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Lloyd Cohen*

In the mid-1980s, the state of Virginia established the Thomas Jefferson High School for Science and Technology (hereinafter TJ) in the suburbs of Washington D.C. as a magnet secondary school for the mathematically gifted and inclined. Each year the school admits slightly more than four-hundred freshmen from the three thousand who apply out of the twenty thousand available in the region. It is the process by which those students are selected that is the subject of this study.

TJ is a remarkable school. As a summary illustration of its intellectual excellence, consider that in twelve of the last thirteen years TJ has led the nation in the number of National Merit Semi-Finalists. But focusing exclusively on the intellectual kudos earned by its students seriously understates TJ’s success and attraction. The school’s culture is one of civility, respect, and moral virtue. Unlike most other public high schools, property and person are completely secure within its walls. Students routinely leave valuable equipment resting on their lockers and find it undisturbed when they return hours, or even days, later. Nor is this school merely an intellectual and moral hothouse. The school is also renowned for its musical and athletic accomplishments. In 2002, for example, the boys’ cross country team won the state championship, while the girls’ team finished second, and since their inception in 1989, both the boys’ and girls’ crew teams have won numerous medals in various championship events.

What is the root of this success? To begin, we can reject the hypothesis that it is a great infusion of funds that is the cause. Expenditure per student at TJ is only slightly more than that at the average conventional high school in the region. Indeed, in part because of the age and size of the facility, TJ actually has less in the way of physical resources than most of its neighbors.

While the faculty deserves some credit, its role should not be overstated. Although the high quality of the student body makes TJ an attractive place to teach, the faculty are, for the most part, neither chosen nor rewarded by criteria markedly different from those that prevail at any other northern Virginia high school. Indeed, in the early years immediately following TJ’s conversion from a neighborhood high school to a magnet school, there was little change in the makeup of the faculty.

The lion’s share of the credit for the success of TJ’s students rests with the students themselves. It is they who have made TJ what it is. Arriving on campus with an abundance of intellectual aptitude and good moral character, they create a culture that nourishes and reinforces those virtues.

For those with the requisite talent and character, the opportunity to attend TJ is a great privilege. It provides an intellectually, morally, and socially enriched environment. To avail themselves of this privilege however, selected students and their families pay a considerable price. First, because TJ draws its students from a wide geographic area, most students endure a long commute and have difficulty maintaining school friendships outside of the building. Second, it is believed-perhaps correctly-by some parents that it is somewhat more difficult for TJ students to gain admission to elite universities than it is for equivalent students from ordinary suburban high schools. But, despite these drawbacks, TJ remains a very attractive choice, and each year, close to three thousand of the brightest eighth graders in the region apply for the four-hundred-plus slots available.

The great success of TJ’s students might lead one to conclude that its admissions regime is a finely tuned machine designed to pluck out the best of the best. That conclusion would be unwarranted. Given the large and intellectually well endowed population on which it may draw, almost any admissions process that was not systematically perverse would yield an outstanding student body. But, that does not mean that the admissions decision is of no moment. For the student chosen-assuming he is a good fit-attending TJ is a valuable privilege. To deny him that privilege for some reason other than merit would be a grave and invidious act of discrimination. In addition, finding students who are best able to partake in the culture provides a real benefit to all the others; each member of the community adds to and supports the ethos of the institution.

I. J’Accuse

The case I shall make, in the pages that follow, is that TJ’s admission process, formed by the push and pull of social, political, and-oh yes-even intellectual forces, has evolved into a wasteful, convoluted, inefficient Rube Goldberg-like mechanism that is designed to admit the most intellectually gifted students in the region subject to two nested constraints. The first constraint is that substantially more African-American students must be admitted than would be chosen on merit alone. The second-because to expressly voice and directly apply the first constraint would be offensive to the assumption of equal intellectual endowment and the principle of equal treatment, and would also be in violation of the Equal Protection Clause of the Fourteenth Amendment of the United States Constitution and of the 1964 Civil Rights Act-is that the first constraint must be satisfied sub rosa. That is, the admissions process must be facially neutral and appear to be based on factors that bear a rational relation to intellectual merit. The result is a process that is best conceived of as something concocted by a mind that vacillates between the dark dreams of Franz Kafka and the comic absurdity of Monty Python.

Do not misunderstand me. I do not believe that anyone has actually designed the process in a self-conscious attempt to promote this goal while accommodating these constraints. Rather, the current regime is the result of something akin to an evolutionary process. Much as the unremitting demands of a market selects and reforms the firms within it, such that those that survive are economically efficient, so, in an analogous process, the goals and constraints subject to which the TJ admissions regime has evolved have given it a grotesque form.

The political pressures that bear on the admissions regime are, at least in part, a matter of public record. Over the last several years there have been a series of pronouncements by the superintendent of the Fairfax County Schools, Mr. Daniel Domenech, as well as public hearings before the Fairfax County School Board (hereinafter FCSB) discussing the problem of less than proportional enrollment of African-Americans at TJ, and possible solutions. On the other side a substantial number of Fairfax County residents, parents of school age children in particular, have been vociferous in their efforts to prevent discrimination. Because of these efforts, and because express consideration of race is considered ethically and legally unacceptable, the proposals put forth and enacted by the FCSB have generally focused on creating a geographic quota that would serve the same purpose. Given the demographics of Fairfax County and the very high minimum standard for admission, no geographic quota has a realistic prospect of materially changing the ethnic makeup of the student body at TJ. There are no middle schools in the county that are so overwhelmingly African-American that merely assigning a quota to each school would likely yield many African-Americans who meet the minimum standards. Indeed, it could very well have a reverse and perverse effect, in that those African-American students with the greatest prospect of admission may attend over-represented schools.

For the class of 2006, the political compromise approved by the FCSB was that, after the committee process described below was followed, and after four-hundred and twenty students were selected in the usual manner, the oversight committee was then empowered to select up to an additional thirty students from the pool of eight hundred previously identified qualified applicants who attended underrepresented middle schools. Though the implicit purpose of this grant of authority was to increase African-American representation, of the twenty-nine additional students admitted under this program, only one was African-American. The principle reason for the absence of additional African-American students in this group is that nine of the eleven African-American students who were eligible for admission by finishing in the top 800 on the index had already been accepted.

While the express proposal of a geographic quota was both feckless and largely unsuccessful, the battle to undermine the principle of race-neutral admissions had already been won. The story to be told is how the use of an elaborate committee structure-staffed sympathetically, given broad discretion to make subjective judgments, informed of the race of the applicants, deprived of vital information, and signaled as to their true purpose-invidiously discriminates among candidates on the basis of race.

II. The Admissions Regime

For most of its history the TJ admissions process has had the same basic structure. The heart of the process is a two-step drill. Step one consists of the construction of an index score for each applicant based principally on objective criteria. This step cuts the field from close to three thousand to eight hundred. Step two consists of screening by an elaborate set of committees. These committees, employing more subjective criteria, cull the over four-hundred matriculants from the eight-hundred highest scorers on the index.

In the first stage, the applicants take a customized version of the Specialized High School Admissions Test, provided by the American Guidance Services. The exam consists of fifty math questions and seventy verbal questions. The index score is constructed by summing: (1) the number of correct verbal answers; (2) 1.4 times the number of correct math answers; and (3) 8.75 times the student’s GPA in his core academic subjects (weighting the first quarter of the 8th year grades at one-quarter of the 7th year grades).

This process is styled by the TJ admissions’ office as an 80/20 weighting of test scores to grades. Meaning, if a student scored the maximum on each portion of the test and had a 4.0 GPA, his total index score would be 175, with 80% of that total coming from the test and 20% from his grades.

Neither the two portions of the index-exam score and grades-nor the relative weights that they are assigned, are exceptionable. The exam itself is fundamentally an intelligence test; though, because it is now unfashionable to recognize differences in intelligence and to employ tools that measure that difference, it is not characterized as such. It is thoroughly reasonable to first, give the lion’s share of weight to intelligence in choosing whom to admit to a school for the intellectually gifted, and second to look to past performance in school as something like a tie-breaker to decide between closely matched students.

One seeming oddity of this initial selection formula is that the math and verbal scores are given the same implicit weight. Because the ultimate question is whether an applicant will be offered admission to a math and science specialty high school, commonsense suggests that more weight should be placed on the math portion of the exam. But, commonsense might be misleading. While it is true that the two parts separately measure distinct math and verbal abilities, their more important function may very well be that each is an independent measure of intelligence.

The characterization of this as an 80/20 weighting system is emblematic of a minor theme of my criticism of the TJ admissions’ process. It suggests that those who administer the process are neither quantitatively adept nor careful. It was only after the FOIA request was made that the precise formula described in the paragraph above was revealed. The other materials published by the FCSB, and made available to parents and students, offer only an enigmatic reference to the 80/20 formula, suggesting that the board believes that the formula is simply too esoteric and difficult for the parents to comprehend.

The obvious message conveyed by the "80/20" reference is that results on the test count four times as much as grades in making the first cut. But does the formula actually achieve that result? The answer is less than clear. Imagine that all the students who applied to TJ had between a 3.5 and a 4.0 GPA, while their test results were evenly spread over the entire range of possible results. Then, differences in GPA would explain considerably less than 20% of who made the first cut. On the other hand, imagine that grades were spread evenly over the entire range of scores while the test was extraordinarily easy such that all applicants answered at least forty math questions and sixty verbal questions correctly. Then, differences in GPA would explain considerably more than 20% of who made the first cut. Thus, it is the dispersion of applicants’ scores and grades that ultimately will determine whether the formula that TJ employs is giving a 20% weight to GPA or not. Given the thesis of this article, this is a minor matter, and so I did not bother to calculate standard deviations for the entire set of 2831 files to determine how close the formula comes to an 80/20 weighting. I did, however, calculate standard deviations for the 791 files that survived to the second stage. Based on that selected (and biased) sample I concluded that the dispersion of GPAs and test scores were such that the claim of an 80/20 weighting was not grossly inaccurate. This, however, seems to be a mere fortuity. I found nothing in the documents made available from the FCSB to suggest that those who crafted this formula had undertaken a similar inquiry.

This lack of clarity in exposition and imprecision in meaning is ultimately small potatoes. Nothing at this first stage of the process is offensive to either commonly held standards of equal treatment by a public body or a rational process for choosing the best of the best. At modest cost and without invidious discrimination, it does more than a tolerably good job of identifying those most likely to benefit from what TJ has to offer.

To characterize the process as inoffensive is not, however, to say that it is ideal. It is curious that there is no information available from the FCSB on how effective the admissions process is at picking winners. If choosing the most intellectually qualified applicants were the singularly important aim of the process, one would expect that some effort would be made by those in charge to validate the process. Such a study would not be inordinately difficult or expensive. As will be discussed later, there is a simple, obvious, and inexpensive method to measure the effectiveness of the first stage of the process-indeed of the entire admissions regime-and improve on it! At a minimum, it would permit the authorities to determine the appropriateness of: (1) the particular aptitude test employed, (2) the relative weight given to its separate parts, and (3) their combined weight vis a vis grades at the first stage. Beyond that, it could also be used to determine and measure what-if anything-is of benefit at the second, more subjective, stage. And, such an examination of the index formula and procedure need not be an annual event-even if only undertaken once, it would yield positive returns for the entire life of the process.

But this lack of validation of the first stage is not crippling. I repeat again, despite its shortcomings, the first stage of the procedure is unobjectionable. It offends neither ordinary notions of equal treatment before the law nor a reasoned approach to choosing the best applicants. It is only after the first stage is completed that the admissions train leaves the intellectual and ethical track.

At the second stage of the process, the top 800 candidates on the index are invited to complete an application. The remainder of the application consists of: (1) three letters of recommendation including one from a science teacher and one from a math teacher; (2) a self-reported personal data sheet indicating special accomplishments and activities with an emphasis on those involving math and science; and (3) several very short essays. In addition, the file created for each student explicitly indicates the applicant’s name, sex, race, and neighborhood school.

After these applications are compiled, the tedious and cumbersome committee process begins. Eight committees, each with six members, convene for four full days to review the files. Each committee examines a representative selection-based on rank on the admissions index-consisting of three-hundred files. Under this system, every file is read by three separate committees, each of which makes its own independent recommendation. If there is a difference in judgment among the committees, the recommendations are sent on to a ninth committee-the oversight committee-to make the final determination concerning which four-hundred-plus applicants will be accepted. Then, (as mentioned earlier) for the first time in selecting the class of 2006, after four-hundred and twenty students were chosen, a third stage was undertaken. The oversight committee reconvened with the power to accept up to an additional thirty applicants from the pool of 800 who attended middle schools from which fewer than ten students had been accepted to TJ in the prior stage. The committee found twenty-nine students worthy of this privilege.

III. The Guidelines

TJ produces a document entitled Guidelines for Selection Committees. The Guidelines describe both the entire admissions process and instruct those who are to carry out its second stage. Rather than summarize, I shall quote at length from the Guidelines, not only to guarantee complete accuracy but also to provide the reader with a feel for the culture that generates such a document and such an admissions process.

Admissions Process For Freshmen

2. Achievement

IV. The Purpose of Stage II

What is one to make of this document and the strange process it outlines? What is the true purpose of this elaborate and expensive committee structure? The benign explanation is that it represents an effort to achieve something closer to perfection in satisfying the putative goal of selecting the most qualified students available while presumably being scrupulously careful to ensure that no one is the object of discrimination on the basis of race, religion, sex, or any other suspect criteria. But that explanation does not survive scrutiny. The remainder of this article is principally an elaboration of the argument-supported with empirical evidence-that the purpose and effect of the second stage of the admissions process is to substantially increase the number of African-American students admitted beyond those that would be chosen on merit alone. This politically and legally problematic goal is accomplished by employing a system that institutionalizes and legitimizes subjective, ad hoc, eclectic judgments. The process is thereby rendered opaque and avoids being explicitly racially discriminatory.

Note once again the very large hound that is not barking. That hound is the validation of the process. Clearly stage two of the admissions process is elaborate and costly. It requires the expenditure of substantial resources-not merely by the school system-but also by the students and their teachers. If the true purpose of the second stage was to more finely tune the process and pick out the overlooked gems of the first stage, then surely some effort would be made to determine whether it actually resulted in a net improvement. The first stage employs standard measures of ability and achievement, so the FCSB might be forgiven for simply assuming that it is an effective screen. The second stage, however, overrides the rankings that were yielded by the first stage and substitutes subjective judgments without the least evidence that those exercising those judgments are particularly skilled at doing so, or have actually demonstrated success in the past.

The substitution of the subjective human judgment of the committee members for the objective mechanical calculation of the first stage is per se neither vice nor virtue. Subjective and objective means of making a decision each have their place. The appropriate inquiry is whether this particular regime for employing human judgment-leaving aside its disproportionate costs-is likely to, or is even intended to, achieve more precise results and whether the grant of discretion to the committees that it necessarily entails is cabined so as to avoid abuse, or, as I believe, to encourage it.

There are two necessary conditions for this subjective second stage to yield systematic returns over the rankings of the admissions index. First, the people making the decision must have some expertise in making such judgments. Second, they must have available valuable information that cannot, or at least has not, been included in the objective quantitative information of the first stage. Does this committee structure satisfy these conditions? Does it bear the earmarks of a means for experts to exercise considered judgment?

First, let us consider how the committee members are chosen. The Guidelines require that "[e]ach of the eight freshman selection committees is composed of six members: a non-voting chairperson, one administrator, one teacher, one counselor, one with experience in human relations, and one representative from the educational staff of a non-FCPS school division participating in the regional school."

But those are not the only criteria for staffing the committees. Christel Payne, the Admissions Coordinator at TJ, informs us that:

In December I request from each of the 8 cluster offices in FCPS as well as from the departments of Instructional Services, Student Services, and Human Resources the names of individuals recommended to serve on the committees. I ask for teachers (from English, math, science, and social studies), counselors, administrators, and people with expertise in human relations (HR people and those in special ed are good candidates.). I specify that I must have a lot of people recommended, and I ask for their gender, ethnic, and school level. I also contact our 5 other participating districts and ask for nominees from them. Then I compose 9 committees, each with 5 people, each balanced in ethnic, gender, and school level. That is, each committee will have a teacher, a counselor, an administrator, a person with expertise in human relations, and someone from one of the other counties/city of whom at least 2 are minorities, 2 are females and 3 are males or vice versa, and 1 is from an elementary school, 1 from a middle school, and 1 from a high school. Eight of these committees do the basic 4-day reading, and the 9th committee serves as the Oversight Committee.

The required credentials of this congeries places no premium on expertise in assessing promise in math and science. Indeed, given the criteria for selection to the committees, one suspects that the committee members are substantially less mathematically and scientifically gifted than those whom they must judge. A lack of expertise is not disabling if the committee members are merely exercising a political franchise, but it is a serious handicap if they are expected to make subtle and nuanced judgments of merit. Thus it is telling that not only are the committees not staffed with mathematicians and scientists, they are instead larded with people expected to promote special-interest agendas.

Beyond the particular categories of individuals chosen to serve on the committees, there is the grotesque proliferation of committees and committee members. The selection process is not some deeply complicated enterprise requiring the input of experts from a variety of arcane fields. How does one explain that in the end, fifty-four people contribute to the overall decision, and that a minimum of eighteen pairs of eyes look at each file?

The large number of people reviewing each applicant’s file serves two ends. First, the committee structure and the decisions it renders are intended to function more as a political exercise than as an academic one. A multiplicity of constituencies must be served and each must be represented. Second, and more importantly, the multiplicity of committees, the large number of participants on each one, and the multi-layered decision-making mechanism supply political camouflage. No one is actually responsible or accountable for any decision.

In addition to the excessive number of committees and committee members, and their singular lack of qualifications to judge promise in math and science, more striking still is the paucity of information which they are to sift and weigh. Not only are they provided with little additional information, they are-in effect-instructed to give that information little weight. More importantly, they are actually deprived of valuable information. They are not supplied with the index score, the index rankings, or the test scores or GPA used to derive that index.

If there is a legitimate rationale for employing a second stage at all-rather than simply relying on the formula used in the first stage-it is that the formula has not been designed to take into consideration qualitative distinctions among the applicants that have not been reduced to something quantitative; it requires human judgment to account for these factors.

The Guidelines instruct on the question of what weight is to be given to the various factors as follows: "Evaluate holistically. No one piece of the application is weighted more than another." To describe the general method as "holistic" is merely to say that it cannot be reduced to a simple linear function. Fair enough. But, as I will shortly show instructions later in the document suggest that the unconstrained tone of the term of "holistic" is not to be taken too far. As for not weighing any piece more than another-if meant literally, depending on what is meant by a piece of the application-it suggests that test scores, grades, letters of recommendation, essays, and personal data sheets are to count equally. Once more, this is inconsistent with later instructions, which grant the committee members discretion to disregard certain portions of an applicant’s file. More importantly, even if meant figuratively, it suggests a radical reduction from the first stage to the second in the weight to be given to the admissions test.

Do the first and second stages of the admissions process bear a rational relation to one another? The 80/20 formula was used at the initial stage because those who designed the process believed 80/20 to be the appropriate weights to be given to at least those two factors. At the second stage, however, as our regression results suggest the Guidelines implicit instruction to employ something closer to a 50/50 weight between scores and grades has been followed. If the 80/20 formula makes sense at the first stage, why not at the second? And, if a 50/50 formula makes sense at the second stage, why not at the first? I can conceive of no way to rationalize the inconsistency in the relative weights employed at the first and second stages.

It is one thing to say that other-non-quantitative-factors will be weighed at the second stage because they do not easily lend themselves to incorporation into a formula, it is quite another to say that the very same factors will be given radically different weights at the two stages of the proceedings. One possible justification is that some of the new factors considered at the second stage are actually more nuanced measures of one or the other factor weighed at the first. Thus, one could say that letters of recommendation from teachers are a richer evaluation of the applicant’s class performance than their grades. But, under what logic could letters of recommendation, personal essays, and data sheets steal more weight from an aptitude test than from a GPA?

Nor is it merely that the test is to be given less weight at the second stage. The test results, index score, ranking, and GPA are not even made available to the committees. Instead, the committees are provided with the percentile ranks of the applicants on each portion of the test and their grades in each core course. This alteration should not be dismissed as equivalent information. The committees are provided with substantially less informative data. The percentile rank merely situates the applicant in terms of all others who took the test. This has the unfortunate effect of: (1) collapsing the range, thereby resulting in applicants with different raw scores earning the same percentile rank; and (2) yielding different percentile spreads between candidates for the same differences in raw scores depending on where in the distribution they lie. Why gratuitously add this measure of imprecision to the process? The only reason, I can think of, is that the members of the committee are not arithmetically gifted enough to compare and comprehend the meaning of different raw scores, math on a fifty-point scale and verbal on a seventy-point scale. Percentile ranks are less mentally challenging. Is it tragic or comical that the admissions committees for one of the preeminent math and science high school in the country require such a pathetic crutch?

And what about the GPA? GPA is a useful summary statistic, widely employed by both employers and admissions committees. The committee members could of course calculate GPA for each applicant, but why make them go to the trouble? At the end of the first stage of evaluation, all this information is obviously available. The raw scores and the GPA were used to calculate the index and to rank the applicants.

Finally, we have the index score and ranking itself. This summary statistic weighs the test and grades in a systematic fashion for all applicants. It was not only considered significant enough to be the sole basis for completely rejecting over 2000 applications, but it was important enough to the process at the second stage that the 300 files assigned to each committee are pre-selected to be strictly representative of the distribution. And yet the index scores and ranks are purposely withheld from the committees.

There is no explanation for the exclusion, limitation, and distortion on the quantitative information made available to the committees consistent with the hypothesis that the committees’ role is to act as a body of trained and experienced professionals bringing their expertise to bear on all the relevant information to make the best admissions decisions. What is really going on here? First, the system is designed to liberate the committees from the tight bonds of precise mathematical measures. The provision of percentile ranks on the admissions test-rather than raw scores-suggests that those who designed the procedure are skeptical of the ability of the committee members to comprehend even rudimentary mathematical information. Moreover, it seems clear that the committee members are being discouraged from employing any mathematical tools in making their decisions. There is more than a little irony at play here in that TJ is one of the premier math and science high schools in the United States.

The process eschews the precision of numbers in favor of some other, more important goal. The intermediate goal is to free the committee members to indulge their tastes without being burdened by either internal or external constraints. They should not be forced to confront the fact that they are accepting an applicant who missed twenty verbal questions and twelve math questions over another who missed less than half those numbers, the former resting seven-hundred places lower in the ranking than the latter.

But what is the ultimate purpose of all this freedom? Is it to give more vigorous weight to the non-quantitative measures: essays, letters of recommendation, and personal data sheets? Such an explanation is belied by the Guidelines themselves. They instruct:

How is it that reading a single essay may prove sufficient? If one is trying to make a nuanced judgment between closely matched brilliant applicants, surely the Guidelines would instruct one to read each essay carefully to determine which applicants display the most polished command of the English language, the most intelligent insight, the most fluid style. On the other hand, reading but a single essay is the more appropriate strategy if you are testing for basic literacy and fluency in the English language. Such a standard would only be appropriate if the essays were to serve as a binary barrier, meant to exclude those who lacked sufficient literacy, rather than as a variable whose weight would add to the likelihood of admission.

As to the letters of recommendation, the Guidelines suggest that its author understands that these letters are composed by unknown strangers whose own fluency, articulateness, and understanding of, and commitment to, the process is even more of a cipher. Thus, the Guidelines implicitly instruct that they are to be given little weight.

As for the data sheets, leaving aside that they are entirely self-reported and unverified, the guidance to the committees seems to suggest little more than a binary counting exercise-zero and more than zero.

To summarize, the committees have considerably less, and less important, information than the computer that derived the list of eight hundred candidates. The true purpose of the elaborate committee structure is not to allow trained experts to exercise their finely honed judgment in selecting subtly superior applicants, but instead, to use the fa�ade of expertise and deliberation to grant a cover for broad discretion to indulge more personal agendas. The committees are then staffed with the expectation that those agendas will correspond to the political agenda of the FCSB and the superintendent.

Should any committee members not already understand their role, the Guidelines instruct them. It mentions race (i.e. "minorities") only once, but its injunction is clear: "Standardized testing for minority students does not necessarily reflect their abilities. The scores may be depressed. If test scores are low, then determine judgements [sic] from other indicators of success (grades, teacher recommendations, writing, and activities)."

This circumspect assertion that "[s]tandardized testing. . . does not necessarily reflect" the abilities of "minorities" is precious. Who has asserted that standardized testing does necessarily reflect their abilities? And what of non-minorities do the tests necessarily reflect their abilities? The vacuous truism is then followed by an invitation to discriminate. The empirical claim that standardized tests underpredict minority performance is not only unsupported both in this document and in the empirical literature on testing, but it is actually directly contrary to that literature.

Given that every file represents someone who scored in the top eight hundred on the index, if they ranked relatively poorly on the test, their grades must be high. And would their teacher recommendations be anything less than supportive? Bingo!-there is now more than enough of a basis to offer the low scoring African-American student admission.

The putative purpose of the committees is to do what no mere computer program can do-that is, to bring human discretion to bear on the issue. But because discretion always entails the exercise of an eclectic, ad hoc judgment, it is also a vehicle for potential abuse. The most pernicious and invidious abuse of discretion that a public official can exercise is to deny individuals equal treatment under the law on account of race, religion, or ethnicity.

The simplest method to preclude, or at least discourage, such abuse would have been to not ask the applicants their ethnicity or at least conceal that information from the committees. But no, the only unadulterated information provided to the committees are the ethnicity and sex of each applicant. Rather than making even the minimum effort to prevent such abuse, the FCSB-speaking through the Guidelines-expressly invites the committees to embrace the opportunity to take account of race in their admissions decisions.

The entire second stage-with its elephantine herd of committees-is in fact nothing more than an elaborate fig leaf. Its purpose is to hide the method by which the principle goal of substantially increasing African-American admissions is satisfied. The multiplicity of decisionmakers and the subjective nature of their judgments allows the racial agenda to remain at least partially concealed.

The absurdly excessive number of committees and committee members serves an additional dual role. First, it reinforces the suggestion that this sorting process is a very serious matter requiring the input of many trained and astute minds. Second, it provides a multi-layered personal cover. When people-children and adults alike-choose to do something morally suspect they prefer company. While the child is inclined to later excuse himself by saying "he did it too," the adult is more likely to justify or excuse himself by saying "it was a consensus determination." By presenting the TJ admissions procedure as a consensus achieving mechanism, based on a gestalt of factors, both the identity of the decisionmaker and the criteria for the decision are rendered indeterminate-no one is individually responsible for any decision and no particular criterion is dispositive.

IV. The Data and Statistical Analysis

Thus far, the structure of the process has been laid bare and the documents analyzed to make the case that the function and purpose of the second stage of the admissions process is to surreptitiously discriminate in favor of African-American candidates. But the proof, as they say, is in the pudding. Does the empirical evidence support that hypothesis?

Pursuant to a FOIA request, I obtained the quantitative data employed to choose the class of 2006. Each of the 2831 applicants for the class of 2006 is encapsulated in a line of information consisting of their ethnicity, sex, percentile rank among the applicants on the verbal test, percentile rank among the applicants on the math test, weighted GPA for the first quarter of the eighth grade and the entire seventh grade in core academic courses, combined index score-which is equal to their raw score on the verbal test + (1.4 x their raw score on the math test) + (8.75 x their GPA in core courses)- and their rank based on their combined index score. Of the 802 finalists invited to complete applications, 791 actually did so. For those 791, the line also lists whether they were accepted or rejected. In addition, the TJ admissions office provided summary statistics. Included in this information is the number who applied, the number of finalists, and the number accepted for each ethnicity, middle school, and sex.

Ethnicity

White : 507 249 49%

African American 11 10 91%

Hispanic 34 20 59%

Native American 3 0 0%

Asian 183 130 71%

Multiracial 49 29 59%

Other 15 11 73%

Sex

Male 450 247 55%

Female 352 202 57%

Total 802 449 56%

The large differences in the rate of acceptance across ethnicities presented in Table 1 is supportive of the hypothesis of invidious discrimination but not by itself determinative. A large difference in the rate of admission might occur for a variety of reasons. It may reflect invidious discrimination. It may be the result of disparities in the qualifications among the candidates of different ethnicities. Or, it may simply be random variation. Likewise, the almost identical rates of admission for males and females suggest that no distinction is drawn on the basis of sex, but this too may not be the case. One sex may have a placed a far higher number of people at the top of the finalist group, and if judged on the merits would be admitted in higher percentages.

In order to answer such questions, a closer look at the data is required to see if-when taking into consideration grades and test results-there is a merit-based explanation for the result. There are a variety of ways to address this question. To begin, we can gain a fair picture of the issue without resorting to any arcane statistical techniques.

The index, which is equal to an applicant’s raw score on the verbal test plus 1.4 times their raw score on the math test, plus 8.75 times their GPA in core courses, is an important measure of an applicant’s qualifications. The index is thought important enough by the FCSB that it is the sole basis of rejecting the applications of 72% of the candidates and then is used to select and balance the 300 files examined by each committee. If the index ranking that was employed to determine the finalists was also employed as the sole basis of determining admissions, then only the top 449 scorers on the index would have been offered admission. So we ask, how does this prospect of admission to TJ change for each ethnicity as the applicant’s index score declines? In general, as one would suspect, those who scored higher on the index were more likely to be admitted. Table 2, below, displays the simple probability of members of the various ethnicities and both sexes being admitted as their rank on the index falls.

In general, as the score on the index falls, the rate of admission drops. The average rate of admission for the entire class of those in the portion of the distribution that would not have been accepted if the index were the sole criterion was 27%. But the pattern of admission for African-Americans was clearly different. The index rank of the eleven African-American students was: 20, 250, 324, 366, 487, 511, 521, 551, 644, 683 and 716. All but the 521st ranked applicant was admitted. Thus, not only were all four in the upper portion of the distribution admitted, but six out of the seven African-American finalists, or 86%, who scored below the 449th were nonetheless offered admission to TJ. At the same time, only eighty-three non-African Americans out of three-hundred and thirty-five in this same range of the distribution-or 25%-were offered admission. For white applicants it was even worse; those who scored below the 449 mark had less than a 20% chance of gaining admission.

While the general pattern is clear, a more precise and rigorous analysis requires the more sophisticated tool of regression analysis. The relationship we seek to discover is that between the decision to admit or reject an applicant and the variables that the committees had before them. Regression analysis is the standard statistical technique employed to answer such questions. It is the standard because it is the most powerful and efficient method-it makes use of all the information the data supplies. The most common form of regression posits a linear relationship between the dependent variable and the explanatory variables. That form of regression is inappropriate in this case because the dependent variable in this study is binary, that is, the applicant is either accepted or rejected. When estimating the equation that models the probability of a binary event, the more appropriate form of the regression equation is one in which the dependent variable (probability of admission) has the shape of an S curve that asymptotically approaches 0 from above and 1 from below. The standard technique for such a regression is Probit.

The potential explanatory variables consist of all the information that the committees have before them: verbal percentile rank (though not the raw score); math percentile rank (though not the raw score); grades in the core courses of seventh and eighth grade (though not the GPA); ethnicity; sex; individual data sheet (consisting principally of self-reported math and science activities); letters of recommendation; and several short essays written by each applicant.

Unfortunately we could not employ every one of these variables in our regression. Since the grades in the individual courses were not provided in response to the FOIA request, the applicant’s GPA was used instead. For a variety of reasons we made no use of data sheets, letters of recommendation, and essays to estimate the admissions probability regression. First, we did not seek this information in our FOIA request. Had we requested it we believe that the request would have been denied on the grounds that the data might reveal, or could be used to discover, the identity of particular individuals. Second, acquiring the information would have entailed financial expenditures that were a large multiple of those actually incurred. Third, translating the information into a quantitative form usable in a regression equation would have been a costly and cumbersome process. Fourth, the Guidelines suggest that this information carried little weight in the selection process. Fifth, and most importantly, unless these variables (and the substitution of grades in individual courses as opposed to GPA) weigh systematically in favor of some ethnicities or either sex, their exclusion from the regression will not in any way bias the estimates of the regression. I assume that no such systematic relationship exists. Should that not be the case I invite the TJ admissions office and the FCSB to demonstrate it.

The basic regression posits that a candidate’s likelihood of admission is a function of their: (1) percentile rank on the math test; (2) percentile rank on verbal test; (3) GPA; (4) sex; and (5) ethnicity. Sex and ethnicity are captured with a series of "dummy" (i.e., binary) variables.

Table 3, below, provides the simple descriptive statistics of all the included variables.

The regression results are presented in Table 4.

Chi square tests were performed on the hypothesis that the coefficients for the various ethnicities were the same.

Test White = Black

Chi2(1) = 10.67; Can reject equality with 99.89% certainty.

Test White = Asian

Chi2(1) = 9.22; Can reject equality with 99.76% certainty.

Test White = Hispanic

Chi2(1) = 6.40; Can reject equality with 98.86% certainty.

Test White = Other

Chi2(1) = 3.13; Can reject equality with 92.34% certainty.

Test White = Multi

Chi2(1) = 2.24; Can reject equality with 86.57% certainty.

Test Black = Hispanic

Chi2(1) = 3.92; Can reject equality with 95.22% certainty.

Test Black = Asian

Chi2(1) = 5.98; Can reject equality with 98.55% certainty.

Test Black = Other

Chi2(1) = 1.74; Can reject equality with 81.28% certainty.

Test Black = Multi

Chi2(1) = 6.04; Can reject equality with 98.60% certainty.

Interpretation of coefficients in Table 5:

The coefficients represent the marginal effect (i.e., dProb/dX) of increasing the independent variable by 1 unit (for discrete variables, moving from X=0 to X=1) evaluated at the mean of each of the explanatory variables. The coefficients can be interpreted as follows:

Holding all else constant,

But these results seriously understate the degree of discrimination that can be derived from the regression equation. Applicants of all races who score high on the index had a very high likelihood of gaining admission. Thus, the percentage advantage in that portion of the distribution to being identified as Black is small. The more significant question is what is the advantage of being Black if one scores poorly on the index?

Table 6 provides a practical sense of the probability of admission as a function of race and sex. We employ the estimated regression equation to determine the probabilities of admission for candidates with varying credentials. Thus, any candidate ranked approximately 100 on the index, that is, scoring at the 96th percentile on the verbal exam, at the 97th percentile on the math exam and having a 4.0 GPA, would have over a 99% chance of admission regardless of their race and sex. But, as the credentials decline, the probability of admission declines at very different rates for candidates of different races and sex.

The hypothesis of this article is that black candidates with inferior credentials will be admitted with alacrity while white candidates would be rejected out of hand. I direct your attention to Table 6. Consider the probabilities of the applicant with the credentials of the 600th and 700th student. If that applicant is a white male, his chances of admission are 6.94% and 0.38% respectively, while if the same applicant were black, his chances would be 66.69% and 22.33%, respectively. Thus, based on the regression equation, the black student is between ten and sixty times as likely to be admitted to TJ with credentials in the 600 to 700 range, as compared a white student.