
DIVERSITY AND EXCELLENCE:
ARE THEY COMPATIBLE?
"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, Diversity:
The game plan
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 thoughtout 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 eighthgrade 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 nonHispanic 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.
"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 eighthgrade 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 allwhite 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 "lowincome" schools,
those with values between $112k and $158k, "middleincome schools." Figure
3 shows the result of this partition for middleincome 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 "middleincome" 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 eighthgrade 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 + b_{1}x_{1} + b_{2}x_{2} , where y is one of four pass rates, and x_{1} and x_{2} are eighthgrade black class percentage and average neighborhood home value, respectively.
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 blackstudent 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 satisfactorylevel
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.
The anomaly
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 meanscore 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 meanscore 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 regressionplane pass rates to compute the performance gaps, finding from satisfactorylevel data a gap of 1.07 standard deviations, and from excellentlevel 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. Twentyone 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 II. Relationship
Between Pass Rates and MeanScore Differences.
Let Δ be the mean difference between the score distributions of Pikesville whites and other whites. Then, the probability distribution for the nonPikesville group is P(x+Δ). The passing fraction of Pikesville whites,
f_{P},
is related to the passing score, λ, by the relation:
Similarly, the passing fraction of
nonPikesville whites,
f_{N} , 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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