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July 30, 1999

Racial Quotas in College Admissions: A Critique of the Bowen and Bok Study

In a new statistical analysis, two former Ivy League presidents argue that racial preferences in college admissions are good for both minorities and society at large. Examining the analysis, however, Hoover fellow Thomas Sowell has discovered that the numbers don’t add up.


Back in 1936, a leading magazine of the time, The Literary Digest, made a prediction about the presidential election of that year, based on a poll with a very large sample—more than 2 million people. Their poll indicated that Governor Alfred Landon of Kansas would defeat President Franklin D. Roosevelt’s bid for re-election. When FDR carried forty-six of the forty-eight states at that time, this not only contributed to the discrediting and demise of The Literary Digest, it taught a lesson about the use of statistics. The size of a sample is by no means as important as its representativeness.

That lesson seems to have been lost amid a chorus of media and academic approval of a recent study of affirmative action in college admissions by ex-college presidents William G. Bowen (Princeton) and Derek Bok (Harvard). Their book, The Shape of the River, has a sample size of more than 90,000 college students, but the sample is highly unrepresentative. Moreover, the authors’ internal breakdown of this sample makes comparisons among colleges that are like comparing apples and oranges. The widespread approval of the Bowen and Bok study may have much less to do with its statistical methods than with its politically correct conclusions.

The central message of their book is that racial preferences and quotas in college admissions—“race-sensitive admissions” is their euphemism—have been beneficial and have not created the problems claimed by critics of affirmative action. But that conclusion rests on their statistics—and on their ignoring other statistics which indicate otherwise.

That the Bowen-Bok sample used is unrepresentative of college students—black and white—is easily demonstrated. In this sample, the graduation rate of black students is 75 percent. In other samples collected by other individuals and organizations, black graduation rates are less than 50 percent. Indeed, black students’ graduation rates are only about half of the graduation rates of white students, many of whom also drop out. At Berkeley, for example, the black graduation rate has been 30 percent—but Berkeley is not part of the Bowen-Bok sample.

The authors of The Shape of the River admit that they are studying students in an atypical group of elite colleges and universities, rather than a representative national sample of either students or colleges. Yet Bowen and Bok repeatedly make sweeping declarations about national policy, just as if they had not admitted the serious limitations of their data.

For example, they make much of an apparent refutation of critics who have blamed racial preferences for high black failure rates at colleges with which these students have been mismatched academically. This apparent refutation is based on comparisons of the graduation rates among black students attending colleges and universities that Bowen and Bok break down into three groups, according to how high the average SAT scores are at the institutions in these groups. Then the authors triumphantly show that black students graduate at a higher rate on the campuses with the highest SAT scores. But there is less here than meets the eye.

First of all, these are not comparisons among individual colleges and universities. Bryn Mawr, Duke, Princeton, Rice, Stanford, Swarthmore, Williams, and Yale are all lumped together as the top group with higher SATs, while Denison, Miami of Ohio, Michigan (Ann Arbor), North Carolina (Chapel Hill), Penn State, and Tulane are lumped together as the bottom group with the lowest SATs within the elite Bowen-Bok sample. Unfortunately, these two sets of colleges differ not only in SAT scores but also—and dramatically—in size.

The median number of undergraduates on campuses in the top group is today less than 3,000, while the median number of undergraduates on campuses in the bottom group is more than 13,000. The largest number of undergraduates at any college in the first group is smaller than the median number at colleges in the second group. These disparities were very similar for the past years covered in the Bowen and Bok study, though the particular numbers varied from year to year.

What then do these statistics really prove? That black students graduate at a slightly higher rate from much smaller colleges than from larger colleges—at least within this highly unrepresentative sample of black students attending highly unrepresentative colleges? But, because the set of colleges with smaller enrollments also has higher SAT scores than the set of colleges with larger enrollments, Bowen and Bok conclude that this refutes the critics of mismatching.

As one of those critics, I have long said that, if you are going to be mismatched, you are better off on a small campus, where you have a chance of getting special help from your professors, rather than at a huge research university where most professors give little attention to undergraduates of any race. Somehow, I don’t feel refuted.

A much more straightforward test of the effects of mismatching would be to separate minority students into those with qualifications (SAT scores, grades, etc.) comparable to their white classmates at the respective institutions they attend and those who were admitted with lower qualifications. When such a comparison was made at Berkeley, it turned out that those minority students admitted with higher qualifications graduated at a much higher rate than those admitted under “race-sensitive” standards. But Bowen and Bok do not risk any such comparison.

By lumping together all the colleges in each group, rather than considering these colleges individually, Bowen and Bok make it impossible to know whether the general patterns they show even apply to most of the institutions within each group, quite aside from problems in comparing the groups with one another. For example, although Bryn Mawr and Duke are both in the top group, the number of students on the Bryn Mawr campus is only a fraction of the number on the campus of Duke University. It is like horse-and-rabbit stew, made with one horse and one rabbit. The overall “flavor” of this statistical stew reflects far more what happens at Duke than what happens at Bryn Mawr.

If there are different results on these two campuses, we have no way of knowing it from these statistics, nor is what happens at Bryn Mawr likely to affect the totals very much. The same size disparities exist within the other groups of colleges that are lumped together for group comparisons. Within the bottom group among these elite institutions, the University of Michigan today has five times as many undergraduates as Denison University—and, in the years covered by the Bowen-Bok data, had more than eight times as many entering freshmen.


A study of the Berkeley student body found that those minority students admitted with higher qualifications graduated at a much higher rate than those admitted under “race-sensitive” standards.


These authors are not merely comparing apples and oranges. They are comparing a collection of apples and oranges with a collection of pears and melons.

The statistics that form the backbone of The Shape of the River were not collected by Bowen and Bok themselves, but were obtained from an organization which refused to permit individual college breakdowns in the published data. While these limitations were not created by the authors, drawing sweeping conclusions from data with such serious limitations is something for which they cannot escape responsibility.

What is most clearly their responsibility is the overall thrust of their argument. That argument is that affirmative action has helped blacks. But what other public policy is assessed in terms of whether its benefits are beneficial to the beneficiaries? The authors claim that society as a whole benefits, but they are short on even flawed evidence for that. What their data primarily seek to show is that the beneficiaries are benefited. Even if they could prove that, do we regard agricultural subsidies or various forms of corporate welfare as socially beneficial because the recipients like what they get and even lobby for more? For that matter, crime benefits criminals and lies benefit liars, but are these reasons to favor crimes and lies?

Nor is it nearly as clear as the authors claim that quotas and preferences benefit black students as a whole. The Bowen-Bok atypical sample of black students in institutions where these students have high survival rates tells us nothing about the fate of black students nationwide, where survival rates are far lower and most do not survive at all.

One of the “successes” and social benefits of affirmative action, according to Bowen and Bok, is that black college graduates go on to provide “leadership” even more so than white college graduates. Yet the arbitrary and stereotypical notions of “leadership” used by these authors tell us nothing about who is being led to what, or with what results. Asian Americans, for example, have no Jesse Jacksons, but they seem to be doing better than those who do. Indeed, as shown by a recent scholarly study by Professors Stephan and Abigail Thernstrom—America in Black and White—blacks were rising economically at a faster rate in the 1940s and 1950s than after acquiring such a plethora of “leaders” at all levels since the 1960s.

Running through The Shape of the River is the suggestion that affirmative action is responsible for the growing black middle class. Yet the rapid growth of that middle class began even before the civil rights revolution of the 1960s, much less the racial quotas and preferences that began in the 1970s. The rise of blacks into professional and similar occupations was faster in the five years preceding passage of the Civil Rights Act of 1964 than in the five years following its passage.

Although Bowen and Bok make much of the number of blacks who went on to postgraduate degrees from the elite institutions studied, until fairly recently most blacks who earned postgraduate degrees came out of the historically black colleges—a group of colleges arbitrarily dropped from the Bowen-Bok sample, on grounds that these institutions did not have affirmative action policies. That is true enough in itself, but very misleading if it suggests that the history of black colleges is irrelevant to the reiterated assertions of Bowen and Bok about the importance of affirmative action at elite institutions in creating a black middle class.

Even today, the role of the non-elite, non-prestigious black colleges is considerable. For the sixth year in a row, Xavier University in Louisiana has led the nation in the number of black alumni who have gone on to medical school. Of the ten top academic institutions in the country in the number of black alumni who go on to become scientists, six are black colleges. This might have been expected back in the Jim Crow era, when most black students went to black colleges, but most black students today do not go to black colleges. There are more blacks at Ohio State than at Xavier.

The continuing role of the black colleges in the creation of a black middle class not only undermines Bowen and Bok’s claims for the imperative importance of education at Ivy League and similar institutions through “race-sensitive” admissions standards. The exclusion of data from black institutions raises further questions as to whether The Shape of the River is a serious attempt to get at the truth, rather than a clever response to growing criticisms of racial quotas.

Understandable as it may be that two former presidents of Ivy League colleges might think that admission to such institutions is the sine qua non of success—that for blacks it is “Yale or jail” in Abigail Thernstrom’s facetious comment—there is much statistical and other evidence to the contrary.

Little-known Cornell College in Iowa has a higher percentage of its alumni end up in Who’s Who in America than the alumni of Cornell University. Harvey Mudd College has a far higher percentage of its graduates go on to earn Ph.D.s than do the graduates of Harvard College. Deans of graduate schools of engineering have ranked graduates of Harvey Mudd College and of the Rose-Hulman Institute over the graduates of Penn, Duke, and UCLA. Deans of leading law schools have ranked graduates of Davidson College over the graduates of most Ivy League schools. Franklin & Marshall graduates score higher than the graduates of the University of California at Berkeley on the national exams for medical school admission.

While Bowen and Bok compare the alumni of selected elite institutions with the alumni of all colleges lumped together, the blatant reality of the academic world is a very wide stratification of colleges, as well as many differences in size and style. A black student turned down by Yale will not need a get-out-of-jail card, but is more likely to be admitted on his merits into Davidson, Franklin & Marshall, or any of a large number of other high-quality institutions whose alumni do very well, thank you.

The Shape of the River makes no serious attempt to assess the backlash against racial quotas and preferences. Worse, a case study from Stanford University is dismissed as reflecting “a particular period of racial tension on a single campus.” Yet surely these former university presidents cannot be unaware that poisonous racial incidents have become more common in recent times on campuses from coast to coast—so much so that the phrase “the new racism” has been coined to describe this phenomenon and has become common currency in academic discussions.

On many campuses, you need only walk into a lunch room and see black students clustered together at their own separate tables to realize how much of the civil rights dream of an integrated America has gone awry in academia. As a black student at Harvard in the 1950s, I never experienced or even heard of the kinds of ugly racial incidents that have occurred on campuses across the country in recent years—and which college administrators have gone to great lengths to try to cover up.

It is not simply conservative critics of current policies who have reported and commented on such racial incidents and general changes for the worse in race relations on campus—especially on campuses that have gone furthest in the direction in which Bowen and Bok want to point us. Radical professors at Berkeley have likewise commented publicly on growing racial resentments that Bowen and Bok try to dismiss as a passing peculiarity at Stanford.

Readers who are interested in seeing a serious analysis of the consequences of admissions preferences, as distinguished from the tendentious brief presented by Bowen and Bok, should read Choosing Elites by Robert Klitgaard. The difference will become immediately apparent in the quality of the questions asked, as well as in the very different answers that result. Sadly, the kinds of institutional data made available to Messieurs Bowen and Bok are unlikely to be made equally available to those who are not defenders of “race-sensitive admissions.” It is hard even to imagine such statistics being turned over to Charles Murray, for example.

The statistical problems in The Shape of the River are not incidental but fundamental. However large the sample and however sophisticated its statistical analysis, its unrepresentativeness makes it no more reliable than the Literary Digest poll which predicted that Alf Landon would defeat FDR. Yet this book tells so many people what they want to hear that it is unlikely to have to bear up under much critical scrutiny. On the contrary, this long and tedious book is likely to end up as something that believers in racial preferences can point to—rather than read—as “proof” that affirmative action is “a good thing.”


Thomas Sowell is the Rose and Milton Friedman Senior Fellow on Public Policy at the Hoover Institution.


This is a slightly revised version of an article that appeared in the April 1999 issue of the American Spectator. Reprinted by permission.

Available from the Hoover Press is Affirmative Action in Higher Education: A Dilemma of Conflicting Principles, by John H. Bunzel, part of the Hoover Essays in Public Policy series. Also available is Barbarians inside the Gates and Other Controversial Essays, by Thomas Sowell. To order, call 800-935-2882.