, such as Texas and California, this statistic measures the *opposite* of integration.  The more evenly distributed that ethnic groups are in schools, the lower the the number. If all schools in California had exactly the same ethnic make-up, there would be no majority white schools, so 0% of black students would be in them!  Indeed, in Table 11 from this report (p. 27), California is given as the most segregated state by this measure.

The other two measures that Dr. Orfield uses have similar problems. Most of the change in all three are probably caused by the increase in the percent of Hispanics and the decrease in the percent of non-Hispanic whites, not by segregation. By most mathematically sensible measures, segregation has decreased and integration has increased over the last 20 years. See "Measuring School Segregation" by David M. Frankel and Oscar Volij for details: http://www.econ.iastate.edu/research/working-papers/p11808

The original post was here.

Comments

I am one of the people who raised this question in comments on the original post, and I am very pleased to see that someone has done better than I did in following up.

I claim that the following statistic is what we should be using to measure segregation and make inter-temporal and inter-geographic comparisons: the population-weighted chi-square value for each school.

While a statistician will likely understand that right away, let me explain for the benefit of others. To compute this, you decide on your set of race categories. (White, black, and hispanic? Or cacuasian, asian, latino, african, native? Take your pick.) Then you compute the expected number of kids from each race in a school, assuming that all races were represented in perfect proportion to their population. Then you compute the difference beween the actual number and the expected number for each race in the school. You then form a quantity called chi-square, which is essentially the square of each difference (so surplus and deficit both contribue positively) normalized by he expected sampling error (because being off by 10 in a group of 20 is much worse than being off by 10 in a group of 200). A satistican will tell you that, in a perfectly mixed society, you would expect a chi-square be just a few (more exactly, the number of races minus one) in each school. In our society, it will be much larger.

To average over a region, compute the average of chi-square for all schools, weighted by the number of students at the school. You are then free to compare chi-suquare between regions and across time. You don't have to worry about your results being contaiminaed by differenting population fractions across regions or population fractions varying over time, because the chi-square measure has taken all of that into account.

If any social scientist has done this analysis (which is what a statistician would tell him to do, if he asked), I would love to know the chi-squares values for the U.S. in 1968 and today.

A quick search of some recent top Sociology journals produced a very informative article on trends in school segregation, 1970-2000, by Logan, Oakley and Stowell ("School Segregation in Metropolitan Regions, 1970–2000: The Impacts of Policy Choices on Public Education", AJS 2008.) The article examines both trends in primary school education, and the connection between desegregation policies and actual desegregation.

Here's the conclusion: "The gains [in integration] were concentrated in shifts within school districts, which is where enforcement actions have almost always been targeted. There was nearly a 40% fall in segregation at this level. But these gains were partly counterbalanced by increasing between‐district segregation that occurred especially between 1970 and 1990. This rise is surprising, because levels of residential segregation were falling moderately in many parts of the country at the same time (in our sample of metropolitan areas, the average was 79 in 1970, 68 in 1990, and 65 in 2000). The trends are consistent with the interpretation that in this era when black‐white separation in schools could no longer be taken for granted, white families with children were systematically selecting homes in school districts with smaller minority populations. We have not measured white flight directly, but we infer it from rising between‐district disparities. White flight was of sufficient magnitude to limit gains from desegregation but not to nullify them."

So things are better in 2000 than in 1970, but the 1990s saw a slight increase in segregation. Also, measured at the district, rather than the school, level, segregation has increased, in spite of residential segregation declining. So, your measures and units of analysis really do matter rather a lot.

Is (voluntary) segregation by itself something to be loathed? Or is it because of its association with other unpalatable concomitants (in the racial and ethnic versions).

Race and ethnicity are the most common ones that accompany the negative connotation. But one could evaluate segregation for wealth, education, familial demographic, occupation etc. Are those execrable too?

Left to themselves, will people naturally segregate or anti-segregate? I suspect the former.

@David Wright: Does that method account for segregation on a city level? For example, I grew up in Milwaukee - one of the most segregated cities in the country (in a Northern town nonetheless!). The city is 39.5% Black, with a large majority of the Black population concentrated in a small area. The percentage of Blacks in Wisconsin is 6.15%. Likewise, the percentage of Blacks in the entire United States is 12.8%.

Now, should we expect schools in Milwaukee to be 39.5%, 6.15%, or 12.8% Black?

As a side note, I attended public school in Milwaukee. I was one of a dozen White kids in a school of over 200. Other Milwaukee Public Schools were equally unmixed, if not worse. It's been my experience that White suburban America is completely out of touch with reality. And either woefully, or willfully, ignorant of race in America.

@Jonathan: You make a point worth calling out. No method will objectively determine what the racial mix in a given school "should" be. The national fractions? The fractions in the school's county? The world fractions? You have to give that as input to the model, and different people way have different ideas about the geographic level at which mixing "should" occur.

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