In November 1996, the voters of California by a 54 to 46 percent margin passed a referendum banning the use of race by the state in hiring and in college and university admissions. It was known as Proposition 209. Several years have elapsed since Prop 209 passed and La Griffe du Lion decided to look into the changes it brought about. We did a back-of-the-envelope calculation with a result so astonishing that we were compelled to take a harder, more careful look.

The campaign leading up to the vote was rancorous. Civil rights activists denounced the law and maligned its sponsors. Ward Connerly, the California regent and businessman, was their chief target. It was Connerly who chaired the California Civil Rights Initiative that campaigned for passage of Proposition 209. Connerly, who is black, was labeled a "houseboy" and "paid assassin" and worse. Jesse Jackson accused him of promoting ethnic cleansing, a theme picked up in the Oakland Tribune, which ran an editorial cartoon depicting a dry-cleaning shop with a sign "Connerly & Co. - Ethnic Cleansers."

In the summer of 1997, the New York Times quoted Connerly as saying, "If you're lying on a gurney, and a black doctor shows up, you're going to get up and crawl out." La Griffe du Lion, having looked at medical education in its March 2000 issue, Standardized Tests: The Interpretation of Racial and Ethnic Gaps, was eager to see how banning race-based admissions affected medical school enrollment in California.

We devised a quartet of tests to check for compliance with the initiative. One is an old standby. Another was suggested by a calculation of Jerry Cook. Two are novel and capable of revealing noncompliance in exquisite detail. They can detect even the subtlest impropriety. We call the foursome:

1. The eyeball test
2. The mean difference test
3. The lottery test
4. The meritocracy test

TESTS FOR COMPLIANCE
Test 1. The eyeball test. Are the credentials of successful candidates independent of race and ethnicity? This test is not rocket science. It is a classic and still one of the best. To perform it, we need unbiased measures of the qualifications of the successful candidates. They might include the results of in-house entrance or promotional exams, or standardized tests like the SAT, LSAT, GRE, and MCAT. For admission to a professional or graduate school, undergraduate grades are also useful.

We look for a partitioning of credentials by ethnicity in the winner's circle. With a race-neutral selection there should be none. Group differences, evident in the applicant pool, are eliminated by meritocratic selection.

Grade-point averages (GPA) are the least reliable of objective measures, because they vary by undergraduate institution and major. Nevertheless, some averaging-out takes place so that group comparisons of GPA are still useful. Table 1 reveals significant group differences in both the GPA and the MCAT. Whites and Asians were admitted with a 3.79 average GPA. Blacks and Hispanics averaged 3.42. In other terms, if students got only grades of "A" and "B," 79 percent of the grades obtained by Asians and whites would be "A" compared to 42 percent for blacks and Hispanics.

The Medical College Admissions Test or MCAT is a better measure of ability. It is a nationally standardized exam produced by the Educational Testing Service. It is required almost universally of US medical-school applicants. The MCAT has four sections: Verbal Reasoning, Physical Sciences, Biological Sciences, and Writing Sample. The test measures more than science knowledge. It assesses thinking ability also. MCAT results are highly correlated with the progress of medical students and the rate at which physicians become board certified. More important for our purposes, the MCAT cuts across differences in undergraduate schools and majors.

MCAT score distributions have a standard deviation of about 2. In 1997, UCLA admitted blacks and Hispanics with average scores of 9.8. Their Asian and white counterparts averaged 11.6. About 0.9 standard deviation separated admits from the two groups. Because test scores and GPAs were available, inspection was enough to show that UCLA used a double standard. The full extent of the transgression will emerge as we perform the remaining tests.

Test 2. The mean difference test. Find the mean differences that, without use of preferences, would best account for the ethnic profile of the selected candidates. Do they agree with expected group differences? Often we do not have access to a breakdown of test scores or GPA's by race and ethnicity. In these circumstances, this test is a winner. In fact, generally we find it our most reliable test. To perform it, we need to know the fraction of each group selected. We assume a meritocratic selection procedure and calculate the mean differences that best account for the actual fractions selected. The mean differences should agree closely with those established by precedent. The calculation goes like this:

Let f_A and f_B be the fractions of candidates from groups A and B, respectively, who would be selected in rank order of some property, x. The quantity, x, might be a standardized test score for example. We choose group A as a reference group with P(x) its normalized probability distribution. We assume P is Gaussian for convenience. The fraction, f_A , is given by,

where λ is the smallest value of x guaranteeing selection. We find its value by numerical solution of (1).

Assume that the distribution function for group B is also Gaussian, and displaced from P by an amount, Δ. That is, the distribution function for group B is given by P(x + Δ). The displacement, Δ, is the difference between the means (A - B) of the two distributions.

The fraction, f_B , may then be written:

where in (2) we have used the transformation,

The mean difference, Δ, is obtained by numerical solution of (2). We expect Δ to fall within the bounds established by precedent. For example, using whites as the reference group, we expect Δ for blacks to be about 1 standard deviation. Cutting a little slack, we could accept between 0.8 SD and 1.2 SD.

We applied the test to the UCLA Medical School admits. From Table 1 we see that 0.104 of black/Hispanic applicants and 0.030 of Asian/white applicants were accepted. Plugging the numbers into (2) gave Δ = -0.62 SD. So in-your-face was UCLA's use of preferences that their admission profile could have been obtained by merit only if the qualifications of blacks and Hispanics exceeded those of Asians and whites by 0.62 SD. If the enormity of UCLA's abuse of the law is not yet apparent, Test 4 will put it in more descriptive terms. Be patient.

Test 3. The lottery test. Find the probability that a random selection from the pool of applicants produces at least as many underrepresented minorities as were actually selected. In a bias-free selection this probability should be close to unity. This test was suggested by a calculation of Jerry Cook. Though not very sensitive, it is easy to apply and can provide a heads up that something is wrong. We need to know the number of applicants and admits from each group. The rational for the test goes like this:

The ability of underrepresented minority applicants is about a standard deviation below the rest of the pack. This guarantees that a bias-free selection process will pick fewer minorities than their proportions in the applicant pool might indicate. Consequently, it is a virtual certainty that a lottery will select more minority applicants than a meritocratic process. Given the ethnic makeup of an applicant pool, we compute the probability of randomly choosing at least as many underrepresented minorities as were actually selected. This probability should be, to many digits, close to one. Anything less implies the use of preferences.

Suppose N_A members of group A and N_B members of group B vie for n slots. We want the probability that the number randomly accepted from group B will be at least n⁰, the number actually selected. The probability that the number of B's selected randomly is exactly n⁰ can be expressed simply in terms of binomial coefficients:

The probability that the number of B's accepted randomly is at least n⁰ is then,

In the 1997 UCLA Medical School freshman class, the number of black/Hispanic applicants, N_B , was 489. The number of other applicants, N_A , was 4675. The applicants vied for n = 191 seats. The number of offers made to blacks and Hispanics, n⁰, was 51. Plugging all into (5), the probability of 51 or more blacks and Hispanics being selected randomly was 1.9 x 10^-12. Not too close to unity, would you say?

Test 4. The meritocracy test. a) Assume a bias-free selection and find the most probable number of candidates selected from each group. Compare with the observed numbers. b) Find the probability of obtaining the observed ethnic profile without the use of preferences.

a. The most probable number selected from each group. Suppose N ethnic groups. The ith group has N_i applicants who vie for one of N_S slots. Let group k be a reference group, and let P_k(x) be its normalized distribution of qualifications (say scores on a standardized exam). Then we can write,

where Δ_i is the mean difference between the ith and kth group means, (k - i). (Δ_k = 0.) All distributions are assumed Gaussian. The quantity, λ, is the score of the least qualified applicant to receive an offer.

Each term on the left side of (6) represents the most probable number of applicants accepted from a particular group. (For a full derivation see Women and Minorities in Science.)

Applying (6) to the 1997 UCLA Medical School applicants, there are two terms in the expression, one for Asians and whites, the other for blacks and Hispanics. We choose Asians and whites as the reference group.

Precedent tells us that the qualifications of black and Hispanic applicants will lag behind those of Asians and whites by about 1 standard deviation. Various standard measures like the SAT, LSAT, MCAT or IQ exams confirm this gap. (For more about ethnic gaps see The Color of Meritocracy and Standardized Tests: The Interpretation of Racial and Ethnic Gaps.) Accordingly, we set Δ = 1 for the black and Hispanic applicants. The number of offers extended, N_S , was 191. The numbers of Asian/white applicants (N₁) and black/Hispanic applicants (N₂) were 4675 and 489, respectively. Plugging all into (6), and solving numerically gave λ = 1.74 SD. That is, the lowest score guaranteeing an offer should be 1.74 SD above the Asian/white mean, and 2.74 above the black/Hispanic mean.

Evaluation of the individual terms on the left side of (6) gives us the most probable number of earned offers for each group. Between 1 and 2 offers should have gone to blacks and Hispanics, and 189 or 190 to Asians and whites. Table 2 shows how the two groups fared in reality and how they would have fared without the use of preferences.

Admissions is a zero-sum game. Because of quotas for underrepresented minorities, approximately 50 Asians and whites were denied admission to the UCLA Medical School. Their places were taken by 50 less-qualified blacks and Hispanics.

b. Probability of obtaining the observed number of acceptances by merit. In the previous section, we found the most probable number of black and Hispanic admits if admitted in rank order of ability. The entry in Table 2 brackets the result (1.48) with integers. The number of applicants actually admitted was 51. We will now estimate the probability of admitting 51 or more blacks and Hispanics. (Hold your breath.)

Suppose we were to repeat the admissions process many times with replicas of the 1997 applicant pool. Each time we would get a somewhat different distribution of qualifications, and an unbiased selection process would produce slightly different results. In this sense, the distribution of earned offers is a sampling distribution. If n* is the most probable value of the number of blacks and Hispanics given offers, we can estimate the standard error of the distribution as σ = [n*( N_S - n*)/N_S ]^1/2. For the UCLA Medical School example n* = 1.48, giving a standard error estimate of σ = 1.21. The actual number of blacks and Hispanics accepted was 51. In standard units, 51 is 40.8 SD away from the most probable number of blacks and Hispanics, i.e., (51 - 1.48)/1.21. The probability of black and Hispanic applicants earning 51 or more berths is the area under the bell curve from 40.8 SD to infinity, or about 10^-364. That is, the chance of admitting 51 or more blacks and Hispanics was 1 in 10³⁶⁴. Nota bene: There are approximately 10¹⁰⁰ fundamental particles in the universe.

Cutting UCLA some slack, we repeated the calculation using a mean difference of 0.8. That would be about right for an all Hispanic (no black) applicant group. If all the minority applicants were Hispanic, the chance of them earning 51 or more seats would be about 1 in 10¹⁰⁹. Still a bit of a long shot, would you say?

UCLA's barefaced violation of Prop 209 was not a transient event. The next two classes at the Medical School were admitted using the same (unlawful) system of preferences.

MEANWHILE, DOWN THE STREET AT IRVINE
   While the UCLA Medical School was contemptuously ignoring the law, its sister school at Irvine was moving toward compliance. The first two years after Prop 209, the number of "underrepresented minority" admits at Irvine dropped sharply from pre-209 levels of about 30 to 8. But was this really compliance? Table 3 shows the 1998 numbers for the freshman class at the UC Irvine Medical School.

In 1998, Asians and whites were admitted to the Irvine Medical School at more than twice the rate of blacks and Hispanics. Irvine was no UCLA, but was it law-abiding? Eyeballing reveals serious problems. Though only 8 offers were extended to blacks and Hispanics, these 8 had MCAT scores that lagged behind those of Asian/white admits by about 0.65 SD. Also there was an apparent GPA gap. In 1998, the UC Irvine Medical School flunked the eyeball test.

Applying the mean difference test, we found that a mean difference of 0.35 SD would best account for the 1998 enrollment figures if selection was by merit. We expect a mean difference of about 1. In 1998, the UC Irvine Medical School flunked the mean difference test.

Applying the lottery test, we found the probability of 8 or more blacks and Hispanics being randomly accepted from the pool to be 0.9945, a borderline result, but suggestive of preferences. In 1998, the UC Irvine Medical School lottery test was ambiguous.

Applying the meritocracy test using a mean difference of 1, the most probable number of minority offers was 2. Cutting Irvine some slack and using a mean difference of 0.8, the most probable number of minority offers increased to 3. (See Table 4.) The probability of obtaining at least the 8 observed minority admits was 0.000445. Or put another way, the chance of 8 or more seats going to underrepresented minorities was about 1 in 2250. In 1998, the UC Irvine Medical School flunked the meritocracy test.

In 1997 and 1998 the Medical School at Irvine made an anemic effort to reform its race-based admissions history. One year later in 1999, perhaps emboldened by UCLA's brazen defiance of the law, Irvine gave up all pretense of compliance. They admitted 28 blacks and Hispanics, up from 8 the previous two years. The meritocracy test exposed them in dramatic fashion. The probability that the Irvine Medical School could have obtained its 1999 enrollment profile without the use of preferences was 10^-88.

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 nation'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 first class to be admitted to the Law School under Hopwood entered in 1997. Table 6 shows enrollment data for that year and results from the meritocracy test.

We cannot perform the eyeball test because we have no LSAT scores. The mean difference test was passed with flying colors, finding that an ability gap of 0.94 SD would best account for the data. This is right where we expect the gap to be. The lottery test was also right on target. We found the probability that a random selection of applicants would result in at least 51 minority admits to be 1.00000000000000. The meritocracy test predicted the most probable number of black and Hispanic admits to be 47, a bit less than the 51 accepted. However, the probability of admitting 51 or more blacks and Hispanics by merit was 0.25, well within reasonable expectation. Hats off to the Law School at the University of Texas. The first year after Hopwood, despite strong faculty sentiment supporting affirmative action, the Law School did what we expect of a law school, it obeyed the law.

But hold on please. In 1998 the admissions profile changed. (See Table 7.) UT Law accepted 69 blacks and Hispanics from an applicant pool of 375, twice the rate of the previous year. With no LSAT data we could not perform the eyeball test. The mean difference test yielded an unacceptably low 0.58 gap to best account for the data. UT Law passed the lottery test, with the probability of randomly selecting 69 or more blacks and Hispanics from the applicant pool being 0.999999999999548. The meritocracy test, was damning. It showed the chance of admitting 69 or more blacks and Hispanics from the applicant pool without preference to be less than one in ten million. UT Law had gone the way of the rest of the University.

Don't let it be forgot,
That once there was a spot,
For one brief shining moment
That was known as Camelot.

WHERE NEXT?
   The future of race-based university admissions was foreshadowed in May 1998 by the Orwellian observations of Herma Hill Kay, Dean of the Boalt Hall Law School at Berkeley. Celebrating the diversity of the Law School's second post-Prop 209 freshman class, she remarked:

"Pursuant to policies adopted by the Boalt faculty in late 1997, we avoided overreliance on numerical indicators, which have never been the sole criteria for admission to Boalt Hall, and we carefully considered the full range of each applicant's accomplishments and experiences. Under Proposition 209 and the UC Regents' decision prohibiting affirmative action, race and ethnicity were not considered in making admissions decisions."

While there may be laws banning the use of race in admissions, there is no political will to enforce them. Even the activists who worked hard to get the laws passed do not have the stomach to bring the fight to an honest conclusion. That goes for Ward Connerly too. While California does an end run around Prop 209, Connerly campaigns for similar laws in other states. Other notables join him in the I-told-you-so hypocrite's corner. Applauding the fact that UC minority enrollment has rebounded to pre-Prop 209 levels, Thomas Wood, co-author of Proposition 209, is quoted by the Salt Lake Tribune as saying that Prop 209 "is not an exclusionary measure, either on its face and application or in its effect." And from Steve Balch, president of the National Association of Scholars, "We are pleased to see that the numbers are rebounding in the absence of preferences."

It will take more than a referendum or a ruling from a court to establish a meritocracy. Precisely what is required remains unclear. One thing, however, is very clear. The politician, like Don Giovanni, is the ultimate cynic. Change "woman" to "issue" below and Da Ponte might have been speaking for Connerly, Wood or Balch.

"This woman or that, to me they're all the same. I don't give my heart to any one of these beauties. Today I'll choose this one, tomorrow another."

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