Volume 3  Number 2
March 2001

In 1954, a unanimous Supreme Court declared that racially segregated schools were inherently unequal. The Court based its decision on studies showing that "segregated schools damaged the psyches of black children and their motivation to learn." But do black students really achieve more in racially mixed classrooms? And what of whites? In this essay we examine how racial diversity affects achievement. Along the way we find and resolve a puzzling anomaly.
"Where I come from, diversity just means you have to lock your bicycle up."
Fred Reed 

   It was not the Supreme Court or a conceited social commentator who revealed how diversity influences achievement. It was multiple regression and standardized tests. The National Education Association used neither when it listed four ways that a diverse student body contributes to education. According to America's largest teacher's union,


  • promotes racial tolerance,
  • contributes to the robust exchange of ideas essential to a quality system of education,
  • breaks down barriers among individuals of different races, and
  • improves academic performance.
   The last proposition is the topic of this essay. The first three are more resistant to analysis. We leave them to puerile op-edery.

The game plan
   To find a link between academic achievement and classroom racial composition, we turn to standardized-test programs used in at least 20 states. The tests enable us to gauge the tangible effects of racial diversity. Our strategy is straightforward: Using racial mix and socioeconomic status (SES) as independent variables, we ask how performance depends on them. Regression provides the answer.

   Ideally, we want SES and racial mix to be uncorrelated. This is the most important requirement we impose on the data. The greater the correlation between these two variables, the more difficult it will be to separate their influences from one another. If they were perfectly correlated, we could learn nothing about their individual effects. Alternatively, if these variables were uncorrelated, their separate influences could be fully disclosed. Notwithstanding that minority groups enjoy fewer economic and cultural benefits than whites, carefully thought-out procedures and selection of data can achieve a nearly complete decoupling of the effects of race and SES.

   With thousands of schools reporting test results, the available information needs culling. A few requirements narrow the choices quickly. We require all students in our sample to take the same battery of tests. That limits us to one state. We insist also that students share a common curriculum, thus avoiding the introduction of a new and nasty variable. That restricts us further to a local jurisdictional unit, most often a county. We want each school in our sample to be small enough to have a neighborhood identity, i.e., have its own SES stamp, while at the same time be large enough to have a statistically meaningful number of test takers. Finally, the test schools must embrace a collection of racial mixes. We will not be looking for data in Iowa.

   The key to separating SES from race is "neighborhood character." We know generally that SES and race are strongly correlated, but only local decoupling of these variables in each school is required. We need to avoid schools, for example, whose black kids are poor and white kids are rich.

   We chose the Maryland School Performance Assessment Program (MSPAP) as best suited to our needs. In an annual spring ritual, all third, fifth and eighth graders are examined. Detailed reports are issued fully disaggregated by race.

   Demographic considerations narrowed our focus to Baltimore County. Its 725,000 residents, 80% white, 16% black and 3% Asian, are almost a racial mirror of America. Its schools span a range of racial mixes, pure white to pure black and lots in between.Middle schools in Baltimore County share a common curriculum. Their classes have statistically adequate numbers of students, yet are drawn from small geographic zones. We used the middle schools for our data, taking eighth-grade mathematics pass rates as the measure of performance.

   In 2000, almost 8000 Baltimore County eighth graders in 27 public middle schools took the MSPAP tests. All but 305 were either black or non-Hispanic white. We excluded nine schools from our sample because in one way or another they were incompatible with our requirements. Four had a statistically inadequate number of black eighth graders. Another was a school for children with behavioral problems. Four more had "magnet" programs, drawing students from outside the school's geographic attendance zone. A ninth school was eliminated because some of its scores were off the charts. We thought its data to be in error, but a harder look revealed that the school has a unique student population. This seeming anomaly is in fact just another manifestation of human biodiversity. It calls for a separate discussion, which we include as the last section of this report.

   To gauge the success of our efforts to decouple SES from race, we constructed a correlation matrix of all the variables. We used average residential real estate values in the attendance zone of each school as a measure of SES. Table 1 displays the matrix.

   Home values correlate strongly with achievement as expected, and insignificantly with racial mix as hoped. Judicious choice of data realized a correlation coefficient of -0.024 for home value and black class percentage. Home value correlates significantly with three of four pass rates. The black pass rate at the excellent level of achievement is the exception. This rate, however, fails to correlate strongly with any variable, even the black pass rate at the satisfactory level. The explanation is simple. At high levels of achievement, black pass rates cluster about zero, leaving little room for variation. In contrast, the black pass rate at the satisfactory level correlates strongly with white pass rates at both the satisfactory and excellent levels, another indication of the "neighborhood character" of the schools in our test sample.

   The message of the correlation analysis is that achievement correlates positively with SES and negatively with racial mixing for both races. SES and racial mix influence performance to about the same extent.
class home black pass rate white pass rate
 % black value satisfac excel satisfac excel

class % black 1.000 
home value -0.024  1.000 
black pass rate sat -0.460  0.551  1.000 
black pass rate excel -0.143  0.161  0.131  1.000 
white pass rate sat -0.718  0.634  0.827  0.207  1.000 
white pass rate excel -0.621  0.685  0.776  0.296  0.928  1.000 

Table 1. Correlation Matrixshowing that SES (gauged by average neighborhood home value) is uncorrelated to classroom racial composition.

"Students of both races achieve more in whiter classes."
The data
   Disaggregated average test scores for each middle school in Baltimore County are given in Appendix I for the year 2000. Pass rates for blacks and whites at both satisfactory and excellent levels of achievement are included there.

   Figure 1 shows a scatterplot of eighth-grade math pass rates at the satisfactory level vs. black class percentage. Each point contains data from a single school. The extent of scatter, caused by failure to control for SES, is conspicuous. Yet, discernible through the noise, is a downward drift in performance with increasing black classroom presence. Both black and white rates decline as classrooms become blacker. Putting it more positively, students of both races achieve more in whiter classes

   Pass rates at the excellent level are shown in Figure 2. Downward drift is again evident, though black pass rates are so low at this level, there is little room left for drift. Even here, however, blacks achieve best in nearly all-white classes.

   Figure 2 has an anomalous point at a 39% black eighth grade. The point is marked in the figure by an inverted green triangle. This school's near 50 percent white pass rate at the excellent level would be high in any racial mix. In a 39% black eighth grade, it sticks out like a sore thumb. We save a discussion of this school for last.

  Finally, before moving to a more thorough analysis, we note from Figure 2 that pass rates for whites appear to be grouped in two distinct branches, one high and one low. On the suspicion that the branches might correspond to SES levels, we constructed a crude SES partition based on average home values. Schools with average neighborhood home values between $70k and $102k were designated "low-income" schools, those with values between $112k and $158k, "middle-income schools." Figure 3 shows the result of this partition for middle-income performance at the satisfactory level.

   Its naïve simplicity not withstanding, the effect of this SES partition is convincing. Most of the scatter is gone. Trends are more evident. The high branch observed in Figure 2, is seen to correspond to "middle-income" pass rates.

"Racial integration raises black performance and lowers white."
The regression
  How does achievement in the classroom relate to SES and racial mix? Regression supplies the answer. We fit pass rates to a linear model, using black eighth-grade percentage and average neighborhood home value as independent variables. The results are summarized in Table 2. Four choices of dependent variable were used: black and white pass rates, each at the satisfactory and excellent levels of achievement. Pass rates were fit to the plane, y = a + b1x1 + b2x2 , where y is one of four pass rates, and x1 and x2 are eighth-grade black class percentage and average neighborhood home value, respectively. 
For whites at the satisfactory level, SES and racial mix account for 90% of the variation in pass rates with a = 14.31, b1 = -0.537, b2 = 0.507.
Regression is significant at the 0.00005% level.
For whites at the excellent level, SES and racial mix account for 83% of the variation in pass rates with a = -14.07, b1 = -0.290, b2 = 0.345.
Regression is significant at the 0.0001% level.
For blacks at the satisfactory level: SES and racial mix account for 50% of the variation in pass rates with a = 4.74, b1 = -0.237, b2 = 0.307.
Regression is significant at the 0.5% level
For blacks at the excellent level: the regression was not significant.

Table 2.  Regression parameters.

   The numbers tell a simple story. Racial integration raises black performance and lowers white. At high levels of confidence, especially for whites, performance declines linearly with increasing black class percentage. At the satisfactory level of achievement, with SES held constant, an increment in black class percentage of 1 percent causes a 0.537 percent decrement in the white pass rate and a 0.237 percent decrement in the black. Performance for both races is lowered by increasing the number of classroom blacks. The effect on whites is more pronounced. Their pass rates decline at twice the rate of blacks. At the excellent level, white pass rates are reduced by a 0.290 percent decrement for each 1 percent increment in black-student percentage. At this level, black performance is extremely poor and is essentially unaffected by the racial mix of a classroom or the SES of its students.

  SES and racial mix exert about equal influences on achievement. Holding racial composition constant, each increment of 1 percent in average neighborhood home value advances white satisfactory-level achievement by a 0.507 percent increment and by a 0.345 percent increment at the excellent level. For the same increment in home value, blacks improve by a 0.307 percent increment at the satisfactory level of achievement. The graphs of Figure 4 tell the story with miserly simplicity.



Figure 4.  Regression planes.  Pass rates at the satisfactory level vs. average neighborhood home value and black class percentage. As classes become blacker pass rates go down more sharply for whites than for blacks. SES positively influences pass rates, white more than black.

   The two regression planes, one for blacks, the other for whites, display the same qualitative characteristics. Students do better in whiter and high-SES classrooms. The planes, however, differ noticeably in steepness. Both SES and racial mix affect whites more than blacks. White performance is influenced 65 percent more than black by SES, and about twice as much by racial mix.
In short, racial diversity in the classroom reduces white achievement more than it improves black.

The anomaly
   The anomalous point of Figure 2 belongs to Pikesville Middle School. In 2000, its eighth grade class was more than 39 percent black. At this racial mix, the regression plane predicts a white pass rate of 17.05 percent at the excellent level. Pikesville whites passed at a rate of 49.53 percent, almost three times that predicted. A similar situation prevailed at the satisfactory level where 88.8 percent of Pikesville whites passed, compared to a predicted 55.6 percent.

   A brief digression is required here. The performance gap between two groups is conveniently represented by the difference in their mean scores. We do not, however, have mean scores. We have only pass rates. Nevertheless, it is possible to estimate mean-score differences from pass rates. In "Standardized Tests: The Interpretation of Racial and Ethnic Gaps," La Griffe du Lion, Vol. 2, No. 3, March 2000, we developed a technique for doing this. We include from that essay, with minor changes, a description of the relationship between pass rates and mean differences. (See Appendix II.)

   Now suppose that Pikesville whites are truly a distinct group, with characteristics measurably different from other whites. We want to find the mean-score difference between them. To control all effects but that due to group differences, we should compare Pikeville whites to other whites at a school with the same SES and racial mix found in Pikesville Middle School. There is, however, no such school. The regression plane solves the problem. It tells us what the pass rates would be in such a school, were it to exist. We used the regression-plane pass rates to compute the performance gaps, finding from satisfactory-level data a gap of 1.07 standard deviations, and from excellent-level data a gap of 0.94 standard deviations. That is, we found that Pikesville whites differ in ability from other Baltimore County whites by about 1 standard deviation!

  The Baltimore yellow pages and a street map confirmed what we now understood. Twenty-one of the 42 synagogues listed in the phonebook were located within a 2.5 mile radius of Pikesville Middle School. (See Figure 5.) The puzzle was solved. White students at Pikesville middle school were nearly all Jewish!

   Calls to Baltimore confirmed our suspicion. In the forty years or so bracketing the end of the nineteenth and the beginning of the twentieth century, waves of Jewish immigrants settled in Baltimore. Succeeding generations moved farther out from their parents' urban ghetto in search of a better life. In Baltimore, as in other cities, ethnic migration does not follow a 1/r law. Ethnic groups migrate in specific directions, preserving their cultural and/or racial environment. Baltimore Jews struck out in a northwesterly direction. Their migration eventually stretched beyond city boundaries into Pikesville. By 1970, Pikesville Middle School was virtually 100 percent Jewish.

   But as Jews drive out gentiles, so they are driven out. Blacks are now moving out from the city along the same northwest corridor traveled by Jews two generations earlier. Pikesville Middle School is now about 60 percent Jewish and 40 percent black. Its anomalous white pass rate corresponds exactly to what we might expect of Ashkenazic Jews. They are a discrete cognitive group with a mean IQ approximately one standard deviation above that of other European whites. (See "Some Thoughts about Jews, IQ and Nobel Laureates," La Griffe du Lion, Vol.2 No. 2, February 2000.) Curiously, Jewish and black migratory patterns, begun in Baltimore fifty years earlier, created in the year 2000 a riddle to delight the readers La Griffe du Lion.


APPENDIX I. MSPAP 2000 Baltimore County Eighth Grade Results
white % black % white % black %
N N percent satisfactory satisfactory excellent excellent
Middle School black white black1 math math math math

Hereford 0 271 0.00 82.29 0.00 33.58 0.00
Holabird 5 194 2.51 41.24 0.00 7.22 0.00
Ridgely 11 291 3.32 82.47 54.55 30.24 27.27
Sparrows Point 7 184 3.66 51.63 28.57 5.43 0.00
Perry Hall 25 418 5.41 79.67 60.00 29.90 8.00
Parkville 22 337 5.99 64.39 36.36 15.13 4.55
Gen. John Stricker 20 260 7.14 45.00 30.00 8.85 10.00
Dumbarton 19 212 7.69 79.72 31.58 40.09 10.53
Pine Grove 27 282 7.99 75.53 51.85 28.37 11.11
Cockeysville 28 226 9.96 76.55 50.00 37.17 0.00
Arbutus 26 196 11.35 55.10 19.23 11.73 0.00
Stemmers Run 41 242 13.85 30.17 9.76 4.55 2.44
Catonsville 25 139 14.79 81.29 44.00 30.22 4.00
Franklin 84 353 17.95 77.34 38.10 28.33 4.76
Lansdowne 42 174 19.44 52.87 19.05 9.77 0.00
Middle River 85 216 28.24 43.06 18.82 4.63 1.18
Dundalk 60 138 30.30 38.41 28.33 6.52 0.00
Deep Creek 95 168 34.80 43.45 28.42 7.14 1.05
Golden Ring 97 129 37.45 48.06 25.77 6.20 2.06
Meadowood Ed Center2 5 8 38.46 0.00 0.00 0.00 0.00
Pikesville 142 214 39.12 88.79 41.55 49.53 13.38
Loch Raven Technical3 137 170 43.22 70.59 30.66 17.06 2.92
Sudbrook Magnet3 155 166 46.97 84.94 63.23 32.53 9.03
Deer Park Magnet3 266 81 72.68 48.15 31.20 13.58 5.26
Southwest Academy3 319 60 78.57 60.00 24.76 10.00 1.25
Old Court 316 6 96.34 33.33 29.43 0.00 3.48
Woodlawn 267 9 96.74 11.11 10.49 0.00 1.50
(1) Percent black is calculated using all students in the denominator, not just the sum of black and white.
(2) Meadowood Education Center is a school for students with behavioral problems.
(3) Schools with magnet programs

APPENDIX II.  Relationship Between Pass Rates and Mean-Score Differences.
  Assume all distributions are Gaussian with a common standard deviation. Standard units are used throughout. Let P(x) be the probability distribution of test scores for Pikesville whites. The function P(x) is centered on x = 0.

  Let Δ be the mean difference between the score distributions of Pikesville whites and other whites. Then, the probability distribution for the non-Pikesville group is P(x+Δ).

  The passing fraction of Pikesville whites, fP, is related to the passing score, λ, by the relation:


   Similarly, the passing fraction of non-Pikesville whites, fN , is


   For computational convenience, A2.2 may be transformed to:


   The mean difference, Δ, and the passing score, λ, (in standard units) are obtained by simultaneous solution of A2.1 and A2.3.

   The distribution function, P(x) is given by



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