Full opinion text
HARLINGTON WOOD, Jr., Circuit Judge. This appeal arises out of an individual and class action brought under Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C. §§ 2000e et seq. (1976 & Supp. V 1981), and the Civil Rights Act of 1866, 42 U.S.C. § 1981 (1976), charging racial discrimination in the pattern and practice of employee discharges between 1974 and 1981 at defendants-appellees’ Midwest Diaper Plant formerly in Park Forest South, Illinois. Plaintiffs-appellants are Wesley Coates, a black employee who commenced this litigation individually after the defendants fired him in April, 1975, members of a class certified as all blacks discharged from the plant from 1974 until the plant closed in 1981, and intervenor Equal Employment Opportunity Commission (EEOC). Plaintiffs appeal from the decision of the trial court finding that defendants did not engage in a pattern or practice of discrimination against blacks in discharging members of the certified class or the class representative, Wesley Coates. Coates v. Johnson & Johnson, 28 Empl.Prac.Dec. (CCH) U 32,-664 (N.D.Ill.1982). Plaintiffs allege that the district court erred in its consideration of plaintiffs’ statistical and nonstatistical evidence and various other issues. I. COMPANY BACKGROUND Defendants constructed the plant in 1978 and operated it until March, 1981 when it was closed for financial reasons. The location for the plant had been selected because the company sought an experienced and racially-integrated work force. As a result of an affirmative action plan developed with the general contractor building the plant, approximately 25% of the work was subcontracted to minority-controlled firms. Although the construction trades were not known at that time for their enthusiasm for an integrated work force, the company managed to obtain a construction work force that was 25% to 30% black. After construction, the total work force at the plant ranged from a low of 437 employees in 1973 to a high of 784 in 1980. The percentage of blacks in the work force ranged from a low of 19.4% in 1973 when the plant opened, to a high of 27% in 1979. The management of the plant consisted of first-line supervisors, department managers, production managers and superintendents, and a plant manager. Over the approximately eight-year life of the plant, a very significant percentage of supervisors and upper-level managers were black, generally increasing each year until just before closing, when the high was reached of 41% black managers and 8% black supervisors. One of the production managers, Ather Williams, Jr., a black, was promoted in 1976 to plant manager, replacing a prior white plant manager, and in 1980 Williams was promoted to director of "operations, although he was not replaced as plant manager. There were two general categories of employees: salaried employees (professional/technical, clerical) and wage employees (production workers). The conditions' of employment of the wage employees were governed by successive union bargaining agreements, but wage employees were not covered by the grievance procedures of the collective bargaining agreement until after a sixty-day probationary period. In 1976, the plant management adopted progressive disciplinary and discharge procedures for all nonprobationary wage and salaried employees. Severity of the discipline increased with the severity of the offense. The more severe category (Group I) included offenses such as insubordination, sleeping on the job, fighting and safety violations; a Group I violation could result in immediate suspension and later discharge. The less severe offenses (Group II) included absenteeism, poor performance and minor safety violations. A Group II violation could result in counseling, reprimand, or suspension and even discharge if repeated. See Coates (POF 128-45). First-line supervisors had direct responsibility for the administration of discipline. Discipline matters could proceed through the grievance procedures to the plant manager, who could uphold or reverse the disciplinary action. If the union was not satisfied, it could proceed to binding arbitration. The successive collective bargaining agreements all contained provisions for a grievance based on any company action perceived to be racially discriminatory. Salaried employees not covered by the grievance procedure had ' a different appeal route through department managers and division heads to the employee relations managers. These procedures, as detailed as they were, necessarily allowed a measure of discretion and judgment to those involved in the process. II. LITIGATION BACKGROUND On April 23, 1975, the company discharged plaintiff Wesley Coates, a wage employee who had survived his probationary period by two months, for sleeping on the job. This incident occurred one day after Coates had been reinstated from a suspension for damaging company property while driving a forklift truck. The company decided not to lessen the punishment because an undercover investigative agent working inside the plant reported that Coates was selling drugs on company property. Coates filed a charge with the EEOC and about three years later brought this suit. The complaint was amended to allege Title VII class discrimination and to add a count alleging individual and class discrimination under 42 U.S.C. § 1981 (1976). Coates contended that he and more than 200 other blacks were discharged “as a consequence of a uniform policy and practice to reduce black employment and discriminatorily discharge black employees at defendants’ plant.” He alleged that defendants maintained a continuing policy and practice of discriminatorily discharging black employees through (1) an articulated plan to reduce the representation of blacks at the plant and (2) a highly discretionary discipline-discharge-reinstatement system under which blacks were treated less favorably than whites. The district court certified the class on May 29, 1981 and Coates, a somewhat less than exemplary employee, became the named class representative. After extensive discovery and a thirteen-day bench trial, the district court ruled for defendants on both the class and individual claims. The court found that plaintiffs’ statistical and nonstatistical evidence was adequately rebutted by defendants, and that plaintiffs failed to meet their burden of persuasion. It is from this ruling that plaintiff Coates, individually and on behalf of the class, and the EEOC appeal. Although there are some questionable and close aspects, they do not, in the context of this case, result in reversible error. We affirm. III. THE LEGAL STANDARDS Plaintiffs’ initial objection to the district court’s decision is that the court analyzed the class action claim according to an “incorrect legal framework” for Title VII class cases. Plaintiffs contend that the district court erred by confusing the kind of evidence required to rebut a private, nonclass disparate treatment prima facie case with that sufficient to rebut a government or class pattern or practice disparate treatment prima facie case. In McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), the Supreme Court provided an analytical framework “intended progressively to sharpen the inquiry into the elusive factual question of intentional discrimination” in private, nonclass Title VII cases. Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 255 n. 8, 101 S.Ct. 1089, 1094 n. 8, 67 L.Ed.2d 207 (1981). Under this McDonnell Douglas-Burdine framework, the plaintiff is required to establish a prima facie case by producing facts that “eliminate[] the most common nondiscriminatory reasons” for the defendant’s alleged action, for example, by showing that he or she is a member of a protected group and is otherwise basically similarly situated to members of the unprotected group. Burdine, 450 U.S. at 254,101 S.Ct. at 1094. It then becomes a reasonable assumption that any differential treatment by the employer was due to discrimination. The facts the plaintiff must show to be entitled to the inference of discrimination will vary according to the type of employment practice involved. McDonnell Douglas, 411 U.S. at 802 n. 13, 93 S.Ct. at 1824 n. 13; Burdine, 450 U.S. at 253 n. 6, 101 S.Ct. at 1093 n. 6. A plaintiff’s prima facie case creates a rebuttable presumption that the defendant unlawfully discriminated against the plaintiff and compels the trier of fact to award judgment for the plaintiff unless the defendant offers evidence that “raises a genuine issue of fact as to whether [the defendant] discriminated against the plaintiff.” Burdine, 450 U.S. at 254-55, 101 S.Ct. at 1094. The defendant’s burden may be met by “articulating] some legitimate, nondiscriminatory reason” for the defendant’s employment action. McDonnell Douglas, 411 U.S. at 802, 93 S.Ct. at 1824; see Burdine, 450 U.S. at 254, 101 S.Ct. at 1094. The purpose of this evidence is to “allow the trier of fact rationally to conclude that the employment decision [was not] motivated by discriminatory animus.” Burdine, 450 U.S. at 257, 101 S.Ct. at 1096. If the explanation provided by the defendant is “legally sufficient to justify a judgment for the defendant,” then “the presumption raised by the prima facie case is rebutted, and the factual inquiry proceeds to a new level of specificity.” Id. at 255, 101 S.Ct. at 1094-95 (footnote omitted). This new level allows the plaintiff to try to persuade the court that the defendant’s explanation is “unworthy of credence” or that “a discriminatory reason more likely motivated” the defendant. Id. at 256, 101 S.Ct. at 1095. The plaintiff retains the ultimate burden of persuasion. Id. The Supreme Court has applied an analogous analytical framework to the liability phase of a government or class action alleging a pattern or practice of disparate treatment. In International Brotherhood of Teamsters v. United States, 431 U.S. 324, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977), the Court explained that: The importance of McDonnell Douglas lies, not in its specification of the discrete elements of proof there required, but in its recognition of the general principle that any Title VII plaintiff must carry the initial burden of offering evidence adequate to create an inference that an employment decision was based on a discriminatory criterion illegal under the Act. 431 U.S. at 358, 97 S.Ct. at 1866. Relying on Franks v. Bowman Transportation Co., 424 U.S. 747, 96 S.Ct. 1251, 47 L.Ed.2d 444 (1976), the Teamsters Court stated that plaintiffs who raise a pattern or practice class claim have as their initial burden the task of demonstrating that unlawful discrimination has been the regular policy of the employer, i.e., that “discrimination was the company’s standard operating procedure — the regular rather than the unusual practice.” 431 U.S. at 336, 360, 97 S.Ct. at 1854, 1867. The focus “often will not be on individual [employment] decisions, but on a pattern of discriminatory decisionmaking.” Id. at 360 n. 46, 97 S.Ct. at 1867 n. 46. The plaintiffs’ prima facie case will thus usually consist of statistical evidence demonstrating substantial disparities in the application of employment actions as to minorities and the unprotected group, buttressed by evidence of general policies or specific instances of discrimination. Once the plaintiffs establish a prima facie case of a pattern or practice of discrimination, “[t]he burden then shifts to the employer to defeat the prima facie showing of a pattern or practice by demonstrating that the [plaintiffs’] proof is either inaccurate or insignificant,” id. at 360, 97 S.Ct. at 1867, or by providing a “nondiscriminatory explanation for the apparently discriminatory result.” Id. n. 46; see also Dothard v. Rawlinson, 433 U.S. 321, 338-39, 97 S.Ct. 2720, 2731-32, 53 L.Ed.2d 786 (1977) (Rehnquist, J., concurring) (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”). “The strength of the evidence the defendant must produce to prevent the plaintiff[s] from carrying the burden of persuasion as to disparity depends, as in any case, on the strength of the plaintiffs’ proof.” Segar v. Smith, 738 F.2d 1249, 1268 (D.C.Cir.1984). Nonetheless, at the liability stage of a pattern or practice suit, the plaintiff always bears the burden of persuasion with respect to discrimination. See Craik v. Minnesota State University Board, 731 F.2d 465, 487-88 (8th Cir.1984) (Swygert, J., dissenting). Although the general framework for analyzing the liability portion of a government or class disparate treatment case is essentially comparable to the framework outlined in McDonnell Douglas-Burdine for individual disparate treatment actions, the content of the specific stages of that framework will be different. The focus in a class action is “on a pattern of discriminatory decision-making,” 431 U.S. at 360 n. 46, 97 S.Ct. at 1867 n. 46, of which specific allegations of alleged discrimination may be a part, although not always controlling if the number of such instances is not significant. The class action “may fail even though discrimination against one or two individuals has been proved.” Cooper v. Federal Reserve Bank of Richmond, — U.S.-, 104 S.Ct. 2794, 2801, 81 L.Ed.2d 718 (1984). The pattern or practice claim may also fail — despite any statistical evidence offered by plaintiffs — if the defendant articulates a nondiscriminatory, nonpre-textual reason for every discharge. See Paxton v. Union National Bank, 688 F.2d 552, 567 (8th Cir.1982), cert. denied, 460 U.S. 1083, 103 S.Ct. 1772, 76 L.Ed.2d 345 (1983). On the other hand, the class claim does not fail just because the district court finds that the company has satisfactorily explained the discharges of the named class representatives and any other testifying employees. Boykin v. Georgia-Pacific Corp., 706 F.2d 1384, 1393 (5th Cir.1983), cert. denied, — U.S.-, 104 S.Ct. 999, 79 L.Ed.2d 231 (1984). Since strong statistical evidence, without anecdotal evidence, may in some cases form a prima facie case, see Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741-42, 53 L.Ed.2d 768 (1977); Segar, 738 F.2d at 1277-78, a defendant’s successful rebuttal of each alleged instance of discrimination weakens, but does not defeat, a plaintiff’s class claim. Neither statistical nor anecdotal evidence is automatically entitled to reverence to the exclusion of the other. Plaintiffs maintain that the district court misunderstood the type of evidence that defendants must offer to rebut a plaintiff’s prima facie pattern or practice suit and treated the class action as a collection of individual lawsuits, thus failing to accord plaintiffs “the stronger presumption of deliberate discrimination” that attends the establishment of a prima facie case of class-wide discrimination. Plaintiffs argue that the district court allowed defendants to rebut their prima facie case by accepting defendants’ proffered explanations for the decisions to discharge the individual class members who testified. We recognize that, had the district court treated the class action solely as a collection of individual lawsuits and allowed defendants to rebut plaintiffs’ prima facie case in the manner claimed by plaintiffs, we would have a different issue. See Teamsters, 431 U.S. at 343 n. 24, 97 S.Ct. at 1858 n. 24; EEOC v. American National Bank, 652 F.2d 1176, 1198 (4th Cir.1981), cert. denied, 459 U.S. 923, 103 S.Ct. 235, 74 L.Ed.2d 186 (1982). Considering all the circumstances of this case, we do not believe Judge Leighton underestimated the showing required to rebut plaintiffs’ prima facie case which he found plaintiffs had established. We are satisfied that the district court assessed the weight of all of defendants’ evidence as he was entitled to do, not just defendants’ explanations of the discharges of the class representatives in concluding that defendants had not discriminated. Heeding the teaching of United States Postal Service Board of Governors v. Aikens, 460 U.S. 711, 103 S.Ct. 1478, 75 L.Ed.2d 403 (1983), we now briefly review all the evidence, although we do not retry the case here, to determine whether the district court’s findings that defendants did not engage in a pattern or practice of discrimination as to the class and did not discriminate against plaintiff Coates are clearly erroneous. Id. at 716, 103 S.Ct. at 1482; Pullman-Standard v. Swint, 456 U.S. 273, 285-90, 102 S.Ct. 1781, 1788-91, 72 L.Ed.2d 66 (1982); Fed.R.Civ.P. 52(a). We consider the evidence relating to the individual claims in our assessment of the class claim, and vice-versa, since evidence relevant to one is also relevant to the other. The class claim is to be considered first, since if the class claim has merit, the named and unnamed individual class members are entitled to the burden-shifting presumption of Teamsters. Craik, 731 F.2d at 471. We will find a factual finding clearly erroneous only if, after reviewing all the evidence, we are “left with the definite and firm conviction that a mistake has been committed.” United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948). IV. CLASS CLAIM Plaintiffs’ class claim charged defendants with engaging in a continuing policy and practice of discriminatorily discharging black employees. This policy and practice allegedly were manifested in an articulated plan to reduce the representation of black employees at defendants’ plant, and in a disciplinary-discharge-reinstatement system under which management personnel had “unbridled discretion” in taking employment actions, and allegedly used that discretion in a discriminatory manner. Plaintiffs relied on the discretionary nature of defendants’ disciplinary system to point out how disparate treatment of blacks and whites could easily result because of racial animus on the part of various supervisory personnel. With their anecdotal and statistical evidence, plaintiffs attempted to demonstrate the existence of racial animus in individual situations and on a regular, class-wide basis. In addition, plaintiffs introduced into evidence a copy of a company memorandum (the “Dean memorandum”) that plaintiffs contended specifically evidenced a race-conscious company policy to reduce the number of blacks in defendants’ work force. A. The Dean Memorandum Plaintiffs offered the memorandum written November 19, 1976, by Dominic Dean, a white who was then director of personnel, and sent to Dean’s supervisor, Bart Corradino, a white who was national director of personnel for Johnson & Johnson Baby Products Company. The memorandum was issued in response to a letter sent by Ben West, director of contract compliance for the United States Energy Research and Development Administration, the government compliance agency for defendants. West had written that defendants’ 1975 affirmative action plan reflected a decline in the percentage of minorities employed by defendants during 1975. The Dean memorandum reflected Dean’s concern that West’s criticism was unjustified, but nevertheless included a statement that plaintiffs contend evidenced defendants’ policy of intending to reduce the number of black employees. The memorandum stated: As you know, last year our compliance officer, Mr. Ben West, had indicated that we should be at higher percentages in the areas of both female and minority employment. He felt strongly about this, to the point of writing a letter to the President of the Baby Products Company, Mr. D. Johnston, indicating that we, rather than increasing our percentage of minority participation, had decreased it. It was our intention to reduce the number of minorities in our plant in 1975, based on maintaining parity with the community, which we found ourselves above. Anderson’s letter written in early October spells out our position on Mr. West’s letter. It was my intention to meet with Mr. West to discuss our downward trend in minority employment. However, per discussions with L. Lar-sonneur and yourself, I have been advised not to do so. You should be aware that the likelihood of the compliance officer again becoming very concerned, perhaps to a greater degree than last time as mentioned in his letter to Mr. Johnston, is a very strong possibility, in my opinion. Perhaps we should write a letter to Mr. West to advise his office that after a review of the statistical information we are making changes in our 1975 Affirmative Action Plan that will affect our ultimate goals and objectives and cause a reduction in minorities in the plant; as opposed to his finding that out at the time that the 1977 Affirmative Action Plan is submitted. Defendants responded to plaintiffs’ interpretation of the memorandum by explaining that the “intention to reduce” language referred to nothing more than the recognition by Dean that, because of normal attrition and some changes in defendants’ hiring policies occurring in the fall of 1974, they expected fewer minorities and women in the plant. The major change in hiring policy was a requirement that new applicants have three to five years industrial work experience. That change was instituted at the suggestion of Ather Williams, Jr., a black who was hired in May, 1974 as manager of administration and whose responsibilities included the task of reducing the number of employee turnovers at the plant. Defendants pointed out that the memorandum merely corroborated the conclusions of Anderson Fain III, a black and the company’s EEO/Affirmative Action coordinator. Prior to the writing of the Dean memorandum, Fain had written a memorandum entitled “1975 Affirmative Action Compliance” in response to the West letter. Fain observed that the small decline in the percentage of blacks in defendants’ work force reflected the effects of the sharp reduction in hiring activity in 1975 and the new requirement of three to five years prior industrial work experience. Fain stated that he thought statistics prepared by the United States Department of Labor would substantiate his view that fewer qualified minorities and females were available. Defendants maintained that after Dean wrote his memorandum, but before he sent it to Corradino, he went over a draft of the memorandum with Williams. In their conversation, Dean allegedly told Williams that he believed Fain’s observations explained the reduction in the percentage of minorities at the plant in 1975 and that this explanation should be communicated to West. Dean stated that although the hiring changes would, given normal attrition, reduce minority representation at the plant, he believed that, because the minority representation in defendants’ work force then actually exceeded the representation of minorities in the available work force, defendants could properly “float above parity” and need not take affirmative steps to hire minorities or females lacking the required industrial work experience. Williams apparently agreed with Dean, but emphasized that in no event could defendants go below the parity level.- The company claims that neither at this meeting nor at any other meeting during the short life of this plant did company officials discuss any intent to discharge black employees. Furthermore, the company generally denies that any such policy or practice was ever formed or adopted. Judge Leighton so found. Dean then wrote the memorandum to Corradino to inquire whether “floating” above parity was consistent with corporate policy. Defendants assert that because of concern about the connotation to which the memorandum was susceptible, Dean wrote on one copy of the memorandum, “Need advice from corporate — where we are.” Plaintiffs maintain that there is no evidence in the record to show that Dean was concerned or that he wrote the phrase. According to defendants, others in the company also expressed concern about the possibility that the memorandum could be misinterpreted. This was the position of Frank R. Steele, a black who was then director of corporate equal opportunity for Johnson & Johnson, and William O’Brien, a white who was then vice president of personnel for Johnson & Johnson Baby Products Company. As a result, Steele prepared a document, dated December 17, 1976, and signed by O’Brien, that was sent to all Baby Products facility directors and personnel managers. The memorandum stated that as part of defendants’ affirmative action policy, they should make every effort to maintain minority and female representation levels, even when the levels exceeded parity. All of this occurred prior to this lawsuit. The district court adopted defendants’ view of the Dean memorandum and found that the memorandum did not and was not intended to express a policy of defendants to discharge black employees in 1975 or in any other year. In commenting on the plaintiffs’ attorneys’ persistence “on a construction of the Dean Memorandum which its content does not reasonably support,” Judge Leighton stated that: A reasonable mind will readily grasp that taking this sentence out of the context of the others to which it refers, giving that one sentence special meaning without regard to the substantive matters that modify its intention, is a deliberate attempt to give it a distorted construction. Only a mind bent on litigation mischief can pursue such a course of conduct. Coates (COL 16). We have no reason to find that Judge Leighton’s view of the memorandum was clearly erroneous. It would be a business faux pas of the first degree for any company, much less a company with a high percentage of upper-level black personnel, to put in writing and circulate a memorandum suggesting discriminatory discharges. Plaintiffs’ insistence on its own distorted and unlikely interpretation may be explained by plaintiffs’ perception that the memorandum plays a crucial role in their case. Plaintiffs’ interpretation of the memorandum, it was no doubt noted, could make up for deficiencies in plaintiffs’ other evidence. B. Statistical Evidence 1. Plaintiffs introduced several statistical studies that purported to show a disparity in discharge rates for black and white employees. Plaintiffs’ statistical expert, Dr. Thomas DiPrete, an assistant professor of sociology at the University of Chicago, conducted analyses of both wage employees and salaried employees. Dr. DiPrete explained that he treated the two groups separately because (1) the process of hiring, training, and evaluation was different for each group, (2) blacks held a larger proportion of wage positions (35.1%) than salaried positions (22.9%) (1973-81), (3) the rates of discharge were considerably higher for wage than for salaried employees, and (4) unlike many of the salaried employees, the wage employees were not transferred from other of defendants’ facilities but were newly hired in 1973 and thereafter, and thus more were susceptible to discharge. Dr. DiPrete’s initial study of wage employees showed that, using the definition of discharge used by defendants in the ordinary course of business, the discharge rate for black wage employees for the years 1973 to 1981 was almost twice as high as the discharge rate for white wage employees. This difference was statistically significant at a level of eight standard deviations. When the discharge rates of black and white wage employees were compared based on the number of “man years” worked, thus controlling for the length of time worked, the disparity in discharge rates was significant at a level of nine standard deviations over the years 1973 to 1981. To discern if factors other than race could explain the marked difference in discharge rates for blacks and whites and thus attempt to preempt defendants’ rebuttal, Dr. DiPrete conducted a series of survival analyses. The most comprehensive of these studies, in which he controlled for seniority, education, years of experience in the work force prior to hire, sex, and absences and tardiness (in his view the only objective indicator of an employee’s reliability, since other components of a worker’s disciplinary history are considered to be subject to supervisor bias) of nonprobation-ary employees, Dr. DiPrete found a disparity significant at the fourth standard deviation level. Plaintiffs’ statistical evidence of salaried employees showed that for the years 1973 to 1981 the discharge rate was 7.17% for white salaried employees but 12.94% for blacks. This difference, without controlling for other factors, was statistically significant at the .02 (P) level. Dr. DiPrete’s survival analysis of salaried employees hired after January 1, 1973, controlling for seniority and for employees who left for reasons other than discharge, showed a disparity significant at a level of three standard deviations (discharge rates of 9.96% for whites and 23.53% for blacks). Defendants attempted to rebut plaintiffs’ statistical evidence by showing that the statistics were “inaccurate or insignificant,” Teamsters, 431 U.S. at 360, 97 S.Ct. at 1867, and by offering a “nondiserimina-tory explanation for the apparently discriminatory result.” Id. at n. 46. Defendants’ expert, Dr. George Neumann, an associate professor at the graduate school of business also of the University of Chicago, made his own statistical studies of black and white discharge rates and offered several methodological criticisms of plaintiffs’ statistical analyses. Dr. Neumann’s studies also analyzed wage and salaried employees separately, but his studies did not use the exact definition of discharge used by defendants in the ordinary course of their business. Instead, Dr. Neumann developed two new discharge designations. The first group included terminations due to technical or organizational changes, layoffs, discharges because of plant closing, failure to return from suspension, and other discharges; the second group included the above categories and added others. Using these alternative definitions of discharge, Dr. Neumann analyzed the data on a yearly basis (instead of aggregating or “pooling” it over the years covered by the class suit) and conducted a multiple regression analysis based on the following variables: race, sex, years of education, seniority, and formal disciplinary actions taken within the twelve months prior to discharge as evidenced in the personnel files. From this analysis, Dr. Neumann concluded that the differences in discharge rates of black and white employees were explained not by race, but by the employment history of the individual employee, particularly disciplinary actions. A similar analysis was conducted for salaried workers, except the disciplinary history variable was excluded. Dr. Neumann again concluded that race did not affect the discharge rates. In addition, Dr. Neumann attacked plaintiffs’ statistical analyses because (1) the data was pooled over the entire seven-year period instead of analyzed year-by-year, (2) the data included discharges from 1973, a year prior to the cut-off date for class liability, (3) the data failed to include an employee’s disciplinary record, (4) the use of survival analyses on the data was inappropriate because of the number of “censored observations,” i.e., many individuals in the sample did not experience the event being studied (discharge), and (5) plaintiffs’ studies did not take into account “time-varying variables” such as changes in the labor market or in plant managers. Plaintiffs’ expert, Dr. DiPrete, responded to Dr. Neumann’s criticisms and conducted his own last-minute, additional statistical studies in an effort to impugn Dr. Neu-mann’s analyses. First, Dr. DiPrete testified that he considered it appropriate to include data from 1973 to more readily establish that a pattern or practice of discrimination existed over the life of the plant, although the plaintiff class included black employees discharged beginning in 1974. Even without the 1973 data, however, Dr. DiPrete claimed that the black discharge rate was higher than the white discharge rate at a level of more than five standard deviations. Second, in response to Dr. Neumann’s assertion that pooling the data over the years was improper, Dr. DiPrete performed a log linear analysis that indicated that aggregating the data was appropriate and produced valid results. Third, Dr. DiPrete argued that it was entirely appropriate not to use an employee’s disciplinary record as a relevant variable because disciplinary actions were subject to the same discriminatory bias as the discharges and therefore would tend to mask the effect of race on discharge. Dr. DiPrete also testified that survival analyses were not significantly affected by the number of censored observations, especially when the sample size was so large (over a thousand), and that time-varying variables, to the extent they should be considered at all, were implicitly accounted for in the log linear test. Dr. DiPrete also criticized Dr. Neu-mann’s studies, particularly Dr. Neumann’s failure to pool the data and his method of defining discharge and seniority. Dr. DiPrete then repeated his own analyses using Dr. Neumann’s data base in an attempt to point out the errors in Dr. Neumann’s analyses. One of Dr. DiPrete’s studies showed that, correcting for all the flaws alleged to be in Dr. Neumann’s analyses and controlling for disciplinary history, sex, education, experience, and seniority, blacks were discharged at a higher rate than whites in each year studied, and that the disparity was statistically significant in three of these years. If the data were pooled for the years 1974-1981, Dr. DiPrete found that the difference between the black and white discharge rates was significant at a level of six standard deviations. Finally, even using Dr. Neumann’s data and variables, except taking into account an employee’s entire disciplinary record rather than only those disciplines issued in the twelve months preceding discharge, Dr. DiPrete found that the disparity in the discharge rates was significant at a level greater than three standard deviations when the data was pooled over the class period. The district court concluded that “the statistical evidence presented by the parties has not been helpful to this court.” Coates (COL 31). The court emphasized that the statistical evidence was ill-suited to take into account the “wide variety of factors” that go into making “individualized discharge decisions,” and that the “failure of both experts to define discharges with any certainty” was itself of grave concern. Id. (FOF 258, 259). As to plaintiffs’ statistical evidence, the court concluded that the failure “to consider an employee’s disciplinary record alone renders the study an unreliable examination of discharge rates.” Id. (FOF 262). In addition, the court agreed with defendants’ expert as to the methodological criticisms that could be lodged against plaintiffs’ statistical evidence and found that the valid criticisms undercut the probative value of plaintiffs’ studies and testimony. The court also rejected plaintiffs’ expert’s reworking of defendants’ expert’s studies, which took into account disciplinary history. The court observed that even as to these studies the resulting disparity was statistically significant only if the data were pooled and if the discipline variable included the entire disciplinary record of an employee — two changes the court thought distorted the results. 2. This case illustrates the problems that can arise when experts for each side construct their own analyses using different theories and then factor various variables in or out. Statistical analysis appears to be a science and, when properly and fairly used, it can be of great assistance to the factfinder. On the other hand, statistics are so manipulable that some skepticism may be justified when set in the evidentia-ry context of the whole case. See, e.g., Soria v. Ozinga Bros., Inc., 704 F.2d 990, 995-96 (7th Cir.1983). In this case, for example, the two experts reached their parties’ desired results, but they relied on different statistical techniques, different definitions of variables, and different statistical tests for pooling. The most apparent consistency between the two experts’ testimony was their insistence that the other’s study contained serious statistical flaws. Given the large number of disagreements between the experts, we can understand the district court’s wariness about the weight to be assigned to these particular statistical studies. Nonetheless, we believe the court erred in its analysis of some of the statistical evidence, but not — in the circumstances of this case — to a reversible degree. Our first concern is with the district court’s reluctance to assign much probative value to the statistical evidence because of the particularized factors that affect each individualized discharge decision. This court has recently held that a district court may not find a plaintiff’s discipline statistics “to be of ‘no value’ because ‘each disciplinary action and/or discharge utilizes a separate factual situation.’ ” Mozee v. Jeffboat, Inc., 746 F.2d 365, 372 (7th Cir.1984). Gross statistical disparities between black and white discharge rates may be a telltale sign of purposeful discrimination. Teamsters, 431 U.S. at 339 n. 20, 97 S.Ct. at 1856 n. 20. Once a plaintiff has eliminated “the most common nondiscriminatory reasons” for the act complained of, Burdine, 450 U.S. at 254, 101 S.Ct. at 1094, i.e., by showing that the minority individual receiving the allegedly discriminatory treatment was otherwise basically similarly situated to nonminorities receiving more favorable treatment, the plaintiff is entitled to “an inference that an employment decision was based on a discriminatory criterion illegal under the Act.” Teamsters, 431 U.S. at 358, 97 S.Ct. at 1866 (footnote omitted). When large numbers of employment decisions are under scrutiny, these comparisons can be accomplished statistically. Statistics may be the most practical means of comparison when groups, rather than individuals, are involved. Accordingly, courts have sometimes relied on statistical evidence as the best means of showing the cumulative effects of employment actions, and courts have inferred unlawful discrimination from statistically significant disparities in the treatment of comparably situated protected and nonprotected groups. See, e.g., Lilly v. Harris-Teeter Supermarket, 720 F.2d 326, 336 & n. 20 (4th Cir. 1983), cert. denied, — U.S.-, 104 S.Ct. 2154, 80 L.Ed.2d 539 (1984); Pegues v. Mississippi State Employment Service of the Mississippi Employment Security Commission, 699 F.2d 760, 765 (5th Cir.), cert. denied, — U.S. -, 104 S.Ct. 482, 78 L.Ed.2d 679 (1983). The difficulty of showing comparability of situations is a significant limitation on the probative value of statistical evidence in discipline cases, Mozee, 746 F.2d at 372, but this difficulty does not justify a finding that statistical evidence is useless. Where, as here, the parties attempt to control for differences in disciplinary records and other factors, statistics have the potential of aiding the fact-finder. We think the district court also was mistaken in its acceptance of some of the other methodological criticisms lodged at plaintiffs’ statistical studies. For example, the court accepted the defendants’ criticism that plaintiffs’ statistical evidence was unreliable because it included data from 1973 and prior to the mid-1974 class liability cut-off date. We note, however, that courts have recognized that data on employment practices that occurred prior to the liability period do have some probative value, though less than data focusing on practices after the liability cut-off date. See Trout v. Lehman, 702 F.2d 1094, 1104 (D.C.Cir.1983), vacated and remanded on other grounds, — U.S. -, 104 S.Ct. 1404, 79 L.Ed.2d 732 (1984). Moreover, this criticism became moot after Dr. DiPrete repeated each of his survival analy-ses and considered only employees hired after August 21, 1974. We need not detail all of our concerns with the district court’s treatment of the statistical evidence, however, because we think this case eventually narrowed down to several discrete issues: (1) whether pooling of the data is appropriate; (2) which party bears the burden of persuasion on the issue of whether a variable is tainted by past discrimination; and (3) what is the appropriate measure of disciplinary history. We will discuss each in turn. The most disputed statistical issue concerned whether the experts should have pooled the data into a single sample or used year-by-year samples. Dr. Neumann, the defendants’ expert, testified that he had performed a Chow test that suggested that pooling the data would be inappropriate, but he never elaborated on this study and defendants never offered it into evidence. Dr. DiPrete, in his rebuttal testimony, testified that he had performed a log linear test that indicated that pooling was permissible. The plaintiffs submitted the results of Dr. DiPrete’s log linear test into evidence; they now argue that it was clearly erroneous for the district court to find that pooling was inappropriate. We disagree. Plaintiffs cite Capaci v. Katz & Besthoff, Inc., 711 F.2d 647 (5th Cir.1983), cert. denied, — U.S. -, 104 S.Ct. 1709, 80 L.Ed.2d 182 (1984), for the proposition that the district court should have rejected the defendants’ claim that the data must be analyzed in year-by-year samples. Capad is distinguishable, however, because the year-by-year samples used by the defendants in this case are considerably larger than the disaggregated groupings in Capad. In Capad, the company’s expert grouped the hire and promotion data by location and by year. For example, of the twenty-six geographical areas where Katz & Besthoff operated drugstores, in 1977 nineteen had two or fewer hires, five had three or four hires, one had eighteen, and one had thirty-nine. With these small numbers of hires (and correspondingly small sample sizes of applicants), the company’s expert found sex statistically significant in only one geographic area, where the company had hired thirty-nine men and no women. 711 F.2d at 654-55. The aggregated figures, on the other hand, revealed that the company had hired eighty-six men but only eight women. Id. A cursory comparison of the aggregated and disaggregated totals in Capad, without any statistical analysis, suggests that the disaggregation was intended to conceal the company’s discrimination. In the present case, the annual data yielded sample sizes that ranged from 509 to 662. Although these samples are smaller than the plaintiffs’ pooled sample of 1803, they are not so small as to preclude a finding of statistical significance. See, e.g., Lilly, 720 F.2d at 336 & n. 19 (sample size of 815 and statistical significance at nearly 10 standard deviations); Capaci, 711 F.2d at 652 & n. 3 (sample size of 490 and statistically significant with probability of result due to chance less than 1 in 1000). We do not intend to imply that the appropriateness of pooling turns solely on the sample size of the disaggregated groups. Pooling data is sometimes not only appropriate but necessary, since statistical significance becomes harder to attain as the sample size shrinks. See D. Baldus & J. Cole, Statistical Proof of Discrimination § 9.221, at 309 (1980) (“All other things being equal, the test statistic and level of significance rise as the sample size increases.”); Fisher, Multiple Regression in Legal Proceedings, 80 Colum.L.Rev. 702, 717 (1980) (“In small samples, t-statistics must be larger for a given significance level.”). The more important distinction between this case and Capad is that here the defendants’ expert testified that he had performed a Chow test that indicated that it was statistically inappropriate to pool the data. Nothing in the Capad opinion suggests that the company’s expert offered any statistical reasons why pooling would lead to inaccurate statistical results. In this case, Dr. DiPrete, the plaintiffs’ expert, disagreed with the Chow test results, but Dr. DiPrete did not directly refute Dr. Neumann’s statements — DiPrete never said that he performed a Chow test that showed pooling was permissible. Instead, Dr. DiPrete testified that he thought the log linear test was the better test and that the log linear test indicated that pooling would not distort the statistical results. Thus the district court was left to decide which was the better test. Both the log linear and Chow tests are statistical tests for whether two or more sets of data may be grouped as a single sample in a statistical model. See S. Fien-berg, The Analysis of Cross-Classified Categorical Data 48-51 (2d ed. 1980) (log linear test); J. Murphy, Introductory Econometrics 237-43 (1973) (Chow test). The basic difference is that the log linear analysis tests the relationships between some but not all of the variables while the Chow test considers the entire model. Having read the statistical explanations of both tests, we readily admit that neither this court nor the district court has enough statistical ex-' pertise to declare that one test should be universally favored over the other. Instead, we believe that in cases such as this one — in which the argument against pooling does not appear to be merely pretextual, cf. Capad —the pooling issue should be decided on the facts of the particular case. In this case, although the plaintiffs’ argument appears to have some merit, we do not believe that Dr. DiPrete’s testimony presented such proof that we are left with a “definite and firm conviction that a mistake has been committed.” United States Gypsum Co., 333 U.S. at 395, 68 S.Ct. at 542. The trial court could reasonably have found that Dr. Neumann, who had more experience in this type of case, was the more credible expert on this issue. The district court therefore could have accepted Dr. Neumann’s testimony that the Chow test was the proper test and could discount the probative value of the pooled analyses. Coates (FOF 286). In short, we conclude that the pooling issue presents a close question, but, ultimately, not one that is clearly erroneous. See Soria, 704 F.2d at 994-95 n. 6. The second major issue concerns the burden of persuasion when a plaintiff claims that variables in the defendant’s statistical analyses reflect past discrimination. In this case, defendants attempted to show that there was an independent factor other than race, namely an employee’s disciplinary record, that correlated with and could explain the statistical disparity in discharge rates. In other words, defendants contended that there was no difference in the way black and white wage employees who had compiled comparable disciplinary records were discharged when they committed the same offense. According to defendants’ statistical expert, the number of disciplinary actions taken against an employee in the twelve months prior to discharge was one of the strongest predictors of discharge. Plaintiffs, however, contend that the company also discriminated in discipline. They maintain that defendants should not be able to offer a possibly biased factor as a legitimate, nondiscriminatory explanation for differences in black and white discharge rates without first showing that the possibly biased factor was in fact unbiased. The few cases that have touched on the issue of the role of possibly biased explanatory factors in the defendants’ rebuttal have not explicitly considered the question in terms of the allocation of the burden of persuasion. Perhaps the leading case discussing this problem is James v. Stockham Valves & Fittings Co., 559 F.2d 310 (5th Cir.1977), cert. denied, 434 U.S. 1034, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978). In Stockham, plaintiffs alleged unlawful discrimination in job assignments that resulted in a significant disparity in the earnings of white and black workers engaged in the manufacture of valves and fittings (blacks earned an average of 37$ less per hour than whites). The defendant responded by introducing a regression study to show that the disparity could be explained in terms of “productivity factors.” The productivity factors used in the study were years of schooling, achievement, seniority, skill level, outside craft experience, outside operative experience, absenteeism, and merit ratings. Id. at 332. Plaintiffs objected to the critical factors of “skill level” and “merit rating” because they claimed these factors were defined in a way that incorporated discrimination. The court agreed. “Skill level” was derived from an employee’s job class, and because plaintiffs had claimed that they had been systematically excluded from job classes with high ratings, “[a] regression analysis defining ‘skill level’ in that way thus may confirm the existence of employment discrimination practices that result in higher earnings for whites.” Id. Similarly, merit ratings were based on the subjective evaluation of defendant’s supervisors, who were overwhelmingly white, so that “[i]f there [was] racial bias in the subjective evaluations of white supervisors, then that bias [would have been] injected into [the] earnings analysis.” Id. (footnote omitted). After noting that the defendant’s statistical expert “concedefd] that he made no attempt to control or check for racial bias in his analysis,” id., the court found that the defendant’s regression in no way refuted the plaintiffs’ prima facie case of racial discrimination in job allocations. Although Stockham does hold that a defendant may not rely on factors that the court concludes are biased, we do not read Stockham as holding that the defendant must persuade the court that an allegedly biased explanatory variable is not biased before the defendant can offer statistics using the variable as evidence rebutting the plaintiffs’ prima facie case. In rejecting the use of the defendant’s two proffered explanatory factors, the Stockham court had before it more than the plaintiffs’ allegation that the factors were biased. The court also had plaintiffs’ statistical evidence that clearly showed a substantial disparity between the representation of blacks and whites in the higher job classes, id. at 329, and evidence showing that the average merit rating given to blacks was significantly less than that given to whites. Id. at 332. Because the plaintiffs had produced evidence from which the court could infer that the defendant’s proffered explanatory factors actually reflected other discrimination, the court could have implicitly concluded that the defendant could not rely on these factors until it had rebutted this inference. Other cases also have suggested that a defendant may not rely on factors that the court concludes are biased, but, again, these decisions have not addressed the question in terms of the burden of persuasion. See, e.g., Trout v. Hidalgo, 517 F.Supp. 873, 886 n. 47 (D.D.C.1981), modified on other grounds sub nom. Trout v. Lehman, 702 F.2d 1094 (D.C.Cir.), vacated and remanded, — U.S. -, 104 S.Ct. 1404, 79 L.Ed.2d 732 (1984); Pouncy v. Prudential Insurance Company of America, 499 F.Supp. 427, 450 n. 14 (S.D.Tex. 1980), aff'd, 668 F.2d 795 (5th Cir.1982); see also D. Baldus & J. Cole, § 8.121, at 254 & n. 31 (1980), § 8.23 (1984); Finkelstein, The Judicial Reception of Multiple Regression Studies in Race and Sex Discrimination Cases, 80 Colum.L.Rev. 737, 738-42 (1980); Gwartney, Asher, Haworth & Haworth, Statistics, the Law and Title VII: An Economist’s View, 54- Notre Dame Lawyer, 633, 656 (1979). Cf. DeMedina v. Reinhardt, 686 F.2d 997, 1008-09 & n. 7 (D.C.Cir.1982) (burden of production, but not persuasion, on defendant in disparate impact case). In Presseisen v. Swarthmore College, 442 F.Supp. 593 (E.D.Pa. 1977), aff'd without opinion, 582 F.2d 1275 (3d Cir.1978), the district court did not explicitly address the burden of proof issue, but the court’s analysis suggests that the plaintiffs bore the burden of persuasion for possibly biased variables. Swarthmore College argued that differences in rank explained differences in salary; the plaintiffs countered that the university also discriminated in promotions and therefore a variable for rank would reflect past discrimination. The district court held that since the plaintiffs failed to meet their burden of persuasion as to the existence of discrimination in promotions, the defendant could include a variable for rank in the regression used to rebut plaintiffs’ statistical evidence. Id. at 619. See also Agarwal v. Arthur G. McKee & Co., 19 Fair Empl.Prac.Cas. (BNA) 503, 512 (N.D.Cal. 1977). But see Valentino v. United States Postal Service, 674 F.2d 56, 71 n. 26, 72 n. 30 (D.C.Cir.1982) (expressing disagreement with the district court’s discussion of the issue, 511 F.Supp. 917, 944-45 (D.D.C. 1981)). Although we generally agree with those courts that have held that plaintiffs need not account for a potentially biased factor in establishing their prima facie case, we think that once a defendant offers statistics using an allegedly biased factor, the plaintiff must bear the burden of persuading the factfinder that the factor is biased. Placing the burden on the defendant would skew the general Title VII framework for allocating burdens and would be inconsistent with the principle that the plaintiffs in a Title VII case retain the ultimate burden of persuasion on the issue of discrimination. See Segar, 738 F.2d at 1284; Clark v. Chrysler Corp., 673 F.2d 921, 929 (7th Cir.), cert. denied, 459 U.S. 873, 103 S.Ct. 161, 74 L.Ed.2d 134 (1982). Plaintiffs should not be able to shift the burden of persuasion by alleging that some factor in defendant’s control has been used by the defendant discriminatorily. A defendant that uses a possibly biased explanatory factor to show that inclusion of the factor changes the result of the plaintiffs’ analysis has effectively met its burden of production within the meaning of Teamsters. See Trout v. Lehman, 702 F.2d at 1102 (“[T]he most effective way to rebut a statistically based prima facie case is to present more accurate statistics.”). By including the factor and showing that the statistics no longer indicate discrimination, the defendant responds to the particular proof used by the plaintiffs to establish their prima facie case and thus raises a genuine issue of fact as to whether the apparent disparate treatment is in fact due to discrimination. Such an approach is not unfair. A plaintiff can meet this burden by introducing evidence sufficient' for the court to infer that the explanatory factor was subject to the control of the defendant and the defendant exercised that control in an unlawful, discriminatory manner. The defendant must then either rebut this evidence or, if possible, come forward with another explanation for the alleged discriminatory result. But the plaintiffs must bear the ultimate burden of persuasion when they claim that an explanatory variable included in the defendant’s statistical analysis merely reflects other discrimination by the defendant. Thus, in the present case, the plaintiffs had the burden of persuading the court that the defendants’ disciplinary system allowed its supervisors to discriminate in discipline and that the supervisors did discriminate. No direct statistical evidence was introduced on the issue of discrimination in the meting out of oral or written disciplinary actions (other than those resulting in discharges). Defendants’ statistical expert, Dr. Neumann, testified that no statistical study could address that question. Similarly, plaintiffs made no attempt to compare the number of written disciplines received by blacks and whites; they evidently assumed that they would not need statistical evidence showing that the defendants meted out written disciplines in a discriminatory manner. This lack of statistical proof greatly weakened their case. See, e.g., Chisholm v. United States Postal Service, 516 F.Supp. 810, 849-50 (W.D.N.C.1980), aff'd in relevant part, 665 F.2d 482 (4th Cir.1981). If plaintiffs had prepared statistical evidence on that issue, then defendants would have been in the possibly difficult position of trying to show that the plaintiffs’ disciplinary statistics were inaccurate, or having to explain why blacks received a disproportionate share of disciplines. Plaintiffs’ evidence consisted of testimony of a former union steward and president that blacks received formal, written warnings for rule violations while whites were given only oral counselings, testimony of class members telling of instances in which they received written warnings without first receiving oral counselings, and exhibits attempting to show that whites were often only orally or informally counseled for violations, including Group I violations for which they should have been suspended pending discharge. Defendants offered exhibits showing that there were in fact other blacks treated more favorably than whites who committed like offenses, and that blacks were also often only informally counseled for Group I violations. Defendants essentially maintained that although they may have distinguished among employees in imposing discipline, there was no evidence they did so on the basis of race. The total evidence introduced by both parties directed specifically toward the issuance of oral and written disciplines (not discharges) was not great, and what evidence was presented was conflicting. Yet the issue of discrimination in the meting out of oral and written disciplines other than those resulting in discharges is important in this case. We would feel more secure in our judgment, therefore, had the issue been aired more fully. However, as we are limited by the evidence presented, we cannot say that the district court, after viewing the witnesses and weighing all the evidence, clearly erred in finding that the evidence failed to show that defendants engaged in a pattern or practice of discrimination in issuing disciplines. See Lee v. National Can Corp., 699 F.2d 932, 936 (7th Cir.), cert. denied, — U.S.-, 104 S.Ct. 148, 78 L.Ed.2d 138 (1983). Consequently, the district court could properly admit defendants’ statistical evidence showing that an employee’s recent disciplinary record provided a nondiscriminatory explanation for any disparity in the discharge rates for black and white wage employees. Plaintiffs rebuttal evidence to the defendants’ statistical analyses raises the third major issue: what is the appropriate measure of disciplinary history. Plaintiffs’ expert, Dr. DiPrete, reworked Dr. Neumann’s analyses and corrected for what Dr. DiPrete considered to be errors. Dr. DiPrete’s studies showed that the disparity in discharge rates between blacks and whites was statistically significant if the statistical model included the employees’ entire disciplinary records rather than the twelve-month records. The district court concluded that the twelve-month measure was more accurate and therefore discounted the probative value of the plaintiffs’ rebuttal statistics. After a careful review of both the statistics and the trial transcript, we conclude that this finding is clearly erroneous but does not constitute reversible error. First, although the defendants’ expert testified that his study indicated that the twelve-month measure was the best predictor of discharge, the plaintiffs’ rebuttal study ND1 (which substituted total disciplinary record for prior twelve months and used logit analysis rather than multiple regression) had better results with respect to the discipline variables. In Dr. Neu-mann’s equations, only about