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Selling Sloppy Statistics


So the Supreme Court has announced it will hear the long-simmering affirmative action case from the University of Michigan law school, in which white plaintiffs sued, claiming to have been denied admission even though they had grades and test scores that were comparable to those of students of color who were admitted.

The case in question–which the Circuit Court decided in favor of the law school and their affirmative action program–will now fall into the lap of a high court that has been increasingly hostile to such policies and tends to consider race-conscious affirmative action efforts little more than illegitimate “racial preferences.”

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 set a precedent for essentially blocking the admission of blacks, Latinos and American Indians to selective schools of higher education.

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 GPA’s and LSAT scores that for whites were met with rejection.

According to the plaintiffs, the odds of one of these “underrepresented minority” students (URM’s) 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 URM’s admitted were unqualified–indeed they conceded that all had been fully qualified–they insist that when URM’s and whites had equal qualifications, minority students were more likely to be accepted, thereby indicating preference.

To make their case at trial, the plaintiff’s attorneys presented grid displays 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 URM’s 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 URM’s in a cell had a 50% chance of admission and whites had a 25% 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 URM’s and whites in a given cell were treated the same–either all accepted or all rejected–Larntz simply threw out their data and refused to consider it.

In other words, by only examining cells where there was a differential outcome, Larntz automatically inflated the size of that difference. Overall, 40% of minority students who applied to the law school were in cells that exhibited no racial differences in admission odds ratios, meaning that claims of massive preference for URM’s depend on ignoring 40% of all applicants of color to the law school.

Secondly, differential odds ratios for white and minority acceptance could just as easily result from a system involving zero preference for URM’s, as from a system with large preference, largely due to the small sample sizes of applicants of color.

For example, in 1996, among the most qualified applicants (students with a 3.75 GPA or better and a 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 and 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 for blacks and a less than certain probability for whites. But surely one cannot infer from one accepted black out of one black 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 racial 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 scores comparable to their own, blacks in a particular range are far 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 the mostly suburban schools attended by whites. Thus, black students can be said to have overcome more and even be more “qualified” than whites who score in the same range or even 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 have agreed there is nothing wrong with considering 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 then 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 differential odds ratios as evidence of “reverse discrimination” are chilling, and would require the rejection of almost all applicants of color to selective schools, simply because there are so few URM applicants.

For example, imagine an applicant pool at a hypothetical school where there is only one URM applicant for each “qualification cell,” perhaps because the school is in a very white location and doesn’t typically attract minority applicants. Under an odds ratio analysis that assumed URM’s couldn’t have more favorable odds of admission without this proving reverse discrimination, most URM’s no matter how competent would have to be rejected simply because to accept one-out-of-one 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 the 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 for admission, 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 mere hypotheticals, there is real evidence of how reliance on odds ratios would work in practice. In 1996, there were only two black students in the country who received LSAT’s over 170 and had GPA’s 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 that 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, or 95; and imagine that both of the blacks with those grades and scores applied. Since admitting both of the blacks would yield odds ratios unacceptably in favor of blacks, 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 U of M indicates the problem with utilizing odds ratio analyses. Larntz notes, for example, that among applicants in 1999 with a 3.5-3.7 GPA and LSAT’s of 156-158, six of seven URM’s were admitted, while only one of seventy-three whites at that level were accepted. This yields an odds ratio of 432:1 in favor of URM’s 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 particular “qualification cell,” it is entirely possible that the admissions officers who decided to accept six of those seven merely examined the files and found that those six had overcome extraordinary obstacles (including racism and perhaps 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 URM’s, 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 that combination of test scores and grades was worthy of acceptance–essentially what the University said that year–this yields an acceptance probability at that level of 8.75%. Applying that probability to each group yields six whites out of 73 who should be accepted and 0.6 URM’s out of seven who should be. In other words, because of the small pool of URM’s 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 URM’s as a group.

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 URM’s and 1 white admitted (the actual numbers for 1999), we would get the opposite: 6 whites and 1 URM. The problem is, even with that “correction,” the probability of acceptance for URM’s would be 14.3%, while for whites it would be 8.2%, 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 odds ratios for people of color, without basically rejecting the vast majority of URM applicants outright.

The fact is, the current attack on affirmative action is based on a lie; the lie 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 (hint: it ain’t the rye side), 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% of black applicants were admitted to the Law School while 39% of white applicants were admitted. More recently, in 2000, 36% of black applicants were admitted, while 41% of white applicants were. If that’s reverse discrimination, I’m having a hard time making out the victims.

Tim Wise is an antiracist writer, lecturer and activist. He can be reached at (and footnotes can be obtained from), timjwise@msn.com

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