In a society based on meritocratic principles, a pattern of color will emerge that reflects the distribution of human attributes among racial and ethnic groups. Such patterns have developed in America in professional sports. In other areas, however, we have been more circumspect. In this essay, La Griffe takes a mostly dispassionate look at how to calculate, by race and ethnicity, the outcome of any competition in which group abilities differ. We focus on cognitive differences, saving other group variations for later consideration. Depending on where in the culture wars you stand, the method can be used to test claims of equity or inequity. Illustrations are provided that range from the promotion of police officers to law school admissions. 

   When circumstances permit, the prediction of human events can be made with impressive accuracy. In nature we find analogies. A typical room contains about 10²⁷ air molecules. They move about more or less free of external forces, bouncing off each other and the walls. The chances of finding them all on one side of a room, leaving the other side a vacuum are infinitesimal. (Figure 1A). You can bet your life it will not happen. In fact, you do. 

   The same room containing only three gas molecules (Figure 1B) finds the three molecules, much of the time, together on one side. Numbers make the difference. As they grow large, certain probabilities grow into virtual certainties. 
 

A CHICAGO POLICE SERGEANTS' EXAM 

   In 1994, The city of Chicago gave an examination to 4700 police officers. The outcome determined who would be promoted to sergeant. There were 114 vacant slots to fill. The test was taken by 2,653 whites, 1,494 African Americans and 506 Hispanics. (Forty-six were listed as "other," and one had no racial or ethnic identity.) The exam had been worked over by consultants at a cost of $5 million to insure its cultural neutrality. Based on test scores alone, promotions were made in rank order to the 114 highest scoring policemen. Promoted were 109 whites, 3 blacks and 2 Hispanics. 

   The affair has been an object of litigation for years, plaintiffs charging that the 1994 sergeants' promotional roster had a significant disparate impact on African American and Hispanic police officers. We ask only one question: Given that 2653 whites, 1494 blacks and 506 Hispanics took the exam, how many from each group would we expect to be in the winner's circle of 114? We digress to introduce a useful principle. 
 

If a large group takes a set of tests, such that each test contains at least one part dependent on cognitive ability, then the test takers will finish in the same rank order on every test. 

   According to the principle of corresponding order, the police officers taking the sergeants' exam should finish in rank order of IQ. In Women and Minorities in Science (WMS), La Griffe du Lion, Vol. 1, No. 1, we solved the problem of how groups fill slots by rank ordering on some property. Specifically, if the distribution function of the property differs for each group by a translation along the property axis, but is otherwise identical, the following relation was shown to hold. 
 
 

(1)

where N_i is the number of people (say, test takers) in the ith group; P(x) is the probability distribution of the property (say, IQ) for a reference group; λ is the cutoff value of the property, at or above which a person will be selected to fill one of the N_S slots; Δ_i is the displacement of the mean for the ith group from that of the reference group. (Δ = 0 for the reference group). Each term on the left side of (1) represents the number of people from a particular group who make the cutoff. The sum is over all groups. Units are standard deviation (SD) throughout. 

   For the Chicago police exam there are three terms on the left of (1) corresponding to three groups, white (W), black (B) and Hispanic (H). We take the white group as the reference group so that the distribution function, P(x), is that of whites. The numbers of test takers from each group were assigned the values 2653, 1494 and 506 for white, black and Hispanic, respectively. The cognitive gaps (Δ) for blacks and Hispanics were assigned values from the National Longitudinal Survey of Youth as measured by the Armed Forces Qualifications Test, i.e., Δ_B = 1.21 SD and Δ_H = 0.93 SD. 

   With these values in place, solution of (1) yields the value 1.74 SD for λ. That is, the cutoff for promotion was 1.74 SD above the white mean. The small number of slots relative to the number of test takers insured a high threshold. Using this value of λ, each term on the left-hand side of (1) was evaluated, giving the expected numbers of promotions from each group. The results are summarized in Table 1. 
 
 

 
A BERKELEY FANTASY 

   The University of California at Berkeley is the crown jewel of the best state university system in the US. Not only is it the best public university in California, it is arguably the best public university in the world. The top universities are those with the top faculties, and UC Berkeley is second to few. No fewer than 12 Nobel laureates received the prize while on the Berkeley faculty. Only Harvard exceeds this number with 28. (Harvard is in a class by itself.) For comparison, other well known university faculties have produced the following numbers of Nobel Prize winners: MIT and Stanford 11 each, Columbia 9, Princeton 8, Yale 5, Johns Hopkins 2. In 1995, the National Research Council of the National Academy of Sciences ranked Berkeley among the top 10 in 35 of 36 graduate departments. It was first in chemistry, mathematics and statistics among others. UC Berkeley ranked fourth in Biochemistry and Molecular Biology, third in geosciences and physics. 

   As a state university, UC Berkeley is a remarkable bargain for California residents. A Berkeley diploma is among the most respected in the world. It is a virtual guarantee of success. Consequently, the University attracts an elite pool of applicants. Nearly 12,000 of the applicants for the Fall 1997 freshman class had 4.0 averages. With a few prized slots filled from a large pool of applicants selected primarily on intellectual endowment, UC Berkeley is a near-perfect model for a gedanken experiment that we propose. Each fall Berkeley admits about 3500 freshmen. Some seats go to nonresidents, but assume for simplicity that Californians fill the 3500 slots. We ask the following question: 
 

Suppose in 1990 every 18-year-old Californian competed for one of 3500 seats in the UC Berkeley freshman class, the seats to be filled in rank order of cognitive ability. What would the ethnic profile of the freshman class look like?  
 

   We used IQ group differences from the psychometric literature. Since Hispanics in California are primarily of Mexican descent, we used the Coleman Report value for the Hispanic IQ gap, Δ_H = 0.84 SD. We set the IQ gap for African Americans, Δ_B, to the National Longitudinal Survey of Youth (NLSY) value of 1.21 SD. For East Asians, i.e., Japanese, Chinese and Koreans, we used the average Δ derived from SAT distributions. In WMS, Δ_EA was estimated from math SAT distributions as -1.24 SD. From verbal SAT distributions, we estimate the verbal component of Δ_EA as -0.27 SD. We used the average of the math and verbal values, or -0.75 SD. The Asian population of California is only about half East Asian, so we split it in half and introduced another category: "Other Asian" (OA). The bimodal character of Asian American cognitive ability was discussed in WMS, where it was found, albeit for mathematical aptitude, that "Other Asians" had a profile like that of Hispanics. Accordingly we used a value Δ_OA = 0.84, matching the value for Hispanics. We had little data on American Indians et al. However, they perform similarly to Hispanics on the combined verbal and math SAT, so we assigned them the Hispanic gap of 0.84 SD. From the 1990 census we counted 18-year-old Californians as follows: East Asians 21,600; "Other Asians" 26,000; non-Latino Whites 210,600; African Americans 33,690; American Indians et al 3990; and Hispanics 148,620. 

   The competition was stiff with nearly half a million 18-year-olds competing for 3500 freshman seats. Solution of (1) yielded a minimum ability for admission, λ, 2.21 SD greater than the white mean. Admission was a formidable obstacle for whites and East Asians, and was near impossible for "underrepresented minorities." The gedanken experiment produced the following result. 

If every 18-year-old Californian in 1990 competed for one of the 3500 seats in the UC Berkeley freshman class, the seats being filled in rank order of cognitive ability, the class would have looked like this: 

7 African Americans 
115 Hispanics 
3 American Indians et al 
1244 East Asians 
20 "Other Asians" 
2111 non-Hispanic Whites 

The odds of making it to Berkeley would have been: 

4912 to 1 for an African American 
1291 to 1 for a Hispanic, "Other Asian" or Indian et al 
   16 to 1 for an East Asian 
   99 to 1 for a non-Hispanic White 
 
 

   Notwithstanding Berkeley's reputation, the University is not the goal of every 18-year-old Californian, though typically there are more than 20,000 first-time freshman applications to the University each fall. La Griffe analyzed Berkeley admissions for Fall 1996. 

   Most of the applicants could be classified as either African American, Hispanic, Asian or non-Hispanic white. A few were nonresident aliens. There were some native Americans, Filipinos, and others of unknown race or ethnicity. 

   No university knows in advance how many applicants will accept offers of admission, but they can guess pretty well. Berkeley, like other universities, plays an admissions guessing game. From experience a university estimates what fraction of offers will be accepted. They do this very well. In the Fall of 1996, UC Berkeley tendered a bit more than 8000 offers to prospective first-time freshmen. Berkeley based admission decisions on academic ability, race, ethnicity and other criteria. Using the above values for the cognitive gaps, we calculated an admissions profile based on cognitive ability. Table 2 presents the results. 
 
 

   In 1996 the University of California was free to discriminate by race or ethnicity. And so they did. Enrollment data for Berkeley shows that most blacks and Hispanics were admitted without meeting standards set for whites and Asians. (This was already known from test score comparisons.) Approximately 84 percent of black and 70 percent of Hispanic admits did not meet the standard achieved by the lowest ranking white or Asian admitted. They secured offers entirely on racial or ethnic grounds. As a result, nearly 1500 Asians and whites were denied offers of admission. Asians took the biggest hit, almost 1000 of them being sacrificed on the altar of diversity. By most objective measures, Asians outperform whites, yet they were admitted at a lower rate. 

   In a post-Prop. 209 California, racial and ethnic diversity can be achieved by opening new doors to the "underrepresented minorities." Do not sell university administrators short. They are a wily crew. Requiring geographic and economic heterogeneity are just two back doors to admission. California plans to grant all students who graduate in the top 4 percent of their high school class automatic admission to the University. La Griffe can only begin to imagine how many more schemes will be devised by committees seated around tables on the top floors of administration buildings. 

   The test of whether or not UC Berkeley complies with its mandate to purge discrimination from its admission process will be the profile of the 3500 or so freshmen who show up each fall. No administrator, regent, judge or elected official will convince La Griffe of compliance with the Civil Rights Initiative if the numbers fail to add up. It is not easy for anyone to get into Berkeley. Nor should it be. Tens of thousands of outstanding young white and Asian Californians have already been denied the benefits of a Berkeley education. We are sorry to observe that the crown jewel is flawed. 
 
 

HOPWOOD AND THE UNIVERSITY OF TEXAS 

   La Griffe was pleased to find a bright spot, however transient, in the diversity wars. The University of Texas at Austin is one of our nations's best. Before 1997, its Law School practiced race norming in its admissions process. White and Asian students formed one pool of applicants admitted from test scores and grades. Blacks and Mexican Americans formed another pool. They were considered separately and admitted on the basis of other factors, including race and ethnicity. Cheryl Hopwood changed all that. She is a white woman who successfully challenged the University of Texas Law School's admissions procedures in federal court. In March 1996, the court ruled in her favor, presumably ending race-based admissions at the University and the region covered by the fifth circuit. 

   The class entering the Law School in Fall 1997 was the first to enroll under the Hopwood ruling. We analyzed the enrollment data, again using (1) and the same values for the cognitive gaps. The Law School offered admission to 907 of 2515 white applicants, 11 of 225 blacks and 40 of 306 Mexican Americans. The Law School also offered admission to 134 "Others." They did not, however, report the number of "Other" applicants. For convenience, we assumed 372 for this number, by treating "others" as whites and applying the white applied/offered ratio to them. (As we have noted, "others" wherever they occur, test more-or-less like whites, though here they are likely to include a number of Asians.) Table 3 summarizes our results. 
 

   The enrollment statistics are in excellent agreement with our predictions for merit-based admissions. The University of Texas Law School complied with the law, admitting the first class under Hopwood by merit and without bias. Without the discriminatory policy employed by the University in the past, offers of admission to white students rose from 841 in 1996 to 907 in 1997. In the last year before Hopwood, at least 66 people were denied admission to the Law School because they were white, more if we include "Others." Be assured that administrators and faculty are at this writing devising ways to do it again. 

   Undergraduate schools in Texas are not subject to the same constraints as the Law School. Following a post-Hopwood move in the direction of meritocratic admissions, they rebounded quickly. A resourceful legislature, observing that school districts are de facto segregated, passed a law guaranteeing to the top 10 percent of every high school graduating class admission to any public college or university in the state. They wasted no time in making an end run around Hopwood. The freshman class at the University of Texas now has a pre-Hopwood ethnic profile. Commenting on the reestablishment of the pre-Hopwood profile, chairman Edward Blum of the anti-quota Campaign for a Color-Blind America  proclaimed, "These enrollment figures at UT are welcome news that apparently come as a surprise to the traditional civil rights advocacy groups who claimed the Hopwood decision was going to permanently re-segregate our institutions of higher education." He went on to say that "the overriding benefit of the top ten percent rule is that it extends the same educational opportunity regardless of race or ethnicity." Blum and Marc Levin, executive director of the Campaign for a Color-Blind America, wrote in the Dallas Morning News, "One thing is for sure: we certainly shouldn't underestimate the ability of minority students again." 

   Here are the facts: A student in the 90th percentile at a predominantly black school would fall approximately in the 53rd percentile in a non-Hispanic white school. A student in the 90th percentile at a predominantly Hispanic school would fall approximately in the 67th percentile in a non-Hispanic white school. University admissions is a zero-sum game. The top ten percent rule is race norming in disguise. Under it, better qualified youngsters are denied admission in about the same numbers as before. We will not contest Blum et al when they point to the UT enrollment as proof that racial preferences are not needed for equal opportunity. Semantic disputes are unproductive. To Blum and Levin, "equal opportunity"  includes the opportunity to enter the University by the back door, bumping those who would enter through the front. 
 
 

DISCRIMINATION AT HARVARD? 

   In two articles, The Dispossession of Christian Americans and Our Self-Selecting Elite, Pat Buchanan lamented the scarcity of white Christians at our most prestigious university, Harvard. Following on the heels of a November 16, 1998 Wall Street Journal article by Ron Unz, Buchanan's articles have become rallying points for Euro-Americans resentful of abuses inflicted upon them by the ruling diversity elite. The articles have been widely posted on the internet, and have spawned congruent essays in sympathetic media. Basically, they lay out the case for white Christians being discriminated against by admissions policies in our elite schools. 

   From Unz we read, "It seems likely that non-Jewish white Americans represent no more than a quarter of Harvard undergraduates, even though this group constitutes nearly 75% of the population at large, resulting in a degree of underrepresentation far more severe than that of blacks, Hispanics or any other minority groups." He also asserts that "Jews and Asians constitute approximately half of Harvard's student body, leaving the other half for the remaining 95% of America." Buchanan echoes with, "50 percent of Harvard's student body is drawn from about 5 percent of the U.S. population," i.e., Jews and Asians. He also complains that "non-Jewish whites -- 75 percent of the U.S. population -- get just 25 percent of the slots. Talk about underrepresentation," says Pat, "Now we know who really gets the shaft at Harvard -- white Christians." Again citing Unz, Buchanan reports Harvard's undergraduate body as 7 percent Hispanic, 8 percent black, nearly 20 percent Asian, and between 25 and 33 percent Jewish. Putting aside rhetorical flourish, we ask what Harvard's student profile would look like under a race-neutral admissions policy? From population statistics and group differences, we provide the answer. It is not an answer that Unz and Buchanan et al will necessarily like. 

   Being the preeminent American university, Harvard is unequaled for a replay of the Berkeley Fantasy, this time with a nation-full of aspirants. As the cream of American youth rises to the top, the best and brightest make themselves known. Most will at least apply to Harvard. We computed the Harvard enrollment profile that would result from a bias-free admissions policy, using census statistics to count 18-year-olds of various ethnic stripes, and (1) to analyze the data. We assigned a cognitive gap of -0.84 SD to the new group, Jews, based on NLSY data. 

   Harvard reports 6704 undergraduate degree students for Fall 1998. Of these 472 (about 7 percent) were international students, leaving 6232 Americans. We estimated the number of freshman seats open to Americans as 1/4 this number or 1558. (The precise number is not essential.) Filling these slots in rank order of cognitive ability from the pool of all American 18-year-olds, we calculated Harvard's ethnic percentages based on merit alone.The percentages are shown in Table 4, from which we note immediately that the predicted Asian and Jewish enrollment is remarkably close to that reported by Unz and Buchanan. 

   We do not know what goes on behind closed doors when an admissions committee gets down to work. At Harvard, the admissions process is further complicated by large numbers of "legacy students" among the applicants. These are children of alumni who through preference are admitted at 3 to 4 times the rate of other applicants. Without more information, we forgo more detailed analysis. 

   So who is getting the shaft? Enrollment at Harvard is not exactly a mirror of America, but in a meritocratic society, our elite schools would no more mirror our population than does the National Basketball Association. Ron Unz's assertion that "Jews and Asians constitute approximately half of Harvard's student body, leaving the other half for the remaining 95% of America," is almost accurate. Strip away the rhetoric and we are left with a reflection of how intelligence is distributed in America.
 

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