Opinion ID: 508923
Heading Depth: 2
Heading Rank: 1

Heading: Adverse Impact.

Text: 21 To make out their prima facie case showing the adverse impact of the Engineer Training Program, the plaintiffs set out a raw statistical comparison of the percentage of blacks who failed the tests in the Training Program with the percentage of whites who similarly failed. 6 According to the district court's assessment of the evidence, of the 497 white students ... 432 or 87% passed. Of the 70 black students ... 42 or 60% passed. Thus the black pass rate was 69% of the white pass rate. Cox v. Conrail, Civil Action No. 85-0514, slip op. at 79 (D.D.C. August 26, 1987) (p 208). 7 22 In addition to the raw numbers, which by themselves are not very instructive, counsel performed several calculations for the district court, only one of which it accepted and used. 23 As is clear from the district court's opinion, the district court took note of the plaintiffs' comparisons of the pass rate for blacks with the rate for whites. The district court also took note of the EEOC's Uniform Guidelines on Employee Selection Procedures, 29 C.F.R. Sec. 1607.4(D), which sets out the four fifths rule that a minority pass rate which is less than four fifths (or 80%) of the majority pass rate will generally be regarded by the Federal enforcement agencies as evidence of adverse impact.... The four fifths rule has also been used with caution by some courts, e.g., Black, supra, 831 F.2d at 133-35 (6th Cir.1987); Fudge, supra, 766 F.2d at 657-59 (1st Cir.1985); Guardians Association of the New York City Police Department, Inc. v. Civil Service Commission of the City of New York, 630 F.2d 79, 87 (2d Cir.1980), cert. denied, 452 U.S. 940, 101 S.Ct. 3083, 69 L.Ed.2d 954 (1981), but has been criticized as unreliable and overly simplistic. Shoben, supra, 91 Harv.L.Rev. at 805-06. In the final analysis, the district court rejected application of the four fifths rule because it found the samples of women (11) and blacks (70) too small to support a finding that the figures are statistically significant. Cox v. Conrail, supra, slip op. at 81 (p 214). That conclusion is consistent with the Uniform Guideline statement that differences [of more than 80%] in selection rate may not constitute adverse impact where the differences are based on small numbers and are not statistically significant.... 29 C.F.R. Sec. 1607.4(D). The Uniform Guidelines do not establish a hard and fast rule for federal agencies, and the courts have followed suit, especially where small numbers are involved. Black, supra, 831 F.2d at 133-35 (6th Cir.1987); Fudge, supra, 766 F.2d at 657-59 (1st Cir.1985). 24 The district court, in rejecting the comparisons, had very little choice. The plaintiffs as a matter of trial strategy decided to avoid an extensive exploration of the use and meaning of statistical analysis by way of expert testimony. The district court was well within the bounds of reason in making an intuitive decision, rather than attempting independently to educate itself in the field of statistical analysis. See Fudge, supra, 766 F.2d at 657 (1st Cir.1985). 25 Second, the plaintiffs performed and proffered a Z statistic calculation. The Z statistic, or test for differences between independent proportions, is one of several used in discrimination cases as a way of assessing the probability that a discrepancy in statistical sample--varying pass rates, for example--is due to chance, rather than discrimination or some other explanation. Baldus & Cole, supra, Sec. 9A.1. As the size of a statistical sample decreases, the probability that a discrepancy is due to chance is heightened. See Segar v. Smith, 738 F.2d 1249, 1282-83 (D.C.Cir.1984), cert. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985). There is always a possibility that a discrepancy is due entirely to chance, but with enough repetition of a test, the likelihood of that possibility diminishes. Ibid. The Z statistic is a calculation which measures in a uniform way the degree of the discrepancy in relation to the size of the sample. It thus allows comparison, from study to study, of the probability that a numerical discrepancy is due entirely to chance. See Shoben, supra, 91 Harv.L.Rev. at 799-800. 26 This information was not communicated to the district court by an expert, because the plaintiffs believed that judicial notice could be taken of it. While that may be true, the district court was not required to take notice of it. Fed.R.Evid. 201(d) (a court shall take judicial notice if ... supplied with the necessary information). The issue apparently was not articulated to the district court in a manner that could permit it to make the legal determination as to whether the level of chance implicated by the plaintiffs' statistics was significant pursuant to the teachings of Palmer v. Shultz, supra, 815 F.2d at 90-97. There is always some possibility that a statistical discrepancy is due to chance. But that does not keep the courts from relying on statistics, when shown to be significant, for the establishment of a prima facie case. The question--the legal question--is what degree of certainty the courts require for a prima facie case to be established. The 5% level--that is to say in 5 (or fewer) out of 100 samples a given numerical discrepancy is, on average, due to chance--is commonly accepted among statisticians as an acceptable degree of uncertainty, and was adopted in Palmer v. Shultz, supra, 815 F.2d at 96. This 5% or less figure corresponds to a Z statistic figure of 1.96 or greater. Shoben, supra, 91 Harv.L.Rev. at 803 & n. 41. 27 In apparent response to the Z statistic proffer, the district court wrote, 28 There is no indication whether, or to what degree, the pass rate percentages are meaningful. Plaintiffs chose not to use a statistical expert and were thus barred at trial from introducing complicated statistical evidence. Such evidence is meaningless to the lay person.... The court is not in a position to evaluate the appropriateness of the formulas selected, whether they are complete and accurate, how they should be applied to the evidence in the instant case, or what the significance of their results are. Without such information, plaintiffs have failed to prove that the pass rate ratios are meaningful. 29 Cox v. Conrail, supra, slip op. at 81-82 (p 216). The appellants press the argument that the district court's refusal to accept the proffered Z statistic was reversible error. We disagree. We do not believe that the adoption of the 5% or less legal standard relieves plaintiffs of the burden of making their statistical analyses intelligible to the finder of fact. Statistical calculations performed on data in discrimination cases are not probative of anything without support from an underlying statistical theory. See Baldus & Cole, supra, Sec. 10. Generally, the plaintiffs present statistics about themselves--for instance, their own performance in a selection device alleged to have an adverse impact on members of a protected minority group. Shoben, supra, 91 Harv.L.Rev. at 797-98. For purposes of analysis, those who actually claim discrimination serve merely as a statistical sample of the relevant population: if the disparity between majority and minority cannot be explained by legitimate reasons, discrimination against the entire minority population at large may exist. Ibid. But the numerical disparity can sometimes be explained by reasons other than discrimination. For instance, the sample itself may not be representative of the population at large, or sufficiently random, or, as the district court in this case observed, the sample may be so small that a slight change in the data would present an entirely different result. Id. at 801. In addition, disparities may be explainable by other factors, such as uncomprehensive statistical treatment, varying levels of qualifications among applicants, errors in definition of groups, inappropriate sampling methods, errors in measurement, or even clerical and computational errors. Baldus & Cole, supra, Sec. 10.112. Perhaps the leading commentators on the use of statistical analysis in discrimination litigation have warned that the statistical tests they recommendprovide a good point of departure, but the accuracy of the inferences they suggest (even when assumptions of random sampling are perfectly satisfied) can be no greater than the validity of the basic research design and methodology that produced the measure of disproportionate impact.... Regardless of the legal theory of the case, the issues of measurement and research design that we have discussed throughout this book should be considered in assessing the pedigree and weight of the critical numbers. Id. at 337. 30 While plaintiffs in a discrimination case need not set up and demolish every conceivable straw man in making out a prima facie case, the statistics must be made meaningful to the finder of fact in order to permit the plaintiffs to carry their burden of showing that their statistics are significant. 31 We are not prepared to say that the Z statistic calculation is so simple and straight forward that an expert is never required to explain it to a finder of fact. Nor do we wish to be understood as holding that an expert is always required. We leave both possibilities open because it would be impossible to anticipate the impact of this theory upon every conceivable factual situation. We believe that in the factual context of this case, the district court made a valid finding that the plaintiffs' proffered statistics were not sufficiently presented to make out a prima facie case of adverse impact. 32