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).1 Plaintiffs allege that *529the 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 com*530pany 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).2 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, 19813 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.4
*531In 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.5
The Supreme Court has applied an analogous analytical framework to the liability phase of a government or class *532action 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.6 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 *533Paxton 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).7
*534IV.
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.8 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 de*535gree 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 stat*536ed 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.9 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,10 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.11 When the discharge rates of *537black 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.12 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.13 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, *538made 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 analysis14 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.15 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 *539all, 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 disci*540plinary 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.16 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 *541had 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.17 711 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.18 Nothing in the Capad opinion sug*542gests 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,19 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 dis*543charge 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 *544& 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,20 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 *545burden 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’ *546rebuttal 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 one-third (15 of 42) of the disciplinary variables (major, minor, and absenteeism) were statistically significant at a level of two standard deviations. By contrast, more than half (12 of 21) of the disciplinary variables in Dr. DiPrete’s study ND1 were statistically significant. Thus the substitution of the entire disciplinary record for the twelve-month measure seemed to improve the results of the statistical analysis. See D. Baldus & J. Cole, § 8.23, at 100 (Supp.1984) (“The size and statistical significance of the controversial qualification will illuminate the question of whether the qualification was in fact considered.”). We therefore conclude that the defendants’ statistical results, by themselves, could not provide a reasonable basis for preferring the twelvemonth measure over the entire disciplinary record measure.
The defendants also argue that the twelve-month measure was better because discipline is a “time-carrying” variable. With the plaintiffs’ variable, an employee with three disciplines in the past year would be considered comparable to an employee with three disciplines over five years. We agree that this misspecification limited the probative value of the plaintiffs’ rebuttal statistics. On the other hand, we believe that Dr. Neumann’s analyses included a misspecification of the twelvemonth period. Dr. Neumann’s model defined the relevant disciplinary period as the calendar year for employees who were still employed on December 31st and as the twelve months prior to discharge for terminated employees. (Defense exhibit TTTT). To be consistent with his underlying theory (i.e., that the twelve-month record is what supervisors considered), however, Dr. Neu-mann should have defined the record in terms of the twelve-month period prior to the last, if any, discipline the employee received during the year. For example, if two employees committed the same violation on April 1, 1977 but only one was discharged, the relevant period (assuming for the moment that twelve months is correct) for both employees is April 1, 1976 to April 1, 1977. With Dr. Neumann’s definition, only the discharged employee’s record would be considered in this time frame. The non-discharged employee could have a worse disciplinary record in the correct twelve-month period but — if the prior violations occurred prior to January 1, 1977 — a better record in Dr. Neumann’s model.
Had the district court heard only the testimony of the experts and counsels’ arguments, we would be hard pressed to find the court’s choice of the twelve-month measure to be clearly erroneous. However, the testimony of John Matson and Ather Williams, two defense witnesses, and the provisions of the 1978 collective bargaining agreement convince us that the entire disciplinary record was the better— though by no means perfect — measure. On cross-examination, Matson, the plant manager from August, 1973 until August, 1974, admitted that under the plant’s “whole man” concept of discipline, supervisors should have made subjective decisions about the employee’s past record, the employee’s attitude, and any other attribute the supervisor considered important. (Tr. at 1592). Williams, the plant manager from 1976 until the plant closed, testified that as plant manager he was involved in the fourth step of the grievance procedure. He further stated that in these meetings he reviewed with the employee whatever past disciplines were recorded in that employee’s file.21 Moreover, in relating his rea*547sons for upholding Cecilia Dampier’s discharge, Williams stated, “Well, I looked at Miss Dampier, that in the four years that she was employed with us, each year— well, three out of four years she had discipline on a different kind of offense.” (Tr. at 1813). Clearly, Mr. Williams considered Miss Dampier’s entire disciplinary record in upholding her discharge. Since Matson and Williams were plant managers and thus helped form the plant’s discipline policies, it seems likely that their practice typified the plant supervisors’ approach. In addition, the 1978 collective bargaining agreement for the Midwest Diaper Plant provided that management could consider only disciplines in the prior three years. The addition of this provision implies that management had previously considered more than three years of an employee’s record. Thus the statistical evidence on this issue was about equal but all of the nonstatistical evidence favored the plaintiffs’ contention. The district court’s finding that the plaintiffs’ statistical analyses were less probative than the defendants’ because the plaintiffs’ expert used the entire disciplinary record as his discipline variable was therefore clearly erroneous.
The district court’s mistake does not amount to reversible error. Although the court’s findings of fact and conclusions of law state that the defendants’ statistics were better than the plaintiffs’ studies, we read such statements as the court’s preference between two studies — both with limited probative value. The district court found that “the results of neither expert’s study speak clearly and unambiguously to the question at hand,” Coates (FOF 258), and concluded that “the statistical evidence presented by the parties has not been helpful to this court.” Coates (COL 31). Citing this conclusion of law and some of the comments made by the court during trial, plaintiffs argue that the court discounted the probative value of the statistics before hearing the evidence. If plaintiffs were correct, the trial court would have erred. See Mozee, 746 F.2d at 372. After reviewing the record and reading the judge’s comments in context, however, we conclude that the court considered all the statistical evidence but found the studies to have little probative value and, consequently, to be of little help in deciding the case. See Coates (COL 43). This finding of limited probative value was not one that leaves this court “with the definite and firm conviction that a mistake has been committed.” United States Gypsum Co., 333 U.S. at 395, 68 S.Ct. at 542.
Both parties’ studies suffered from a number of statistical problems that limited the studies’ probative value. As we noted above, the defendants’ expert used a poor measure of prior discipline. On the other hand, the plaintiffs’ disciplinary variable, the entire disciplinary record, was by no means a perfect measure because it failed to reflect the “time-carrying” nature of discipline. And even if the district court had found the entire disciplinary record to be a good measure, Dr. DiPrete’s study ND1 (which substituted the entire disciplinary record for the twelve-month measure) had no year with a statistically significant coefficient on the race variable. Thus this study confirmed the defendants’ results of no discrimination. Dr. DiPrete’s other models, which corrected for a number of alleged errors by Dr. Neumann, had better results (from the plaintiffs’ viewpoint), but our review of the record indicates that it was not clearly erroneous for the district court to disagree with Dr. DiPrete about these alleged flaws.22 We note that the *548district court also gave less weight to Dr. DiPrete’s testimony because Dr. DiPrete lacked familiarity with the particulars of his work — a shortcoming which the district court found was not reflective of a careful study. Coates (FOF 261). In short, we believe that neither party offered a compelling statistical case but that, instead, both parties offered statistical analyses of approximately the same, limited probative value. Therefore the district court properly turned to the nonstatistical evidence as the deciding factor.
3.
The nonstatistical evidence consisted of testimony by plant supervisors and documentary evidence that purported to compare defendants’ treatment of black employees with its treatment of white employees. The documentary evidence included summaries of the employee personnel files of some four hundred black and white employees whom the company had discharged.23 The defendants offered comparisons of these summaries as proof that the actual disciplinary records of discharged employees were similar — regardless of race. One comparison showed that disciplinary records of 205 discharged black employees were similar to the disciplinary records of white employees discharged for the same reasons. Relying on this evidence, the district court concluded that disciplinary history explained the allegedly disparate treatment.
Although the testimony and comparisons that explained the discharges of the testifying class members were hardly sufficient to undermine plaintiffs’ prima facie discharge case, Boykin, 706 F.2d at 1393; American National Bank, 652 F.2d at 1198, the comprehensive comparisons of the disciplinary records of four hundred discharged employees provided more probative evidence than the contradictory and inconclusive statistical studies. We have already found no error in the district court’s conclusion that disciplinary actions were meted out in a nondiscriminatory manner, and therefore we believe that the district court’s reliance on the documentary evidence as supporting its conclusion that defendants adequately rebutted plaintiffs’ charge of a pattern and practice of discriminatory discharges is not clearly erroneous. Although plaintiffs are able to point to some discrepancies and errors in the comparisons made by defendants that might reflect individual instances of some discriminatory treatment, that is not enough to undercut the value of the evidence as tending to show the absence of any pattern or practice of discriminatory conduct in the particular circumstances of this case. See Cooper, 104 S.Ct. at 2801. The burden was on plaintiffs to show that blacks and whites discharged for similar offenses had very different disciplinary records if plaintiffs were to respond successfully to defendants’ comparisons showing that an employee’s disciplinary record, not the employee’s race, affected whether the employee would be discharged for a rule violation.
We are satisfied that the district court fulfilled its obligation of “conductpng] a thorough inquiry into the treatment of comparable employees.” Worthy v. United States Steel Corp., 616 F.2d 698, 703 (3d Cir.1980). The district court considered all the evidence as to whether there were whites with records comparable to blacks who were not discharged when blacks were and concluded that the evidence did not support a finding of a pattern or practice of disparate treatment. The district court concluded that the evidence “does not show that any Negro employee of defendants was treated less favorably than was any Caucasian employee, nor was any Negro *549employee subjected to discriminatory treatment, either with regard to discipline or discharge, because of his or her race.” Coates (COL 28). The court doubted the credibility of the testimony of certain black supervisors called by plaintiff after the plant had been closed on the basis that until the trial none of them had ever claimed that a pattern of discrimination existed at the plant, even though there had been a number of channels through which they could have safely lodged complaints (e.g., grievance process, complaint to the plant manager [a black], to the company’s EEOC/Affirmative Action coordinator [also a black], or to the EEOC). The district court similarly discounted the testimony of the union officials, finding that their testimony was inconsistent with their conduct during the time they had held positions of responsibility. As to the individual class members, the court found that none of them had been discriminated against and that each had been legitimately disciplined and discharged. The court rejected the argument that blacks were discharged in situations in which whites were not. Because we take the clearly erroneous standard seriously and can find no overall error in the district court’s finding, we must accept its conclusion.
V.
SALARIED EMPLOYEES
The court also rejected the plaintiffs’ allegation that the defendants discriminated in discharging salaried employees. Although plaintiffs offered statistical evidence on this issue, the plaintiffs’ expert admitted that his study of salaried employees was less thorough than his study of wage employees. (Tr. at 916-17). The defendants’ expert, on the other hand, offered regressions in which the coefficients on the race variables were small, and as likely to be positive (suggesting that blacks were discharged at a higher rate than whites) as negative (suggesting that blacks were discharged at a lower rate). The race coefficient was statistically significant at a level of two standard deviations in two of the fourteen equations, but one of these two coefficients was positive and the other negative. (Defense Exhibit VVVV). Given these statistical results and the testimony of the defense witnesses, the district court’s finding of no discrimination in the discharges of salaried employees is not clearly erroneous.
VI.
EVIDENTIARY ISSUES
A. Admission of Employee Disciplinary Records and Summaries.
Plaintiffs maintain that the disciplinary memoranda that defendants’ lawyers’ paralegal used in preparing the summaries, as well as the summaries themselves, should not have been admitted into evidence. Plaintiffs argue that the disciplinary memoranda are hearsay and do not fall within any of the exceptions, such as the business records exception provided by Rule 803(6) of the Federal Rules of Evidence. In addition, plaintiffs contend that the summaries were in any event inadmissible under Rule 1006 because they were inaccurate and because they were produced too late. The district court has broad discretion in admitting evidence under Rules 803(6) and 1006, and we will not disturb its decision unless there has been an abuse of that discretion.
Rule 803(6), the business records exception to the hearsay rule, was intended to permit the admission of records maintained in the regular course of business, unless “the source of information or the method or circumstances of preparation indicate a lack of trustworthiness.” United States v. Chappell, 698 F.2d 308, 311 (7th Cir.), cert. denied, 461 U.S. 931, 103 S.Ct. 2095, 77 L.Ed.2d 304 (1983). Plaintiffs argue that the disciplinary memoranda were prepared and kept primarily for use in the grievance procedure, and that consequently there is a high risk that the versions of the rule violations represented by the memoranda are biased. They compare the memoranda to company reports about accidents, *550see, e.g., Palmer v. Hoffman, 318 U.S. 109, 63 S.Ct. 477, 87 L.Ed. 645 (1943), or to reports prepared by prison guards about inmates’ alleged misconduct, see, e.g., Bra-cey v. Herringa, 466 F.2d 702 (7th Cir. 1972), that have been held to be inadmissible. We believe, however, that the district court’s determination that the disciplinary memoranda had sufficient indicia of reliability so as to be admissible under Rule 803(6) was not an abuse of discretion. See Paxton, 688 F.2d at 567 (defendants introduced employment records that listed reasons why each employee was discharged to rebut plaintiffs’ classwide prima facie case); McDowell v. Safeway Stores, Inc., 575 F.Supp. 1007, 1063 (E.D.Ark.1983) (defendants’ employment records, along with other evidence, were admissible to rebut plaintiffs’ allegations of discriminatory discharges). Unlike the accident report in Palmer, the memoranda here were part of the systematic conduct of running a business; they were kept according to a regular procedure and for a routine business purpose — memorializing employee performance — that tended to insure accuracy. In this way they are also different from the prison guards’ reports in Bracey, since the disciplinary memoranda were not prepared primarily with a view toward their use in a subsequent adversarial proceeding. . The memoranda related not only to the more extreme examples of employee behavior, e.g., insubordination, but also to the more routine but equally important gauges of employee performance, e.g., competence in the completion of work assignments. Accordingly, the district court did not abuse its discretion in admitting these business records.
Next, plaintiffs argue that even if the disciplinary records themselves were admissible, the summaries of those records prepared by defendants’ counsels’ paralegal were not admissible as summaries under Rule 1006.24 Plaintiffs maintain that the admission of the summaries was inappropriate because they were not made available to plaintiffs at a reasonable time and place and because they are inaccurate. As defendants correctly point out, however, only the underlying documents, and not the summaries, must be made available to the opposing party so as to give them a reasonable time to respond, United States v. Foley, 598 F.2d 1323, 1338 (4th Cir.1979), cert. denied, 444 U.S. 1043, 100 S.Ct. 727, 62 L.Ed.2d 728 (1980), and there is no question that the underlying personnel records here were made available to plaintiffs well before trial. In addition, we find nothing wrong with the district court's acceptance of the summaries as basically accurate. The trial court heard testimony as to specific incidents of misconduct and had no trouble finding the summaries reliable. Had we been conducting the trial we may have permitted plaintiffs more time to respond to defendants’ summaries than they were given by the district court, but we cannot say that the district court abused its discretion in admitting the summaries.
B. Destruction of Departmental Files
Plaintiffs also argue that they should have had the benefit of an evidentiary presumption because certain documents were destroyed by defendants during the closing of the plant. One group of documents destroyed was the departmental files, which were maintained plant-wide beginning in 1976 and contained duplicates of all disciplinary documents. Although only the personnel files were relied on by defendants in considering discharge decisions, the departmental files were allegedly important to plaintiffs’ case because they allegedly contained the only record of oral counseling given to employees, which plaintiffs contended were given to white employees in situations in which blacks were issued written warnings. Plaintiffs argue *551that because of defendants’ spoilation of this evidence, plaintiffs were entitled to an evidentiary presumption that the records of the oral reprimands would corroborate plaintiffs’ testimonial evidence that blacks were “written up” in situations in which whites were not. In addition, defendants’ manager of labor relations, Thomas Ro-chon, destroyed a small group of disciplinary letters that were in his possession at the plant closing. These letters had been removed from some personnel files after March, 1978, in connection with an agreement with the union that disciplinary letters more than three years old would be removed. Plaintiffs maintain the presumption should also have applied to these letters.
The prevailing rule is that bad faith destruction of a document relevant to proof of an issue at trial gives rise to a strong inference that production of the document would have been unfavorable to the party responsible for its destruction. S. C. Johnson & Son, Inc. v. Louisville & Nashville Railroad, 695 F.2d 253, 258-59 (7th Cir.1982); Vick v. Texas Employment Commission, 514 F.2d 734, 737 (5th Cir. 1975). However, considering the circumstances surrounding the destruction of the documents in this case, nothing gives rise to an inference of bad faith by defendants. The district court accepted the testimony of Williams, the black plant manager, that the personnel files were destroyed only after he consulted with the EEOC/Affirmative Action coordinator regarding which files needed to be maintained in light of the pending class action. Williams was told that these files, in view of the closing of the plant, did not have to be kept. He then decided that they could be destroyed considering that (1) the departmental files were not official records and the management had agreed with the union not to rely on them in issuing discipline, and that (2) to Williams’ knowledge, the departmental files included only incomplete duplications of documents kept in the official files and were not well maintained. Similarly, the district court found that Rochon was unaware at the time he destroyed the disciplinary letters that there was any pending litigation regarding defendants’ disciplinary policies, although Rochon was aware that one employee had filed a suit regarding his discharge. These circumstances suggest that the documents were destroyed under routine procedures, not in bad faith, and thus cannot sustain the inference that defendants’ agents were conscious of a weak case.
C. Refusal to Disclose Self-Critical Portions of the Affirmative Action Plans.
Plaintiffs also maintain that the district court erred in its “pervasive reliance” on evidence of defendants’ affirmative action efforts in areas unrelated to discharges and in refusing plaintiffs’ request to discover self-critical portions of defendants’ annual affirmative action plans. Plaintiffs also contend that even if the self-critical portions of defendants’ affirmative action plans were subject to a qualified privilege and thus not discoverable, whatever privilege existed was waived when defendants affirmatively offered evidence of their affirmative action efforts on the issue of the existence or nonexistence of a pattern or practice of discrimination. Plaintiffs complain that the district court thus erred in allowing defendants to offer evidence of their affirmative action efforts without allowing plaintiffs to discover defendants’ self-critical evaluations of those efforts.
The prevailing view is that self-critical portions of affirmative action plans are privileged and not subject to discovery by plaintiffs, see, e.g., Jamison v. Storer Broadcasting Co., 511 F.Supp. 1286, 1296-97 (E.D.Mich.1981), although courts have sometimes permitted discovery in conjunction with a protective order maintaining the confidentiality of the self-critical studies, see, e.g., Ford v. University of Notre Dame, 24 Empl.Prac.Dec. (CCH) 1131,203 (N.D.Ind.1980). The precise bounds of the privilege depend on the extent to which the policy of equal opportunity in employment will best be served in the particular circumstances presented by each case. O’Connor *552v. Chrysler Corp., 86 F.R.D. 211, 26 Fair Empl.Prac.Cas. (BNA) 459, 464 (D.Mass. 1980). We need not decide, however, whether the district court’s order denying pretrial discovery of defendants’ self-critical evaluations was proper in this case (the court had first examined the documents in camera). The voluntary use by defendants at trial of their affirmative action efforts to prove nondiscrimination opened the door and waived whatever qualified privilege may have existed. The district court therefore should have permitted plaintiffs to have access to defendants’ subjective evaluations of their own affirmative action efforts. The policy behind a qualified privilege for self-critical affirmative action evaluations is to promote the overall goal of removing discriminatory practices from the workplace. Allowing self-critical evaluations to remain confidential is thought “to assure fairness to persons who have been required by law to engage in- self-evaluation ... and to make the self-evaluation process more effective by creating an effective incentive structure for candid and unconstrained self-evaluation,” O’Connor, 86 F.R.D. at 218, 26 Fair Empl.Prac.Cas. (BNA) at 464, thus encouraging conscious efforts to engage in fair employment practices. But an employer should not be able to offer its affirmative action policy before the trier of fact as a manifestation of nondiscrimination and at the same time be able to hide self-critical evaluations that may undercut the employer’s portrayal of its efforts. Fairness requires that the qualified privilege not be allowed to mask discrimination when the overall policy behind the privilege is directed toward eliminating it.
Although we believe that the district court abused its discretion in denying plaintiffs’ request, we believe that plaintiffs were not substantially prejudiced. Despite plaintiffs’ contention to the contrary, we believe the district court’s reliance on the evidence of defendants’ affirmative action efforts as probative of nondiscrimination was not “pervasive.” Certainly the court paid some attention to this evidence. Although we have recognized that evidence of an employer’s behavior in nonchallenged employment practices may relate only obliquely to the issue of discrimination in the challenged practices, we have held that trial courts should “at least consider” such evidence. Soria, 704 F.2d at 999. Here the district court did that, and we are unconvinced that its reliance on the evidence was beyond what the evidence merited when weighed in the context of this case. The evidence of seeking minorities for construction, and for employees, supervisors and managers at a level above the relevant available work force, which is unrebutted, strongly suggests that plaintiffs would have found little help in the company’s self-analysis. In any event, defendants’ other evidence was sufficient to undercut plaintiffs’ prima facie case so that we would still conclude that, even without its reliance on the affirmative action evidence, the district court’s finding of nondiscrimination was not clearly erroneous.
VII.
INDIVIDUAL CLAIM
Because we affirm the district court’s conclusion that defendants did not engage in a pattern or practice of discharging employees on the basis of race, plaintiff Coates was not entitled to any presumption that defendants had unlawfully discriminated against him. The district court concluded that Coates was “discharged for legitimate reasons and not because of his race.” Coates was discharged when three supervisors found him sleeping on the job, a Group I violation. He had been suspended two days earlier for damaging weight scales while driving a forklift truck, and an investigative agency working for defendants reported that Coates had been selling drugs on company property. The district court found that:
[Coates] is the only employee at defendants’ diaper plant who within three days committed two serious violations of company rules, was reinstated once and the following day was again suspended pending termination. He is also the only em*553ployee at the diaper plant whose work record was considered for possible leniency by a member of his own race [plant manager Williams] but whose judgment was swayed when he was shown reports of activities which disclosed Coates was selling drugs on company property____ Sleeping on the job, as Coates was found in this case, when it is not a pretext for race discrimination, is a legitimate ground for discharging an employee____ There is no evidence in the record to show that any Caucasian employee was permitted to engage in the same or similar conduct as was the plaintiff Coates without discipline or discharge. Further, this court has not seen or heard any evidence which shows that any Caucasian employee who was being considered for disciplinary discharge was cited in reliable investigative reports for selling drugs on company property. The absence of such evidence ... is fatal to [the] claim that plaintiff Coates was a victim of discrimination.
Coates (COL 18) (citations omitted).
Plaintiffs have not pointed to any evidence in the record or made any legal arguments that would lead us to disturb the district court’s findings and conclusions. Accordingly, we affirm the district court’s judgment that defendants did not unlawfully discriminate against plaintiff Coates.
VIII.
CONCLUSION
Although Coates may have been a poor choice as the named plaintiff for the class, the case failed for other reasons. Because we feel this was a close case, however, we do not believe that defendants should be awarded attorneys’ fees. See Christiansburg Garment Co. v. EEOC, 434 U.S. 412, 421, 98 S.Ct. 694, 700, 54 L.Ed.2d 648 (1978) (prevailing defendant in a Title VII case may recover attorneys’ fees only if the district court finds that the plaintiff’s action was “frivolous, unreasonable, or without foundation”); Ekanem v. Health and Hospital Corp., 724 F.2d 563, 574-75 (7th Cir.), cert. denied, — U.S. -, 105 S.Ct. 93, 83 L.Ed.2d 40 (1984). Each party shall bear its own costs on appeal. The district court’s judgments in favor of the defendants on both the class claim and the individual claim are AFFIRMED.
. All future citations to portions of the district court decision will refer to its findings of fact (FOF) or conclusions of law (COL), rather than to specific page numbers. E.g., Coates (FOF 14, COL 2).
. All persons within the jurisdiction of the United States shall have the same right in every State and Territory to make and enforce contracts, to sue, be parties, give evidence, and to the full and equal benefit of all laws and proceedings for the security of persons and property as is enjoyed by white citizens, and shall be subject to like punishment, pains, penalties, taxes, licenses, and exactions of every kind, and to no other.
42 U.S.C. § 1981 (1976).
. The class certified was defined as:
All members of the Negro race discharged by defendants after June 8, 1974, as to Count II (Section 1981), and after August 20, 1974, as to Count I (Title VII), as a consequence of a uniform policy defendants employed and administered during these time periods.
Coates (FOF 32).
. The Supreme Court has distinguished between two kinds of Title VII cases — disparate treatment and disparate impact. According to the Court in International Brotherhood of Teamsters v. United States, 431 U.S. 324, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977),
[djisparate treatment ... is the most easily understood type of discrimination. The employer simply treats some people less favorably than others because of their race, color, religion, sex, or national origin. Proof of discriminatory motive is critical, although it can in some situations be inferred from the mere fact of differences in treatment____ Undoubtedly disparate treatment was the most obvious evil Congress had in mind when it enacted Title VII.
******
Claims of disparate treatment may be distinguished from claims that stress "disparate impact.” The latter involve employment practices that are facially neutral in their treatment of different groups but that in fact fall more harshly on one group than another and cannot be justified by business necessity____ Proof of discriminatory motive, we have held, is not required under a disparate-impact theory-
Id. at 335 n. 15, 97 S.Ct. at 1854-55 n. 15. Plaintiffs contend that although they tried their case mainly on a theory of disparate treatment, they also alleged disparate impact, and that the district court erred in ignoring this theory. The district court did in fact mention plaintiffs’ disparate impact allegation, Coates (COL 31, 41; FOF 38), although the court prop*531erly tried the case as one involving disparate treatment; plaintiffs’ complaint alleges facts appropriate for disparate treatment analysis for both the individual and class claims, and indeed this is the way they presented their case. Plaintiffs never argued that there were facially neutral termination rules that had a disproportionate impact on blacks; rather, they alleged that the rules were more severely applied, through supervisory discretion, to blacks than to whites. In fact, plaintiffs’ attorney devoted his entire closing argument to disparate treatment analysis without once mentioning disparate impact. Cf. Ste. Marie v. Eastern Railroad Association, 650 F.2d 395, 399 n. 2 (2d Cir.1981). Thus, this case is susceptible to a disparate treatment, and not a disparate impact, theory. Burdette v. FMC Corp., 566 F.Supp. 808, 817 (S.D.W.Va.1983) (”[i]n a disparate discharge situation, the effects] of facially neutral policies are not at issue"). See EEOC v. Federal Reserve Bank of Richmond, 698 F.2d 633, 638-39 (4th Cir.1983), rev’d on other grounds sub nom. Cooper v. Federal Reserve Bank of Richmond, — U.S.-, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984); Pouncy v. Prudential Insurance Company of America, 668 F.2d 795, 799-802 (5th Cir.1982); Mortensen v. Callaway, 672 F.2d 822, 824 (10th Cir.1982).
. The framework is analytical only, and does not suggest a specific order of proof at trial. Craik v. Minnesota State University Board, 731 F.2d 465, 470 n. 7 (8th Cir.1984); McCluney v. Jos. Schlitz Brewing Co., 728 F.2d 924, 926 (7th Cir.1984); Capaci v. Katz & Besthoff, Inc., 711 F.2d 647, 663 (5th Cir.), cert. denied, - U.S. -, 104 S.Ct. 1709, 80 L.Ed.2d 182 (1984). ”[I]t is merely a sensible, orderly way to evaluate the evidence in light of common experience as it bears on the critical question of discrimination.” Furnco Construction Corp. v. Waters, 438 U.S. 567, 577, 98 S.Ct. 2943, 2949, 57 L.Ed.2d 957 (1978).
. Teamsters, for example, involved statistical "proof of the expected result of a regularly followed discriminatory policy,” 431 U.S. at 360 n. 46, 97 S.Ct. at 1867 n. 46, and testimony by forty individuals of specific instances of discrimination. In some cases, a plaintiffs statistical evidence alone might constitute a prima facie case. See Segar v. Smith, 738 F.2d 1249, 1278 (D.C.Cir. 1984).
. Plaintiffs point out that the district court adopted nearly all of defendants’ proposed findings of fact. When this occurs, we examine the findings especially critically when deciding whether they are clearly erroneous. Photovest Corp. v. Fotomat Corp., 606 F.2d 704, 731 (7th Cir.1979), cert. denied, 445 U.S. 917, 100 S.Ct. 1278, 63 L.Ed.2d 601 (1980). Here, the trial court apparently considered proposed findings by each party and allowed each party ample time to criticize the other’s, see Coates (FOF 39); the court made some modifications, although the bulk of the findings are those proposed by defendants. Nevertheless, the adopted findings *534are formally those of the trial court, and it is with regard to these findings that we review the record for the requisite support. Garcia v. Rush-Presbyterian-St. Luke’s Medical Center, 660 F.2d 1217, 1220 (7th Cir.1981). Nothing suggests that Judge Leighton did not carefully and properly weigh and consider all the evidence in making his decision.
. Plaintiffs’ evidence attempted to demonstrate that defendants’ supervisory personnel:
(i) overlooked rule violations committed by their white employees while at the same time building files of disciplinary letters against black employees who were accused of comparable conduct; (ii) suspend[ed] or termi-nat[ed] black employees while retaining white employees for comparable rule violations; (iii) reinstated] white employees after the processing of grievances while refusing to similarly reinstate black employees with comparable employment and disciplinary histories who [had] committed comparable offenses.
. Defendants also introduced evidence showing that the percentage of blacks, exclusive of other minorities, decreased only one percent from 1974 to 1975, and that in every year the plant was in operation the representation of blacks in defendants’ work force, as reflected in defendants’ EEO-1 reports filed with the government, exceeded the percentage of potential black employees available in the relevant community.
. Defendants’ payroll master tape codes distinguished between employees who "quit,” those who were “discharged,” and those who retired, died, or were no longer employable because of permanent disability. The "discharge” category used by Dr. DiPrete included employees terminated for excessive absenteeism, incompetency, insubordination, violation of Group I or Group II rules, training difficulties, or administrative separation. Dr. DiPrete did not use the classification “discharged for lack of work.”
. Dr. DePrete explained that:
The determination of the statistical significance of differences in discharge rates was computed using either Z-scores or Pearson chi-square statistics (X2)____ The probabilities associated with the Z and X2 statistics were taken from a probability table based upon the normal distribution and a probabili*537ty table based upon the chi-square distribution with one degree of freedom, respectively. Plaintiffs’ Exhibit 23-A, at 4 n.*.
The "standard deviation” is a number that quantifies the degree to which disparities spread out above and below the mean of distribution, thus describing the probability that chance is responsible for any difference between an expected outcome and the observed outcome in a sample consisting of two groups (a binomial distribution). The greater the number of standard deviations, the less likely it is that chance is the cause of any difference between the expected and observed results. The Supreme Court noted in Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977), that under a "two-tail” test of statistical significance, "[a]s a general rule for ... large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that the [disparity] was random would be suspect to a social scientist.” Id. at 497 n. 17, 97 S.Ct. at 1281 n. 17. The general rule should be applied with caution, however, and its particular applicability may vary from case to case. See D. Baldus & J. Cole, Statistical Proof of Discrimination § 9.03, at 293-97 (1980), 108-12 (Supp. 1984); see also American National Bank, 652 F.2d at 1190-93. Here, a binomial model would appear to be appropriate. See, e.g., Lilly v. Harris-Teeter Supermarket, 720 F.2d 326, 336 n. 18 (4th Cir.1983), cert. denied, — U.S. -, 104 S.Ct. 2154, 80 L.Ed.2d 539 (1984).
. "Survival analysis is a loosely defined statistical term that encompasses a variety of statistical techniques for analyzing positive-valued random variables.” R. Miller, Survival Analysis 1 (1981). The particular type of survival analysis used by Dr. DiPrete was a proportional hazards study. This analysis was employed, rather than the more common multiple regression analysis, in order to try to refine the data by studying employees who quit the plant only for the length of time they were employed there, and thus, at risk of discharge. Plaintiffs never attempted to explain precisely how the methodology of a proportional hazards study differs from that of a multiple regression study.
. In addition to describing statistical significance in terms of levels of standard deviation, statistical significance also may be expressed as a probability value (P) on a continuous or relative scale ranging from 0 to 1.0. The level of statistical significance rises as the value of the (P) level declines. Chi-square (X2) test statistics, see supra note 11, can be converted into a probability statement — (P) level — or a standard deviation expression. D. Baldus & J. Cole, supra note 11, § 9.22, at 308. A (P) value below .05 is generally considered to be statistically significant, i.e., when there is less than a 5% probability that the disparity was due to chance. For large samples, statistical significance at a level in the range below 0.05 or 0.01 is "essentially equivalent" to significance at the 2 or 3 standard deviation level. Id. § 9.03 at 297.
. Multiple regression is a statistical technique for making quantitative estimates of the effects of several independent factors on a single dependent variable. Fisher, Multiple Regression in Legal Proceedings, 80 Colum.L.Rev. 702, 702 (1980). This form of statistical analysis has been used in countless Title VII cases. E.g., Trout v. Hidalgo, 517 F.Supp. 873, 877-78 (D.D. C.1981), modified sub nom. Trout v. Lehman, 702 F.2d 1094 (D.C.Cir.1983), vacated and remanded, — U.S. -, 104 S.Ct. 1404, 79 L.Ed.2d 732 (1984).
. Dr. Neumann testified that he did not include a variable for disciplinary actions in his salaried workers regression because there were no formal disciplinary actions for managers, professionals, and technical and clerical workers. (Tr. 2248).
. The ability to compare groups statistically, such as through a survival or multiple regression analysis, may depend on several considerations. One court has listed four such considerations:
(1) the "significance” of the influence factors discovered through the analysis, (2) the quantity of data used to evaluate a particular dependent variable, (3) the quality of that data, and (4) the ease with which independent variables may be converted to numerical equivalents.
Agarwal v. Arthur G. McKee & Co., 19 Fair Empl.Prac.Cas. (BNA) 503, 506 (N.D.Cal.1977).
. Disaggregating by years, the defendant’s expert had sample sizes of 12, 20, 28, 31, 32, 42, 47, 54, 71, 94, 58, 72, 93, and 12. See Capaci v. Katz & Besthoff, Inc., 525 F.Supp. 317, 326 (E.D. La.1981), aff’d in relevant part, 711 F.2d 647 (5th Cir.1983), cert. denied, - U.S. -, 104 S.Ct. 1709, 80 L.Ed.2d 182 (1984).
. Plaintiffs, citing United States v. City of Chicago, 549 F.2d 415, 432 (7th Cir.), cert. denied sub nom. Arado v. United States, 434 U.S. 875, 98 S.Ct. 225, 54 L.Ed.2d 155 (1977), assert that the district court could not reasonably accept Dr. Neumann's testimony about his Chow test results over Dr. DiPrete’s contradictory log linear test testimony because Dr. DiPrete submitted his results but Dr. Neumann did not. We do not find City of Chicago controlling. In that case, this court held that a district court could find that an expert’s testimony that studies in the 1960’s showed a correlation between patrolman examinations and training academy success was insufficient to prove job relatedness when the studies were not introduced into evidence. Thus in that case we affirmed a finding of fact whereas here the plaintiffs ask us to overrule one. In addition, the expert in City of Chicago had no connection with the studies he cited; Dr. Neumann, on the other hand, testified *542that he performed the Chow test and that it was the appropriate test for pooling. In light of these distinctions, we conclude that City of Chicago is not controlling and that the district court could consider the testimony about the Chow test.
. Prior to this lawsuit, Dr. Neumann had testified in matters dealing with ethnic discrimination, race discrimination, and sex discrimination in federal district court in Illinois and on age discrimination in Milwaukee. He also had advised other firms and, on one occasion, prepared material for the EEOC for a case that later settled. By contrast, this was the first case in which plaintiffs’ expert, Dr. DiPrete, had ever testified. (Tr. 924) He admitted that his experience with analyses based on data from a single company basically consisted of reading several studies in the "literature” (Tr. 2888) and that he was a sociologist, not a labor economist. (Tr. 924-25).
. Most courts agree that a plaintiff need not control for every conceivable factor in order to present a statistical prima facie case of disparate treatment. See, e.g., Segar, 738 F.2d at 1274-75, 1287 (plaintiffs’ failure to account for specialized prior experience in criminal investigations does not prevent their salary regression from establishing a prima facie case). On the other hand, an employee’s prior discipline record seems likely to be a major, if not the most important, factor in a discharge decision. When a factor is this obvious an influence, it may be appropriate to require a plaintiff either to include the factor in his statistical analysis or to offer proof that the factor reflects past discrimination. See Burdine, 450 U.S. at 254, 101 S.Ct. at 1094 (prima facie case "eliminates the most common nondiscriminatory reason^" for the employment decision). We need not decide this issue, however, because here the plaintiffs offered some testimony that the defendants discriminated in discipline.
. On cross-examination, plaintiffs' attorney asked Williams: "And under [the whole man] *547approach you would look at an employee’s total disciplinary record, wouldn’t you?” Williams answered, "That’s true.” (Tr. at 1955).
. Even in Dr. DiPrete’s most modified model, he found race to be statistically significant in only three of the seven years, and only one of those years was significant at a level of three standard deviations. Because courts "should be extremely cautious in drawing any conclusions” from statistical significance at the two-to-three standard deviation level, American National Bank, 652 F.2d at 1192, the relatively low statistical significance — especially in a case with numerous definitional problems — did not require the district court to conclude that the statistics conclusively proved discrimination. See Teamsters, 431 U.S. at 340, 97 S.Ct. at 1857 (the *548usefulness of statistical evidence ‘‘depends on all of the surrounding facts and circumstances").
. These four hundred personnel files were part of approximately 3,200 personnel files which were made available to plaintiffs during discovery. Plaintiffs could have made their own study of the files. Lacking plaintiffs’ study, it is too much to be forced to assume that considering the minority construction, hiring, and promotion practices of this company and other evidence, that the company had immediately begun to keep biased personnel files and business records to undo its otherwise excellent affirmative action efforts.
. Rule 1006 provides:
The contents of voluminous writings, recordings, or photographs which cannot conveniently be examined in court may be presented in the form of a chart, summary, or calculation. The originals, or duplicates, shall be made available for examination or copying, or both, by other parties at reasonable time and place. The court may order that they be produced in court.