
    Alston A. EMANUEL and Leon Paige, Appellants. v. John O. MARSH, Jr., Secretary of the Army, in his official capacity; Department of the Army, HQ U.S. Army Troop Support and Aviation Material Readiness Command, Appellees.
    No. 86-1282.
    United States Court of Appeals, Eighth Circuit.
    Submitted Oct. 9, 1989.
    Decided March 7, 1990.
    Rehearing Denied May 14, 1990.
    
      Edward L. Welch, East St. Louis, Ill., for appellants.
    Major Cathy P. Cates, U.S. Army, Washington, D.C., for appellees.
    Before MCMILLIAN and FAGG, Circuit Judges, and HEANEY, Senior Circuit Judge.
   HEANEY, Senior Circuit Judge.

This matter is before us for a second time. When it was first here, we held that Alston A. Emanuel, a black civilian employee of the Army, was not entitled to recover on his claim for employment discrimination. We reasoned that he had not established discrimination under a disparate treatment analysis and that under existing precedent the case could not be considered under a disparate impact analysis. Emanuel appealed to the Supreme Court, which remanded the matter for our reconsideration under a disparate impact analysis. 487 U.S. 1229, 108 S.Ct. 2891, 101 L.Ed.2d 925. Having made that analysis, we hold that Emanuel has established a prima facie case of disparate impact and remand the matter to the district court with directions that it make the following determinations: [1] whether the Army’s use of subjective performance awards serves, in a significant way, legitimate employment goals; and [2] whether other tests or selection devices, without a similarly undesirable effect, would also serve the Army’s legitimate employment goals.

BACKGROUND

In Emanuel v. Marsh, 828 F.2d 438 (8th Cir.1987), this Court affirmed the district court’s holding that disparate impact analysis was not proper because Emanuel challenged subjective employment practices rather than a facially neutral objective employment test. See, e.g., Talley v. United States Postal Serv., 720 F.2d 505, 506 (8th Cir.1983), cert. denied, 466 U.S. 952, 104 S.Ct. 2155, 80 L.Ed.2d 541 (1984). We noted, however, that a split in the circuits existed and the issue was before the United States Supreme Court in Watson v. Fort Worth Bank & Trust, 798 F.2d 791 (5th Cir.1986), cert. granted in part, 483 U.S. 1004, 107 S.Ct. 3227, 97 L.Ed.2d 734 (1987).

Emanuel appealed this Court’s decision to the Supreme Court. The Supreme Court subsequently decided Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988). Watson involved a black employee rejected in favor of white applicants for promotions to supervisory positions. The employer did not use precise and formal criteria to determine promotions; instead, it relied on the subjective judgment of white supervisors familiar with the candidates and the nature of the jobs concerned. Both the trial court and the Fifth Circuit rejected the employee’s contention that a disparate impact analysis was proper in such circumstances. The Supreme Court vacated the judgment of the lower courts and remanded the matter for further consideration.

Justice O’Connor, speaking for all the Justices, stated that: [1] if the disparate impact analysis of employment discrimination was rejected for decisions based on subjective criteria; employers could avoid liability by infusing their employment practices, discriminatory or not, with criteria subjective in nature; and [2] no principled difference exists in the confines of Title VII between subjective and objective employment criteria. Watson, 487 U.S. at 989, 108 S.Ct. at 2786, 101 L.Ed.2d at 842. “In both circumstances, the employer’s practices may be said to ‘adversely affect (an individual’s) status as employee, because of such individual’s race, color, religion, sex, or national origin.’ ” Id. (quoting 42 U.S.C. § 2000e-2(a)(2)).

Following its decision in Watson, the Supreme Court remanded this case to us for consideration of Emanuel’s claim under a disparate impact analysis. We, in turn, remanded the matter to the district court.

On remand, the district court rejected Emanuel’s disparate impact analysis. It reasoned that the statistical evidence did not permit an inference that the Army discriminated against blacks in promotion decisions. Emanuel v. Marsh, No. 83-055C(5), slip op. at 2 (E.D.Mo. Apr. 12, 1989). Alternatively, and assuming that Emanuel had established an inference of discrimination, the court concluded that the Army had demonstrated legitimate reasons for using subjective criteria — performance awards, amount of training and SKAP ratings — in its decisionmaking process and that less restrictive alternatives to achieve the Army’s legitimate employment goals did not exist. Id. at 3.

DISCUSSION

Emanuel first asserts that the district court erred in concluding that no relevant statistical disparities exist in the TSAR-COM workforce. The district court stated:

Plaintiff contends the disparate impact is seen at the highest grade levels (GS-12 and above). It is at these positions the plaintiff argues blacks are underrepresented. As the Supreme Court recognized in Watson, statistical evidence is often misleading and can be interpreted in different ways. The evidence presented in this case is a classic example of how the numbers can be turned around to fit any argument being made.

Quoting from its earlier opinion denying certification of the class of black males employed in all divisions at TSARCOM, the district court continued and found that the statistics presented did not show any disparities.

[Pjlaintiff cannot point to any statistical data which can allow the Court to draw an inference that there is widespread race and sex discrimination against black males. The statistics of TSARCOM’s workforce in late 1982 showed that approximately fifty-six percent (56%) of TSARCOM’s workforce served in the mid to upper employee grade levels. Of all black employees at TSARCOM, approximately sixty-three percent (63%) were employed in the mid to upper grade levels. The evidence shows that the percentages have remained relatively constant since 1982.

Assuming arguendo the accuracy of the district court’s statistical analysis, the analysis misses the point. While the data relied on by the district court does not permit an inference of discrimination, it also fails to reach Emanuel’s allegation that blacks were not promoted to GS-12 and above because of their race.

We initially note that our analysis is complicated by the incomplete record on appeal. Despite repeated requests, the parties have not filed with the Court all of the statistical evidence introduced in the district court. Nevertheless, for reasons discussed below, the statistical breakdown of persons employed within Emanuel’s division at TSARCOM, the Directorate of Material Management (DMM), adequately fulfills Emanuel’s burden of establishing the existence of statistical disparities between black employees at middle and lower levels as opposed to black employees at supervisory levels. See Watson, 487 U.S. at 993, 108 S.Ct. at 2788, 101 L.Ed.2d at 845.

A. DISPARATE IMPACT ANALYSIS OP SUBJECTIVE EMPLOYMENT PRACTICES

When this case was first tried at the district court and first appealed to our Court, the law of the Eighth Circuit was that an individual could not prove a violation of Title VII by means of disparate impact analysis of subjective employment practices. See, e.g., Talley v. United States Postal Service, 720 F.2d 505, 507 (8th Cir.1983); Harris v. Ford Motor Co., 651 F.2d 609, 611 (8th Cir.1981). Subsequently, the Supreme Court concluded, however, that an individual could prove a violation of Title VII by an employer’s use of subjective employment practices through the use of disparate impact analysis, Watson, 487 U.S. at 989, 108 S.Ct. at 2786, 101 L.Ed.2d at 842, and clarified the direction that a disparate impact analysis must follow in Wards Cove Packing Co. v. Atonio, — U.S. -, -, 109 S.Ct. 2115, 2121-27, 104 L.Ed.2d 733, 747-54 (1989).

As the result of Watson and Wards Cove, the Supreme Court has adopted a nine-prong analysis to assure that the disparate impact test of employment discrimination comports with the goals and limitations of Title VII:

1) The plaintiff must be a member of a protected group;

2) the plaintiff must have made or attempted to make or have been deterred from making application for the job or promotion;

3) the plaintiff must show that new hiring or promotion has been made by the employer, and that the employer has hired or promoted individuals not from the plaintiffs protected group;

4) the plaintiff must show relevant statistical disparities permitting an inference of racial imbalance in defendant’s workforce, Wards Cove, — U.S. at -, 109 S.Ct. at 2122, 104 L.Ed.2d at 749; Watson, 487 U.S. at 993, 108 S.Ct. at 2788, 101 L.Ed.2d at 845;

5) the defendant can rebut such an inference with relevant statistics, Wards Cove, — U.S. at -, 109 S.Ct. at 2123, 104 L.Ed.2d at 750; Watson, 487 U.S. at 994-98, 108 S.Ct. at 2789-90, 101 L.Ed.2d at 846-47;

6) the plaintiff must identify specific employment practices that he or she is challenging as discriminatory, Wards Cove, — U.S. at -, 109 S.Ct. at 2124, 104 L.Ed.2d at 751; Watson, 487 U.S. at 993, 108 S.Ct. at 2788, 101 L.Ed.2d at 845;

7) the plaintiff then must show that the identified employment practices caused the exclusion of applicants for jobs or promotions because of their membership in a protected group, Wards Cove, — U.S. at -, 109 S.Ct. at 2124, 104 L.Ed.2d at 751; Watson, 487 U.S. at 993, 108 S.Ct. at 2788, 101 L.Ed.2d at 845;

8) once causation has been established, the defendant must demonstrate a business justification for his employment practice, Wards Cove, — U.S. at -, 109 S.Ct. at 2125-26, 104 L.Ed.2d at 752-53; Watson, 487 U.S. at 997-98, 108 S.Ct. at 2790, 101 L.Ed.2d at 847;

9) if a business justification is established, the plaintiff must demonstrate that other tests or selection devices, without a similarly undesirable racial effect, would also serve the employer’s business justification, Wards Cove, — U.S. at -, 109 S.Ct. at 2125-26, 104 L.Ed.2d at 752-53; Watson, 487 U.S. at 997-98, 108 S.Ct. at 2790, 101 L.Ed.2d at 847.

The Army does not question whether Emanuel met the first three prongs of the Watson-Wards Cove analysis. He was a qualified black applicant for promotion to GS-13. He made application for promotion to a GS-13 position at the correct time. A white employee was selected for promotion instead of Emanuel. Furthermore, Emanuel identified during both the class certification hearing and the case-in-chief specific employment practices which he claims have' a discriminatory effect, thereby, meeting the sixth prong of the Watson-Wards Cove analysis. The specific employment practices are the use of performance awards, training and SKAP ratings in promotion decisions. Each practice uses subjective criteria.

B. RELEVANT AND SIGNIFICANT STATISTICAL DISPARITIES EXIST IN DEFENDANT’S WORKFORCE

The district court compared the composition of blacks in both supervisory and non-supervisory positions with the composition of the total workforce in both supervisory and non-supervisory positions throughout TSARCOM. The proposition the district court appears to be stating is, even if there is discrimination preventing blacks from reaching supervisory positions, this conduct does not violate Title VII provided the employer employs a significant number of blacks at middle level positions. This cannot be the law. See Wards Cove, — U.S. at - n. 8, 109 S.Ct. at 2123 n. 8, 104 L.Ed. at 749 n. 8 (“bottom-line racial balance is not a defense under Title VII”). Rather, the essential question is whether discrimination impairs black employees’ attempts to rise from non-supervisory to supervisory positions.

The district court also erred by relying on the statistical breakdown of the entire TSARCOM facility. The relevant labor pool is the DMM, the large division within TSARCOM for which Emanuel works.

Unlike the hiring practice in Wards Cove, promotions were, in practice, made from within each directorate at TSARCOM; thus, the pool of lower level employees represents the pool of qualified applicants for promotion. The Army alleges that “more than an insignificant” number of promotions were from outside Emanuel’s directorate but fails to support this allegation with evidence. Also, unlike the employment practice in Wards Cove, nothing in this record demonstrates that the qualifications for the various GS-levels within the DMM are vastly different or at all exclusive of each other, thereby, making it a near certainty that promotions to supervisory levels within the DMM were given to individuals working within the DMM.

Consequently, the most relevant data with respect to whether the Army discriminated against blacks seeking promotions to a supervisory position within the DMM is the statistical breakdown of the DMM isolated from the other directorates within TSARCOM. See Wards Cove, — U.S. -, 109 S.Ct. at 2119, 104 L.Ed.2d at 745 (the relevant labor pool is the pool of employees likely to be hired or promoted). Furthermore, lack of statistical disparities throughout a total workforce does not disprove statistical disparities existing within a large subset — for example, the DMM accounts for about one-quarter of TSAR-COM’s employees — of the total workforce. Id.; see also note 9.

Within the DMM, a total workforce of 994 of GS-3 and above exists. Of the 994, there are 304 black employees and 685 white employees. In GS-12 and above, there are 164 employees. Of whom, 28 are black (17% of the GS-12 and above employees within the DMM), and 136 are white (83% of the same unit). In GS-11 and below, there are 830 employees. Of the 830, 276 are black, constituting 33% of the GS-11 and below employees within the DMM, and 554 are white, constituting 67%. Thus, blacks comprise 33% of the workforce classified at GS-11 or below, but only 17% of the workforce classified at GS-12 or above. Using the number of employees in the workforce classified GS-12 and above as the sample, see Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977), the standard deviation is 6. The expected number of blacks in positions classifed GS-12 and above is 54. The difference between the expected number of blacks and the observed number of blacks is 26, and this difference is more than four standard deviations. In light of all the underlying circumstances, including past racial discrimination against Emanuel by the appel-lee, such a result is suspect, statistically significant and makes a prima facie case of statistical disparity. See also id. (“if the difference between the expected value and the observed number is greater than two or three standard deviations,” the statistical disparities are significant).

Similar, statistically significant results occur using either GS-11 and above or GS-13 and above as the relevant sample.

Even if one uses an approach similar to the approach employed by the district court and compares the percentage of the total workforce in upper levels with the percentage of the black workforce in upper levels, significant statistical disparities are apparent. Of the 994 employees in the total workforce within the DMM, 356 are at GS-11 or above (36% of the total workforce). Of the 304 black employees, 63 are at GS-11 or above (21% of the black workforce within the DMM). Assuming — because promotions are made from within the DMM — that the same percentage of blacks would be employed in the upper levels as the general DMM population, the standard deviation is 9.1. The expected number of blacks in upper levels is 109. The difference between the expected number of blacks and the observed number of blacks is 46, and this difference is nearly five standard deviations. Again, such a result is suspect, statistically significant and demonstrates a prima facie case of statistical disparity. Id.

We can draw but one conclusion from the employment data regarding the DMM: the disparities between blacks and non-blacks in upper level or supervisory positions are statistically significant and, in light of the earlier discrimination by the Army against Emanuel and other circumstances of this case, permit an inference of racial imbalance. See Watson, 487 U.S. at 995-96 n. 3, 108 S.Ct. at 2789 n. 3, 101 L.Ed.2d at 845-46 n. 3.

Furthermore, the data depicting the employment of blacks throughout TSARCOM does not rebut disparities found within the DMM. It relates to an irrelevant labor pool because the promotion in question was from a position within the DMM to another position within the DMM. In addition, bottom-line racial balance does not necessarily cure an inference of racial discrimination. Wards Cove, — U.S. at - n. 8, 109 S.Ct. at 2123 n. 8, 104 L.Ed.2d at 749 n. 8. Thus, Emanuel has shown relevant statistical disparities permitting an inference of racial imbalance within the DMM workforce, and the Army has not rebutted this inference.

Three prongs of the Watson-Wards Cove analysis, however, remain.

C. CAUSATION

On remand but without a further trial or evidentiary hearing, the district court concluded that Emanuel did not show that any of the identified employment practices caused the exclusion of black applicants for promotions within the DMM. The district court erred in so concluding.

Once the employment practice at issue has been identified, causation must be proved; that is, the plaintiff must offer statistical evidence of a kind and degree sufficient to show that the practice in question has caused the exclusion of applicants for jobs or promotions because of their membership in a protected group. Our formulations, which have never been framed in terms of any rigid mathematical formula, have consistently stressed that statistical disparities must be sufficiently substantial that they raise an inference of causation.

Watson, 487 U.S. at 993-95, 108 S.Ct. at 2788-89, 101 L.Ed.2d at 845. In essence, the data must show that the employment practices in question tend to select applicants for promotion to supervisory positions within the DMM in a racial pattern different from that of non-supervisory positions within the DMM. See id. In other words, finding that a filtering out of black employees has in fact happened, a plaintiff must now show that the identified employment practices have caused this filtering. This requirement is necessary to avoid the implicit requirement of employment quotas and to assure that the identified employment practices, and not some other factor, caused the underrepresentation of blacks in supervisory positions within the DMM.

The evidence shows that the Army’s use of performance awards prevented black employees from reaching supervisory level positions. Within the DMM, blacks received 18.2% of the awards while constituting 30.5% of the DMM workforce. Equal Employment Opportunity Plan of Action, Appendix III to Part C at 76, US Army Troop Support and Aviation Material Readiness Command (FY 1979). Using the total number of awards received by DMM employees as the sample, the standard deviation is 4.9. The expected number of awards blacks within the DMM should receive is 55, and the difference between the expected number of awards and the actual number of awards is 22. This difference is more than 4 standard deviations. The data demonstrates that the use of performance awards had a significant disparate impact on blacks. Moreover, the Army concedes:

TSARCOM employees received a total of 919 awards, which represents 20.6% of the total work force. Minorities received 14.9% (137) and females received 50.6% (465) of total awards. Analysis of the awards program reflects that awards granted females exceeded their percent in the total work force composition by 3.3%. However, minorities granted awards reflect underrepresentation by 7.3%.

Id. at 36. “Minority employees are not receiving Performance Awards in proportion to their representation in the work force.” Id. at 37. A causal connection between the bottom-line statistical disparities in the workforce and the Army’s use of performance awards in promotion decisions exists. Hence, performance awards acted to filter blacks from supervisory positions.

By proving the existence of relevant statistical disparities within the Army's workplace and a causal connection between these disparities and the Army’s use of subjective performance awards, Emanuel has established a prima facie case of disparate impact.

D. BUSINESS JUSTIFICATION AND LESS RESTRICTIVE ALTERNATIVES

Two prongs of the Watson-Wards Cove analysis remain.

If [a plaintiff] establishes] a prima facie case of disparate impact with respect to any of [the employer’s] employment practices, ... the dispositive issue is whether a challenged practice serves, in a significant way, the legitimate employment goals of the employer. The touchstone of this inquiry is a reasoned review of the employer’s justification for his [or her] use of the challenged practice. A mere insubstantial justification in this regard will not suffice, because such a low standard of review would permit discrimination to be practiced through the use of spurious, seemingly neutral employment practices....
Finally, if [the plaintiff] cannot persuade the trier of fact on the question of [employer’s] business necessity defense, [the plaintiff] may still be able to prevail. To do so, [the plaintiff] will have to persuade the factfinder that “other tests or selection devices, without a similarly undesirable racial effect, would also serve the employer’s legitimate [promoting] interest; ” by so demonstrating, [plaintiff] would prove that [defendant was using its] test merely as a ‘pretext’ for discrimination....

Wards Cove, — U.S. at -, 109 S.Ct. at 2124-25, 104 L.Ed.2d at 752-53 (citations omitted). The purpose of these two prongs of the Watson- Wards Cove analysis is to prevent the inducement of employers to covertly adopt Title VII-violating quotas. Id.

We are unable to determine on the basis of the record before us whether or not the Army's use of subjective performance awards is justified by a legitimate employment interest or whether or not other practices, without similarly undesirable effect, would also serve the employer’s legitimate interests. Thus, we believe a remand is necessary, and the parties should be permitted to present additional evidence on these issues.

Our reasons for remanding are the following. First, while Emanuel asserted both disparate impact and disparate treatment theories, our review of the proceedings indicates that the case proceeded under a disparate treatment theory. Such an approach, considering the Eighth Circuit law at the time, was both reasonable and an efficient allocation of resources. See, e.g., Talley v. United States, 720 F.2d 505, 507 (8th Cir.1983); Harris v. Ford Motor Co., 651 F.2d 609, 611 (8th Cir.1981); supra Part A. Second, neither the district court nor Emanuel was in a position at the time of trial to know, beyond requiring relevant statistical disparities, the narrowly drawn elements necessary under Watson and Wards Cove to prove Title VII discrimination through a disparate impact analysis. Third, neither the Supreme Court’s nor our initial remand order adequately directed the district court in this regard. Finally, remanding the matter for further eviden-tiary hearings on these issues is consistent with the results in Watson, 487 U.S. at 998-99, 108 S.Ct. at 2791, 101 L.Ed.2d at 848, where the Supreme Court remanded the matter to the court of appeals to determine whether the matter could be resolved without further proceedings in the district court, and in Wards Cove, — U.S. at - -, 109 S.Ct. at 2124-27, 104 L.Ed.2d at 750-54, where the Court remanded the matter for further proceedings at which new evidence on the issues of causation, business justification and equally effective, non-discriminatory alternatives could be presented.

Accordingly, we remand this matter to the district court with directions that evi-dentiary hearings be held on the issues of whether the use of subjective performance awards is justified by legitimate employment goals and whether other non-discriminatory practices would also serve those goals. If such alternatives exist or if subjective performance awards are not justified, the statistical disparities in the DMM workforce resulted from, for purposes of Title VII, discrimination by the Army.

At this trial, the district court is directed to permit both parties wide latitude in proof. First, the Army must produce a substantial employment justification for the use of subjective performance awards. If the Army meets its burden of production, Emanuel must persuade the trier of fact that subjective performance awards are not justified by a substantial employment goal. Second, and only if the Army prevails on the first issue, Emanuel must prove that any asserted alternative also would serve the employer’s substantial employment goal. He must then prove that the asserted alternative will not, or is less likely than the complained of practice to, result in discrimination against any protected group. 
      
      . For a detailed recitation of the facts underlying this litigation, see Emanuel v. Marsh, 828 F.2d at 439-41.
     
      
      . Alston A. Emanuel alleged that he and other black male civilian employees at the United States Army Troop Support and Aviation Material Readiness Command (TSARCOM) were denied promotions or deterred from applying for promotions because of racial discrimination.
     
      
      . Justice Kennedy took no part in the consideration or decision of Watson.
      
     
      
      . While Emanuel had received several certificates of merit and letters of appreciation, he had not received a Sustained Superior Performance Award (SSPA). Lt. Col. Straeb, who made the ultimate promotion decision, testified that he relied heavily on the fact that the white employee had received the SSPA. The SSPA is bestowed upon an employee at the sole discretion of the employee’s direct supervisor, who, in this instance, was the same white supervisor who, according to the Army, had previously discriminated against Emanuel.
     
      
      . Employees at TSARCOM generally volunteered for training. The record indicates, however, that a significant amount of training was available to an employee at the sole discretion of the employee’s supervisor. See Emanuel v. Marsh, Transcript of Trial at 1-16 (E.D.Mo. June 25, 1985). Emanuel asserts that his supervisor made training available to white employees rather than to him. The amount of training was an important factor, according to Lt. Col. Straeb, in determining whether a particular employee would be promoted.
     
      
      . SKAP ratings appraise an applicant’s skills, knowledge, ability, and personal characteristics. SKAP reports are updated annually, although an employee has the right to update the SKAP report at any time. In preparing a SKAP, the employee and his or her immediate supervisor rate the employee’s performance in key areas. Neither the employee nor the immediate supervisor may give a rating higher than a "B." A higher level supervisory officer, called a reviewing officer, may upgrade an employee's SKAP rating to an “A" at his or her discretion.
     
      
      . For a statistical analysis of TSARCOM’s employment data, see infra note 18.
     
      
      . We have been informed that the exhibits were not filed with the district court on remand. Some are in the possession of the appellant, some are in the possession of the appellee, and some are now in the possession of this Court.
     
      
      .The Supreme Court qualifies the conclusion that the plaintiff must show bottom-line racial imbalance.
      We qualify this conclusion — observing that it is only "probable” that there has been no disparate impact on minorities in such circumstances — because bottom-line racial balance is not a defense under Title VII. See Connecticut v Teal, 457 U.S. 440, 73 L Ed 2d 130, 102 S Ct 2525 (1982). Thus, even if petitioners could show that the percentage of selected applicants who are nonwhite is not significantly less than the percentage of qualified applicants who are nonwhite, respondents would still have a case under Title VII, if they could prove that some particular practice has a disparate impact on minorities, notwithstanding the bottom-line racial balance in petitioners’ workforce. See Teal, supra, at 450, 73 L Ed 2d 130, 102 S Ct [at 2532] 2525.
      
        Wards Cove, — U.S. at - n. 8, 109 S.Ct. at 2123 n. 8, 104 L.Ed.2d at 749 n. 8.
     
      
      . The preclusive effect of such evidence is in doubt. See supra note 9. At most, the Supreme Court considers such evidence relevant to, but not presumptive of, the question of whether Title VII discrimination exists.
     
      
      . While the burden of production is with the employer, the burden of persuasion remains with the disparate impact plaintiff. Wards Cove, — U.S. at -, 109 S.Ct. at 2126, 104 L.Ed.2d at 753.
     
      
      . The following graph illustrates the statistical breakdown between blacks and whites employed at various levels at the DMM:
      
        
      
      Our inquiry is limited by the static quality of the employment data provided by the employer. The Army argues that the use of static data is a conclusive defect in Emanuel’s case. We disagree. Rather, the static quality of the data relates only to its probative value.
      
      
      . Within the DMM, one American Indian is employed at GS-3. Three Hispanics are employed at GS-9, and one is employed at GS-11.
     
      
      . The standard deviation is the square root of the product of the sample (164) times the probability of selecting a black (.33) times the probability of selecting a non-black (.67). Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977).
     
      
      . Comparing blacks employed at GS-11 and above with blacks employed at GS-9 and below, the difference between the expected number of blacks and the observed number of blacks is 76, and this difference is nearly eight standard deviations. Comparing blacks employed at GS-13 and above with blacks employed at GS-12 and below, the difference between the expected number of blacks and the observed number of blacks is 11, and this difference is more than three standard deviations.
     
      
      . The same holds true if one uses either GS-12 and above or GS-13 and above as the relevant point. Using GS-12 and above, the difference between the expected number of black employees and the observed number of black employees is 21, and this is more than four standard deviations. Using GS-13 and above, the difference between the expected number of black employees is 9, and this is more than five standard deviations.
     
      
      . During the class certification hearing, the Army presented expert testimony that the statistics relied on by Emanuel, and now by this Court, fail to allow an inference of discrimination. The expert gave three reasons for this conclusion: [1] Emanuel’s statistics do not demonstrate racial imbalance between supervisory and non-supervisory positions; [2] Emanuel did not prove the statistical significance of his data; and [3] Emanuel did not provide data tending to show that qualified blacks made application for promotion to supervisory positions within the DMM but were spurned in favor of non-black applicants. We reject the expert’s interpretation of the statistics for the reasons stated above.
     
      
      . If the statistics depicting employment practices throughout TSARCOM were relevant, they too would permit an inference of racial imbalance in the entire TSARCOM workforce.
      TSARCOM has a total workforce of 4,187, 1,022 black employees and 3,165 non-black employees. In GS-12 and above, there are 850 employees. Of whom, 73 are black (8.6% of the GS-12 and above employees throughout TSAR-COM), and 753 are white (88.6% of the same unit). In GS-11 and below, there are 3,337 employees. Of the 3,337, 949 are black, constituting 28.4% of the GS-11 and below employees throughout TSARCOM, and 2,337 are white, constituting 70%. Thus, blacks comprise 28.4% of TSARCOM’s workforce classified GS-11 or below, but only 8.6% of the workforce classified GS-12 or above. Using the number of employees in the workforce classified GS-12 and above as the sample, see Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977), the standard deviation is 13. The expected number of blacks classified GS-12 and above is 241. The difference between the expected number of blacks and the observed number of blacks is 168, and this difference is more than 12 standard deviations. In light of all the underlying circumstances, such a result is statistically suspect. See abo id. (more than three standard deviations is significant).
      We have been unable to determine which data the district court employed to make its findings. The data reflecting the composition of the entire TSARCOM workforce supplied by the Army does not, according to our calculations, permit such findings. It may be that these findings are derived from an exhibit not part of the record on appeal.
     
      
      19. Blacks received 14.0% of awards given at TSARCOM. Appendix III to Part C of Equal Employment Opportunity Plan of Action at 77, U.S. Army Troop Support and Aviation Material Readiness Command (1979).
     
      
      . The evidence does not, however, support Emanuel’s allegation that the Army's use of training in promotion decisions resulted in the statistical disparities one finds within the DMM. The only data in the record on appeal demonstrates that blacks received 22.5% of the training in TSAR-COM while constituting 24.4% of TSARCOM workforce. This difference is insignificant. No data depicting the amount of training within the DMM was available on appeal.
      Finally, the record on appeal contains no data depicting the effect the SKAP ratings had on blacks attempting to receive promotion.
     