Selling Sloppy Statistics: “Reverse Discrimination” and the Perpetuation of Right Wing Fraud

Published as a ZNet Commentary,, December 19, 2002

So the Supreme Court says it will hear the long-simmering affirmative action case from the University of Michigan law school, in which white plaintiffs claim to have been denied admission, even though they had grades and test scores comparable to students of color who were admitted. The case in question, which the Circuit Court decided in favor of affirmative action, will now fall into the lap of a high court that has been increasingly hostile to such policies and tends to consider any race-conscious affirmative action little more than illegitimate “racial preference.”

But in truth, the plaintiff’s claims of reverse discrimination (pieced together by the right-wing Center for Individual Rights) are so flimsy they would be almost laughable were they not so dangerous. Understanding how the right manipulates data to make their case is important for those who hope to stanch the movement to roll back key civil rights gains. Indeed, the data is not only flawed but also dangerous, for its acceptance as legitimate social science, as will be seen below, could result in essentially blocking the admission of most students of color to selective schools.

By utilizing questionable statistical techniques, the plaintiffs claim that black, Latino and American Indian applicants to the U of M law school received preference over whites because they were often accepted with GPAs and LSAT scores that for whites were met with rejection. According to the plaintiffs, the odds of one of these “underrepresented minority” students (URMs) being admitted were often hundreds of times better than the odds of a white applicant with similar scores and grades. Although the plaintiffs have never presented evidence that the URMs admitted were unqualified — indeed they conceded that all were fully qualified — they insist that when URMs and whites had equal qualifications, minority students were more likely to be accepted, thereby indicating preference.

To make their case, the plaintiffs presented grid displays at trial that broke down those who applied and were admitted to the law school by “qualification cells,” separating students into groups by GPA and LSAT (i.e., 3.5-3.75 GPA and 156-158 on the LSAT, on a 120-180 scale). Within each cell, statistician Kinley Larntz calculated the odds of admission for each student, concluding that URMs in many cells had greater chances of admission than whites with the same grades and test scores. He then calculated the odds ratios for each cell, so that if URMs in a cell had a 50 percent chance of admission and whites had a 25 percent chance, the odds ratio would be 2:1. The larger the odds ratio, the greater the degree of presumed preference.

But such an analysis is flawed. First, the data used to calculate admissions odds ratios was limited. Whenever URMs and whites in a given cell were treated the same — all accepted or all rejected for example, or accepted and rejected at the same rate, say, thirty percent — Larntz threw out the data and refused to consider it. As such, by only examining cells where there was a differential outcome, Larntz automatically inflated the size of that difference. Forty percent of minority applicants were in cells with no racial difference in admission odds, meaning that claims of URM preference depend on ignoring 40 percent of all URM applicants to the law school.

Secondly, different odds ratios for white and minority acceptance could just as easily result from a system with zero preference for URMs, as from a system with large preference, due to small sample sizes of applicants of color. For example, in 1996, among the “most qualified” applicants (3.75 GPA or better and 170 or higher on the LSAT), only one black with these numbers applied to the U of M. This applicant was accepted. 151 whites applied with these numbers; 143 were accepted. While most everyone at this level was admitted, since there was only one black who applied and got in, the “odds ratio” in favor of blacks at that level appears infinite, a guarantee, with a less than certain probability for whites. But surely one can’t infer from one accepted black out of one applicant at that level that there is some pattern of preference operating.

As proof that one could produce odds ratios favoring blacks even in the absence of preference for any individual URM, consider the implications of a study by the Mellon Foundation and the Urban Institute, which found that blacks tend to have faced greater educational obstacles than whites with comparable scores on standardized tests. When compared to whites with comparable scores, blacks in a particular range are more likely to have come from low-income families and families with less educational background. These black students are also more likely to have attended resource-poor inner city schools where course offerings are more limited than in suburban schools mostly attended by whites. Thus, blacks can be said to have overcome more and even be more “qualified” than whites who score in the same range or a bit higher on standardized tests.

As such, it becomes easy to see how differential admissions odds ratios could obtain even without “racial preferences.” Simply put, if whites tend to be better off and face fewer obstacles to their educational success than blacks, and if blacks tend to be worse off and face more obstacles, then any black applicant to a college, law school or graduate school will likely have a greater claim for their merit at a given test score level than a white who scored the same. To visualize the point, imagine a four-leg relay race. If whites tend to start out two laps ahead of blacks and the runners finish the race tied, is it fair to say they were equally good as runners; or would we instead say that the black runner was superior, having made up so much ground?

Since even the plaintiffs say it’s fine to consider the obstacles faced by applicants, including the effects of racism, it is quite possible that admissions officers could look at applicant files, see whites and blacks with comparable scores, and on an individual basis make the determination that the black applicants were more qualified, having overcome obstacles faced by far fewer whites. But if individual analyses were completed with such a result, they would produce the same odds ratios as discovered by Larntz. In other words, differential odds ratios themselves prove nothing.

Indeed, the implications of accepting different odds ratios as proof of “reverse discrimination” are chilling, and would require the rejection of almost all applicants of color to most schools, simply because there are so few URM applicants. For example, imagine an applicant pool at a school where there are only one or two URM applicants for each “qualification cell,” perhaps because the school is in a very white location and doesn’t attract minority applicants. Under an odds ratio analysis that assumed URMs couldn’t have more favorable odds of admission, most URMs no matter how competent would have to be rejected simply because to accept one-out-of-one or two-out-of-two would represent “infinite odds” and require the acceptance of every white in the same cell, merely to keep the odds ratios the same.

So although we could expect whites and students of color at the lowest level of scores to all be rejected and those at the top to all be accepted, in the middle such a situation would create chaos. If one black student applied with scores and grades that were good but not a sure thing, and 200 whites applied with those same numbers, the school would have to accept every white in that cell if they accepted the one black, or else face a lawsuit for reverse discrimination on the basis of an unacceptably pro-black admissions odds ratio.

Beyond hypotheticals, we can see how reliance on odds ratios would work in practice. In 1996, there were only two black students in the U.S. who received LSATs over 170 and had GPAs of 3.75 or better. If one of these applied to a given law school, that person would have to be rejected under an odds ratio analysis unless the law school was ready to accept every white applicant with the same score and GPA, irrespective of other aspects of their application file. Now imagine that the same year, 100 whites with those numbers applied to the same school, and 80 of them were admitted, or 90; and imagine that both of the blacks with those scores applied. Since admitting both blacks would yield odds ratios unacceptably in their favor, the school would have to reject one of the clearly qualified blacks with those numbers (thereby producing a large odds ratio in favor of whites) just to avoid being sued for reverse discrimination!

Even the strongest evidence of URM racial preference at Michigan indicates the problem with odds ratio analyses. Larntz notes, for example, that among applicants in 1999 with a 3.5-3.75 GPA and LSATs of 156-158, six of seven URMs were admitted, while only one of seventy-three whites were. This yields an odds ratio of 432:1 in favor of URMs at that level: a seemingly huge racial preference. But there are two problems.

First, with only seven black, Latino or Indian applicants to the U of M School of Law in that “qualification cell,” it is entirely possible that the admissions officers who accepted six of those seven merely examined the files and found that they had overcome extraordinary obstacles (including racism and economic hardship), unlike the white applicants. Thus, the ratio itself, absent other evidence about the particular decision-making of admissions officers, cannot prove a preference for URMs, as the pool is simply too small. Secondly, to balance the odds ratios for this cell would have been impossible. If seven of eighty applicants with those test scores and grades were worthy of acceptance — essentially the school’s position that year — this yields an acceptance probability at that level of 8.75 percent. Applying that probability to each group yields 6 whites out of 73 who should be accepted and 0.6 URMs out of seven who should be. In other words, because of the small pool of URMs in that group, it wouldn’t be possible to admit even one, let alone one black, one Latino and one American Indian, without giving a much higher probability of admission to URMs. But for the sake of argument, let’s say the school rounded up the six-tenths of a person to one full person and admitted one URM with these numbers. Thus, instead of 6 URMs and 1 white admitted, as in 1999, we would get the opposite: 6 whites and 1 URM. The problem is, even with that “correction,” the probability of acceptance for URMs would be 14.3 percent, while for whites it would be 8.2 percent, meaning there would still be an unacceptable odds ratio favoring people of color simply as a function of sample size. So even under a “race-blind” process that sought to avoid different probabilities for different groups, it would be impossible to eliminate favorable ratios for people of color, without rejecting the vast majority of URM applicants outright.

The burden that odds ratio analysis would place on students of color in a case like this is enormous. Indeed, if Michigan was required to admit URMs at the same rate as whites in each qualification cell, they would have to reject all URMs in the above-mentioned cell (3.5-3.7 and LSAT of 156-158) until there were seventy-three URM applicants at that level: ten times the current number and unlikely to ever occur given population demographics. Once again, it would amount to punishing minorities for merely being minorities.

The fact is, the current attack on affirmative action is based on a lieãthat of “reverse discrimination.” The statistics used by groups like the CIR and their clients in court to demonstrate supposed racial preference for people of color are bogus and prove nothing, except the old adage that you can make numbers say just about whatever you wish. It is incumbent upon those of us who support affirmative action to confront these lies and flawed data head-first; to demonstrate conclusively on which side of the bread one continues to find the butter in this society, and to show beyond any doubt that the right-wing crusade against racial equity is supported by smoke and mirrors, not hard facts.

The facts are plain. There is no racial preference for minority students at the University of Michigan Law School. In 1997, for example (one of the years covered by the lawsuit), 34 percent of black applicants were admitted to the Law School while 39 percent of white applicants were admitted. More recently, in 2000, 36 percent of black applicants were admitted, while 41 percent of white applicants were. If that’s reverse discrimination, I’m having a hard time making out the victims

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