30 Fair empl.prac.cas. 1137, 30 Empl. Prac. Dec. P 33,269, 12 Fed. R. Evid. Serv. 279 Equal Employment Opportunity Commission Sylvia Cooper Constance Russell Helen Moore and Elmore Hannah, Jr. v. Federal Reserve Bank of Richmond, Phyllis Baxter Brenda Gilliam Glenda Knotts Alfred Harrison and Sherri McCorkle v. Federal Reserve Bank of Richmond

698 F.2d 633 30 Fair Empl.Prac.Cas. 1137, 30 Empl. Prac. Dec. P 33,269, 12 Fed. R. Evid. Serv. 279 EQUAL EMPLOYMENT OPPORTUNITY COMMISSION; Sylvia Cooper; Constance Russell; Helen Moore and Elmore Hannah, Jr., Appellees, v. FEDERAL RESERVE BANK OF RICHMOND, Appellant. Phyllis BAXTER; Brenda Gilliam; Glenda Knotts; Alfred Harrison and Sherri McCorkle, Appellees, v. FEDERAL RESERVE BANK OF RICHMOND, Appellant. Nos. 81-1536, 82-1259. United States Court of Appeals, Fourth Circuit. Argued July 21, 1982. Decided Jan. 11, 1983. George R. Hodges, Charlotte, N.C. (Robert D. Dearborn, Moore & Van Allen, Charlotte, N.C., on brief), for appellant; Colleen M. O'Connor (Michael J. Connolly, Gen. Counsel, Philip B. Sklover, Associate Gen. Counsel, Vella M. Fink, Asst. Gen. Counsel, Washington, D.C., on brief). J. LeVonne Chambers, John T. Nockleby, Charlotte, N.C. (Chambers, Ferguson, Watt, Wallas, Adkins & Fuller, P.A., Charlotte, N.C., on brief), for appellees. Before RUSSELL, WIDENER and HALL, Circuit Judges. DONALD RUSSELL, Circuit Judge: — 1 — This is an action initially begun by the Equal Employment Opportunity Commission [EEOC] against the defendant Federal Reserve Bank of Richmond. The defendant, chartered under the Federal Reserve Act,1 operates a branch in Charlotte, North Carolina, which provides (1) services to the member banks and the public in the Charlotte area in check collection, adjustment, and provision of cash and securities and (2) services to the United States Treasury and governmental agencies in handling savings bonds and government securities, including food stamp activities. In performing these functions, the bank distributed its various employees, numbering from 350 to 450 in the period 1974-78, largely of a clerical or managerial type, among 16 departments. The job ratings of its employees ranged from pay grade 3 to pay grade 16, with an ungraded officer group of about 8. New employees were generally assigned to pay grades 3 or 4 and assignments among departments were based on "educational background and prior work experience." All employees were evaluated annually on a scale of 1 (unsatisfactory) to 5 (exceptional). Since 1973, the branch had generally posted notices of vacancies by advertising in Southern Accent, a news circular prepared by and distributed to bank employees. Employees were invited to indicate their interest in any posted vacancy. Promotions were generally made within the work force. — 2 — In its complaint the EEOC charged the defendant with engaging in racially discriminatory practices and policies in failure to promote blacks at its Charlotte, North Carolina, branch in violation of Section 703(a) of Title VII, 42 U.S.C. Sec. 2000e. After the commencement of the action, four former or present employees of the defendant at the Charlotte branch petitioned to intervene in order to assert under Sec. 1981, 42 U.S.C., and Title VII individual and class claims of racial and sex discrimination "in promotions, wages, job assignments and terms and conditions of employment" on behalf "of all blacks and females who worked for the defendant at any time since July 2, 1965." The petition to intervene was allowed and the intervenors were, by a consent order, certified as the class representatives to maintain an action charging racial discriminatory practices and policies in the particulars stated in the petition for certification filed by the intervenors but with the class narrowed to include only employees who may have been hired after January 3, 1974. In the same consent order, the EEOC itself agreed to limit its claim of discrimination to "only ... those black persons who worked for the defendant since January 3, 1974." — 3 — After joinder of issues and considerable discovery, the actions both of the EEOC and of the plaintiffs-intervenors came on for trial in September, 1980. Following the completion of the trial, the District Court on October 29, 1980, filed its "Memorandum of Decision." It ruled in this Memorandum: (1) That the defendant had discriminated against the intervenor Cooper "by failing to promote her from her job as a settlement clerk ... to a position as utility supervisor" and against the intervenor Russell "by failing to promote her to a utility clerk position from her position as a utility operator" and "by discharging her ... in retaliation for her filing charges of discrimination with the Equal Employment Opportunity Commission;" (2) that the intervenors Moore and Hannah had not "shown the court that they suffered any discrimination on account of their race" and that their claims should be denied; and (3) that defendant had engaged in a pattern and practice of discrimination from 1974 through 1978 by failing to "afford black employees opportunities for advancement and assignment equal to opportunities afforded white employees [only] in pay grades 4 and 5." The "Memorandum" concluded with the direction to "[c]ounsel for plaintiffs ... to propose and submit by December 1, 1980: 1. Proposed findings of fact and conclusions of law consistent with the above findings ...." — 4 — The District Court filed on May 29, 1981, findings of fact and conclusions of law. In these it found discrimination by the defendant in the class action, in pay grades 4 and 5, and in individual discrimination claims of the intervenors, Russell and Cooper. It dismissed the individual discrimination claims of Hannah and Moore. While the District Court, as had the District Court in Amstar Corp. v. Domino's Pizza, Inc., 615 F.2d 252, 258 (5th Cir.), cert. denied, 449 U.S. 899, 101 S.Ct. 268, 66 L.Ed.2d 129 (1980), stated that "[t]he findings and conclusions herein, however, as well as the Judgment which follows are those of the Court based on an independent review of the record and consideration of the submissions of the parties," such statement was adopted verbatim from the plaintiffs' proposed findings and conclusions; in fact, the statement appears in exactly the same words and in the exact same place as footnote 3 in both the proposed findings and conclusions submitted by the plaintiffs and in the District Court's findings of fact and conclusions of law. Moreover, the Court's 37-page findings and conclusions were almost word for word copies of the findings and conclusions submitted by the plaintiffs. — 5 — From the judgment entered pursuant to the findings and conclusions of the District Court, as well as from an order granting an interim allowance of attorney's fees to the intervenors-plaintiffs' counsel, the defendant has appealed. The plaintiffs did not appeal the dismissal of the individual claims of the intervenors Hannah and Moore or the denial of relief in the class claim in all pay grades above pay grade 5. We reverse. — 6 — In considering such appeal we shall treat first the decision in the class action claim and, second, the decision on the individual claims of intervenors Cooper and Russell. Before addressing the substantive merits of the class action claim, however, it is necessary to resolve two preliminary points pressed by the defendant. The first of these relates to the nature or type of the class action claims, i.e., are they disparate treatment or disparate impact claims or both? The District Court's "Memorandum of Decision" does not identify the class action claim as either a disparate treatment or a disparate impact claim but in the findings and conclusions later adopted by the Court it is clear that the class action is being treated as both a disparate treatment and disparate impact claim. The defendant, on the other hand, asserts that the class action should be treated solely as a disparate treatment action. We agree. — 7 — In Stastny v. Southern Bell Tel. & Tel. Co., 628 F.2d 267 at 274, n. 10 (4th Cir.1980), we stated the necessary elements of a disparate impact claim. These elements, as there declared, are: — 8 — "As is now well recognized, the class action commonality criteria are, in general, more easily met when a disparate impact rather than a disparate treatment theory underlies a class claim. The disparate impact 'pattern or practice' is typically based upon an objective standard applied evenly and automatically to affected employees: an intelligence or aptitude test, e.g., Griggs v. Duke Power Co., 401 U.S. 424, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971); an educational requirement, id.; a physical requirement, e.g., Weeks v. Southern Bell Tel. & Tel. Co., 408 F.2d 228 (5th Cir.1969). Both the existence and the 'common reach' of such objectively applied patterns or practices are likely to be indisputable from the outset, so that no real commonality problems for class action maintenance ever arise in this regard. On the other hand, the disparate treatment pattern or practice must be one based upon a specific intent to discriminate against an entire group, to treat it as a group less favorably simply because of its sex (or other impermissible reason). The greater intrinsic difficulty in establishing the existence and common reach of such a subjectively based practice is obvious. See Hauck v. Xerox Corp., 78 F.R.D. 375, 378 (E.D.Pa.1978). In the instant case, it is clear that plaintiffs' ultimate reliance would of necessity have been upon showing a pattern of disparate treatment. There is no suggestion in the record of a Griggs-type objectively imposed practice having discriminatory disparate impact." — 9 — We reiterated those criteria for a disparate impact claim in the recent case of Pope v. City of Hickory, N.C., 679 F.2d 20, 22 (4th Cir.1982): — 10 — " 'The disparate impact model applies only when an employer has instituted a specific procedure, usually a selection criterion for employment, [such as an aptitude or intelligence test, or height and weight requirements] that can be shown to have a causal connection to a class based imbalance in the [employer's] work force' and has been said not to be 'the appropriate vehicle from which to launch a wide ranging attack on the cumulative effect of a company's employment practices.' Pouncy v. Prudential Ins. Co. of America, 668 F.2d 795, 800 (5th Cir.1982). It is obvious that the plaintiff is not complaining in this case of some employment practice or procedure of the defendant, which, though neutral or fair on its face, has a discriminatory impact on blacks and thus does not fit within the model disparate impact claim." — 11 — It is manifest that the plaintiffs' class action claim does not meet the criteria for a disparate impact claim as those criteria are identified in Stastny and Pope. There was no evidence whatsoever of any "objective standard, applied evenly and automatically" in promotions, such as a physical requirement with respect to height, as in Dothard v. Rawlinson, 433 U.S. 321, 324, 97 S.Ct. 2720, 2724, 53 L.Ed.2d 786 (1977), or a high school diploma, as in Griggs v. Duke Power Co., 401 U.S. 424, 427, 91 S.Ct. 849, 851, 28 L.Ed.2d 158 (1971), or a minimum passing score on an aptitude test, as in Albemarle Paper Co. v. Moody, 422 U.S. 405, 410-11, 95 S.Ct. 2362, 2368, 45 L.Ed.2d 280 (1975) and Connecticut v. Teal, --- U.S. ----, 102 S.Ct. 2525, 73 L.Ed.2d 130 (1982). The claim here is a pattern or practice of intentional discrimination against an entire group by treating it less favorably because of race. That is the typical disparate treatment case. This case should accordingly be properly treated as such. However, the result reached by us would not be substantially different whether the class action be considered as a disparate impact or a disparate treatment case. Cf., Wright v. National Archives & Records Service, 609 F.2d 702 (4th Cir.1979). — 12 — Secondly, the defendant questions the weight, if any, to be accorded by us to the findings of fact and conclusions of law in this case. It is defendant's contention that the circumstance that these findings and conclusions were prepared by plaintiffs' counsel at the direction of the District Court and were adopted by the Court practically verbatim weakens, if it does not undermine completely, the reliability of and the weight to be accorded such findings and conclusions.2 There can be no dispute that the District Court itself, in its "Memorandum of Decision," actually made no findings of fact or conclusions of law as those terms are used and construed in Rule 52(a), Fed.R.Civ.P. It confined itself in this Memorandum to a purely conclusory statement that "the defendant [had] engaged in a pattern and practice of discrimination from 1974 through 1978 by failing to afford black employees opportunities ... afforded white employees in pay grades 4 and 5." Such a statement of ultimate fact is not a finding of fact reviewable under the "clearly erroneous" rule, and sustainable only if adequate supportive subsidiary findings are made. Hicks v. United States, 368 F.2d 626, 631 (4th Cir.1966); Castaneda v. Pickard, 648 F.2d 989, 1001 (5th Cir.1981) (with particular reference to a "discrimination" finding in Title VII actions). Apart from this statement, the District Court stated only that the "[d]efendant [had] not submitted statistical evidence rebutting plaintiff-intervenor's case with respect to discrimination in those grades." It did direct counsel for the plaintiffs to submit "Proposed findings of fact and conclusions of law consistent with the above [conclusory] findings" of discrimination and of non-rebuttal. It is the findings and conclusions so submitted by plaintiffs' counsel which the defendant attacks as entitled to little or no weight for accepting without question the plaintiffs' contentions as stated in the submitted findings, and for disregarding entirely in those findings the evidence and contentions offered by it. — 13 — We, along with other courts, have on a number of occasions--one as recently as a few months ago in Holsey v. Armour & Company, 683 F.2d 864 (4th Cir.1982)--expressed our disapproval of a trial court's practice of announcing its decision and then requesting the prevailing party to prepare findings of fact and conclusions of law which the court adopts almost word-for-word in support of its previously announced decision. The reason for such disapproval is inherent in Rule 52(a), Fed.R.Civ.P., a fair compliance with which "requires the trial court to find the facts on every material issue, including relevant subsidiary issues, and to 'state separately' its conclusions thereon with clarity." Kruger v. Purcell, 300 F.2d 830, 831 (3d Cir.1962); De Medina v. Reinhardt, 686 F.2d 997, 1011 (D.C.Cir.1982).3 As the Court in Sims v. Greene, 161 F.2d 87, 89 (3d Cir.1947), said in language quoted and approved by us in Consolidation Coal Co. v. Disabled Miners of So.W.Va., 442 F.2d 1261, 1269 (4th Cir.), cert. denied, 404 U.S. 911, 92 S.Ct. 228, 30 L.Ed.2d 184 (1971), "[t]he conclusion is inescapable that since a district court is required by the rule [Rule 52(a) ] to make findings of fact, the findings must be based on something more than a one-sided presentation of the evidence," or, as the Court in the same opinion repeated, "[f]inding facts [under Rule 52(a) ] requires the exercise by an impartial tribunal of its function of weighing and appraising evidence offered, not by one party to the controversy alone, but by both."4 See to the same effect: McManus v. Midland Valley Lumber Co., 348 F.2d 898, 900 (4th Cir.1962) ("... must necessarily consider all available evidence bearing upon the issue"); Burgess v. Farrell Lines, Inc., 335 F.2d 885, 889 (4th Cir.1964); Sligh v. Columbia, Newberry and Laurens Railroad Co., 250 F.Supp. 490, 491 (D.S.C.1966), aff'd. 370 F.2d 979 (4th Cir.), cert. denied, 386 U.S. 1007, 87 S.Ct. 1349, 18 L.Ed.2d 434. — 14 — This application of Rule 52(a), it is true, does not require the trial court to deal with every piece of evidence in the record or every argument made during the proceedings, whatever their value, but it does mean that "[t]he reviewing court deserves the assurance [given by even-handed consideration of the evidence of both parties] that the trial court has come to grips with apparently irreconcilable conflicts in the evidence ... and has distilled therefrom true facts in the crucible of his conscience." Golf City, Inc. v. Sporting Goods Co., Inc., 555 F.2d 426, 435 (5th Cir.1977). — 15 — All these considerations prompted the Supreme Court in U.S. v. Crescent Amusement Co., 323 U.S. 173, 184-85, 65 S.Ct. 254, 259-260, 89 L.Ed. 160 (1944) to comment that the adoption of "findings [proposed by one of the parties to the suit and adopted by the trial judge] leave much to be desired in light of this function of the trial court," under the Rules. This is so because an appellate court will " 'feel slightly more confident in concluding that important evidence has been overlooked or inadequately considered' when factual findings were not the product of personal analysis and determination by the trial judge." James v. Stockham Valves & Fittings Co., 559 F.2d 310, 314, n. 1 (5th Cir.), cert. denied, 434 U.S. 1034, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978). Nor is that disquiet, prompted by the trial court's adoption of one party's findings and conclusions, relieved by any statement in such findings and conclusions that the trial court had " 'individually considered' them and adopted them because it 'believed them to be factually and legally correct'; [even though] a cursory reading of the district court's memorandum leaves one with the impression that it was indeed written by the prevailing party to a bitter dispute." Amstar Corp. v. Domino's Pizza, Inc., supra, 615 F.2d at 258. — 16 — The adoption by the District Court of proposed findings and conclusions, though disapproved, will not, however, warrant reversal of the cause per se nor does it mean that the " 'clearly erroneous' " rule of Rule 52(a) will not be applied at all, simply because the findings and conclusions were developed by one of the parties and adopted in course by the judge. As the Court in Flowers v. Crouch-Walker Corp., 552 F.2d 1277, 1284 (7th Cir.1977), after observing that "the district court [had] adopted [in that case] without change findings of fact and conclusions of law prepared by the defendant," said: "[a] critical view of a challenged finding is appropriate where, as here, the findings of fact and conclusions of law of which it is a part were not the original product of a disinterested mind." Again, in Photo Electronics Corp. v. England, 581 F.2d 772, 777 (9th Cir.1978), the Ninth Circuit expressed itself similarly, declaring that, while "the fact that the trial judge has adopted proposed findings does not, by itself, warrant reversal ... it does raise the possibility that there was insufficient independent evaluation of the evidence and may cause the losing party to believe that his position has not been given the consideration it deserves. These concerns have caused us to call for more careful scrutiny of adopted findings." See also, United States v. State of Wash., 641 F.2d 1368, 1371 (9th Cir.1981), cert. denied, 454 U.S. 1143, 102 S.Ct. 1001, 71 L.Ed.2d 294, ("Verbatim adoption of proposed findings of fact by the district court ... calls for close scrutiny by an appellate court"); and Shlensky v. Dorsey, 574 F.2d 131, 149 (3d Cir.1978) (such adoption requires the appellate court to "examine them more narrowly"). — 17 — When the findings of fact and conclusions of law adopted by the District Court have been given that "careful scrutiny" by the appellate court that is required under such circumstances and have been "more narrowly" examined than findings and conclusions which, because developed independently by the trial judge, provide assurance that the District Judge making the findings and conclusions "did indeed consider all the factual questions thoroughly and ... guarantee[s] that each word in the finding [was] impartially chosen," Louis Dreyfus & Cie. v. Panama Canal Co., 298 F.2d 733, 738 (5th Cir.1962, Wisdom, J.), and when, the reviewing court, on the entire record, "is left [after such review] with the definite and firm conviction that a mistake has been committed," United States v. Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 541, 92 L.Ed. 746 (1948), or it is convinced that "the result in a particular case does not reflect the truth and right of the case," Armstrong Cork Co. v. World Carpets, Inc., 597 F.2d 496, 501 (5th Cir.1979), cert. denied, 444 U.S. 932, 100 S.Ct. 277, 62 L.Ed.2d 190, it is the duty of the appellate court to reverse the findings and conclusions as clearly erroneous. — 18 — It is important, too, to note, before addressing the merits of the case, the limited nature of the District Court's finding of discrimination in the class action, as declared by it in both its "Memorandum of Decision" and in the subsequent findings of fact and conclusions of law adopted by it. In its "Memorandum," the District Court, while finding discrimination in affording "black employees opportunities for advancement and assignment equal to opportunities afforded white employees in pay grades 4 and 5," made it clear that "[o]ther than in the above particulars, [i.e., in promotions in pay grades 4 and 5], however, there does not appear to be a pattern and practice of discrimination pervasive enough for the court to order relief." — 19 — This narrowing of the issues in the class action to promotions out of pay grades 4 and 5 was restated in the later findings and conclusions. Thus, finding of fact # 56, as adopted by the District Court is: — 20 — "Except for promotions from pay grades 4 and 5, plaintiffs' and defendant's data ... indicated no statistically significant difference in the initial job assignments and pay grades, performance evaluations or promotion of black and white employees." — 21 — The same ruling was included in the District Court's conclusions of law # 27: — 22 — "The Court concludes that there was no showing that the bank had discriminated against black employees with respect to promotions out of grades 6 and above, and that defendant did not violate Title VII or 42 U.S.C. Sec. 1981 with respect to promotions out of grade 6 and above." — 23 — Moreover, the finding of discrimination in pay grades 4 and 5 was one of a pattern and practice of discrimination in those grades. The establishment of a pattern or practice of discrimination requires proof of "more than the mere occurrence of isolated or 'accidental' or sporadic discriminatory acts" and depends upon a finding by "a preponderance of the evidence that racial discrimination was the [defendant's] standard operating procedure--the regular rather than the unusual practice." Teamsters v. United States, 431 U.S. 324, 336, 97 S.Ct. 1843, 1854, 52 L.Ed.2d 396 (1977). — 24 — With the issues in the class action claim thus limited the District Court proceeded to state its conclusions on those issues (Conclusion # 17): — 25 — "Black employees assigned to pay grades 4 and 5 have, during the relevant time period, been retained in these grades for longer periods than comparable white employees and passed over for promotion solely because of their race and color. Using two statistical methods, plaintiffs demonstrated disparate treatment by defendant of black employees in these grades, that black employees have been retained in these grades for significantly longer periods even when their relative qualifications are equal to white employees and that the disparate treatment is statistically significant at the 5 percent level." — 26 — The Court earlier in its findings had set forth the factual basis for that conclusion. It declared in such findings that the statistical evidence proffered by the plaintiffs and the defendant as well as "[t]he oral testimony of class members" had established "a prima facie case that black employees in pay grades 4 and 5 [had] been denied promotions from these grades solely because of their race," that, in response, the defendant had "offered no explanation for its unfavorable treatment of black employees in pay grades 4 and 5," and "therefore [it found], based on all of the evidence of record, that black employees who [had] been assigned to pay grades 4 and 5 between 1974 and the date of trial [had] been deprived of rights under Title VII." It is manifest from these statements that the District Court's findings and conclusions rest on "the statistical evidence" in the record and "the oral testimony of class members."Before examining the statistical evidence relied on by the District Court for support for these findings and conclusions, we would review the "oral testimony of class members" which the District Court found supplemented the statistical evidence in establishing discrimination in pay grades 4 and 5. There were only three "class members" who testified, and to whom the finding of supportive "oral testimony of class members" could apply in connection with discrimination in promotions out of pay grades 4 and 5. These were Alfred Harrison, Elmore Hannah and Emma Ruffin, they being the only live employee-witnesses who were members of a class of employees not promoted out of pay grades 4 and 5.5 The claim of Elmore Hannah, one of the three non-promoted witnesses in pay grades 4 or 5, was fully discussed and the District Court made very clear findings on his claim. The Court found that Hannah had been "employed through the Bank's handicapped program" at pay grade 3 and, when tried, at higher grade level jobs, had "failed to demonstrate that he was qualified or able to perform the job positions he requested." His claim was accordingly dismissed by the District Court as without merit. The claim of Hannah was accordingly unavailable as a support for any finding of discrimination; indeed, the defendant's efforts at placing Hannah in higher level jobs demonstrated, if anything, an absence of discriminatory practice on defendant's part against handicapped blacks. That leaves the "oral testimony" of Ruffin and Harrison6 as that of the only "class members," out of the countless numbers who had been employed in these two classes, who could be said to support the statistical evidence on which the District Court rested its findings of a pattern of discrimination, as found in this case. — 27 — This case accordingly presents quite a contrast with Teamsters where the "oral testimony of class members" demonstrated 40 cases of specific instances of discrimination in support of the statistical evidence offered by plaintiffs or with that in our own case of Chisholm v. United States Postal Service, 665 F.2d 482, 495 (4th Cir.1981), where there were 20 "class members" testifying of individual discrimination. Here all we have is the testimony of but two class members testifying of individual discrimination in promotion out of either pay grade 4 or pay grade 5 on which a finding of discriminatory practices can be rested. This is even less of a presentation of oral testimony in support of a pattern of discrimination than that found wanting in Ste. Marie v. Eastern R. Ass'n, 650 F.2d 395, 405-06 (2d Cir.1981), where the Court declared that the small number of incidents of discrimination in promotion over a period of years in that case "would be insufficient to support the inference of a routine or regular practice of discrimination ...,"7 or, in Goff v. Continental Oil Co., 678 F.2d 593, 597 (5th Cir.1982), where the Court held that "even if all three witnesses' accounts of racial discrimination were true, this evidence would not have been enough to prove a pattern or practice of company-wide discrimination by Conoco." It follows that these two incidents of failure to promote Ruffin or Harrison, even if regarded as discriminatory, (which we assume only arguendo ), would not support the District Court's finding of a pattern of class discrimination in promotions out of grades 4 or 5 or offer any reinforcement to an inference of discrimination derived from statistical proof; under Ste. Marie v. Eastern R. Ass'n and Goff, there was an absence of sufficient evidence, based on class members' testimony, to provide a basis for a finding of a pattern of discrimination in promotion out of pay grades 4 and 5. — 28 — It is true that a number of "live" witnesses other than Ruffin and Harrison testified for the plaintiffs. This number included the four plaintiffs Cooper, Moore, Hannah and Russell and certain other past or present employees who moved, after adverse decision, to intervene as plaintiff-intervenors. This latter group consisted of Phyllis Baxter, Brenda Gilliam, Glenda Knott, Alfred Harrison and Sherri McCorkle. In denying the motion the District Court stated that all intervenors "in grades higher than grade 5" were not members of the class in whose favor the District Court had found "classwide discrimination." By this test, Cooper, Moore, Russell, Baxter, Gilliam, Knott and McCorkle were not members of the class in which discrimination was found and their testimony could not have been included within the District Court's term "oral testimony of class members," complaining of promotion out of either pay grade 4 or pay grade 5; only the testimony of Ruffin and Harrison met that qualifying standard. However, it is interesting to review the employment records of these witnesses, other than Ruffin and Harrison, in order to see how they were promoted out of pay grades 4 and 5. Thus Baxter hired at pay grade 5, was promoted to pay grade 6 seven months after she was hired. Gilliam, hired at pay grade 4, was promoted to pay grade 5 within approximately 17 months, and within eleven months afterward to pay grade 6; McCorkle, hired at pay grade 4, had in 24 months been promoted two grades to grade 6; and Knott, hired at grade 5, was promoted to grade 6 within 6 months after employment at the Charlotte branch. Russell was employed at pay grade 4, was promoted twelve months later to pay grade 5, and within a month or so, to pay grade 6. Cooper was employed initially at pay grade 3, was promoted two months later to pay grade 4, fifteen months later to pay grade 5, eleven months later to pay grade 6. The intervenor Hannah was found by the District Court not to have suffered discrimination. — 29 — The experiences of these seven black employees, (Cooper, Russell, Moore, Baxter, Gilliam, Knott and McCorkle) all of whom, with the exception of Ruffin, Harrison and Hannah, had promoted out of pay grades 4 and 5 in periods either less than or equivalent to the average of white employees, far from supporting any proof of discrimination in promotions out of pay grades 4 and 5, represented strong proof of the absence of class-wide discrimination in promotion out of pay grades 4 and 5; and since Ruffin's and Harrison's testimony, which is the only "oral testimony of class members" that could in any circumstances be said to support a charge of a pattern of class discrimination, is insufficient, the District Court's finding of a pattern of class discrimination can find no support in the "oral testimony of class members" in pay grades 4 and 5 and must find its basis in the statistical evidence and in that evidence alone.8 — 30 — Statistics, when properly authenticated, constitute an accepted form of circumstantial evidence of discrimination and may sometimes be sufficient to establish without more prima facie proof of discrimination. But statistics "come in infinite variety" and their usefulness or weight "depend[s] on all of the surrounding facts and circumstances," Teamsters v. United States, 431 U.S. at 340, 97 S.Ct. at 1856, and on " 'the existence of proper supportive facts and the absence of variables which would undermine the reasonableness of the inference of discrimination which is drawn' " therefrom, White v. City of San Diego, 605 F.2d 455, 460 (9th Cir.1979). Inaccuracies or variations in data or in the formulae used to test such data may easily lead to different, contradictory, or even misleading conclusions by experts. This fact prompted one court to comment that too often statistical conclusions "appear to depend in large part on the side producing them ...." Stastny v. Southern Bell Tel. & Tel. Co., 458 F.Supp. 314, 324 (W.D.N.C.) aff'd. in part and rev'd. in part, 628 F.2d 267 (4th Cir.1980). And the sophisticated way in which supporting data may be used in developing statistical models in discrimination cases has lead another Court to caution about "the manipulability of statistics in inquiries of [that] sort," Bilingual Bicultural Coalition, Etc. v. F.C.C., 595 F.2d 621, 625, n. 7 (D.C.Cir.1978), and still another to suggest that Title VII cases too often develop into "contests between college professor statisticians who revel in discoursing about advanced statistical theory" and propounding increasingly complex statistical models. Otero v. Mesa Cty. Valley Sch. Dist. No. 51, 470 F.Supp. 326, 331 (D.Colo.), aff'd., 628 F.2d 1271 (10th Cir.1980).9 — 31 — We do not mean to suggest that statistical conclusions, supported by adequate and accurate supporting data and developed through the use of neutral and impartial tests, are not to be given weight, sometimes compelling weight if there is no rebutting evidence, in resolving claims of racial and sex discrimination. We have repeatedly relied on such evidence in a proper case in reaching our decisions and the Supreme Court itself has approved the use of such evidence. In fact, as we said in Equal Employment Opportunity Com'n v. Am. Nat. Bank, 652 F.2d 1176 (4th Cir.1981), a "prima facie showing may in a proper case be made out by statistics alone (citing Teamsters,10 Hazelwood,11 and Barnett12 ), or by a cumulation of evidence, including statistics, patterns, practices, general policies, or specific instances of discrimination." Id. at 1188. But statistical evidence, like any other type of circumstantial evidence, "must not be accepted uncritically," Logan v. General Fireproofing Company, 521 F.2d 881, 883 (4th Cir.1971), and, because of the sophistication and complexity of many of the statistical models being used in discrimination cases by professional econometricians, courts must give "close scrutiny [to the] empirical proof" on which the models are erected, Pettway v. American Cast Iron Company, 494 F.2d 211, 231, n. 44 (5th Cir.1974), in order to guard against the use of statistical data which may have been "segmented and particularized and fashioned to obtain a desired result," Equal Employment Opportunity v. Data Point Corp., 570 F.2d 1264, 1269 (5th Cir.1978). As one authority in the field of discrimination litigation has stated: "[T]he Supreme Court's directives in Teamsters and Hazelwood to evaluate statistical proofs clearly in light of all relevant circumstances reinforce decisions like Robinson v. Dallas,13 Olson v. Philco-Ford14 and Keyes v. Lenoir-Rhyne15 and make clear that in no case should there be a blind adherence to the proposition that mere statistical imbalance equals discrimination." Morris, Current Trends in the Use (and Misuse) of Statistics in Employment Discrimination Litigation, Second Edition, 1979, Equal Employment Advisory Council, p. 51.16 "To be legally cognizable, the pattern [of disparity] revealed must be at least 'significantly discriminatory,' Dothard v. Rawlinson, 433 U.S. 321, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977); at minimum, the percentages must be 'markedly disproportionate,' Griggs v. Duke Power Company, 401 U.S. 424, 91 S.Ct. 849, 852, 28 L.Ed.2d 158 (1971);" and "[s]tatistical proof failing to show a 'marked disproportion', Griggs, 91 S.Ct. at 852, by definition cannot show the 'gross disparity,' Teamsters [97 S.Ct.] at 1856, n. 20, necessary to sustain allegations of disparate treatment." Rivera v. City of Wichita Falls, 665 F.2d 531, 534-35 and 535, n. 5 (5th Cir.1982). — 32 — Of course, statistical evidence, like any other evidence, is always subject to rebuttal and this rebuttal may assume a number of forms. In Dothard v. Rawlinson, Justice Rehnquist, concurring, said that the defendants in a discrimination case "may endeavor [in rebuttal] to impeach the reliability of the statistical evidence, they may offer rebutting evidence, or they may disparage in arguments or in briefs the probative weight which the plaintiffs' evidence should be accorded." [433 U.S. at 338-39, 97 S.Ct. at 2731] And in Teamsters, the Supreme Court declared that statistical evidence may be rebutted by "demonstrating that [the plaintiff's] proof is either inaccurate or insignificant." [431 U.S. at 360, 97 S.Ct. at 1867.] A similar observation was made by us in Roman v. ESB, Inc., 550 F.2d 1343, 1350 (4th Cir.1976): — 33 — "We do not believe that isolated bits of statistical information necessarily make a prima facie case when divorced from other and contrary statistics and from the statistical picture of all the employment at the plant. We also think the absence of other evidence of discrimination should be considered in determining whether a prima facie case is made, just as the presence of other evidence of discrimination should be considered in arriving at the same conclusion." — 34 — To sum up, statistical evidence is circumstantial in character and its acceptability depends on the magnitude of the disparity it reflects, the relevance of its supporting data, and other circumstances in the case supportive of or in rebuttal of a hypothesis of discrimination. And, in reviewing statistical evidence and its supporting data, the Court must give consideration and evaluate fairly such conflicting opinions and hypotheses as may have been presented, tempering its conclusion with what one Court has described as "a pinch of common sense." Otero v. Mesa Cty. Valley Sch. Dist. No. 51, [470 F.Supp. at 335]. — 35 — We should also note an important issue that arises in any review of statistical evidence and this is the determination of the meaning of the term statistical significance in this context.17 There are numerous rules stated by econometricians for determining "statistical significance" in discrimination cases, though as Agid, Fair Employment Litigation, at 541 puts it, "[t]here are no hard and fast rules as to how much of a disparity, is 'enough' to establish a prima facie case or withstand various defenses." Some statisticians base their opinion on the "five per cent level" of disparity in black and white employment as the measuring standard for statistical significance in discrimination cases. A few even in some circumstances, using "a one-tailed probability level to facilitate obtaining 'significant' results," employ a level of 1.64 standard deviations for their opinion of statistical significance. See Friedman, Introduction to Statistics, 146 (Random House, 1972). However, "[t]he adoption of a particular level or test of statistical significance, ... is arbitrary," Smith and Abram, Quantitative Analysis and Proof of Employment Discrimination, 1981 U.Ill.L.Rev. 33 at 43, and a recent commentator has wisely cautioned that "modern statisticians are critical of using five percent or any other level as an absolute standard of significance" in this connection.18 — 36 — The Supreme Court itself, though disclaiming any intention "to suggest that precise calculations of statistical significance are necessary in employing statistical proof," has stated that standard deviations of more than "two or three" represent a minimum for statistical significance.19 Obedient to our understanding of this rule of the Supreme Court in Hazelwood School District v. United States, 433 U.S. at 311-12, n. 17, 97 S.Ct. at 2743, n. 17, and Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977), we have adopted the rule that the proper method for determining "legal significance" on the basis of statistical evidence is through the use of the standard deviation analysis, and in the cases where either the Supreme Court or we have used that standard, we have followed the binomial distribution test. Moultrie v. Martin, 690 F.2d 1078 (4th Cir.1982). Moreover, in American National Bank, supra, we held in interpreting the decisions in Hazelwood and Castaneda, as we understood them, that courts "should be extremely cautious in drawing any conclusions [of legal significance] from standard deviations in the range of one to three," but that a statistical analysis "with standard deviations of more than three" could "safely be used ... absolutely to confirm" an inference of some "disparity."20 It will be noted that we have used the term "legal significance" in this context, rather than "statistical significance." We have done so advisedly for in this connection "statistical significance" to the econometrician may not be and often is not the same as "legal significance," the determination of which, after all, is an issue solely for the court and not for an expert witness.21 This is recognized in Baldus and Cole, Statistical Proof of Discrimination, 308 (McGraw-Hill, 1980) in which the authors state that "what is or is not statistically significant, that judgment is a legal determination properly made by the court and not by an expert." Thus, we emphasize that number comparisons which have statistical significance may not necessarily have legal significance but, while statistical significance as measured by the standards of acceptable statistical principles will not necessarily be legally significant, a finding of legally significant variations based on statistical evidence may not be made in the absence of a finding of statistical significance within acceptable confidence levels in any event. — 37 — With these principles in mind, we approach the statistical evidence on which the District Court in this case relied for the result it reached. The centerpiece in the statistical findings made by the District Court is represented in its Finding # 57, which basically consists of two Tables. It was primarily on the basis of these two Tables, as submitted in the testimony of plaintiffs' expert, that the District Court found "statistically significant disparity" in promotions of blacks in pay grades 4 and 5 in this case. These Tables are an exact reproduction of exhibits 34a and 35a (except that the tables in the finding omit the standard error figures as they appear on the exhibits) as introduced by the plaintiffs through their expert witness Dr. Hoffman. These two exhibits purport to show (1) the exact number of employees in the two relevant pay grades of 4 and 5 for the four years in question, (2) the percentage of blacks among such employees, (3) the total promotions in each year during such period, (4) the number of such promotees who were black, (5) the expected number of black promotees if black promotions had coincided precisely with the black percentage of the overall employee force in the two grades, and finally, (6) the difference between the expected number of black promotions and the actual number of blacks promoted in such pay grades in the relevant years. — 38 — There are a number of significant facts to be observed about the numbers used in these two Tables which are crucial in any examination of the District Court's findings derived therefrom. First, the number of employees in each pay grade for any one of the four years in issue, as listed in these Tables, is neither "Total Incumbents at Beginning of Interval" (that is, at the beginning of the year in question) nor, as the Tables themselves state, "Total Incumbents at End of Interval" (that is, after the end of the year in question). The number of employees in the pay grade for any year, as used in the Tables, is the number of employees who were employed in the pay grade at the beginning of that year and who remained in the pay grade at the end of that year. In other words, any employee who quit, was promoted out, or was fired, or was replaced during the year is not counted in this calculation. This method of calculating the employee numbers out of which promotions were to be made in any stated year increased, particularly in pay grade 4, the percentage of black employees over what it would have been had the Tables used the actual number of employees in the pay grade at the beginning of the stated year, or the actual number at the end of the year, or any average of the two. — 39 — More important for meaningful analysis than this method of calculating the employee mass for determination of the sample is the manner in which the expert calculated the number of black promotions made in the grades for each of the years in question. It was undisputed that the actual number of black promotions in pay grade 4 for the years 1974-1977, for instance, was 39 but the Tables used by the District Court gave this number as 35. The reason for the difference is that any employee, whether black or white, who, after promotion might have terminated voluntarily or involuntarily, was simply eliminated from the calculations of black promotees during that year, as set forth in these Tables. Plaintiffs' witness admitted that such a procedure where only the number of black promotees who, after promotions, continued to be employed and not the actual, correct number of black promotions was used in the calculations, "change[d] the statistics dramatically in the case of grade 4."22 — 40 — The reasons assigned by the expert witness for the use of such artificial numbers on promotions of blacks during the relevant years in his Tables were that, to quote the expert, "there may be promotions that are given to individuals which are not permanent in nature, which leave, which the incumbent leaves quickly after he is promoted and for a variety of reasons--either he's going back to school or he's dissatisfied with his work or he's dissatisfied with the promotions or he fails at the promotion and wishes to leave employment." All of these promotees should be eliminated in the calculations of annual black promotions in the expert's judgment. The District Court did not inquire into the reasonableness of this justification for the omission of such promotees in stating the number of black promotions for a fair and impartial analysis in the critical years, nor are we able to find any basis in the record for such a justification. It seems difficult to assume that when an employee, whether white or black, has requested a promotion to a particular job vacancy (that is the way the evidence shows promotions were generally made) he would be "dissatisfied with the promotion" he had sought and would quit because he got it. Similarly, it is a little odd that, when it is the plaintiffs' contention (which, incidentally, is somewhat specious, as we see later) that it took an average of almost four years for a black to be promoted out of grade 4, the defendant would be promoting a black schoolboy, whose work life would normally be no more than the three school vacation months and who would quit at the end of his school vacation. Moreover, if the question is whether the defendant intentionally failed to promote blacks in pay grades 4 and 5 in a particular year, it would seem that the correct test figure should be the actual promotions made in that particular year out of those pay grades. We are unable to perceive any rational basis for using an inaccurate figure for promotions during the pertinent years for black promotions in exhibits 34a and 35a unless it was "to obtain a desired result" of a standard deviation in excess of -2. Cf., Equal Employment Opportunity v. Datapoint Corp., 570 F.2d 1264 (5th Cir.). Certainly, by reducing the number of promotions, the expert increased the standard deviation but it was an increase achieved not by analyzing the actual numbers but by reducing the number of the actual promotions, thereby diminishing significantly the validity of any calculation of standard deviation based on such artificial numbers. We find exhibits 34a and 35a are fatally flawed by the manner in which they were prepared and by the assumptions on which they were based. — 41 — It is, however, equally interesting to see the method which was adopted without question by the District Court in its critical finding of standard deviations as shown by these Tables. The District Court, in these findings, accepted without question the plaintiffs' expert's calculation of standard deviations in both grades 4 and 5 as shown in exhibits 34a and 35a. There are, however, two tests used in calculating standard deviation in a case such as this. The first and the one used by the Supreme Court in Castaneda and Hazelwood and by us in American National Bank, is the binomial distribution formula; the other is the hypergeometric distribution formula. Some statisticians indicate that the latter test may be used when small numbers are involved and when these numbers are "finite ... without replacements." Winkler and Hays, Statistics: Probability, Inference, and Decision, 225 (2d Ed. 1975; Holtetc); Hoel and Jessen, Basic Statistics for Business and Economics, 132-33 (2d Ed., 1977; Wiley); Hoel, Introduction to Mathematical Statistics, 67-68 (1971; Wiley). Baldus and Cole, in their 1982 Supplement suggest at p. 82, on the other hand, that the binomial test is proper when the sample is "at least 30" or more.23 The samples in exhibits 34a and 35a which incidentally use for the calculations the tables for all four of the relevant years combined and not the tables for one year, are substantial in number and more than meet these minimum number requirements. In pay grade 4 the sample number is 154 and in pay grade 5 it is 269. The size of the sample in either case warrants the use of the binomial test. Moreover, any terminations of employees during the period presumably were replaced and thus the numbers in the sample were not "finite without replacements." It would appear, therefore, that neither of the two reasons generally given for preferring hypergeometric distribution test over the binomial existed in this case. The two tests did, though, result in different standard deviations and different standard deviations more favorable to the plaintiffs. The hypergeometric test thus gave larger standard deviation results. This fact is demonstrated by the Table appearing in note 24 below,24 which is based on the same numbers as are used in exhibits 34a and 35a, comparing specifically the results under both a hypergeometric distribution test and a binomial test (a test, incidentally, the expert did not employ). — 42 — It will be observed that in computing the standard deviations in pay grade 5 even under the hypergeometric test, we reach a different result from that which the plaintiffs' exhibit 35a showed. Our Table shows a standard deviation of -1.87 and that of the plaintiffs' expert, accepted by and set forth by the District Court in its Finding of Fact # 57, is stated as -2.01. The reason for the difference is the difference in what the exhibit (as included in the Appendix at pages 1115-1117 but omitted in the District Court's findings) describes as "standard error." In the expert's Table, this figure is 3.73 and in the one used by us is 4.02. The basis on which we arrived at our result is shown in note 25.25 If our computation is correct, the standard deviation for pay grade 5 was -1.87, which, under the standard null hypothesis, as stated by plaintiffs' expert, would not be statistically significant. Further, if we compute the standard deviation under the binomial test for pay grade 4, the standard deviations for grade 4 in exhibit 34a would be -2.07 and for pay grade 5 in exhibit 35a would be -1.45. Neither standard deviation, as derived under the binomial test, would be statistically significant, since for pay grade 4 the deviations are but marginally over -2, and for pay grade 5 well below -2. Moreover, there are, as we shall see later, special circumstances which render the standard deviation in pay grade 4, even calculated as the plaintiffs' expert did under the hypergeometric test as -2.69, to be without legal significance. — 43 — NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLE — 44 — NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLE — 45 — NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLEThe District Court cited and relied on another Table prepared by plaintiffs' expert. It was described by the expert as a "buddy" study in which, as he explained it, he sought to match black and white employees, with similar lengths of service, similar grades, similar educational levels, similar department and similar lengths of service in grades. The number of matches covered but a fraction of the defendant's workforce, and their number was not confined to employees in pay grades 4 and 5 but embraced employees selected from all levels of defendant's workforce. If we accept the expert's opinion that the study indicated discrimination in promotions between white and black employees, then the study would have indicated discrimination at all levels of employment in the Bank and would actually contradict the District Court's express finding that discrimination in promotions was confined to pay grades 4 and 5. It is unnecessary, however, to examine the reliability of this aspect of the study, since it was conceded by the expert that such study showed a finding of -1.79 standard deviations, which he said was ".037," evidence of disparity between black and white employees in promotions, or well below the standard of "between two to three," or even -1.95. — 46 — It was obvious at this point in the expert's testimony that he had given no firm opinion on this aspect of his study which would support a conclusion under the econometrician's standards of statistical significance in promotions out of pay grades 4 and 5. The plaintiffs' counsel apparently recognized this and, in seeking to overcome this obvious deficiency in proof, requested the expert to explain at this point "what does this (i.e., the buddy study) tell us about '74 through '77 with your buddy system." To that question the expert replied, "[t]hat if you had reason to believe that blacks were being treated differently than whites, that there was a significant difference." Apparently finding the answer ambiguous, counsel followed that answer with this question to his own expert: — 47 — "Q Must we assume that there was a difference in order to reach a conclusion? — 48 — "A If you assume that there was no difference and that blacks at this point in all of the studies that I've done were equally likely to be above or rated more highly than whites and promoted at a faster rate than whites as they were to be promoted at a slower rate than whites, you would have a 'P' value that was approximately twice as large as that, or .07, or 7 times in 100. Using the standard on a two-tailed test of 5 percent you would not have a significant difference." — 49 — When the expert gave this explanation of his results, the District Judge interrupted to inquire, "I say where in this data is it possible statistically to generate a hypothesis [or 'presumption'] which will beef up the actual results of the statistical analysis? .... where then does that hypothesis come from that race played a part?" (Italics added) The expert's answer was: — 50 — "A The two-tailed test or the test that assumes that blacks are as equally likely to be higher as they are to be lower, which is the alternative. In statistics you say, I believe that there is no difference. You then look to see if there is some relationship in this case between race and promotion. If you truly have no reason to suspect that blacks would be higher or lower, you must use the two-tailed test, but in an experimental design, for instance, where there is a substantial amount of information gathered prior to performing the study that indicates that there is a relationship between race or between what you're studying and an outcome-- — 51 — "COURT: Are you saying that if you draw the conclusion by inspection that the figures are skewed on a racial basis then your statistical opinion depends of whether you put the question in the positive or negative? — 52 — "A Yes, and if you assume that the processes that are gone through in order to determine whether or not discrimination has occurred in order to get a right to sue letter or in the initial evaluation that there is a reasonable chance that it could have occurred in this spot is a proper assumption, you have the ability to use a stronger and a more powerful alternative hypothesis." — 53 — After hearing the expert's explanation, the District Judge inquired: "You weren't stating the hypothesis that is the speculative proposition that you're going to test against the figures you've got. You're talking in terms of a presumption or a reason to start out favoring one side or the other of the question." (Italics added) To that inquiry the expert responded: "It is a presumption, yes." Under these admissions of the expert, a finding of statistical significance, of a magnitude sufficient to support, even for the econometrician, an inference of discrimination could only be arrived at if one begins his review of the statistical evidence with a "stronger and more powerful alternative hypothesis" or "presumption" and one that admittedly favors the plaintiff in a discrimination case that there is "a reasonable chance" that there has been discrimination. Such an assumption, which arbitrarily favors one party to the controversy, cannot be considered a reliable basis for a finding of discrimination. — 54 — Moreover, any finding of discrimination in this case, based on the statistical evidence is compellingly rebutted by two other Tables prepared by the expert before he produced the Tables in exhibits 34a and 35a. These Tables were listed in the record as exhibits 34 and 35 and covered employees in the pertinent pay grades 4 and 5 for the same four years as exhibits 34a and 35a. Such Tables began by taking as the employee pool in the two relevant pay grades for analysis the "Total Incumbents [in those pay grades] at Beginning of Interval." Unlike the numbers in exhibits 34a and 35a, this is an accurate and exact number, and similarly, in setting forth the "Total Black Promotion" in any given year within the relevant time period for both pay grades the actual number of black promotions made during the year was used. In short, these Tables deal with actual, not artificial or tailored numbers and they present a precise picture of the percentage of black promotions in the relevant years for pay grades 4 and 5. The results stated in terms of standard deviations, as measured by the binomial test, are significantly different than those in the exhibits relied on by the District Court, i.e., -1.52 for pay grade 4 and -1.24 for pay grade 5, as shown by the compilation appearing in note 26.26 — 55 — It will be observed that under Tables 34 and 35 the standard deviations, computed under the binomial test, are such that "the hypothesis that the [selection process] (for black promotions in pay grades 4 and 5) ... would be suspect to a social scientist," is not proved.27 The expert, however, did not use the binomial test in his Tables; he used again the hypergeometric test. The expert conceded that the standard deviation difference between whites and blacks in promotions out of pay grade 4 for the pertinent years under the hypergeometric test, as shown by these tables, was -1.89. On the statistical significance of this result, he testified: — 56 — "A 1.89 standard deviation difference between blacks and whites. This is a significant difference if one makes the assumption that it's reasonable to believe that blacks have been discriminated against. The value of that standard error given that assumption is 1.65 standard errors. That corresponds to 5 times in 100. If one makes the assumption that I don't know, that I can't tell and I have no reason to believe whether blacks were discriminated against or not, that is not a significant difference at the .05 level, which I believe the standard error would be 1.95. — 57 — "Q So for the year 1974 does this table reflect that blacks have not promoted out of grade 4 on a comparable basis with whites? — 58 — "A Not statistically." — 59 — As the Court remarked, after hearing this testimony: — 60 — "... to give any meaning to the conclusion expressed in Table 34 [sec. 4] you've got to have pretty well decided the case before you read Table [sec. 4] 34? — 61 — "That's true." — 62 — The expert did testify that exhibit 35 showed a significant statistical disparity in grade 5 under a hypergeometric test, (i.e., -2.24).28 But, as we have already seen, this was because of the expert's own error in calculation.29 The correct figure was such that (i.e., -1.56), even under the expert's own test it would not have been statistically significant. It follows that in both cases the standard deviation is less than -2. — 63 — It will be noted that the expert would test the results of his calculations of standard deviations both in exhibits 34a and 35a and in his buddy studies (but, significantly, not exhibits 34 and 35) by a "one-tail" test of significance and it is on the basis of this test that his opinion of statistical probability of discrimination rests. Since the findings of the plaintiffs' expert thus depend on the use of the "one-tail" test, it is necessary to understand first the difference between a "one-tail" test and a "two-tail" test and to determine under what circumstances, if any, it is proper to use a "one-tail" test. The "two-tail" test, which was the one used by the Supreme Court in Castaneda and Hazelwood, and which, as we have already noted, is the other test used in this connection, proceeds on the basis of a "null hypothesis," which was described by us in American National Bank at page 1191 as "the hypothesis that underrepresentation of a protected minority group in any sample made up of a protected and nonprotected group (binomial distribution) might be attributable to normal fluctuations of chance rather than to discriminatory design." In the application of this "one-tail" test to any compilation, however, one begins with the assumption or hypothesis, based on other evidence than that in the actual compilation being analyzed, that the defendant has been guilty of discrimination and adjust the results on the basis of that assumption. The difference in result between the two tests is significant and dramatic. Plaintiffs' expert conceded as much, and this is evident from the standards themselves for determining statistical significance under the two tests. The rule in Castaneda and Hazelwood requires standard deviations in the range of "more than two or three," and under the "two-tail" test, as often stated by statisticians "about two" standard deviations are the necessary predicate for a finding of statistical significance under the view of some social scientists. But when the "one-tail" test is used, the plaintiffs' expert testified that 1.65 standard deviations warranted a finding of statistical significance.30 — 64 — Both the District Court and the plaintiffs' expert recognized that the "one-tail" test is a dramatically stricter standard for statistical significance than the "two-tail" test. In fact, the court in Brown v. Delta Air Lines, Inc., 522 F.Supp. 1218, 1229, n. 14 (S.D.Texas 1980), declared, on the basis of Dr. Hoffman's testimony to such effect in that case, that, — 65 — "Moreover, Dr. Hoffman's use of a one-tailed, rather than two-tailed, test favors the plaintiff's viewpoint even further (because with a one-sided test, it takes less of a variation from expectation to reach '.05 significance')." — 66 — A commentator has made the same observation about the "one-tail" test, describing it as " 'data mining' per se" which is "the statistician's term for manipulating data to prove a desired result." Harper, supra, 32 Hastings L.J. at 1355, n. 65, citing Freedman, Pisani and Purves, Statistics, 494-96 (1978). Still another text is more specific in its description of the "one-tail" test. In Friedman, Introduction to Statistics, 146-47 (Random House, 1972), the author explains: — 67 — "Note that, although at value of 1.96 is required to reject Ho at the 5 percent level with a two-tailed test, a value of only 1.64 is needed if a one-tailed test is used. Many investigators find it tempting to use a one-tailed probability level to facilitate obtaining 'significant' results. — 68 — "... the safest procedure in virtually all situations is to use two-tailed values. Using one-tailed values to make rejection of Ho (i.e., the null hypothesis) 'easier' serves to increase type I errors, while the size of the difference, as measured by rm is unaffected. A strict application of one-tailed values includes the danger of overlooking important results in the non-predicted direction, and any attempt to test for such outcomes leads to inaccurate probability values. Analysis of data based on two-tailed probability levels can be reported without apology, while it is almost always necessary to 'explain away' the use of one-tailed probability levels." — 69 — The District Court itself characterized the use of the "one-tailed" test in this case as a method of "beef[ing] up" the statistics and the expert himself employed the adjectives "stronger" and "more powerful" in his characterization of the test in his exposition of the test. Because of this fact (i.e., the more favorable aspect of the "beef[ed] up" test for the plaintiffs in a discrimination claim), plaintiffs' expert testified that its use in any case is conditioned upon the presence in the record of other evidence which would justify a belief or an assumption that the defendant had been guilty of discrimination. The evidence in this case which, according to the expert, justified the use of such test in this case, consisted of certain data gathered by him and incorporated in exhibits identified and introduced before introducing exhibits 34 and 35. Such evidence, at least that which it thought pertinent, was presumably that which was identified by the District Court in its findings before it accepted the results of the expert's "one-tail" test results. Whether the use of the "one-tail" test was appropriate in this case even under the expert's theory thus depends on whether this evidence on which the District Court relied was sufficient to generate a legitimate belief or assumption of discrimination. Though we do not conclude that this is a case in which the "one-tail" test should not have been used in any event, we have reviewed the evidence cited and relied on by the expert for his assumed justification for his use of the results of the "one-tailed" test. — 70 — In his assumed justification, the plaintiffs' expert relied on multiple regression studies, submitted by him in addition to exhibits 34, 35, 34a, 35a. Similar studies were offered in Stastny v. Southern Bell Tel. & Tel. Co., supra, 628 F.2d 267. The District Court commented on the reliability of such studies thus: — 71 — "Regression analysis begins with the assumption that certain independent variables in fact determine the outcome of decisions to raise pay and promote. Such assumptions are intellectually questionable and not grounded upon any solid evidence." 458 F.Supp. at 323.31 — 72 — Whether this is a fair comment on regression studies is a matter we need not concern ourselves with in this case. The studies in this case are insufficient, even under the expert's faulty theory of justification, to provide a reasonable basis for an inference, hypothesis or belief that the defendant had been guilty of discrimination. We accordingly proceed to examine the studies on which presumably the District Court justified its approval of the expert's use of a "one-tail" test in establishing statistical significance by its standards in this case. — 73 — The first multiple regression of the studies to which the District Court referred in his findings was a comparison of earnings of black employees for the defendant's workforce taken as a whole. The records used by the expert, however, show that there was a greater percentage of whites in the upper pay grades than blacks. This, as the District Court found, could not have been because of any "significant difference in initial job assignments and pay grades, performance evaluations or promotion of black and white employees;" the District Court expressly found that there was no difference.32 Moreover, almost all the employees in the managerial category, which consisted of the higher pay grades, were long-time employees; in fact, the employment of many of them extended back beyond the effective date of the Act itself. In addition, the expert's studies did not show that there was any discrimination in pay rates between whites and blacks in pay grades 4 and 5. Moreover, there was a greater proportion of white employees in the higher clerical levels than of black employees, though the proportion of blacks in these pay grades was considerably above the proportion in the black force qualified for such pay grades, according to the defendant's figures. It would seem reasonable to assume that, because of the greater concentration of whites in pay grades above pay grade 5 carrying higher pay rates than pay grades 4 and 5, white employees, taken as a group throughout the defendant's work force, would receive higher wages than blacks. For this reason (the inclusion of all employees, those at the lowermost level of pay and those at the highest), regressive tables involving an overall comparison of salaries of employees have been widely dismissed by the courts as completely unreliable. — 74 — In Agarwal v. Arthur G. McKee and Co., 19 FEP Cases 503 (N.D.Cal.), aff'd. 644 F.2d 803 (9th Cir.1981), the plaintiffs, just as plaintiffs' expert here, attempted to use a regressive analysis in support of discrimination based on a comparison of salaries of minority and non-minority employees at all pay levels in an employer's work force. In finding the study meaningless, the Court said (p. 512): — 75 — "[P]laintiff's regression analyses contain a number of defects. Plaintiff failed to treat salary as a function of job position and salary grade. Furthermore, plaintiff treated all job positions as fungible, involving equal levels of knowledge, skill, and responsibility. Therefore, plaintiff's statistics do not refute defendant's contention that salary differences between minorities and non-minorities within each job position are not substantial." (Italics added) — 76 — Valentino v. U.S. Postal Service, 511 F.Supp. 917, 957 (D.C.D.), aff'd, 674 F.2d 56 (D.C.1982), involved the use of a like comparison of salary difference for the defendant's workforce as a basis for a claim of racial discrimination in salary. Again referring to the erroneous treatment of "all jobs as fungible" and finding the study unreliable, the Court said: — 77 — "Plaintiff treated the wide variety of positions in USPS Headquarters at level 17 and above as fungible items. For example, her regression compared the position of the Postmaster General to that of his secretary. Common sense dictates that these positions are not comparable, are not fungible, and that any difference in salary cannot be presumed to be the result of sex discrimination by the USPA."33 — 78 — Again, the Court in Vuyanich v. Republic Nat. Bank of Dallas, 505 F.Supp. 224 at 280 (N.D.Tex.1980), dismissed as valueless salary comparisons between white and black employees at all levels of employment on the issue of discrimination. The Court said: — 79 — "Not surprisingly, where an employer has employees in differing occupations and of different backgrounds, a simple comparison of the average wage of all white employees and all black employees (or all male employees and all female employees) will not be enough to prove salary discrimination. See, e.g., Pouncy v. Prudential Insurance Co. of America, supra at 449 [499 F.Supp. 427] 23 Emp.Prac.Dec. n. 66, at 16,751 ('The Court believes that the proper inquiry in an analysis of salaries by race should focus on whether black and white employees with the same tenure at the same job level are paid the same salaries') ...." — 80 — Keely v. Westinghouse Electric Corp., 404 F.Supp. 573 (E.D.Mo.1975) is another case where a salary comparison was attempted to be used to support an inference of discrimination. The Court dismissed, as "meaningless" the evidence, saying: — 81 — "Plaintiff has submitted evidence showing that blacks were earning less on the average than were defendant's white employees. Such statistics, however, are meaningless without more. Were evidence produced which showed that black employees with the same length of employment and the same qualifications were paid lower rates for similar jobs, or that no black employee earned more than any white employee, this Court might feel compelled to conclude that the disparity was due to racial discrimination."34 [p. 578] — 82 — Similarly, in this case, the salary comparison referred to in the District Court's findings and used by the plaintiffs' expert as a basis for his "hypothesis" or belief of discrimination against the defendant treated the vice president of the bank as comparable to the cafeteria waitress and considered the eight officers (all of whom are above the pay grade 16) as comparable with employees in pay grade 3, the lowest pay grade in the existing workforce of the defendant. Many other comparisons, almost as lop-sided, could be cited as demonstrating the same flaw. Just as the court ruled in Valentino and in Ste. Marie, this table of salary comparison cannot be used to give support to any presumption of discrimination. Moreover, we are concerned solely with alleged discrimination in pay grades 4 and 5. It would have been appropriate, however, if we had compared wages in those pay grades alone. See Vuyanich, supra, 505 F.Supp. 224. Yet the fact is that the District Court found that there was no discrimination in pay in any specific pay grade, including pay grades 4 and 5. — 83 — A second set of statistics cited by the District Court relates to the assignment of employees "to cleaning positions and the Cafeteria" and to assignments in pay grades 6 to 14. We are unable to find any basis for presuming discrimination on this basis since the District Court both in its "Memorandum of Decision" and in its findings concluded that there was no pervasive evidence of discrimination in the job assignment of employees. Moreover, the employment records reviewed by the plaintiffs' expert demonstrated that over 85% of the bank employees employed in service and cafeteria jobs had requested that type of work and/or that their work experience before hiring was in that type of work. So far as those blacks employed in this work who had not requested jobs in those departments, they, with hardly an exception, had submitted records that indicated work experience only in those areas and, in particular, had no background in clerical work. It is agreed in the District Court's findings that initial employees when employed, were assigned, whether they were black or white, on the basis of "educational background and prior work experience." In view of the District Court's finding of no discrimination in assignments, it is difficult to understand how the expert could have relied on assignments for his presumption of discrimination. — 84 — The District Court also made a finding, based on some data prepared by the expert, that "Fifty-three (53) percent of the black employees, however, were in pay grades 6 and below, as compared with 26 percent of the white employees." This, too, was cited and relied on as authority for a belief that the defendant had engaged in discrimination. What, however, this finding fails to note is that, for pay grades above grade 6 added qualifications are required. There is in the record the percentage of black employees in pay grades 7 to 13 which are the pay grades requiring special qualifications. The percentage of black employees of the defendant in such pay grades is 17.5 percent as compared with a 10.4 percentage of blacks having such special qualifications in the qualified black labor force in the Charlotte employment area as shown by official Labor Department figures. Moreover, the District Court itself found as a fact, and the plaintiffs have not disputed such finding, that there has been no discrimination in promotions or hirings in pay grades 6 and above or in job assignments or in pay in such grades. If this fact be assumed (and the District Court so found) it would appear impossible to derive an inference of discrimination based on a comparison of black and white employees in those pay grades. The situation here is similar to that in Pouncy v. Prudential Ins. Co. of America, 668 F.2d 795, 801-02 (5th Cir.1982), in which the plaintiffs in a discrimination case made a like contention based on a statistical table which "show[ed] that, on the whole, blacks [were] overrepresented in the lower levels of Prudential's work force." The Court dismissed such evidence as meaningless, saying: — 85 — "But this might result from any number of causes. Absent proof that the disparate impact is caused by one or more of the challenged employment practices, we do not require the employer to justify the legitimacy of any (or all) employment practices." — 86 — In this case, any disparity reflected in this table could not, as we have said, be the result of any discrimination in hiring or assignment; the District Court has found the absence of any such discrimination and the plaintiffs have not excepted to that finding. If it be said it is due to discrimination in promotions out of pay grades 4 and 5, the statistical evidence in the tables submitted by the plaintiffs will not support such a finding, if we follow the Hazelwood and American National Bank test (statistical deviations in the range of "about two or three," with only the existence of at least three deviations being sufficient for an absolute inference of discrimination). — 87 — The District Court noted that there was a disparity in the average time rate of promotions out of pay grade 4 (but not pay grade 5 ) between white and black employees in the expert's studies. However, the studies compiled by plaintiffs' expert showed the comparative rates in promotion overall of black and white employees and in pay grades 4 and 5 for the relevant years. Specifically, the expert testified that black employees had less or equivalent time at the bank in each of the grade levels above grade 4 (that is, for pay grades 5 and above), in all the years in issue and that "the promotion rate of blacks [all grades included] was greater than for whites" in the same years. — 88 — Moreover, the studies prepared by the expert himself in connection with his regressive studies, indicated quite clearly why there should have been a disparity in promotion of blacks out of grade 4. These studies showed that a far greater proportion of black hirees brought to their employment an experience in service and cafeteria jobs than white hirees and, conversely, the white hirees brought a far greater work experience in clerical work than black employees. Since it was found that job assignments for hirees were based on educational background and work experience, it was reasonable to expect that a far greater proportion of black hirees than white hirees would be assigned to service and cafeteria jobs and that a far greater proportion of white employees than black employees would be assigned to clerical jobs. And these expected assignments of black and white hirees were justified by the admitted fact that a far greater proportion of black hirees than white hirees requested service and cafeteria jobs and a far greater proportion of white hirees than black hirees applied for clerical jobs. — 89 — In a bank where the opportunities for promotion primarily were in the clerical or office fields, it is to be expected that those whose work and experience were in those fields would have an advantage in promotions over employees in service and cafeteria jobs.35 Experience in a cafeteria or in cleaning hardly offers training that qualifies one for clerical work in a bank such as a Federal Reserve Bank. These are the very reasons which prompted the Court in Ste. Marie to find flawed statistics showing disparity in the employment of whites over minorities in a discrimination case. In that case, Judge Friendly said:"Plaintiff's statistics were hopelessly flawed by the lumping of these secretarial jobs into the clerical category, since these positions did not offer the incumbents the opportunity to acquire the skills and experience that would enable them to qualify for promotion to technical and still less to managerial posts. There is no principle requiring an employer following a policy of promoting from within to make this applicable across the board rather than only to those employee groups whose work gives them the opportunity to acquire the skills needed for promotion. Yet plaintiff's statistics gave the same weight to failure to promote secretaries and typists to posts requiring specialized substantive knowledge and experience as they did to failure to promote women working in other clerical positions that would permit them to obtain the essential skills. This methodology failed to heed the warning in Hazelwood School District v. United States, supra, 433 U.S. at 308 n. 13, 97 S.Ct. at 2742 n. 13: 'When special qualifications are required to fill particular jobs, comparisons to the general population (rather than to the smaller group of individuals who possess the necessary qualifications) may have little probative value.' " [pp. 400-01] — 90 — See also Pouncy v. Prudential Ins. Co., supra, 668 F.2d at 804. The difficulty in our case, as it was in Ste. Marie, is that the difference in the experience acquired on the job assigned in a non-discriminatory way may reasonably account for promotion to higher clerical jobs, rather than discrimination. These considerations are the manifest reasons for the disparity in promotions between whites and blacks at the grade 4 level in this case. They should have been noticed and taken account of by the plaintiffs' expert in his calculations as well as by the District Court. They do not justify a presumption of discrimination in connection with promotions at pay grade 4. — 91 — It follows that, assuming for the moment, it was permissible for plaintiffs' expert to look to other statistics in order to justify the use of the "one-tail" test which was favorable to the plaintiffs, the fact is that none of the statistics he relied on fairly would have justified the assumption of discrimination on which he predicated his right to use this "one-tail" test. We repeat, however, that we are not persuaded that it is at all proper to use a test such as the "one-tail" test which all opinion finds to be skewed in favor of plaintiffs in discrimination cases, especially when the use of all other neutral analyses refutes any inference of discrimination, as in this case. — 92 — Finally, in summary, the expert's opinion on statistical significance based as it is on the use of both the hypergeometric test and the "one-tail" standard of statistical significance, which, as we have seen, is the linchpin for the District Court's conclusion of discrimination, depends for any meaning on the complete acceptance of a sequence of dependent adjustments made in the relevant data and applicable formulae, as demonstrated by our review of the plaintiff's statistical evidence, coupled with a complete disregard of all contrary conclusions evident in the statistical evidence. To recapitulate, we begin this sequential review with exhibits 34 and 35, as prepared initially by the plaintiffs' expert (never discussed in the District Court's Findings) which use the actual promotions of blacks over the relevant period 1974-78 in the pertinent pay grades of 4 and 5. If we apply in these exhibits the binomial test, followed in Castaneda and Hazelwood and accepted by us in Moultrie, and American National Bank, supra, 652 F.2d at 1193, n. 12, for determining the applicable standard deviations for measuring any disparity in promotions out of pay grades 4 and 5, the result in standard deviations for disparity in promotions of black employees stated in both pay grades show a variance well below 2 (i.e., -1.52 in pay grade 4 and -1.24 in pay grade 5).36 Even if we use the hypergeometric, rather than the binomial, test, as did plaintiffs' expert in his statement in his tables 34 and 35, the result in standard deviations is below 2 (i.e., 1.90 in pay grade 4 and 1.56 in pay grade 5). There was thus no basis for a finding of statistical significance as a result of tables 34 and 35, irrespective of whether one employs the binomial or the hypergeometric test. These tables are not mentioned in the Findings proposed by the plaintiffs and adopted by the District Court. — 93 — The expert's presentation then shifts to exhibits 34a and 35a. In these exhibits, accepted by the District Court and included in its Findings, the expert, has, however, changed the number of employees in the sample, both overall and divided between white and black, and more importantly, changed the number of actual black promotions made during the relevant years. In these samples, a number of employees in the pay grades and a number of the black promotions are eliminated. With the pertinent data thus abbreviated, the expert came up with a new set of results in standard deviations. He did not state these results in terms of a binomial test, under which the standard deviations in pay grade 4 would have been barely over 2 (i.e., -2.07) and less than 2 in pay grade 5 (i.e., -1.45).37 On the contrary, he used the hypergeometric test in his tables 34a and 35a. The use of the hypergeometric test in this context is not warranted under the conditions stated by some respected commentators. Under this hypergeometric test, however, the standard deviations for pay grade 4 were -2.69 and -1.87 for pay grade 5. Even if this test result is accepted, there would be no basis whatsoever for inferring discrimination in pay grade 5, and, under our rule as stated in American National Bank, ("... courts of law should be extremely cautious in drawing any conclusions from standard deviations in the range of one to three," 652 F.2d at 1192), a finding of statistical significance, much less legal significance, in pay grade 4 would be accepted only with extreme caution, an injunction particularly apt in view of the undisputed fact that a disproportionate number of black employees in this pay grade were employed in the cafeteria and service departments from which promotion into clerical jobs at the higher pay levels would be less likely than for those in that pay grade having clerical experience. See Ste. Marie, supra, 650 F.2d at 401. — 94 — The expert apparently recognized and even conceded that, for the reasons already given, statistical significance could not be derived from the results of either the binomial or the hypergeometric test under exhibits 34, 35, 34a, 35a or the "buddy" test study which he conducted (in which the standard deviations were less than 2) but he testified that he was entitled to use a 1.65 standard of standard deviations as a test of statistical significance (i.e., the "one-tail" test). The propriety of the use of such a test, admittedly favorable to the plaintiffs, depended, even according to plaintiffs' expert, on the right of the expert to assume on the basis of other data accumulated by him that the defendant had been guilty of discrimination and to analyze the results of exhibits 34, 35, 34a and 35a on that basis. As we have said, the facts and data cited by the expert and included in the District Court's Findings simply did not justify such a belief or assumption, and therefore, did not justify the use in this case of a "beef[ed] up" "one tail" test, to use the District Court's own description of the test. But it is only by the use of such a test that he reached a result of standard deviations of -2.69 in pay grade 4 and of -2.01 in pay grade 5, (both of which are below the "safe" figure of -.3). In short, plaintiffs' expert has achieved his opinion of statistical significance by discarding all tests except one which he has admitted in Brown (522 F.Supp. 1218) favors the plaintiffs, and even where he limited himself to that test, he has reached a result which we said in American National Bank was to be accepted with extreme caution. We are of the opinion that the District Court was in clear error in accepting the opinion of plaintiffs' expert on statistical significance when that opinion rested on such skewed analyses and which disregarded the far more reliable tables, (i.e., tables 34 and 35), which demonstrated no basis for a finding of statistical significance, much less legal significance. — 95 — Before concluding the class action aspect of this case, we should observe that the defendant offered considerable expert testimony in support of its defense of no discrimination, little of which was noticed or discussed by the District Court in its Findings, and then only in an effort to support its finding of discrimination. The evidence submitted by the defendant was clearly relevant to the defendant's defense that it had never subjected its black employees, either in pay grades 4 and 5, or in any other pay grades, to discriminatory treatment and deserved consideration by the District Court. It consisted largely of various statistical studies made by defendant's expert. One of these studies showed, for instance, that between 1966 and 1978, white employment at the bank dropped from 82.3% to 64.3% while black employment increased from 17.7% to 35.7% and that in the period between 1974 and 1978 thirty-five percent of all employees hired by the bank were black, although the black representation in the relevant labor market was but twenty percent. — 96 — In another chart, the bank's employees were divided into groups based on type of job corresponding to the Labor Department classifications. The percentage of blacks in each group classification in the Charlotte metropolitan area as shown by the relevant Labor Department statistics was ascertained. Pay grades 3 through 6 under the defendant's employment procedures were classified as a group which "require[d] relatively little training and persons from the general labor market [could] perform at those jobs" in that group. 46.4% of the black employees in 1978 were within the class. This was practically two times the available black employees in the general labor force in the Charlotte area (i.e., 19.9%). The second grouping covered the employees in pay grades 7 through 13 qualifying within the classification of "labor force clerical employees." In this group were 16.2% of the bank's black employees as contrasted with available blacks meeting the qualifications of such group in the relevant labor market of 10.4%. Again, the percentage of black employees in these pay grades is considerably more than the available qualified blacks in such group in the Charlotte area. The final group embraced pay grades 14 through 16 plus all officers and it was classified in the labor statistics as "non-farm managers and administrators." In this group there was a single black in defendant's labor force but because of the small number involved, this represented 5.6% of those employed in such group as contrasted with 3.75% among the available qualified blacks in such classification in the relevant labor area. These comparisons, as set forth in these tables, follow the model set forth in Hazelwood School District v. United States, 433 U.S. 299, 97 S.Ct. 2736, 53 L.Ed.2d 768, under which the Supreme Court measured disparity by comparing the percentage of black hirees to the percentage of blacks available in the relevant labor market. This method of analysis has been declared to be probative of both an employer's actual hiring practices and its recruiting practices. Clark v. Chrysler Corp., 673 F.2d 921, 929 (7th Cir.1982). In this case, the fact that blacks were more heavily represented at all levels than their representation in the relevant qualified labor pool would be probative of an absence of discrimination in recruiting, in assignments and in promotions. — 97 — Another chart of the defendant traced the promotion rate of black and white employees employed at all pay grades in the period 1974 to 1978, within the fifteen-month period after they had been hired. This data showed the percentage of black employees in the entire workforce of the bank in the 1974-78 period, was 33%; during this period black employees received 35% of all the promotions. The defendant's expert calculated from his charts that "[t]he probability of [a] white [employee] being promoted [in the 1974-78 period] was about 18%, whereas the probability of a black being promoted [was] 20%." This calculation was not questioned by the plaintiffs. Moreover, all this information on rate of promotion was verified in the charts developed by plaintiffs' expert. Thus, looking at the years 1974-78, the plaintiffs' statistics established that, except in grade 4, blacks had either less or equivalent time than whites in every pay grade from 5 on. Thus, in pay grade 5 in 1974, whites remained in that pay grade 45 months, whereas blacks remained only 31 months. That disparity in favor of blacks continued for the remaining years in the period except for the year 1977 when the two groups were "equal." These results were confirmed by other studies made by the plaintiffs' expert. In this period of 1974-75, the promotion rate for whites overall was 13% and that of blacks 17%; in the 1975-76 period, the promotion rate for whites was 16% and for blacks 19%; and in the 1976-77 period, the promotion rate for whites was 11% and for blacks 15 1/2%. It is plain from this summary of the plaintiffs' expert's statistics that, as the expert admitted, in the critical period 1974-78 the promotion rate for black employees by the defendant overall was greater than the promotion rate for whites. — 98 — The District Court, however, states in its Findings that these exhibits of the defendant confirm the finding of discrimination in pay grades 4 and 5, even if they disprove it in all other pay grades. To support this statement it refers to the defendant's exhibit 111 and particularly the record of black promotions in pay grades 4 and 5 for the years 1967-78, which it finds were less percentage-wise than their representation percentage-wise in the defendant's labor force. The reason for this, however, was obvious. Prior to 1966, according to the District Court's Findings, black employees were limited to assignment to "basically cleaning positions and the cafeteria," positions that did not provide the experience to qualify for promotion to clerical work at levels above 4 and 5. This would mean in the early years of this compilation the heavy concentration of blacks in these labor areas would result in lower rates of promotion for them. This in turn would manifestly skew the figures significantly for a large period of the time concerned by the exhibit in pay grade 4 especially and to a lesser extent in pay grade 5. See Ste. Marie, supra, 650 F.2d 395. But the crucial years in this case are 1974 to 1978 and it is for those years that we must look for discrimination or not at all. That represents the period to which the claim of discrimination in promotion was limited by agreement of the parties and the period within which class discrimination in promotion had to be established by the plaintiffs.38 It is appropriate to look to pre-January 3, 1974 evidence "[o]nly if we conclude that the employees proved certain title VII violations during the actionable period," Croker v. Boeing Co., 662 F.2d 975, 990 (3d Cir.1981). The District Court seemingly recognized this, but incorrectly declared that "[d]efendant's exhibit 113 for 1974 through 1978 shows this same disparity by year."39 These exhibits to which the District Court refers are, so far as pay grades 4 and 5, no more than a restatement of the very information set forth in plaintiffs' exhibits 34 and 35 and with some significant changes already discussed, in their exhibits 34a and 35a. The plaintiffs' expert conceded that, viewing these exhibits alone, it was not possible to say that there was a statistically significant disparity in the promotions of blacks out of pay grades 4 and 5 in the period 1974-78. It is only when these figures are "refined" by the application of hypergeometric tests and by the use of a 1.65 standard deviation rule, as contrasted with an "about two or three" test, can disparity be found. We have already indicated why we conclude that such standards (i.e., the hypergeometric test and the 1.65 level for standard deviation disparity) are inappropriate and we need not repeat those reasons here. It is sufficient that, if we consider plaintiffs' own exhibits 34 and 35, or even exhibits 34a and 35a themselves, for the crucial years 1974-78, we are left with no statistical basis for a finding of discrimination in promotion out of pay grades 4 and 5. In fact, plaintiffs' expert witness, during his testimony on recall, answered the question, "[i]n using the directional (i.e., the 1.65 level of significance) test, it's (i.e., the result stated in standard deviations] barely significant, isn't it?" with an affirmative, "Yes." Accordingly, even after the use of his hypergeometric and "one-tail" test (which he has recognized favors the plaintiffs in this case) can he find even "barely significant" statistical basis for an inference of discrimination in promotion out of pay grades 4 and 5 on these exhibits of the defendant. This is manifestly no comfort to the plaintiffs in the findings in the defendant's exhibits. — 99 — It follows that a finding of either a prima facie case or of a pattern of class discrimination in promotions out of pay grades 4 and 5 or a finding of fact of such a pattern is not supported by any substantial evidence either of live testimony or evidence in plaintiffs' presentation or in defendant's statistical tables and any conclusion of class discrimination in those pay grades is clearly erroneous and without any substantial support in the record. We accordingly reverse the District Court's Findings and Conclusions of class discrimination in promotions out of pay grades 4 and 5 and direct the entry of a dismissal of such claim. — 100 — We now turn to the two individual cases of discrimination. The first of these is the claim of the intervenor-plaintiff Russell. The District Court found that the defendant had discriminated against her (1) by denying her promotion to a supervisory position in 1974 despite her qualifications and the existence of a vacancy and (2) by harassing and intimidating her and (3) finally in discharging her in retaliation for her filing an EEOC charge against the defendant. — 101 — The claim of a denial of a promotion did not arise out of any application or request for a promotion by Russell. The defendant, through its supervisor, approached Russell and inquired whether, to use Russell's own words, she would be willing to return to "low speed in order that she could train new employees," the supervisor explaining, according to her, that, if she agreed, she "would be promoted in grade, and she would have supervisory status and responsibilities." According to the District Court's findings, she accepted but was "denied supervisory status and a pay grade increase," though, after complaining, she "later received a pay grade increase but has continuously been denied supervisory status." — 102 — Actually, Russell's own testimony was somewhat different from this summarization by the District Court. Her reply to the job offer made her by her supervisor was "that [she] would accept the job on the basis that we agreed to [dependent on] what [her] job title would be, what [her] job duties would be, and if the agreement didn't work out that [she] would return to [her] position as checker." Pressed by her attorney as to whether she had been "told anything about supervisory responsibilities," she added that she was told she "would be offered a job as a utility clerk, which at that time meant supervisor, and that [she] would have supervisory responsibilities over the new girls that were coming into the first-run section, and that [she] would aid them in training and with any problems that they would have; but [she] would also keep the work kept up if it should get behind." Russell accepted the offer and transferred to the new job. — 103 — After she had transferred, Russell testified that she "didn't see my job title or grade 6 right away." (Italics added.) She went to her supervisor's office to complain "about not receiving [her] job title and [her] grade when [she] was handed [her] raise slip with [her] job title of utility clerk and [her] Grade 6 and the amount of [her] raise." At this point she said, "I was all right then." In short, then, by her own testimony, Russell had gotten precisely what she had been promised. She had received the exact title, pay grade and pay raise she had been promised. She was satisfied. So far as the record shows, she never missed one pay date at her increased pay status; her pay at pay grade 6 began as of the time she began work at her new position. She had at the time no complaints. — 104 — Sometime later, however, she observed two other employees in her department who attended what she understood was a supervisors' meeting. She testified she was not invited or allowed to attend the meeting.40 She contended she was doing the same type of work as these two employees and that the failure to invite or allow her to attend the meeting established that she was not being treated like white employees in similar status to her. She, however, admitted that both of these other employees, Ina Mauney and Joanne Moore, had been employed longer at the bank than she--in fact, she testified that Mauney in particular had worked "a lot longer" at the bank than she, and that both Mauney and Moore had been promoted to pay grade 7 with job classification of "utility clerks A" some months before Russell had received her promotion to pay grade 6. In any event, Russell by her own testimony, was plainly not comparable to Mauney or Moore either in pay grade or in title status and had never been. She never claimed that she was promised job status as "utility clerk A" or a pay grade of 7 comparable to the title and pay grade of Mauney and Moore. She had gotten what she herself said she had been promised, i.e., the title of "utility clerk" at pay grade 6. Despite this, the District Court concludes that Russell had been discriminated against by not being given the classification of "utility clerk A" at pay grade 7 because such a classification and pay grade were "more relevant to the job duties Russell was assigned." This is the theory on which the District Court found that Russell had been discriminatorily denied a promotion. There is no basis or justification for such a finding in this record, and the finding of discrimination in this respect is reversed. — 105 — The second ground for finding discrimination in favor of Russell, as stated by the District Court, arose out of her discharge in January, 1975. Prior to 1974 Russell had been a valued employee and had received satisfactory evaluations annually for several years. The defendant had recognized this service and had rapidly advanced Russell to pay grade 6, with appropriate pay increases. But in 1974 Russell's conduct as an employee deteriorated seriously. This is not just the defendant's testimony; Russell herself candidly testified to such fact. When asked, "[y]ou did have an attendance problem in your last year with the bank?" she responded, "Yes." She identified various forms titled "Explanation by Employee of Absences and Attendance Reports," signed and acknowledged by her, covering excessive absences or tardiness in the year 1974 and continuing into the month of January, 1975. Without attempting to deny her absenteeism she would excuse her absenteeism, testifying that "[p]art of the time I was ill. Part of the time my children were ill, and I had, I was on medication that I had gotten from the doctor because I was under a lot of stress." She admitted being counseled by her supervisor about her "absenteeism and tardiness" a number of times throughout 1974. She was given at least one and perhaps two reprimands for absenteeism and tardiness, low work evaluations and finally was placed on probation in that year. She had other difficulties beyond that of absenteeism as an employee. These too were discussed with her and she was counseled about them. She, for instance, did not dispute that she did not get along with her supervisor or with another black employee in the department. — 106 — After she received her first reprimand and had been placed on probation for absenteeism, she filed in mid-July, 1974, her first charge of discrimination against the defendant. In this charge, she said "[t]he above Company demoted me because of my race,41 Negro, refuses to promote and train Negro employees because of their race,42 and discriminated against me with respect to terms and conditions of Employment (Job Assignment), because of my Race (Negro)." Even after she had filed this claim of discrimination and after she had been placed on probation for her admitted record of excessive absenteeism, Russell's absenteeism continued without any noticeable improvement. Finally, her immediate supervisor Cain, in November told her he was recommending her termination. Cain submitted his recommendation to his supervisor, Walker, whose title was assistant vice-president. The latter told Cain he thought Russell should be "assigned to other duties in another department." He made this decision "[in] the hope that Ms. Russell, by virtue of a new assignment and new environment, might correct the problems that we had pointed out to her in previous months." — 107 — On January 20, 1975, Walker talked to Russell. He reviewed with her her unsatisfactory employment record during 1974 and, then, by his account, "offered her an opportunity to transfer to the Adjustments Department," explaining to her "that we felt that a change in supervision and work atmosphere might help the situation, so we might preserve the training and experience that she had, which is valuable to us in this operation." Russell responded, as Walker testified, that "she liked to work in the Check Operations better than working in Adjustments." She added that "[a]lthough she was familiar with it, she had not had much opportunity to work in that area ... and asked if she might be allowed to return to the Check Collection Department at some point in time." Walker said his response was that "if her attendance improved, her tardiness record and overall work attitude in her new assignment, if improvement occurred, she [might] be considered for reassignment in Check Operations at some point in time." Walker saw Russell again on January 22 and told her that she would be transferred to Adjustments on January 27. According to Walker, Russell replied, "that her attorney had advised her and that she was refusing the transfer and that she had also amended her charge against the bank to include retaliation." Finally, on January 24, Walker, with Cain present, saw Russell for the third time and "again offered her the opportunity to transfer to the Adjustments Department and informed her that if she refused the transfer that we would have no alternative but to terminate her employment with the bank immediately." She refused the transfer and her termination was then processed. — 108 — This account is not substantially different from that of Russell, except that she disputed that she had said that she was refusing the transfer on advice of her lawyer. In her sworn charge as filed with the EEOC, however, Russell said that she was "refused permission to transfer after [she had previously requested a transfer to that division, i.e., Adjustments] refusing same." At the trial several years later, she testified she "refused to go into that [Adjustments] department because [she] had already volunteered to work in that department, and I was told that I did not have enough experience and there was no one to train me; and I refused it because I felt then that I didn't have any job knowledge." This testimony, that she had earlier volunteered to work in Adjustments but had been refused because of a lack of experience, is contradicted, however, by other testimony given by Russell herself at trial. She testified at trial that when she had volunteered to go to Adjustments, her supervisor "acted as though he didn't hear me," not that her supervisor told her that she "did not have enough experience ... [or] any job knowledge." She, in turn, sought to explain away the language in her EEOC charge that she had previously requested a transfer to that division some two months before her discharge in January, 1975 by repudiating the language in the charge, saying that she was "under pressure" when she gave the statement and denied she had ever "ask[ed] for a transfer" to Adjustments, only that she had "volunteered" to go to Adjustments. The statement, however, was drafted in the EEOC office in conjunction with an EEOC employee without any employee of the defendant being present. — 109 — The District Court finds that her discharge in January, 1975, was "in retaliation" of Russell's action in filing an EEOC charge in July, 1974. In support of this conclusion, the District Court found that, after the filing of the EEOC charge, Russell was given "unfair adverse performance evaluations, [and] threatened with termination of her employment," although such unfavorable evaluations, reprimands and threats of termination "were not based on any deficiencies in Russell's performance" and "can only be explained on the basis of Russell's race." As we have already indicated, her work performance before her probation, by her own explicit admission, was deficient; the findings of the District Court to the contrary simply have no support in the record. It cannot, therefore, be said in the light of the record and Russell's own admissions that the reprimands, the counseling and the evaluations of Russell's job performance were "unfair." Equally without any real basis in the record is the statement that the reprimands, the probations and the evaluations only occurred after Russell had filed her complaint with the EEOC. When asked, "[w]hat happened, Ms. Russell, after you filed your charge with the EEOC?" Ms. Russell replied, "[w]ell, I started, I got a low progress report, and I was put on 60 days probation, no, that was before I filed. I was just being harassed." (Emphasis added) She offered no explanation of how she was harassed. — 110 — But even though she had poor job performance Russell claims she should not have been placed on probation or given the option of transferring or being fired because other employees, with equally bad absenteeism and tardiness records had not been so treated. This explanation was accepted without question by the District Court. Ms. Russell identified three employees who, she said, had similar or worse absentee records than she and who were treated more leniently. These three were Joyce Norwood, Joyce Gibbs and Donna Stokes; of the three, Norwood was black and Gibbs and Stokes were white. Norwood and Stokes were counseled about their absenteeism about the same time as Russell and both, according to the defendant's undisputed testimony, responded by improving their attendance record. Norwood had had, according to her head supervisor, only two absences after counseling and had since been promoted twice. Since Norwood is black as is Russell, the difference in treatment between the two could not be racially motivated, and would appear to have been based on Norwood's response to her counseling. Stokes, like Norwood, was retained after she corrected, following counseling, her attendance. But Gibbs, a white, who did not respond, was terminated. Russell contends, however, that Gibbs' absenteeism had been more protracted than hers. The defendant, also, identified two other employees in the same department as Russell, both of whom were white and both of whom were fired at about the same time as Russell for excessive absenteeism without any offer of a transfer. Again, the plaintiff-intervenor counters that the absenteeism of these two whites was more exaggerated than Russell's. The fact of the matter, though, is that the defendant terminated both white and black employees for excessive absenteeism and that Russell was guilty of such absenteeism is unquestionably established. — 111 — The District Court seems to accept that, under the Burdine rule,43 the defendant rebutted the intervenor-plaintiff's prima facie case by articulating a legitimate reason either for her discharge or her transfer because of her absenteeism and tardiness, as well as because of the friction between her and her employer and fellow employees in her existing department. The District Court, however, found that the defendant's reason for discharging Russell, as claimed by it, was pretextual. What the District Court purported to ground its finding of pretext in discharging Russell for absenteeism was that the offer to Russell of a transfer without loss of pay grade or salary level to another department was pretextual. It bases this conclusion on the alleged failure of the defendant to assure Russell that she would be given training for the new job and that she was not told specifically what the new job would be. The defendant's witness testified that Russell made no inquiries along this line but abruptly refused the transfer. It is admitted that she went straight from the bank to the EEOC office and filed a charge in which she justified her refusal on the ground that the defendant had earlier refused her request to transfer her to Adjustments.44 She made no such claim as that stated by the District Court in her charge. It is also significant that, when she requested a transfer to that department two months earlier, there had been no discussion of what her job would be, presumably because Russell, who had worked at the bank for several years, knew what the work was in the Adjustments Department, and because she knew that it was the policy of the bank to provide any training an employee might need where there was a transfer of jobs by employees. — 112 — Nor is there any reason to doubt the good faith of the bank in the offer of a transfer. Walker, the top official over Russell, indicated quite clearly to Russell he wanted to try to enable her to overcome her difficulties and to resume her career as a valuable employee of the bank. There was nothing in his conduct in the final interview, as testified to by Russell, herself, which would indicate abruptness, indifference, or hostility. On the contrary, Walker's attitude was, if we take his account (and Russell does not dispute it), friendly and conciliatory. He refused earlier to approve a recommendation to fire Russell and in selecting a department to assign her to on transfer, he chose the very one which Russell had earlier filed a complaint because she had not been transferred to it. We are unable to find any substantial evidence in the record to support a finding that the alternative offer of a transfer or termination was racially motivated45 or motivated by an intention to retaliate, or that the defendant's action was pretextual. This is a case of an employee, whose work performance, under her own testimony, was unsatisfactory and the mere fact that she had filed an EEOC charge could not immunize her from legitimate disciplining for unsatisfactory performance. Section 704(a) was never intended to be a shield for the admittedly delinquent employee. See Dickerson v. Metropolitan Dade County, 659 F.2d 574, 580-81 (5th Cir.1981); Hochstadt v. Worcester Foundation, Etc., 545 F.2d 222 (1st Cir.1976). To make out a case of retaliatory discharge, it was necessary under some of the decisions for Russell to show that "but for" her EEOC charge she would not have been discharged. Jackson v. City of Killeen, 654 F.2d 1181, 1186 (5th Cir.1981) ("Plaintiff failed to show that the defendant's reasons for her discharge were pretextual, i.e., that her race was a 'but for' cause or determining factor for her discharge"); Mack v. Cape Elizabeth School Bd., 553 F.2d 720, 722 (1st Cir.1977) ("... that but for them she would have been re-employed"); Staniewicz v. Beecham, Inc., 687 F.2d 526, 528 (1st Cir.1982); cf., Lovelace v. Sherwin Williams Co., 681 F.2d 230 (4th Cir.1982), and Brodin, The Standard of Causation in the Mixed-Motive Title VII Action: A Social Policy Perspective, 82 Col.L.Rev. 292 (1982).46 We find in all this no evidence of pretext in order to conceal a retaliatory intent and beyond question there was no racial bias involved. We accordingly reverse any finding of discrimination in Russell's treatment in this regard. — 113 — The second claim of the other intervenor-plaintiff Cooper presented a less complicated set of facts. She had been initially employed at pay grade 3 but she had been given what was, except for a delay occasioned by a maternity leave, roughly annual promotions until her promotion on August 12, 1974, when she had reached the level of pay grade 6. At that time her supervisor inquired of her whether she would like to move to the position of settlement clerk with an increase in pay grade to 7 and with a salary increase. She accepted the offer and on August 12 began her duties as a settlement clerk at pay grade 7. Later, when she discussed her job evaluation report with her supervisor, the latter told her, according to her account of the conversation, that she "was at the maximum for Grade 7, that [she] would have to get a promotion in order to get a raise" and that "he would let [her] know if any job came up that he felt [she] could do." In the latter part of June, 1975, she learned that John Morgan, a white, had been promoted from pay grade 6 to pay grade 8 and given a supervisory position. She complained to her supervisor that she had not been given the promotion and proceeded instantly to file her complaint of racial discrimination on July 8, 1975, with the EEOC. — 114 — John Morgan, who had received the promotion, had been employed in early 1974 by the defendant at pay grade 6 and had been assigned to the department where Ms. Cooper was working. On August 12, 1974, which interestingly was the same date on which Ms. Cooper had been promoted out of pay grade 6, Morgan was assigned as a reader-sorter operator in the department. This operation was connected with the computer division in the department and was housed in a compartment separate from and not observable from other parts of the department, including where Cooper worked. On February 10, 1975, Morgan was promoted to pay grade 8. There is dispute about his title as a result of the promotion. Morgan's superior testified that his promotion was to the position of reader-sorter supervisor; the employment record describes his new job as utility supervisor. The defendant contended it was a clerical mistake to list Morgan as a utility supervisor. It is not necessary, however, to resolve whether the title given or the record was in error. Whatever his formal title, it is beyond dispute under all the evidence that his primary duties from the first were connected for all practical purposes exclusively with the reader-sorter operation. Ms. Cooper's testimony corroborates indirectly this conclusion. From February until June, 1975, Ms. Cooper never saw Morgan in the department outside of the computer room and he exercised no supervisory duties in any area except in the computer room where the reader-sorter operation was located. In fact, Ms. Cooper testified she never came into contact with Morgan and never knew that Morgan had been promoted to a supervisory position even though they were working in the same department on the exact same shift, until, at a meeting of employees in late June, some five months after Morgan had been promoted, the department head told all the employees Morgan was a supervisor. Assuredly, if Morgan had been promoted in February to utility supervisor with authority over Cooper and others in the department, Cooper would have come in contact with him and would have known that he was her supervisor. All of this confirms that Morgan's primary responsibility, as the department head testified, was the reader-sorter operation and only that operation, though the department head indicated that, as time went on and Morgan became more proficient, he expected to extend Morgan's duties. — 115 — The District Court included in its findings a note to the effect that "[i]n view of the testimony regarding Morgan's duties, the demeanor of the witnesses and the record evidence, the Court refuses to accept defendant's assertions that J. Morgan was a reader-sorter supervisor. Even if J. Morgan were reader-sorter supervisor, Cooper was more qualified than J. Morgan according to defendant's records to fill the position and was more experienced in the Bank," and had higher performance evaluations. This finding was taken verbatim from plaintiffs' proposed findings, in which it appears, as it does in the District Court's findings, as note 9. This finding, however, though somewhat ambiguous, seems to accept that, under the facts, the issue revolves about the respective qualifications of Morgan and Cooper for reader-sorter supervisor. And the testimony of the parties was specifically directed to that issue. — 116 — Under these circumstances, we begin, as did the District Court, with assuming that Ms. Cooper had made out a prima facie case and that the defendant had responded with a legitimate, non-discriminatory reason for selecting Morgan because of his greater understanding and ability in operating the reader-sorter machine. The issue, under Burdine, then becomes whether Ms. Cooper has established by the preponderance of the evidence that such reason was pretextual and not asserted in good faith. We note at the outset that there is no showing anywhere that the defendant or any of its supervisors had demonstrated any racial prejudice or taken any discriminatory action against Cooper because of her race; nor is there any evidence of racial slurs or discourtesies directed at Ms. Cooper or any other black employees by the defendant or any of its managers or supervisors. On the contrary, the conduct of the defendant towards Cooper in particular had been uniformly considerate and helpful. Her record of steady promotions attested to that. In fact, her last promotion resulted not from any request by her for a promotion but was initiated wholly by Cooper's own supervisor. Nor was there any evidence of any practice of racial discrimination in promotions at Cooper's pay grade. The District Court found to that effect and the plaintiffs have not contested that finding. There simply is not any evidence in this case of any racial motivation in the defendant's act of preferring Morgan over Cooper for the particular job available on February 10. — 117 — There can be little argument that, if the primary responsibility of the job to which Morgan was promoted was the reader-sorter operation, Morgan's qualifications were superior to those of Cooper. It is not of moment whether Cooper had been longer employed over-all than Morgan. The question was: Was Morgan or Cooper better qualified to supervise the reader-sorter operation? The answer to that question turned on the experience and competency of the two parties in the operation of the reader-sorter machine, which unquestionably was an operation requiring considerable experience and skill. One could not well supervise such a complicated operation if one did not possess competency in the operation of such machine, particularly if the employee had not acquired the skill herself to operate the machine. Morgan had been an operator of the machine for some six months. He had shown proficiency as such an operator. He was able to operate the machine alone. He was in a position to supervise and to relieve the operators. He knew how to make minor repairs on the machine. Cooper had worked at most two and a half months in the reader-sorter room. She never had been able to operate the machine alone. She admitted she didn't know how to put the data in the machine and that such procedure was necessary in operating the machine. Her ability to work on the machine was confined to cleaning. It is impossible to understand how she could have relieved an operator or could have aided an operator who had trouble with placing data in the machine or could have supervised the employees working in the reader-sorter operations. Moreover, she did not like working in the reader-sorter room and had been transferred out of that operation at her own request. — 118 — The employer has the right to fix the qualifications that are "necessary or preferred" in selecting the employee for promotion, and, in order to make out a prima facie case, a plaintiff must establish that she meets these qualifications. This is the purport of the decision in Waters v. Furnco Construction Corp., 688 F.2d 39 (7th Cir.1982), on remand from 438 U.S. 567, 98 S.Ct. 2943, 57 L.Ed.2d 957 (1978), where the employer had established as qualification for hiring as bricklayers only those known by the foreman to be experienced and capable from former employment. Under the earlier decision of the Supreme Court in that case, that test was upheld though it denied experienced minority bricklayers who had not previously been employed by the defendant consideration for employment. This was, also, the holding in Aikens v. U.S. Postal Service, Bd. of Governors, 665 F.2d 1057, 1059 (D.C.Cir.1981), cert. granted, 455 U.S. 1015, 102 S.Ct. 1707, 72 L.Ed.2d 132,47 wherein the Court said: — 119 — "A plaintiff who demonstrates that he possesses the absolute minimum qualifications for a job [in promotion], therefore, does not necessarily make out a prima facie case; if the employer has indicated that certain additional qualifications are necessary or preferred, the plaintiff must demonstrate that he has those qualifications as well." Later, the Court added (Id., at 1060): — 120 — "At the prima facie stage ... the plaintiff may be required to go beyond a showing of minimum qualifications to demonstrate that he possesses whatever qualifications or background experiences the employer has indicated are important."48 — 121 — The defendant in this case clearly "indicated" that a qualification for the promotion in question was experience and competency in operating a reader-sorter machine, and the District Court recognized this. As we have already observed, by her own admission, Cooper could not operate a reader-sorter machine. She couldn't load the machine; neither had she ever operated the machine by herself. Absent that qualification, Cooper's claim of a prima facie case is open to serious doubt. But, even if we agree that she had made out a prima facie case, it is manifest, as the District Court found, that the defendant had "articulated" a legitimate reason for selecting Morgan over Cooper for the vacancy. In order to overcome the defendant's articulation of a legitimate reason for giving the vacancy to Morgan because of his greater experience and competency in the reader-sorter operations, Cooper had, according to Aikens, "to show [her] superiority" over Morgan in the reader-sorter operations "in order to prove discrimination," in her non-selection for the promotion, [665 F.2d at 1060] and thereby to establish that the defendant's reason was pretextual. Cooper failed entirely to meet this burden and the finding of the District Court to the contrary is without substantial support in the record and was clearly erroneous. — 122 — After Ms. Cooper learned of Morgan's promotion in late June, she determined to quit or, as she expressed it in her charge as filed with the EEOC, "[a]s a result [of] the defendant's denial of consideration of her for a new position], I was forced to terminate." The District Court held that Cooper quit "only because of the Bank's preferred treatment of Morgan and the embarrassment and unfavorable working environment to which Cooper was thereafter subjected," and that, "[u]nder the circumstances, the termination of her employment constituted a constructive discharge in violation of 403(a) [sic] of Title VII ...." This claim would appear mooted by the fact that Cooper failed to show that the defendant's ground for promoting Morgan was pretextual. But, even if the claim were not pretextual and the issue of constructive discharge was proper, there was no basis in the record for a finding of constructive discharge. To establish "constructive discharge" under Title VII, "the employee must [have been] subjected to employment practices which are discriminatory and which make the working conditions intolerable, thus forcing the employee to quit. Further the employer's actions must be intended by the employer as an effort to force the employee to quit." Irving v. Dubuque Packing Co., 689 F.2d 170, 172 (10th Cir.1982). See, also, J.P. Stevens & Co., Inc. v. N.L.R.B., 461 F.2d 490, 494 (4th Cir.1972); Grigsby v. North Miss. Medical Center, Inc., 586 F.2d 457, 461 (5th Cir.1978); Nolan v. Cleland, 482 F.Supp. 668, 672 (N.D.Cal.1979). There is absolutely no evidence that the defendant sought by its action "to force [Cooper] to quit." The evidence is quite clearly to the contrary. Cooper's supervisor sought to persuade her not to quit. Moreover, her only complaint of unfair treatment, even under her own testimony, was the failure to be promoted. Yet, "[t]he cases applying the doctrine of constructive discharge have held that failure to promote, in and of itself is not sufficient to result in a constructive discharge." Irving v. Dubuque Packing Co., supra, 689 F.2d at 172. Cooper claims that she was embarrassed by not being promoted. That occurs any time an employee is not promoted. Moreover, in this case, the embarrassment, if any, was short-lived. Cooper only learned of the promotion when she was working on the night shift and she immediately quit when she got off work that night. There was no harassment "to which Cooper was thereafter subjected." The only basis for a claim of "constructive discharge" is failure to promote and that simply is insufficient, particularly under the facts of this case, to establish a "constructive discharge." — 123 — We are confirmed in this opinion in this case by the response of the defendant when Cooper expressed her intention to quit. When told of her intentions, her supervisors, as we already pointed out, counseled her against quitting. Despite their counsel, she went to the Personnel Office and asked for a form of resignation. The employee in the Personnel Office attempted to dissuade Cooper from quitting. Cooper testified that the Personnel employee finally gave her the resignation form which Cooper signed. At this point, the testimony diverges. Cooper testified that the Personnel employee told her that she would not turn in the resignation until 12 o'clock that day and that, if Cooper wanted to withdraw it, to call her before 12 o'clock. Wilson, the Personnel officer involved, denied such understanding. Cooper claimed she called Wilson about 11:30 A.M. but that Wilson told her she had inadvertently shown the resignation to her superior and the latter had processed it. Wilson denied that such conversation took place. Whether the facts were as Cooper gave them or as Wilson testified, there is no evidence that there was any racial motivation which prompted the mix-up, if there actually was a mix-up, and nothing to support a finding of discriminatory purpose. — 124 — The claim of Cooper is remanded to the District Court with directions to dismiss. — 125 — There is another appeal connected with the class claim and consolidated with it for disposition by us, which remains for decision. It arose initially out of a motion by the individuals Phyllis Baxter, Brenda Gilliam, Glenda Knott, Alfred Harrison, and Sherri McCorkle to be permitted to intervene in the class action. These petitioners for intervention asserted in the proposed complaint, as attached to their petition to intervene, injury as a result of discrimination in promotions because of their race and color in violation of Sec. 1981,49 42 U.S.C. Except for the claim of Alfred Harrison, these claims related to denials of promotions out of pay grades above pay grade 5 occurring after January 3, 1974. — 126 — All of the petitioners, however, were clearly within the class certified by order of the District Court at the beginning of the class action on March 22, 1977, i.e.: — 127 — "All black persons who have been employed by the defendant at its Charlotte Branch Office at any time since January 3, 1974 [6 months prior to the first charge filed by the intervenors with EEOC], who have been discriminated against in promotion, wages, job assignments and terms and conditions of employment because of their race." — 128 — They received notice of that certification along with plainly stated advice that, if they desired, they could exclude themselves from the class by notifying the Clerk of the District Court, but that the Court would "include [them] in the class in this action unless [they] request[ed] to be excluded from the class in writing." The consequences of not opting out for a class member were distinctly spelt out in the notice: "... the judgment in this case, whether favorable or unfavorable to the plaintiff and the plaintiff-intervenors, will include all members of the class; all class members will be bound by the judgment or other determination of this action ...." The notice, also, stated the consequences of opting out: "... [they] would not be bound by any judgment or other determination in this action and you will not be able to depend on this action to toll any statutes of limitations on any individual claims that [they might] have against the defendant ...." The petitioners, though thus noticed, did not opt out but instead they cooperated with the class action by testifying at trial. On October 30, 1980, the District Court filed its "Memorandum of Decision" in the class action. It was not until March 23, 1981,--almost five months after the District Court had filed its Memorandum of Decision and four years after the class action was begun--that these petitioners appeared by the same counsel as had represented the plaintiffs in the class action, filed their motion for leave to intervene and to file complaint-in-intervention. — 129 — The District Court denied the motion to intervene, holding that petitioners claiming discrimination above pay grade 5, "are not entitled under the ruling of the court to be treated as members of the class which has gained rights in this litigation" and that petitioners having claims of discrimination below pay grade 5 "are in the class as to which relief has been ordered by the judgment in this case and their rights will be dealt with in Stage II proceedings" of this action. The denial was made without prejudice to any underlying rights the intervenors may have, and included a dictum to the effect that the Court saw "no reason why, if any of the would be intervenors are actively interested in pursuing their claims, they cannot file a Section 1981 suit next week, nor why they could not file a claim with EEOC next week." There was no appeal from this order. — 130 — The petitioners thereafter on May 13, 1981, filed their action in the District Court, setting forth their individual claims of discrimination in promotions because of their race and color occurring after January 3, 1974, in violation of Sec. 1981. The defendant moved to dismiss the action as barred under principles of res judicata by the adverse decision in the class action. The District Court entered an order denying the motion to dismiss without a statement of reasons but properly certified the issues raised by the motion to dismiss for interlocutory appeal under Sec. 1292, 28 U.S.C. Interlocutory appeal was granted to us and the appeal was consolidated for appeal purposes with the main appeal in this proceeding. — 131 — The rule for determining when a judicial determination in a properly certified class action will bind a class member, not opting out after notice, in asserting thereafter an individual claim within the range of charges determined in the class suit was settled by us in Dalton v. Employment Sec. Com'n. of N.C., 671 F.2d 835 (4th Cir.1982), cert. denied, --- U.S. ----, 103 S.Ct. 138, 74 L.Ed.2d 117; Woodson v. Fulton, 614 F.2d 940 (4th Cir.1980); Dorsey v. Smith, 91 F.R.D. 261 (D.Md.1981); see also, Kemp v. Birmingham News Co., 608 F.2d 1049 (5th Cir.1979). The class member in such a case seeking relief individually on charges of discrimination within the charges determined in the class action is precluded by res judicata from maintaining subsequently an individual action claiming discrimination in a particular ruled on in the class action. The only exceptions to this rule are grounded on due process, which requires that there be proper certification of the class, adequate notice to class members, and adequate representation of absent class members. Thus, if there were not class certification, res judicata does not apply. Simer v. Rios, 661 F.2d 655 (7th Cir.1981); see 48 A.L.R.Fed. Sec. 3, 679. Similarly, if the individual class member or his sub-class were not adequately represented, due process is violated and res judicata will not attach. Lewis v. Philip Morris, Inc., 419 F.Supp. 345 (E.D.Va.), rev'd. on other grounds, 577 F.2d 1135 (4th Cir.1978); Grigsby v. North Miss. Medical Center, Inc., 586 F.2d 457 (5th Cir.1978); Haas v. Howard, 579 F.2d 654 (1st Cir.1978). None of those circumstances is present here. The class was properly certified; proper notice was given class members; and the class was completely and adequately represented. The class certified and the charges litigated in the class action included the claims and charges asserted by the plaintiffs in these subsequent individual suits. They (except Harrison), are, therefore precluded by the determination of the District Court in the class action suit that there was no practice of discrimination in promotion out of pay grades above pay grade 5 in the years 1974 forward. The plaintiff Harrison, however, is precluded by our determination on this appeal that there was no practice of discrimination in pay grade 5 and below. — 132 — The plaintiffs seek to escape the bar created by the determination in the class action suit by arguing that they were prevented by the District Court in proving their individual claims in the class action trial. This argument would disregard the fact that the trial was bifurcated by agreement of the parties. Accordingly, the first issue to be resolved in this case was that of liability for discrimination by the defendant. If liability were not found at this stage, the second stage which would relate to establishing the individual claims of class members, such as these plaintiffs, would be mooted. However, specific evidence of individual acts of discrimination in promotion was relevant, but, under the practice in a bifurcated trial, it was not admitted to establish the class members' right to relief, but to provide support for the prima facie class claim of liability.50 This was made clear in the ruling of the District Court that any right of a class member to participate in a favorable judgment was a matter to be resolved only after the issue of liability had been resolved. Sledge v. J.P. Stevens & Co., Inc., 585 F.2d 625, 637 (4th Cir.1978), cert. denied, 440 U.S. 981, 99 S.Ct. 1789, 60 L.Ed.2d 241; Payne v. Travenol Laboratories, Inc., 673 F.2d 798, 828 (5th Cir.1982). The plaintiffs' counsel, who were also counsel in the class action suit, plainly recognized and acquiesced in this decision. See Newman v. Prior, 518 F.2d 97, 100-01 (4th Cir.1975). — 133 — The plaintiffs, also, press the point that the District Court in its order denying intervention, stated, by way of dictum, that it saw no reason why the plaintiffs could not file their individual suit under Sec. 1981 or why the EEOC could not validate a suit under Title VII by issuing now a right to sue letter. This comment was made by the District Court four and a half months after it had decided the class action suit and about four years after the plaintiffs had been noticed of their obligation to opt out if they wished to preserve their right to maintain an individual suit. The opinion expressed was plain dictum and could not constitute a basis for contending that the plaintiffs had been misled or prejudiced in any way. — 134 — Finally, the plaintiffs have cited to us Dickerson v. United States Steel Corp., 582 F.2d 827, 831-32 (3d Cir.1978). There is dictum in that case which, it could be argued, suggests that the proof is "different between class action claims and individual claims of discrimination" and that there is not such commonality of law or fact between the two claims, that of the class action and that of the individual's claim of discrimination, as to support res judicata. However, that is not the manner in which the ruling in Dickerson has been interpreted by the Third Circuit. In an en banc opinion in Croker v. Boeing Co., 662 F.2d at 997, that Circuit dismissed under res judicata two individual claims "because they were not named plaintiffs but rather were class-member witnesses whose classwide claims had been unsuccessful" in the earlier class suit and it cited Dickerson in support. — 135 — It is to be remembered that a judgment in a class action suit is not a one-way street for the benefit solely of the plaintiffs, as the plaintiffs would argue; its determination is available as either a weapon for the plaintiffs or a shield for the defendant, dependent on its result. Moreover, one of the reasons for Rule 23 is to relieve the burden on the courts of successive trials of the same issues. This purpose would be thwarted if a properly filed and prosecuted class action did not result in a determination binding on all members of the class as well as on the defendant. — 136 — We accordingly remand the individual cases of the five plaintiffs to the District Court with directions to dismiss. — 137 — In view of our determinations, the claim of plaintiffs' counsel for attorneys' fees in No. 81-1536 is mooted and the grant of such is vacated. — 138 — The judgments of the District Court in both cases are — 139 — REVERSED. Footnotes [1] 12 U.S.C. Sec. 341, et seq [2] Both plaintiffs' counsel and counsel for the defendant have submitted to the Court the proposed findings and conclusions as prepared by plaintiffs' counsel. A comparison of such findings and conclusions with the District Court's findings and conclusions supports the statement in the text [3] In De Medina, the court said: (p. 1011) "It is established that the requirement of fact findings cannot be met by a 'statement of ultimate fact without the subordinate factual foundations for it which must be the subject of specific findings.' O'Neill v. United States, 411 F.2d 139, 146 (3d Cir.1969). Further, the fact findings must touch all material issues. 'For this court to exercise adequately its power of review, the district court must make specific findings about the nature and truth of [plaintiffs'] allegations.' Borrell v. ICA, 682 F.2d 981 at 992 (D.C.Cir.1982)." [4] Quoted with approval in Hershey-Creamery Co. v. Hershey Chocolate Corp., 269 F.Supp. 45, 48 (S.D.N.Y.) [5] That only employees in pay grades 4 and 5 were "class members" in evaluating promotions out of those pay grades is indicated in the District Court's order filed on May 29, 1981, denying intervention by Phyllis Baxter, Brenda Gilliam, Glenda Knott, and Sherri McCorkle because these "were in grades higher than grade 5 [and] are not entitled ... to be treated as members of the class which gained rights in this litigation." It did recognize the rights of Alfred Harrison and Emma Ruffin as members of the class [6] Ruffin applied, according to her testimony, for a typist position. She, along with other applicants, took a typing test. There is no evidence that her test qualified her for the promotion nor that her qualifications were superior to the person selected. The same is true in the case of Harrison. While the District Court made the bald statement that he "made an adequate showing on the tests for the position," there is no evidence in the record to support a finding that Harrison's showing on the tests was the same as the one selected for the vacancy, much less that he was better qualified. It is true he had been in the Army but his only assignment was, by his own testimony, "processing requisitions and in handling computer printouts." See Aikens v. United States Postal Service of Governors, 665 F.2d 1057 (D.C.Cir.), cert. granted, 455 U.S. 1015, 102 S.Ct. 1707, 72 L.Ed.2d 132 (1982) discussed later in connection with the plaintiff Cooper's claim. Upon oral argument of this case in the Supreme Court, even counsel for the plaintiff-employee conceded that a prima facie case of alleged discriminatory denial of promotion would be rebutted by a showing of superior qualifications of the person employed over the plaintiff; the contention of the defendant, which was the issue on which certiorari had been granted, was that, in order to establish a prima facie case, superior qualifications of the plaintiff had to be proved. Unquestionably, there is no evidence in this record that either Ruffin or Harrison was superior in qualifications to the person selected for the vacancy in question [7] To the same effect, see United States v. Jacksonville Terminal Co., 451 F.2d 418 (5th Cir.), cert. denied, 406 U.S. 906, 92 S.Ct. 1607, 31 L.Ed.2d 815 (1972) [8] It should be noted that the District Court found--and the plaintiffs do not contest this finding--that there was no class discrimination in promotions in pay grades 6 and above [9] This very manipulability of statistical modeling caused the writer in the Note, Judicial Refinement of Statistical Evidence in Title VII Cases, 13 Conn.L.Rev. 515, 525-26 (1981), to warn: "Statistics can be exaggerated, oversimplified, or distorted to create support for a position that is not otherwise supported by the evidence. Samples with built-in biases, unqualified statements of 'average' values, and improper mathematical operations with statistics are areas of statistical manipulation that can misrepresent the data." In S. Agid, Fair Employment Litigation: Proving and Defending a Title VII Case, 540 (2d ed. 1979), the author speaks of the "legendary amenability to manipulation and abuse" of statistical evidence. And in Wilkins v. University of Houston, 654 F.2d 388, 395 (5th Cir.1981), vacated and remanded, --- U.S. ----, 103 S.Ct. 34, 74 L.Ed.2d 47 (1982), the Court referred to the "inherently slippery nature" of statistical evidence. See also United States v. Test, 550 F.2d 577, 593 (10th Cir.1976), "We will not accept movants strategic manipulation of their data for the sole purpose of fabricating a 'group' of such size as to circumvent the normal evidentiary requirements of cognizability." [10] International Brotherhood of Teamsters v. United States, 431 U.S. 324, 339, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396 (1977) [11] Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977) [12] Barnett v. W.T. Grant Co., 518 F.2d 543, 549 (4th Cir.1975) [13] Robinson v. City of Dallas, 514 F.2d 1271 (5th Cir.1975) [14] Olson v. Philco-Ford, 531 F.2d 474 (10th Cir.1976) [15] Keyes v. Lenoir-Rhyne College, 552 F.2d 579 (4th Cir.1977), cert. denied, 434 U.S. 904, 98 S.Ct. 300, 54 L.Ed.2d 190 [16] For a good illustration of the Court's careful analysis of statistical evidence and its supporting data, see the opinion of Justice Stevens in New York City Transit Authority v. Beazer, 440 U.S. 568, 585-87, 99 S.Ct. 1355, 1365-1366, 59 L.Ed.2d 587 (1979) and Chance v. Board of Examiners, 458 F.2d 1167, 1173 (2d Cir.1972). In the latter case, the Court said: "After all the technical statistical jargon like 'one-tail' or 'two-tail' tests and 'Chi-Square Test (Yates-corrected)' as well as the less esoteric numbers and percentages [as] were placed before the trial judge, it was his job to resolve the issues." [17] In this context, "[t]he level of significance is a statistical method of identifying the probability that the observed cause-effect relationship (correlative) occurred by chance." Agid, supra, p. 553 [18] Harper, Statistics as Evidence of Age Discrimination, 32 Hast.L.J. 1347, 1354 (1981) Baldus and Cole, Statistical Proof of Discrimination, (1982 Cumulative Supplement), stated the point well: "An easily avoided problem is the treatment of the test of statistical significance as a rule of law rather than as an aid to interpretation. A test of significance is treated as a rule of law when the court asks whether the observed disparity is statistically significant at the .05 level or whether it satisfies the two or three standard deviations rule. If the answer is yes, the prima facie case is established or the evidence is credited. If the answer is no, the prima facie case fails or the evidence is disregarded. This approach was never intended by the United States Supreme Court in Castaneda and Hazelwood and completely misses the point that in discrimination suits, as in all other contexts, tests of statistical significance and confidence intervals do not lay down arbitrary rules for accepting or rejecting data. Rather the tests provide information to assist one in assessing the degree of reliability of the data and in answering specific questions of interest." Sec. 9.4, p. 88. See Note, Beyond the Prima Facie Case in Employment Discrimination Law: Statistical Proof and Rebuttal, 89 Harv.L.Rev. 387, 393, n. 26 (1975): "... what constitutes a substantial disparity has not clearly been resolved." [19] 32 Hastings L.J., supra, at 1354 [20] We said in Equal Employment Opportunity Com'n. v. Am. Nat. Bank, 652 F.2d at 1192: "From all this we conclude that courts of law should be extremely cautious in drawing any conclusions from standard deviations in the range of one to three. Above this range, with standard deviations of more than three, the analysis may perhaps safely be used absolutely to exclude chance as a hypothesis, hence absolutely to confirm the legitimacy of an inference of discrimination based upon judicial appraisals that disparities are, to the legally trained eye, 'gross.' This we conclude is all that the Supreme Court has ever directly approved by its own use of the process." [21] See Hallock, The Numbers Game-The Use and Misuse of Statistics in Civil Rights Litigation, 23 Villanova L.Rev. 5, 12 (1977-78): "Statistical significance must be distinguished from 'legal significance.' " [22] Actually the testimony of the expert was that after eliminating any black promotee who left the defendant's employ before the end of the year under review and then reviewing the data, "we find that there is now a significant difference in grade 4 no matter what assumption you make and there is also a significant difference in grade 5." [23] Actually, there is considerable authority for the rule that statistical deviations, based on samples of 30 or below, are unreliable [24] The method of applying the two tests is: year N total n p q § 1 § 2 blacks in grade ---- -- --------- -- -- -- --- --- Grade 4 ------- 1974 68 45 43 0.66 0.34 1.90 3.11 1975 41 24 13 0.59 0.41 1.48 1.77 1976 22 15 7 0.68 0.32 1.04 1.23 1977 23 16 3 0.70 0.30 0.76 0.79 --- --- --- total 154 100 66 0.65 0.35 2.94 3.87 Grade 5 ------- 1974 80 34 37 0.43 0.57 2.22 3.01 1975 86 44 24 0.51 0.49 2.09 2.45 1976 62 34 31 0.55 0.45 1.97 2.77 1977 41 23 15 0.56 0.44 1.55 1.92 --- --- --- total 269 135 107 0.50 0.50 4.02 5.17 l2-5 N = total grade l2-5 n = total in grade promoted l2-5 p = proportion blacks in N l2-5 q = proportion blacks in N l2-5s1 = standard error under l2-5 hypergeometric test l2-5s2 = standard error under l2-5 binomial test TABLE CONTINUED expected actual difference number § 1 number § 2 black black b/w expected standard standard promotions (np) promotions and actual deviations deviations (diff. / § 1) (diff. / § 2) ------------------ ----------- -------------- --------------- ------------- 28.4 * 25 3.4 * 1.79 1.09 7.7 * 7 0.7 * 0.47 0.40 4.8 2 2.8 2.69 2.28 2.1 1 1.1 1.45 1.39 -- 42.9 35 7.9 2.69 2.07 15.9 13 2.9 1.31 0.96 12.2 12 0.2 0.10 0.08 17.0 16 1.0 0.51 0.36 8.4 5 3.4 2.19 1.77 -- 53.5 46 7.5 1.87 ** 1.45 Table I. BASED ON DATA FROM PLAINTIFFS' TABLES 34a and 35a (J. App. at 1117). [25] * Differs from Table 34a because of rounding here to nearest tenth in expected black promotions. [26] ** Unclear how plaintiffs got 2.01 in Table 35a. (i.e. unclear how plaintiffs got § 1 value of 3.73 instead of the correct number 4.02). [27] N = total grade [28] n = total in grade promoted [29] p = proportion blacks in N [30] q = proportion blacks in N [31] s1 = standard error under hypergeometric test [32] s2 = standard error under binomial test [25] Our formula for calculating the "standard error" and the standard deviation level is under the hypergeometric distribution test as follows (P. Noel, supra, at 70): And for the binomial distribution test (as applied in Hazelwood and Castaneda ): Applying the hypergeometric formula to exhibit 35a, the result is: [26] The exhibit as prepared by plaintiffs' expert for "Promotions Out of Grade 5" in exhibit 35 lists the standard deviation for black promotions in that pay grade for the years in question as -2.24. This is the figure the witness used in his testimony. Such calculation, however, is erroneous. The error in the expert's calculation arose out of his own calculation of the difference between total black promotions and expected black promotions in that grade. He lists the difference as -8.80. Actually, the difference between 58.80 and 52 is 6.8 and not 8.80. This error is apparent on the face of the exhibit itself. Yet it is on this erroneous calculation that the expert testified that, "using a hypogeometric [sic] difference" of -2.24 between black and white promotions out of pay grade 5 as shown in exhibit 35 year N total n p q § 1 § 2 blacks in grade ---- -- --------- -- -- -- --- --- Grade 4 ------- 1974 85 52 47 0.61 0.39 2.25 3.34 1975 51 31 14 0.61 0.39 1.57 1.82 1976 33 21 9 0.64 0.36 1.25 1.44 1977 30 20 3 0.67 0.33 0.79 0.81 --- --- --- total 199 124 73 0.62 0.38 3.31 4.15 Grade 5 ------- 1974 92 39 39 0.42 0.58 2.35 3.08 1975 107 53 28 0.50 0.50 2.28 2.65 1976 79 41 37 0.52 0.48 2.23 3.04 1977 45 24 16 0.53 0.47 1.62 2.00 --- --- --- total 323 157 120 0.49 0.51 4.35 *** 5.48 TABLE CONTINUED expected actual difference number § 1 number § 2 black black b/w expected standard standard promotions promotions and actual * deviations deviations (np) * (diff. / § 1) (diff. / § 2) ---------------- ---------- --------------- ---------------- -------------- 28.7 27 1.7 0.76 0.51 8.5 8 0.5 0.32 0.27 5.8 3 2.8 2.24 1.94 2.0 1 1.0 1.27 1.23 -- 45.3 39 6.3 1.90 * 1.52 16.4 14 2.4 1.02 0.78 14.0 14 0 0 0 19.2 19 0.2 0.09 0.07 8.5 5 3.5 2.16 1.75 -- 58.8 52 6.8 ** 1.56 1.24 Table II. BASED ON DATA FROM PLAINTIFFS' TABLES 34 and 35 (J. App. at 1115). [35] * Values differ slightly from Tables 34 and 35 because of rounding here to nearest tenth in expected black promotions. [36] ** Erroneously recorded in Table 35 as 8.80 [37] *** Unclear how plaintiffs got § 1 value of 3.93 [27] EEOC v. American National Bank, 652 F.2d at 1192, quoting from Castaneda, 430 U.S. at 497, n. 17, 97 S.Ct. at 1281, n. 17 [28] "COURT: Why don't we go to Table 35? "A Table 35 is the same for grade 5 as the previous table was for grade 4. In that table if we sum across all individuals, we find a significant difference between blacks and whites. "Q What is the standard deviation of Table 35? "A 2.24, using a hypergeometric distribution. (It will be observed that the expert is basing this opinion upon his own incorrect computation of the standard deviations resulting from the numbers in the exhibit. See note 26. If we use the correct deviation level, this number is similarly not statistically significant.) "Q Is that a statistically significant difference? "A Yes, it is. "Q Does one need to make the same assumption in 35 that one needs to make in 34 as to-- "A No. "Q --as to whether there has been discrimination before finding that significant difference? "A No." [29] See note 26 [30] As we have already observed, many statisticians today frown on a blanket statement of statistical significance, based on any specific number of standard significance and suggest that the disparity shown by the calculation of standard deviation is just one circumstance to be weighed by the trier of fact. We do not need, however, to address this question here beyond noting the contrary views among statisticians [31] For a more favorable view of multiple regression studies, see Fisher, Multiple Regression in Legal Proceedings, 80 Col.L.Rev. 702 (1980) and Finkelstein, The Judicial Reception of Multiple Regression Studies in Race and Sex Discrimination Cases, 80 Col.L.Rev. 737 (1980) [32] Finding of Fact # 56 [33] See also Ste. Marie v. Eastern R. Ass'n., 650 F.2d 395 at 400 (2nd Cir.1981) where, in dismissing a comparison of salary gap between male and female employees at all levels, Judge Friendly said "that the gap between male and female employees in salary and salary expectations occurred because of the low representation of women in higher salaried positions." [34] To make plain its opinion of such evidence, the Court in that case added (p. 579): "This leads the Court to conclude that too many use statistics as a drunk man uses a lamppost--for support, and not illumination." [35] See Ste. Marie, (650 F.2d at 401): "There is no principle requiring an employer following a policy of promoting from within to make this applicable across the board rather than only to those employee groups whose work gives them the opportunity to acquire the skills needed for promotion." [36] It will be noted that the standard deviations under this test are actually less than the 1.65 standard, stated by plaintiffs' expert, for a "one-tail" test [37] See note 24 [38] In United Air Lines, Inc. v. Evans, 431 U.S. 553 at 558, 97 S.Ct. 1885 at 1889, 52 L.Ed.2d 571 (1977), the Supreme Court said: "A discriminatory act which is not made the basis for a timely charge is the legal equivalent of a discriminatory act which occurred before the statute was passed. It may constitute relevant background evidence in a proceeding in which the status of a current practice is at issue, but separately considered, it is merely an unfortunate event in history which has no present legal consequences." [39] The language of the District Court was that in this case there was "significant disparity at the 5 percent level of reliability" "with respect to each year [for pay grades 4 and 5, as shown by exhibits 34a and 35a, later discussed] and for the combined years 1974-78." Without regard to whether we are to accept "the 5 percent level" as reliable, this statement is plainly incorrect, as a cursory review of the very tables quoted by the District Court in its Findings, which used the more favorable hypergeometric test, will demonstrate. For the years 1975 and 1977 the disparity in pay grade 4, as shown on exhibit 34a as quoted by the District Court, is -.6 and -1.1, which under any test stated by plaintiffs' expert was not "statistically significant." Similarly, in pay grade 5 for 1975 and 1976, the standard deviations were -.2 and -1.0, neither of which would be considered by econometricians as sufficient statistically [40] The District Court speaks of "meetings." The complainant referred to a single meeting [41] There was no evidence that she was ever demoted. Russell, however, apparently based this claim upon her contention that she was denied the same prerogatives of attending a meeting as had Mauney and Moore. This denied her, as she asserts, supervisory status. However, the only supervisory status she was ever promised by her own testimony was "to train new employees" and that, by her own testimony, she did. Actually, her charge was filed in retaliation for being placed on probation for absenteeism [42] This apparently refers to an inquiry by Russell about the opportunity for experience in the use of a particular machine. The supervisor explained, according to Russell, that the existing machine was being replaced by a more sophisticated machine and he was not providing training on the old machine but would provide it when the new machine was received [43] Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981) [44] Russell had earlier filed three charges against the defendant with the EEOC. The first was in July, 1974, after she was placed on probation, the second was in October, 1974, when she was told her supervisor was recommending her termination, the third on January 23, 1975 and the final one on January 24, 1975, after she had been terminated [45] There is no evidence that, in its dealings with employees, the defendant or its supervisors had ever evidenced any racial bias. There is no testimony of racial slurs by supervisors, as in many cases. There was no harassment of minority employees because of their race. If anything, the minority was, as we have seen, actually favored over-all in promotions [46] The author concludes: "Although the Supreme Court has said little regarding mixed-motive causation in individual Title VII cases, its teaching in Title VII class-action cases and elsewhere seems to point toward the adoption of a test that permits a defendant who is found to have been motivated by an unlawful consideration to escape liability if he can establish that he would have arrived at the same decision even absent the unlawful consideration." [Page 293] [47] Certiorari was granted on the petition of the employer, the United States Postal Service in Aikens. The petition assailed the holding of the Court of Appeals that a minority employee, claiming discrimination in a promotion, need not establish that he was either as well or better qualified than the employee selected for the promotion in order to make out a prima facie case. See Note, Relative Qualifications and the Prima Facie Case in Title VII Litigation, 82 Col.L.Rev. 553, 563 (1982). We assume that the employee in this case had made out a prima facie case but we decide this case upon the failure of the claimant to meet the test established in Aikens for proving that the employer's reason for failing to promote the claimant was pretextual. In that latter case, the burden is on the claimant to show her "superiority" or, at least, equality, in competency over the one selected [48] Certiorari was granted on the petition of the Solicitor General appearing on behalf of the defendant contending that the rule enunciated by the Court of Appeals on proof of a prima facie case, as required of the plaintiff, was too lenient [49] It is plain they did not assert claims under Title VII because their claims under that statute would have been untimely [50] See Valentino v. United States Postal Service, 674 F.2d at 68: "Even when the statistical proof is so compelling that it might, in itself, satisfy the plaintiff's initial burden, the prima facie case is bolstered and the court's evaluation is aided by testimony recounting personal experiences of class members."