From the wikipedia article you link to: "Desegregation efforts of the 1970s and 1980s led to substantial academic gains for black students; as integration increased, blacks' educational attainment increased while that of whites remained largely unchanged.[17]"
I follow footnote 17 and download the paper, and there is nothing in the paper about academic gains. I think the footnote must be going to the wrong place.
I have heard a similar claims elsewhere, but when I looked at the data it is not at all convincing. Here is Professor David Armor, who researched integration and desegregation for decades analyzing the data (From page 93. of Forced Justice):
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"Figure 2.7 shows black and white reading achievement between 1971 and 1990 for thirteen-year olds (most of whom are eighth-graders). In 1971, when most blacks in this age group had been educated in segregated schools, black thirteen-year-olds trailed whites by 39 points. Over the next two decades, white scores remained virtually constant, starting at 261 and ending the period at 262 points. In contrast, black scores rose steadily for most of the period, starting at 222 and ending at 242 points (following a drop of a point in the latest assessment)..."
"A number of studies and several noted educators have invoked the harm and benefit thesis by suggesting that black achievement gains observed in the NAEP might be attributed in part to school desegregation....Ironically, the desegregation explanation has never been tested by examining the relationship between achievement and racial composition of schools using the most appropriate source of data, the NAEP itself. Since the NAEP established achievement trends for blacks in the first place, it makes sense to test the desegregation theory by comparing achievement trends for blacks in segregated versus desegregated schools. If the desegregation theory is correct, larger achievement gains would be expected for blacks in desegregated schools than for blacks in segregated schools..."
"Achievement trends for blacks in desegregated versus segregated schools has only recently become available for NAEP data. ...Figure 2.9 shows trends in reading achievement for black thirteen-year-olds according to the racial composition of their schools. The desegregation theory is clearly not supported by the NAEP data. While blacks in majority-white schools generally score somewhat higher than blacks in predominantly minority schools (although not in every year), the trend in reading between 1975 and 1988- when the largest black gains occurred-shows that thirteen-year-old blacks in predominantly minority schools have gained virtually the same as blacks in majority-white schools. In the case of math trends, blacks in predominantly minority schools actually gain 10 points mare than blacks in majority-white schools. By 1990 there was only a 2-point difference between the math scores of segregated and desegregated black students....This pattern of gains for segregated versus desegregated black students in the NAEP is replicated for other age groups as well."
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That was from 1995. More recent NAEP scores show the same thing -- https://nces.ed.gov/nationsreportcard/subject/studies/pdf/sc... The racial achievement gap is the same size no matter the school composition. Black students do little better in schools that are more white. (And that little difference is probably correlation not causation -- higher achieving black parents both have higher achieving kids and are able to afford schools in more white areas, when you control for socioeconomic status the correlation almost disappears).
One of the few John Oliver segments that I actually liked was his one on how so many academic studies are bogus ( http://fortune.com/2016/05/09/john-oliver-scientific-studies... ). There are all sorts of problems with confounding variables, p-value hacking, cherry-picking data, etc. But what he missed is that all the problems he criticizes about health studies also plague the social science literature. And then he does exactly what he complains about when he cites that Rucker Johnson paper. You need to look at the entire literature not just one paper. And you need to put much more weight on papers with clear and straightforward methodology and where other people have checked the math and replicated the results. Rucker Johnson's paper fails on all accounts. It strikes me that Rucker may have made some obvious mistakes, but I cannot tell for certain because he has not published his data and calculations.
To the extent that I myself have looked over the entire literature, my conclusions are in line with these conclusions that were made when the U. S. Department of Education did a review in the 1980s of all the case studies of integration (From David Armor's Forced Justice, page 91):
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"Desegregation did not cause any decrease in black achievement. On the average, desegregation did not cause an increase in achievement in mathematics. Desegregation increased mean reading levels. The gain reliably differed from zero and was estimated to be between two and six weeks [of a school year] across the studies examined.
The median gains were almost always greater than zero but were lower than the means and did not reliably differ from zero."
"Studies with the largest reading gains can be tentatively characterized [as having] small sample sizes two or more years of desegregation, desegregated children who outperformed their segregated counterparts even before desegregation began, and desegregation that occurred earlier in time, involved younger students, was voluntary, had larger percentages of whites per school, and was associated with enrichment programs. None of the above factors can be isolated, singly or in combination, as causes of any of the typically large achievement gains."
"Because of the small samples and apparently non-normal distributions, little confidence should be placed in any of the mean results presented earlier. I have little confidence that we know much about how desegregation affects reading "on the average" and, across the few studies examined, I find the variability in effect sizes more striking and less well understood than any measure of central tendency."
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My take is that if desegregation has any impact on achievement, it is small and drowned out by other factors.