This suit was brought on June 16, 1976, by Dr. Mary Craik1 against St. Cloud State University (SCSU), the Minnesota State University Board, the Inter-Faculty Organization/Minnesota Education Association (IFO/MEA), and various individuals,2 alleging classwide and individual sex discrimination in employment at SCSU in violation of Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 1983, and the Fourteenth Amendment. Specifically, the plaintiffs allege that they and other female faculty members at the University have been subjected to unlawful discrimination with regard to (1) appointment to chair positions, (2) rank, (3) compensation, (4) appointment to administrative positions, and (5) sexual harassment. The District Court certified a class consisting of
females who are or have been employed by St. Cloud University in a teaching capacity and who have been, continue to be, or may in the future be discriminated against because of their sex with respect to promotion, compensation ... and other conditions and privileges of employment.
Designated Record (D.R.) 29.3 The case was tried by a United States Magistrate under the consent provision of 28 U.S.C. § 636(c) (Supp. V 1981). After a trial which lasted 32 days the magistrate concluded that the defendants were not guilty of unlawful discrimination either as to the class or as to the individual claims of the named plaintiffs. After reviewing the briefs, record, and arguments, 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), as to certain claims. Accordingly, we reverse in part, affirm in part, and remand for reconsideration of some of the individual claims for relief.
I. LEGAL STANDARDS
A.
Most of the plaintiffs’ claims are based on the theory of disparate treatment.4 All disparate-treatment claims brought under Title VII5 turn on one basic *469issue: whether the employer intentionally treated “some people less favorably than others because of their race, color, religion, sex, or national origin.” International Brotherhood of Teamsters v. United States, 431 U.S. 324, 335 n. 15, 97 S.Ct. 1843, 1854 n. 15, 52 L.Ed.2d 396 (1977). In order “to sharpen the inquiry into the elusive factual question of intentional discrimination,” 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), courts require Title VII plaintiffs to establish a prima facie case — “a legally mandatory, rebuttable presumption,” id. at 254 n. 7, 101 S.Ct. at 1094 n. 7 — on that issue. The “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.” Teamsters, supra, 431 U.S. at 358, 97 S.Ct. at 1866 (footnote omitted). How the prima facie case is established and the consequences of its establishment, however, depend on whether the case is (1) brought by a single plaintiff on his or her own account or (2) a class action alleging a pattern or practice of discrimination.
In McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), the Court prescribed a model for the establishment of a prima facie case in “private, non-class” Title VII actions, id. at 800, 93 S.Ct. at 1823. The plaintiff must prove that he or she belongs to a protected class, applied for an available job for which he or she was qualified, but was rejected under circumstances which allow the court to infer unlawful discrimination. Id. at 802, 93 S.Ct. at 1824; Burdine, supra, 450 U.S. at 253, 101 S.Ct. at 1093. 6 The court may infer discrimination because, by establishing the prima facie case, the plaintiff has eliminated the two most common legitimate reasons for failure to hire: that there was no vacancy in the job for which the plaintiff applied or that the plaintiff was not qualified for the job. Teamsters, supra, 431 U.S. at 358 n. 44, 97 S.Ct. at 1866 n. 44. As the Court explained in Burdine,
Establishment of the prima facie case in effect creates a presumption that the employer unlawfully discriminated against the employee. If the trier of fact believes the plaintiff’s evidence, and if the employer is silent in the face of the presumption, the court must enter judgment for the plaintiff because no issue of fact remains in the case.
450 U.S. at 254, 101 S.Ct. at 1094 (footnote omitted).
Once the prima facie case is made out, the burden of production shifts to the defendant “to articulate some legitimate, nondiscriminatory reason for the employee’s rejection.” McDonnell Douglas Corp., supra, 411 U.S. at 802, 93 S.Ct. at 1824; Burdine, supra, 450 U.S. at 253-55, 101 S.Ct. at 1093-95. For example, in McDonnell Douglas Corp., the employer met this burden by producing evidence that it refused to rehire the plaintiff because he had participated in illegal demonstrations at the employer’s plant. 411 U.S. at 803-04, 93 S.Ct. at 1824-25. If the defendant carries its burden, thus raising a genuine issue of fact, the presumption of illegal discrimination drops from the case. The plaintiff at all times retains the burden of persuasion and must prove, by showing that the defendant’s explanation was not the true reason for the employment decision, that he or she was the victim of intentional discrimination. Burdine, supra, 450 U.S. at 254-56, 101 S.Ct. at 1094-95.
On the other hand, for cases brought by private plaintiffs or by the government on behalf of many employees, charging that an employer engages in discriminatory practices throughout most or all of its operations, the Supreme Court, in Franks v. Bowman Transportation Co., 424 U.S. 747, 96 S.Ct. 1251, 47 L.Ed.2d 444 *470(1976), and Teamsters, supra, prescribed a different order of proof. The trial of class actions is usually bifurcated into a liability phase and a remedial phase. See Teamsters, supra, 431 U.S. at 360-62, 97 S.Ct. at 1867-68. First, in the liability phase of the action, the plaintiff must prove by a preponderance of the evidence that the defendant engaged in a pattern or practice of unlawful discrimination in various company policies, that “discrimination was the company’s standard operating procedure — the regular rather than the unusual practice.” Teamsters, supra, 431 U.S. at 336, 97 S.Ct. at 1855. Normally, the plaintiff will produce statistical evidence showing disparities between similarly situated protected and unprotected employees with respect to hiring, job assignments, promotions, and salary, supplemented with other evidence, such as testimony about specific incidents of discrimination. The defendant, in rebuttal, will attempt to show that the plaintiff’s “proof is either inaccurate or insignificant.” Id. at 360, 97 S.Ct. at 1867. If it fails, the “trial court may then conclude that a violation has occurred and determine the appropriate remedy.” Id. at 361, 97 S.Ct. at' 1867.7
By proving that the defendant engaged in a pattern or practice of discrimination, not only is the plaintiff class’s eligibility for appropriate prospective relief established, a prima facie case with regard to the remedial phase of the suit, in which relief for individuals is considered, is also made out. Id. at 359, 97 S.Ct. at 1866. Thus, the court presumes that the employer unlawfully discriminated against individual class members. In pattern or practice cases, however, the presumption shifts to the employer not only the burden of production, but also the burden of persuading the trier of fact that it is more likely than not that the employer did not unlawfully discriminate against the individual.8
The [plaintiffs] need only show that an alleged individual discriminatee unsuccessfully applied for a job and therefore was a potential victim of the proved discrimination .... [T]he burden then rests on the employer to demonstrate that the individual applicant was denied an employment opportunity for lawful reasons.
Id. at 362, 97 S.Ct. at 1868; see also Franks, supra, 424 U.S. at 772, 96 S.Ct. at 1268. The burden of persuasion shifts to the employer with regard to the claims of both named plaintiffs and unnamed class members. E.g., Taylor v. Teletype Corp., 648 F.2d 1129, 1136-38 (8th Cir.), cert. de*471nied, 454 U.S. 969, 102 S.Ct. 515, 70 L.Ed.2d 386 (1981).9
In this case we squarely confront the necessity of distinguishing the analysis required for broad-based class actions from that required for individual, non-class actions. Our recent precedents are inconsistent. For example, in Taylor v. Teletype Corp., supra, we followed the Franks-Teamsters analysis. First, we affirmed the District Court’s finding of classwide discrimination. Then we examined the claims of the four named plaintiffs to see whether the employer had proved “that the individual employment decision was free from that discrimination.” Id. at 1136. In contrast, in Coble v. Hot Springs School District No. 6, 682 F.2d 721 (8th Cir.1982), we first analyzed the named plaintiffs’ claims under Burdine and concluded that the District Court had erred in rejecting them. Only then did we consider the class claims. Finally, in Paxton v. Union National Bank, 688 F.2d 552 (8th Cir.1982), cert. denied, — U.S.-, 103 S.Ct. 1772, 76 L.Ed.2d 345 (1983), we analyzed first the class claims and then the individual claims, using the Burdine framework. Even though we found classwide discrimination with regard to promotion, we did not, in examining the named plaintiffs’ claims regarding promotion, place the burden of persuasion on the employer. See 688 F.2d at 556-57 n. 3. However, since none of these cases addressed the question of precisely how the burdens of production and persuasion should be allocated in Title VII class actions, we do not believe that our approach in this case, which conforms with the Franks-Teamsters model, is forbidden by Coble or Paxton.
B.
The magistrate did not analyze the evidence according to the class-action framework we set out above. Rather, he first considered the plaintiffs’ individual claims under the McDonnell Douglas-Bur-dine framework and rejected them. Then he addressed and rejected the class claims. In our view this was error; but if we agreed that' the class claims were properly rejected, it would be harmless, because in that case the individual plaintiffs would not be entitled to the burden-shifting presumption of Franks and Teamsters. But we disagree with the magistrate’s holdings on some of the class claims, in large part because of the manner in which the evidence was considered. In addressing and rejecting the plaintiffs’ individual claims, the magistrate considered only the evidence relating to the specific incidents about which the plaintiffs complained. Then, in addressing and rejecting the class claims, he considered statistical evidence and evidence about university policies and practices, but not the plaintiffs’ evidence relating directly to their individual claims. We take a different view of how to approach the weighing of the evidence in Title VII class actions. With regard to both the individual and class claims, all the evidence was relevant and should have been considered together. The statistical and other evidence is relevant to the individual claims because it “is often a telltale sign of purposeful discrimination.” Teamsters, supra, 431 U.S. at 340 n. 20, 97 S.Ct. at 1856-57 n. 20. The evidence of specific incidents of alleged discriminatory treatment is relevant to the class claims because it may bring “cold numbers convincingly to life.” Id. at 339, 97 S.Ct. at 1856. Much of the probative force of the plaintiffs’ evidence was dissipated by placing it into discrete analytical compartments. Cf. EEOC *472v. American National Bank, 652 F.2d 1176, 1188-89 (4th Cir.1981), cert. denied, 459 U.S. 923, 103 S.Ct. 235, 74 L.Ed.2d 186 (1982) (District Court erred by evaluating statistical and non-statistical evidence independently). Accordingly, while, for the sake of clarity, we shall discuss the plaintiffs’ claims separately, it should be remembered that the evidence relating to one claim may be relevant to and persuasive with regard to others.
II. BACKGROUND: AFFIRMATIVE-ACTION EFFORTS
Neither Title VII, 42 U.S.C. § 1983, nor the Fourteenth Amendment requires an employer to institute an affirmative-action program, 42 U.S.C. § 2000e-2(j) (1976); Burdine, supra, 450 U.S. at 259, 101 S.Ct. at 1096; Rizzo v. Goode, 423 U.S. 362, 375-76, 96 S.Ct. 598, 606, 46 L.Ed.2d 561 (1976), but evidence that an employer has failed to live up to an affirmative-action plan is relevant to the question of discriminatory intent. E.g., Teletype Corp., supra, 648 F.2d at 1135 n. 14. And, although a trial judge need not make specific findings on all facts nor refer to every item of evidence introduced in a lengthy trial, “[t]he reviewing court deserves the assurance that the trial court has come to grips with apparently irreconcilable conflicts in the evidence ... and has distilled therefrom true facts in the crucible of his conscience.” Keystone Plastics, Inc. v. C & P Plastics, Inc., 506 F.2d 960, 962 (5th Cir. 1975). The magistrate’s near-complete failure to address the evidence concerning the defendants’ affirmative-action efforts reduces our confidence in his ultimate conclusions.
The Minnesota State University system has had an affirmative-action plan since 1972. The defendants often did not abide by the plan. They did not set goals and timetables for promotion through the academic ranks, V.15.33-39, 160, or for chair positions, V.15.133-34. Nor did they set timetables for appointing women to administrative positions. V.15.111-15. The defendants advance a number of reasons for these omissions. They assert that it was not the intent of the plan to require goals and timetables for “promotions” in academic rank, but only for “appointment” to new or vacant positions. E.g., V.15.33-40. They further aver that they do not set goals for chair positions because the selection process is prescribed by the collective-bargaining agreement between SCSU and IFO/MEA and is beyond their control. E.g., V.15.133-34.10 In fact, the plan adopted in 1974 provided:
Hiring practices shall be structured to increase the number of qualified ... women in the Chancellor’s office and at each college within the system.
* * * * * *
The Chancellor’s office and each college within the system shall forthwith move towards an equitable balance of ... women for all positions within the system and shall put into effect immediately a program to promote ... women.
* * * ‘!s * *
The Chancellor and each of the college Presidents shall require of the Vice-Chancellors and each department within the colleges the development of numerical goals and timetables for overcoming present imbalances of ... women in all job classifications.
Px. 272-d, at 4, 6, 8. The plan currently in force provides:
*473Qualified persons shall be considered for selection and promotion without regard to ... sex____
ifc !■! ij. Hi
A primary objective of the state universities’ Affirmative Action/Equal Opportunity programs is to have a workforce which is reflective of the availability of women ... in the appropriate labor market. To meet this objective, each university ... shall annually analyze its workforce to determine if there are components of the workforce which are not reflective of the labor market. Goals are to [be] set to overcome any deficiencies which are found, and timetables for reaching these goals shall be set.
Px. 272-g at 4. In view of the plain language of the plans, the defendants’ explanations of why they failed to set goals and timetables are untenable.
In addition, the plaintiffs demonstrated that the affirmative-action committee met irregularly and did not meet at all from late 1978 until December 1980. Px. 116; Grachek II at 27-30. The defendants claim that the committee failed to meet during this latter period because the affirmative-action director wanted to use an individual rather than a committee approach. V.20.-26. We do not believe that this rather lame explanation is adequate. The plan unequivocally states that “[t]he committee shall meet at least monthly.” Px. 272-g at 3; see also 272-d at 12.
Finally, it is uncontested that many members of SCSU’s administration and faculty are ignorant about the meaning of affirmative action. The defendants have not made efforts to remedy this situation through formal training programs. V.7B.32-35, 47.
The magistrate did not make findings on any of these points, and we cannot be sure that he gave this evidence proper weight in considering the plaintiffs’ substantive claims. We believe that the defendants’ explanations, where given, are inadequate to rebut the inference that SCSU officials were not committed to their affirmative-action plan. This is another factor in our conclusion that the magistrate clearly erred in rejecting certain claims of the plaintiffs.
III. CLASS CLAIMS
A. CHAIRPERSONS
Department chairs at SCSU are members of the faculty who are released from teaching duties. The chair manages the department and makes recommendations to the President on personnel actions, budgetary matters, teaching assignments, and so forth. Chairs are appointed by the President of the university.
In March 1976 the university and IFO/MEA entered into a collective-bargaining agreement which, in Article XX, sets out the procedure for selecting chairs. First, a search is held, which may be internal (within the university) or external (including candidates from outside the university). The faculty of the department holds an election by secret ballot. The candidate receiving the majority vote is submitted to the President as the department’s nominee. The President must either appoint or decline to appoint the nominee within 10 working days. If the President declines to appoint, the department holds a second election and selects a different nominee. If the President declines to appoint the second nominee, he or she appoints an interim chairperson. Px. 271-a to -c.
The plaintiffs showed, and the defendants acknowledged, that women were underrepresented in chair positions at SCSU, e.g., Px. 305-b; V.15.134, although in recent years their position has improved, Px. 228 at 2; Px. 305-b, -r. From 1970-1971 11 through 1979-1980, only 3 of 71 chairpersons were women. M. 67. From 1973-1974 through 1978-1979, men were from 10.9 to 5.5 times more likely than women to hold chair positions. Px. 305-b; V.10.26-29. In addition, the plaintiffs showed that women were effectively excluded from any chair positions because, between 1975-1976 and 1979-1980, SCSU conducted, for de*474partments which had all-male faculties, external searches in only 3 out of 21 instances. They also demonstrated that no woman had ever defeated a man in a contested election. Moreover, they showed that the administration had taken no direct steps to increase the number of female chairpersons. E.g., V.15.133-36; Grachek I at 64. See also Part II., supra. Finally, the plaintiffs presented telling evidence relating to Dr. Craik’s unsuccessful chair bid. See Part IY.A, infra.
The defendants pointed to several nondiscriminatory reasons for the dearth of chairwomen. First, they argued that they were unable to conduct external searches unless a faculty position was open in the department, because the chair is a member of the department’s budgeted faculty. Second, the defendants maintain that almost all chairpersons have held doctorates, and that women did not obtain the doctorate in any substantial number until the mid-1970s, so that there was a very limited pool of qualified female candidates. Finally, they attempted to show that women were uninterested in chair positions. Of the 53 elections held between 1975-1976 and 1979-1980, 29 were uncontested, and all nominees — 28 men and one woman — from uncontested elections were appointed. Of the 24 contested elections, women ran in 7. In only 5 of these elections, however, did a woman run against a man. In these 5 male-female contests, the woman ran against an incumbent, and, the defendants maintain, incumbents are hard to defeat. Dx. 77.
The magistrate concluded that the plaintiffs failed to prove that women had been unlawfully discriminated against with respect to chair appointments. He found that “16.67% of the female candidates in contested elections were eventually appointed as chairs; 18.64% of the males in contested elections were appointed chairs,” and concluded that this disparity was too small to give rise to an inference of discrimination. M. 68. He agreed with the defendants that budget constraints made external searches in departments which had no faculty openings impossible, M. 69. Finally, he rejected the plaintiffs’ argument that the administration’s failure actively to recruit and support female candidates was indicative of discrimination, because the faculty’s hostility toward the administration would render such efforts the “kiss of death” to the female candidate. M. 69-70. The magistrate’s discussion is conscientious and shows a great deal of industry. But we disagree in several respects with his method of weighing and analyzing the evidence.
(1) By comparing the percentage of successful female and male candidates in contested elections, the magistrate failed to recognize that female candidates were successful only when they ran against other women, but never when they ran against a man.
(2) By failing to consider cumulatively the effects of the selection process, the magistrate overlooked several important points. Before March 1976, when the collective-bargaining agreement became effective, the President had unfettered discretion in appointing department chairs. After that time, departments — most, if not all, of which had male majorities — held elections to select, by majority vote, a nominee. The President still had the right to reject any nominee and appoint an interim chairperson of his own choosing.
A selection process that is subjective and dominated by men requires particularly close scrutiny. E.g., Paxton, supra, 688 F.2d at 563 n. 15; Royal v. Missouri Highway & Transportation Commission, 655 F.2d 159, 164 (8th Cir.1981). It might account not only for women’s failure to win elections against men, see discussion of Craik’s unsuccessful chair bid, Part IV.A, infra, it might also account for women’s reluctance to run. Cf. Dothard v. Rawlin-son, 433 U.S. 321, 330, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977) (“The application process itself might not adequately reflect the actual potential applicant pool, since otherwise qualified people might be discouraged from applying because of a self-recognized inability to meet the very stan*475dards challenged as being discriminatory.”). Moreover, the defendants’ evidence relating to elections failed to address the period from 1970-1971 through 1975-1976, when the President could appoint chairpersons without considering an elected nominee. In addition, the President appointed the incumbents who, according to the defendants, never lose. Finally, the argument that administrative support would be the “kiss of death” to a female candidate cannot stand in light of the President’s ultimate authority to select the chair.
(3) Finally, no consideration was given to the evidence relating to the Craik-Peterson election, see Part IV.A, infra, and to the defendants’ general failure to pursue affirmative action with regard to chair positions, see Part II., supra.
We firmly believe that, properly analyzed and weighed, the evidence demonstrates that the defendants discriminated against women with regard to chair positions. The plaintiffs showed that the defendants discriminated against women vis-a-vis chair positions both before and after this suit was filed. Women never held more than two chair positions during any one year. Px. 228 at 2, 305-r. Women lost contested elections against men in 1975-1976, 1976-1977, and 1978-1979. Dx. 77. At all times, the President had authority to appoint chairpersons. Even after this suit was filed, the defendants made no direct efforts to increase the number of female chairs. Even though the representation of women as chairpersons increased somewhat in 1977-1978 and 1978-1979, Px. 305-b, this phenomenon was not the result of any change in the defendants’ practices during the post-suit period. Accordingly, we hold that the plaintiffs proved a pattern or practice of discrimination during the period from the time when chair appointments were made for 1970-1971 through the time when those appointments were made for 1979-1980.12
B. RANK
There are four academic ranks at SCSU: professor, associate professor, assistant professor, and instructor. Faculty members are assigned a rank when they are hired, and they may later attain a higher rank through promotion. There are both subjective and objective criteria for appointment and promotion. The subjective criteria include teaching ability, scholarly achievement, and professional activities. Dx. 15-18; Px. 271-c, art. XXV. The objective criteria are degree, experience, time in rank, and length of service. Ibid. Various committees and officials make recommendations for promotions, but the President has final authority to approve or disapprove both initial appointments and promotions. Dx. 15; Px. 271-c, arts. XXI, XXV.
The plaintiffs contend that the defendants discriminate against women with regard to rank. They demonstrated that as academic rank increases, the percentage of women holding that rank decreases, while the percentage of men increases. Px. 305-a. This phenomenon, of course, could be due to factors other than sex discrimination; for example, a smaller percentage of women than men might possess Ph.D.’s. Accordingly, the plaintiffs presented multiple linear regression analyses controlling for such factors as highest degree, time elapsed since highest degree, and experience. These analyses, which covered each year from 1973-1974 through 1979-1980, showed that women held lower academic, rank, at a statistically significant rate,13 *476than men with similar qualifications. Px. 305-O, 337-39. For example, in 1973-1974, 2.9 out of every 10 women were, on the average, one rank lower than men with comparable backgrounds. Px. 305 — o; V.10.73-74. The plaintiffs also showed that, in many cases, women wait longer for promotion than similarly situated men. Px. 305-p, -q.
The defendants were required to rebut the plaintiffs’ evidence by showing that it was inaccurate or insignificant or by providing a nondiscriminatory explanation for the apparently discriminatory result. Teamsters, supra, 431 U.S. at 360, 97 S.Ct. at 1867 and n. 46. Their rebuttal consisted of evidence (1) that the plaintiff’s methodology was faulty, (2) that eligible women are promoted as quickly as eligible men, (3) that women get a high percentage of “exception” promotions, and (4) that women are not discriminated against in hiring.
1. Statistical Methodology. The defendants argue that multiple linear regression is an inappropriate statistical method for examining discrepancies in rank. The plaintiffs assigned numerical values to the different ranks for purposes of the analysis: the rank of “professor” was assigned a one, “associate professor” was assigned a two, “assistant professor” was assigned a three, and “instructor” was assigned a four. The defendants argue that assigning numerical values to “qualitative” data— data which, unlike height, weight, or salary, are not inherently numerical (or “quantitative”) — undermines the validity of the results. Accordingly, they presented studies based on logistic regression fitting analysis,14 which showed that, when five degree categories — Ph.D., M.A. + 90 quarter-hour credits, M.A. + 45 quarter-hour credits, M.A., and B.A. — were controlled for, sex was not a statistically significant factor in rank differentials. Dx. 154b.
*477The magistrate did not rely on the defendants’ logistic regression fitting analy-ses in reaching his conclusion that the plaintiffs had failed to prove discrimination with regard to rank. M. 49. We agree that these analyses did not rebut the plaintiffs’ studies based on multiple linear regression. The defendants’ studies examined data for only one post-suit year, 1977-1978, while the plaintiffs’ studies examined data covering seven years. Moreover, the defendants did not show that the values which the plaintiffs assigned to the various ranks in their multiple linear regression analyses produced misleading results.15
2. Defendants’ Flow Statistics. The defendants, in Dx. 54, presented a “flow” analysis comparing the movement rank to rank of men and women eligible for promotion. The exhibit is broken down by year from 1974-1975 through 1979-1980 and shows that, overall, 52.1 per cent, of the eligible women, but only 38.3 per cent, of the eligible men, were promoted. In Dx. 70 and 161, the defendants showed that women and men who were promoted between 1973-1974 and 1979-1980 had comparable years in rank and years of experience at the time of the promotion and that it took both men and women 15.5 years to advance from instructor to full professor.
3. Exception Promotions. Over the years, a number of persons have been promoted even though their credentials did not meet the requirements of the written guidelines. The defendants presented evidence showing that between 1973-1974 and 1979-1980 women received more than half of these “exception” promotions. Dx. 161, 169. The plaintiffs’ evidence showed, however, that during 1972-1973 and 1973-1974, there were no female, but several male, exception promotions. V.17A.69-83; V.22.-30-33, 59-62.16
4. Hiring. The defendants showed that from 1974-1975 through 1979-1980 comparable percentages of men and women were hired at the highest rank for which they were eligible. Dx. 69. The magistrate did not consider, however, that for the ranks of assistant professor and associate professor, this was not true during the period before the lawsuit was filed. For example, over the entire period covered by Dx. 69, 82.8 per cent, of the women and 82.5 per cent, of the men were appointed to Assistant Professor, which was the highest entry rank possible. But during the pre-suit period, 76.9 per cent, of the women were hired as Assistant Professors, as opposed to 87.2 per cent, of the men. V. 27.42-44.
We believe that it was clear error to find that there was no discrimination with regard to rank during the pre-suit period. Again, our conclusion is based on the cumulative effects of several factors.
It is clear that the defendants’ practices changed after this lawsuit was filed. They appointed women to their highest appropriate ranks in a markedly smaller percentage than men during the pre-suit period. They *478also, at least during 1972-1973 and 1973-1974, gave women no exception promotions, while they gave several to men. Finally, the rate of female promotions almost doubled after the suit was filed. While we do not agree with the plaintiffs that post-suit evidence is irrelevant, “[A]ctions taken in the face of litigation are equivocal in purpose, motive and permanence.” James v. Stockham Valves & Fittings Co., 559 F.2d 310, 325 n. 18 (5th Cir.1977), cert. denied, 434 U.S. 1034, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978) (quoting Jenkins v. United Gas Corp., 400 F.2d 28, 33 (5th Cir.1968)). The magistrate did not recognize the different probative values of pre- and post-suit evidence. Rather, he mistakenly gave post-suit evidence as much weight as pre-suit evidence.
Nonetheless, we would hesitate to overrule the magistrate on this issue in light of Dx. 54, the exhibit which showed the yearly movement rank to rank of persons eligible to advance. Evidence such as this is quite probative because it focuses precisely on the decisions made during the relevant time frame; it does not, like “snapshot” statistics, incorporate “the residue of past discrimination.” Movement for Opportunity & Equality v. General Motors Corp., 622 F.2d 1235, 1245 (7th Cir.1980). However, Dx. 54 is fatally flawed.
First, “eligibility” as used by the defendants is an imprecise and poorly understood concept. For example, the defendants, on Dx. 139a, classified many persons as eligible for promotion who were not eligible under the written guidelines. V.17A.69-83. Moreover, the volume of exception promotions and appointments indicates that the defendants did not rigorously apply the eligibility criteria. See, e.g., Dx. 70; Px. 258; V.22.30-80. Finally, various individual defendants disagree on precisely what the standards are. Some said that they were aware of no standards other than those which are contained in the collective-bargaining agreement. Grachek I at 71-72; V.14.135. These standards are vague, speaking of, for example, “[l]ength of service,” without referring to any particular length of time. Px. 271-e at 25. The “Guidelines for Retention, Tenure, and Promotion,” Dx. 15-18, are much more specific, but have not been distributed to the faculty or to department chairs. V.14.134-36; V. 19.41-42. See Paxton, supra, 688 F.2d at 563-64. This omission is especially suspect since the promotion process normally begins with a recommendation by the department chair. Px. 271-b at 27; Px. 271-c at 25. Consequently, there is substantial doubt whether Dx. 54 includes all persons eligible for promotion and excludes all persons not eligible for promotion.
Second, the effects of the defendants’ tendency, during the pre-suit period, to appoint a greater percentage of men than women to their highest appropriate rank undermine the validity of Dx. 54. One criterion for promotion is time in rank. Since women tended to begin in lower ranks, they would become eligible for promotion to their appropriate ranks later than men. The flow statistics disguise this inequity.
Accordingly, we hold that the plaintiffs proved that the defendants discriminated against women with respect to rank from the time that appointments and promotions were made for 1973-1974 until June 16, 1976, when this suit was filed. Although the effects of this discrimination lingered, and the defendants took no direct steps to compensate for it, we cannot say that the magistrate clearly erred in finding that there was no intentional discrimination in later years, when the defendants’ appointment and exception-promotion policies changed.
C. SÁLARY
The plaintiffs claim that the defendants discriminate against women with respect to salary. They contend that female faculty members receive lower salaries overall and that they receive fewer market-factor and performance increases. The magistrate rejected each of these contentions.
1. Overall Salary. Through multiple-regression analyses covering 1974 through *4791980 the plaintiffs controlled for factors such as experience, degree, and so forth and showed that female faculty members received lower salaries than similarly situated men, and that the differential is statistically significant. Px. 305-O, 337-339. The magistrate found, however, that only one study analyzed the correct group of people — only full-time faculty — and corrected for the proper factors — experience, degree category, division, and rank — -and that it showed that there were no significant differences in salary. Px. 339. He also relied on studies prepared by the defendants which “matched” each woman on the faculty with all men who had (1) the same rank, degree, and experience, Dx. 55, 57, 59, and (2) the same rank, degree, and experience and who were in the same division, Dx. 56, 58, 60.
In light of our holding that the plaintiffs proved sex discrimination with regard to rank during the pre-suit period, this finding cannot stand.
For example, a female assistant professor may be getting a salary comparable to her fellow male assistant professor. But, if she rightfully should be an associate professor and is not because of discriminatory treatment, she should have been earning more money.
Mecklenburg v. Montana State Bd. of Regents, 13 Fair Empl.Prac.Cas. (BNA) 462, 468-69 (D.Mont.1976). See also James v. Stockham Valves & Fittings Co., supra, 559 F.2d at 332; Finklestein, The Judicial Reception of Multiple Regression Studies in Race and Sex Discrimination Cases, 80 Colum.L.Rev. 737, 741-42 (1980).
Nor do we believe that “division” was a proper independent variable. The defendants invented the “division” categories for trial, V.28.171, in an attempt to account for the fact that engineering teachers are paid more than English teachers. Each of the three “divisions” consisted of two colleges: (1) Fine Arts and Liberal Arts and Sciences, (2) Business and Industry, and (3) Education and Miscellaneous. V.21.166-71. These categories are too broad to be meaningful, and the defendants do not use them in making salary decisions. Cf. Wilkins v. University of Houston, 654 F.2d 388, 402 (5th Cir. Unit A 1981), vacated and remanded on other grounds, 459 U.S. 809, 103 S.Ct. 34, 74 L.Ed.2d 47 (1982), affd on remand, 695 F.2d 134 (5th Cir. 1983) (the college in which a professor teaches is the most important factor in determining salary). Accordingly, “division” was not a proper factor.
When all persons holding academic rank are examined,17 controlling for (1) experience and highest degree plus time from highest degree or (2) experience and degree category, the salary differentials for each year from 1975 through 1980 are statistically significant at either the five per cent, or one per cent, level. Px. 305-O, 337-338. Gross statistical disparities alone may, in a proper ease, prove a pattern or practice of discrimination. Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741-42, 53 L.Ed.2d 768 (1977); Teamsters, supra, 431 U.S. at 339-40, 97 S.Ct. at 1856-57. Here, there is, depending on the year, less than a five per cent, or a one per cent, probability that the salary differentials are due to chance. In light of all the other evidence that we have examined, we believe that the salary differentials are a facet of the pre-suit, intentional discrimination regarding appointments and promotions. Thus, we hold that the defendants unlawfully paid women lower salaries than similarly situated men during the same period that they unlawfully discriminated against women with regard to rank. Although it is a close question, we again affirm the magistrate’s finding of no discrimination during the post-suit period. The effects of prior discrimination undoubtedly continued to affect salary, but the plaintiffs point to no evidence that the defendants paid women who were newly *480hired to their appropriate ranks less than similarly situated men.18
2. Market-Factor Increases. In 1980 SCSU began distributing market-factor increases in five traditionally all-male disciplines identified as “scarce market areas”: Business Administration, Computer Science, Economics, Engineering Technology, and Mathematics. Seventeen men and one woman received awards; the woman was the only woman in any of these departments who had a terminal degree.
The discriminatory impact of the awards is evident: the one woman who received the award represented 6 per cent, of the recipients at a time when women constituted more than 20 per cent, of SCSU’s faculty. The magistrate agreed, however, with the defendants' argument that the awards were necessary to maintain a strong faculty in these disciplines. M. 59. We cannot say that this conclusion is clearly erroneous in view of the greater market demand for professionals in these disciplines than for professionals in disciplines such as English and Education, where more women have traditionally specialized. See V.15.67-68.
3. Performance Increases. From 1975-1976 through 1980-1981, 23.1 per cent. of the female faculty members and 26.6 per cent, of the male faculty members received performance, or merit, increases. Px. 43. The plaintiffs point out that the discrepancy is higher for 1975-1976 and 1976-1977. The magistrate held that this evidence was insufficient to establish discrimination with regard to performance increases, particularly since the earlier awards were apparently made after the defendants learned that this lawsuit had been filed. We cannot say that this conclusion is clearly erroneous, so we affirm on this point.
D. ADMINISTRATIVE POSITIONS
The plaintiffs claim that the defendants intentionally excluded women from administrative positions. To the extent that the category of “administrative positions” includes department chair positions, we agree. See Part III.A., supra. We shall confine our discussion here to the higher administrative positions.
The plaintiffs showed that women are and have been markedly underrepresented in upper-level management positions. From 1969-1970 through 1975-1976, the highest position held by a woman was that of dean; from 1976-1977 through 1979-1980, the highest position held by a woman was that of assistant vice president. No more than one woman held these high positions in any one year. Px. 44. The plaintiffs also showed that the defendants had *481set no timetables within which to increase the number of women in administrative positions. V.15.111-15; see Part II., supra.
The magistrate concluded, however, that the plaintiffs failed to prove that this un-derrepresentation was due to sex discrimination, and we cannot say that this conclusion is clearly erroneous. The defendants showed that from 1974-1975 through 1979-1980 women were appointed to administrative positions at more than twice the rate of their percentage in the applicant pool. Dx. 47. While this evidence did not cover the period from 1969-1970 through 1973-1974, it was not totally irrelevant in determining the defendants’ practices during that time. Accordingly, we affirm the magistrate’s conclusion on this point.
E. SEXUAL HARASSMENT
Finally, the plaintiffs claim that the general work atmosphere at SCSU was sexist. “Employer toleration of a racially discriminatory work atmosphere clearly violates Title VII,” Taylor v. Jones, 653 F.2d 1193, 1199 (8th Cir.1981), and the same principle applies to sex discrimination. The plaintiffs’ brief refers to about 50 incidents which occurred over a ten-year period. We refer to some of these incidents below, in discussing Dr. Craik’s individual claim, see Part IV.A, infra, and we have considered them along with all the other evidence of classwide discrimination. Nevertheless, the situation depicted by the evidence simply does not approach the oppressive work atmosphere which forced the plaintiff in Taylor to resign. Thus, we cannot say that the magistrate clearly erred in rejecting this claim.
IV. INDIVIDUAL CLAIMS
A. CRAIK
Craik alleges that she was subjected to unlawful discrimination when she was not appointed chair of the Psychology Department in 1976. The magistrate, analyzing the evidence under the McDonnell Douglas test, held that while Craik had made out a prima facie case, the defendants articulated legitimate, nondiscriminatory reasons for selecting Dr. Peterson, a man, over Craik, and that Craik had failed to show that those reasons were pretextual. In light of our holding that the defendants were guilty of classwide discrimination with respect to chair appointments, this method of analysis was erroneous. The Franks-Teamsters model should have been applied, under which the defendants would have the burden of persuading the trial court that they had not discriminated against Craik. Normally, we would remand this claim for reconsideration under the proper standard. Here, however, we believe that even under the McDonnell Douglas test, the holding against Craik was clear error, and we therefore reverse.
In the spring of 1975 the incumbent chair of the Psychology Department, Dr. Knut-son, announced that he would not continue as chair beyond the end of that quarter. The department selected a committee to conduct a search for a permanent chair, and, since there was an opening on the faculty, held an external search. Craik was one of the candidates for the chair position.
After seven finalists, including two women, had been selected, members of the search committee and members of the department faculty at large began to disagree about the requirements of affirmative action. The search committee discussed the issue at great length. When the committee decided to recommend that four candidates be interviewed, Dr. Murphy, the committee chair, resigned. Murphy felt that affirmative action required a woman to be hired, since it appeared that the female applicants were qualified, and that the department would be “playing games” by having male candidates come for interviews. Px. lr; Knutson at 46-47. He eventually voted for Peterson. Other members of the department reacted with “hostility and anger” to the idea that they would not have any choice but to hire a woman. Kleiber at 23-25. Dr. Charles Boltuck and Dr. Lesar made statements to *482the effect of “this means we’ll be stuck with a woman.” V.31.60; V.31.104-05. Both of these men eventually voted for Peterson. Boltuck asked that his name be removed from the selection proceedings (although he was not on the search committee) so that he would not be liable for reverse discrimination. Kleiber at 20-21. Then the faculty decided to suspend the search altogether and try to reorganize the department. The search process was promptly reinstituted, however, when the administration told the department that cancelling it might give rise to affirmative-action suits. Px. lx, ly. Gillett, the Acting Vice-President for Academic Affairs, met with the department and explained the meaning of affirmative action. Boltuck responded, “Well, that means, then, that we won’t get stuck with an inferior woman.” V.24.150.
The search committee then recommended that four candidates, ranked in order of preference, be brought in for interviews: Joan Bean, Louis Aiken, Mary Craik, and Robert Riedel. Bean and Aiken withdrew their names, however, and Terrance Peterson and Neil Wylie, ranked fifth and sixth, were added to the list. Craik, the only female candidate, was then top-ranked among the finalists. Dx. 25 at 3.
All four candidates were brought in for interviews. While not all faculty members interviewed all candidates, each candidate’s application materials were available for inspection. During the interviews, Boltuck asked Craik if she would sue if she were not selected. V.31.64.
The election was held on May 17, 1976. Under the procedure adopted by the department, after each ballot the name of the person receiving the least votes was to be dropped. The person who, at the end, had the greatest number of votes would be the department’s nominee. On every ballot, Craik received the same 10 votes and Peterson received the same 7 votes. On the last ballot, all the votes for Wylie shifted to Peterson:
Ballot 1 Ballot 2 Ballot 3
Craik 10 10 10
Peterson 7 7 13
Wylie 6 6 dropped
Reidell 0 dropped dropped
Peterson became the department’s nominee.
After the election, Craik complained to Dean Ames, the dean of the college in which the Psychology Department was located, and to President Graham and asked for an investigation. She told them about the voting pattern, the “stuck with a woman” statement, and about having been asked whether she would sue if not chosen. On May 28, 1976, Graham met with Ames, Gillett, Kitchen (the affirmative-action officer), and Robert Becker (Special Assistant to the President) to discuss the appointment. They discussed the information Craik had relayed, and, relying on the recommendations of his advisors, Graham approved Peterson as the new department chair.
No investigation of Craik’s charges was held prior to Peterson’s selection. The officials did not contact Knutson, who was in charge of preparing the affirmative-action report, to determine what his views were; they did not attempt to discover who had made the “stuck with a woman” statement; and they did not ask the union for an extension of time in which to look further into the situation and to receive the affirmative-action report. Knutson finally filed the report about two weeks later, and it stated:
[T]he majority of the search committee does not feel that the action of the department and the administration in this matter is in compliance with affirmative action policies or law ... [W]e hope that it will be reconsidered.
Dx. 25b at 4.19
The magistrate held, however, that the defendants had articulated legitimate, non*483discriminatory reasons for Peterson’s selection, and that the plaintiffs had failed to prove that those reasons were pretextual. He found that the department was deeply divided into factions based on academic interest groups and that members of certain groups voted for Peterson because they believed his interests to be similar to theirs or because he was from outside the department. The magistrate found further that many members of the department were impressed by Peterson’s qualifications. Finally, he found that President Graham, when he approved Peterson’s selection, had virtually no evidence to suggest that the vote might have been tainted by sex discrimination.
We believe that this finding was clearly erroneous. While no one factor is determinative, the cumulative effect of the evidence compels this conclusion. For example, there was evidence that a number of the men involved in the selection process were hostile to the idea of a woman’s being the department chairperson. Boltuck’s and Lesar’s statements about “being stuck with a woman” suggest such an attitude. This inference is strengthened by Boltuck’s later remark, after Gillett had explained that affirmative action did not require choosing a woman without regard to her comparative qualifications, that the department would not “get stuck with an inferior woman,” as well as his inquiry as to whether Craik would sue if not selected.
The plaintiffs presented other evidence indicating that discriminatory attitudes were pervasive in the department. For example, Mason, a man who voted against Craik, while interviewing a prospective graduate student, told her that women like her made good para-professionals and that she probably did not need a graduate degree. V.12.57-58. Lesar told Knutson that he had trouble working with Mary Dwyer because she reminded him of a “prison matron.” V.31.100-01. In 1970, Passini, then chairperson of the Psychology Department, assigned Craik to teach statistics and then revoked the assignment, telling her that men on the faculty had objected to her teaching the course. V.l.47-51. Although we do not know exactly why these objections were made, it is reasonable to infer that they were based on the stereotyped view that women are not good at mathematics.20 There was also evidence that when women spoke in faculty meetings, some of the faculty, especially Murphy and Nunes, would snicker at their suggestions. V.9.83-84.
The plaintiffs also presented evidence indicating that certain male members of the department resented Craik’s assertiveness and feminist viewpoints. Kleiber, for instance, did not vote for Craik because he felt that there were “communication barriers,” stemming largely from sexist attitudes, between Craik and other members of the department. Pdx. 6; Kleiber at 11. He perceived a pervasive atmosphere of resistance to Craik, which he thought might result from her being an assertive woman, including her assertiveness on issues relating to women’s rights. Kleiber at 14-15. Knutson substantially agreed with this assessment. He said that some men in the. department often made remarks which, Knutson believed, indicated that they were threatened by Craik because they believed that she had a lot of power which she and other feminists would use against them. Knutson at 31-36.
Finally, we are struck by the administration’s failure to investigate Craik’s charges before confirming Peterson as the new department chair. The voting pattern alone is highly suggestive; there is a 1.6 per cent, probability that the shift of all of *484Wylie’s votes to Peterson was due to chance (one-half to the sixth power). In light of the furor in the department about affirmative action and its requirements, bias against women is the most plausible explanation. Under these circumstances, given the information that Graham, Ames, Gillett, and Kitchen possessed, the administration had ample cause to suspect that sex discrimination influenced the election. Considered in light of the evidence outlined above, the evidence of the defendants’ general lack of commitment to affirmative action, see Part II., supra, and our conclusion that the defendants discriminated against women as a class with regard to chair positions, see Part III.A, supra, these officials’ complete failure to take any steps to investigate Craik’s charges, or even to ascertain the contents of the affirmative-action report which Knutson was to file, persuades us that Craik was the victim of illegal discrimination.
B. ANDRZEJEWSKI, HEMMER, AND GOEMER
The intervening plaintiffs brought individual claims charging that the defendants had discriminated against them with regard to assignment to rank, promotion, salary, and work atmosphere. As in the case of Craik, the magistrate analyzed and rejected these claims under McDonnell Douglas. In light of our holding that the defendants were guilty of some classwide discrimination, this was error. Accordingly, we vacate and remand so that the lower court may reconsider these claims under the guidelines we set out below for the consideration of the claims of unnamed class members. Additionally, since a holding in favor of the intervening plaintiffs on one or more claims encompassed by our holdings of classwide discrimination might affect the analysis of claims not so encompassed, we vacate and remand for reconsideration of those claims as well under the McDonnell Douglas standard.
VI. CONCLUSION
On remand, the lower court should consider whether injunctive relief is appropriate to ensure that the defendants no longer discriminate against women with regard to chair positions. Such relief should normally be granted. It should also consider the claims of all individuals, including the named plaintiffs and the unnamed class members,21 who show that they were “potential victim[s] of the proved discrimination,” Teamsters, supra, 431 U.S. at 362, 97 S.Ct. at 1868 regarding (1) chair positions, (2) rank during the pre-suit period, and (3) salary during the pre-suit period. The defendants will have the burden of proving by a preponderance of the evidence that they did not discriminate against these individuals with respect to these claims.22 Further, in granting individual relief, the court should ensure that persons who continued to suffer the effects of pre-suit discrimination during the post-suit period are fairly compensated for the entire period. For example, a woman who has discrimina-torily denied a promotion in 1975, and thus remains at a lower rank and salary than comparable men, should be placed in the same position at which she would be today but for the effects of the pre-suit discrimination.
With respect to the classwide claims of post-suit discrimination in rank and salary, and discrimination in administrative positions and work atmosphere, the judgment is affirmed.
Affirmed in part, reversed in part, and remanded with instructions.23
. Dr. Julie Andrzejewski, Dr. Joan Hemmer, and Ms. June Goemer later intervened as plaintiffs.
. SCSU is one of seven state universities governed by the Minnesota State University Board, which is comprised of 10 members appointed by the Governor. The Board, in turn, appoints a Chancellor, who serves as the chief executive of the System. V.15.8-9. SCSU is headed by a President, who is charged by the Board and the Chancellor with the overall management of the university. V.16.10. It offers bachelors' and masters’ degrees, has about 10,000 students, and employs about 600 full-time faculty. V. 16.11-12, 16. IFO/MEA is the exclusive bargaining representative of faculty members within the State University System. Px. 271-a to -c.
. We shall use the following abbreviations throughout this opinion:
(a) Px. or Dx.: Plaintiffs’ Exhibit or Defendants’ Exhibit.
(b) Pdx.: Plaintiffs' Deposition Exhibit.
(c) PB. or DB.: Plaintiffs’ (Appellants’) Brief or Defendants’ (Appellees') Brief.
(d) M.: Magistrate's memorandum opinion.
(e) D.R.: Designated Record.
(f) V.1.163: Transcript volume 1, page 163.
(g) Grachek II at 10: Grachek deposition, volume 2, page 10.
. We shall address only one claim — market-factor salary increases — under a disparate-impact theory. For the differences between the two theories, see International Brotherhood of Teamsters v. United States, 431 U.S. 324, 335-36 n. 15, 97 S.Ct. 1843, 1854-55 n. 15, 52 L.Ed.2d 396 (1977).
. The issue of discriminatory intent is common to analyses under the Fourteenth Amendment, § 1983, and Title VII. See Washington v. Davis, 426 U.S. 229, 240, 96 S.Ct. 2040, 2047, 48 L.Ed.2d 597 (1976) (referring to “the basic equal protection principle that the invidious quality of a law claimed to be racially discriminatory must ultimately be traced to a racially discriminatory purpose.”); Schlei & Grossman, Employment Discrimination Law 693-94 (2d ed. 1983); 2 Larson & Larson, Employment Discrimination § 52.61 (1983). Accordingly, like the magistrate, we shall confine our discussion to Title VII.
. The precise requisites of a prima facie case will vary, of course, if the plaintiff chállenges employment practices other than hiring. See 411 U.S. at 802 n. 13, 93 S.Ct. at 1824 n. 13; 2 Larson & Larson, Employment Discrimination § 50.22, at 10-10 to -11 (1983).
. The Court in Teamsters spoke of the plaintiffs . initial burden in the liability phase of "making out a prima facie case of discrimination,” 431 U.S. at 336, 360, 97 S.Ct. at 1855, 1867, which the defendant must attempt to rebut, id. at 342, 360, 97 S.Ct. at 1858, 1867. Accordingly, many courts, including this one, have used the McDonnell Douglas-Burdine model to analyze the evidence in the liability phase of class actions. E.g., Paxton v. Union Nat’l Bank, 688 F.2d 552, 567-68 (8th Cir.1982), cert. denied, — U.S.-, 103 S.Ct. 1772, 76 L.Ed.2d 345 (1983); Croker v. Boeing Co. (Vertol Div.), 662 F.2d 975, 990-91 (3d Cir.1981) (en banc). We agree, however, with Judge Higginbotham, then on the District Court, that "[i]n a complex class action, utilizing statistical proof and counterproof, the value of the Burdine sequence — to highlight the issues in contest — is about as relevant as a minuet is to a thermonuclear battle.” Vuyanich v. Republic National Bank, 521 F.Supp. 656, 661 (N.D.Tex. 1981), vacated and remanded, 723 F.2d 1195 (5th Cir.1984); accord, Perryman v. Johnson Prod. Co., 698 F.2d 1138, 1143 (11th Cir.1983). Therefore, in considering the merits of the class claims, we shall focus on whether the plaintiffs proved that the defendants engaged in a pattern or practice of discrimination, thereby establishing a prima facie case with regard to the claims of individual class members, without attempting to fit the evidence into the McDonnell Douglas-Burdine framework. For reasons explained below, post, pp. 470-471, we do not believe that our Paxton opinion outlaws this form of analysis.
. We decline to follow the lead of the District of Columbia Circuit in imposing a "clear and convincing evidence" burden on the employer. See, e.g., McKenzie v. Sawyer, 684 F.2d 62, 77-78 (D.C.Cir.1982). The normal standard of proof in civil litigation is that of a preponderance of the evidence, and we do not believe that the public and private interests involved require altering that distribution of the risk of error between the litigants. See generally Santosky v. Kramer, 455 U.S. 745, 754-57, 102 S.Ct. 1388, 1394-96, 71 L.Ed.2d 599 (1982).
. "[T]he allocation of burdens in a case of class-wide discrimination” was not altered by Bur-dine. Taylor, supra, 648 F.2d at 1137 n. 18. The prima facie case established by a finding that an employer is guilty of a pattern or practice of discrimination goes far beyond the prima facie case contemplated by McDonnell Douglas and Burdine. See Burdine, supra, 450 U.S. at 253, 101 S.Ct. at 1094 ("The burden of establishing a prima facie case of disparate treatment is not onerous.”). The Court in Teamsters recognized this difference. A finding of a discriminatory pattern or practice creates "a greater likelihood that any single decision was a component of the overall pattern,” 431 U.S. at 359-60 n. 45, 97 S.Ct. at 1866-67 n. 45, and changes "the position of the employer to that of a proved wrongdoer,” ibid.
. This argument is plainly without merit. "The rights assured by Title VII are not rights which can be bargained away — either by a union, by an employer, or by both acting in concert.” United States v. St. Louis-San Francisco Ry., 464 F.2d 301, 309 (8th Cir.1972) (en banc), cert. denied, 409 U.S. 1116, 93 S.Ct. 913, 34 L.Ed.2d 700 (1973) (quoting Robinson v. Lorillard Corp., 444 F.2d 791, 799 (4th Cir.), cert. dismissed, 404 U.S. 1006, 92 S.Ct. 573, 30 L.Ed.2d 655 (1971)). Moreover, there is nothing in the collective-bargaining agreement to prohibit affirmative action in the selection of chairpersons. Indeed, the agreement expressly states that both the employer and the union will not discriminate on the basis of sex. Px. 271-a to -c, art. II.
. This refers to the academic year.
. The plaintiffs correctly point out that the liability period under § 1983 is governed by Minn.Stat.Ann. § 541.05 (West Supp.1983), which establishes a six-year period of limitations. Occhino v. United States, 686 F.2d 1302, 1307-08 (8th Cir.1982). Accordingly, the defendants are not liable under § 1983 for any chair appointments made before June 16, 1970. Nor, of course, are the defendants liable under Title VII for actions taken before March 24, 1972, when they became subject to its provisions. Equal Employment Opportunity Act of 1972, § 14, Pub.L. No. 92-261, 86 Stat. 103, 113. The District Court, on remand, should determine when the appointments were made and other discriminatory actions were taken.
. Statistical significance is a measure of the probability that an observed disparity is not due *476to chance. Baldus & Cole, Statistical Proof of Discrimination § 9.02, at 290 (1980). A finding that a disparity is statistically significant at the 0.05 or 0.01 level means that there is a 5 per cent, or 1 per cent, probability, respectively, that the disparity is due to chance. Normally, courts and social scientists, when confronted with such low probabilities, conclude that something other than chance is causing the disparity. The courts must decide whether that "something” is illegal discrimination or some other, nondiscriminatory influence.
The Supreme Court recognized a variation of this principle when it noted that "[a]s a general rule ..., if the difference between the expected value and the observed number is greater than two or three standard deviations,” the disparity is not due to chance. Castaneda v. Partida, 430 U.S. 482, 496-97 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977). Accord, Hazelwood School Dist. v. United States, 433 U.S. 299, 311 n. 17, 97 S.Ct. 2736, 2743 n. 17, 53 L.Ed.2d 768 (1977). For large samples, this test "is essentially equivalent to a rule requiring significance at a level in the range below 0.05 or 0.01,” Baldus & Cole, supra, § 9.03, at 297.
The parties in this case presented evidence in terms of statistical-significance rates rather than in terms of the "two or three standard deviations” rule. This presents a potential problem only because both parties also used what statisticians call "one-tailed tests” in determining the rates. Apparently, a disparity that is significant at the 0.05 level under a one-tailed test is only 1.645 standard deviations away from the expected (nondiscriminatory) result, V.32.25, while a disparity that is significant at the 0.05 level under a two-tailed test is 1.96 standard deviations away from the expected result, see Weinberg & Schumaker, Statistics: An Intuitive Approach 169 (3d ed. 1974). We agree, however, with the court in EEOC v. American Nat’l Bank, supra, 652 F.2d at 1192, that
If a legal rule of analysis can properly be derived from the Castaneda footnote, it can only be that standard deviations greater than two or three necessarily exclude chance as a cause of underrepresentation. The converse of this — that standard deviations of not "more than two or three” necessarily exclude discriminatory design as the cause — is nowhere implied.
Statistical evidence showing less marked discrepancies will not alone establish that something other than chance is causing the result, but we shall consider it in conjunction with all the other relevant evidence in determining whether the discrepancies were due to unlawful discrimination.
. There is some argumentation in the briefs about the relative merits of multiple linear regression and logistic fitting analysis. Neither side, however, either in the briefs or at the oral argument, bothered to explain, in intelligible terms or otherwise, what these terms mean. Our conclusion is not based on any holding that either of these statistical methods is superior as a matter of law. They are simply two different ways of analyzing facts, and they may or may not be persuasive in any given case.
. The defendants also argued that Px. 305-O is misleading because it includes some administrators and other non-teaching personnel who have academic rank and because it does not account for the degree categories of M.A. + 45 and M.A. + 90. We do not believe that the inclusion of administrators in the data base undermines the validity of the plaintiffs’ studies. Administrators (defined as President, Assistant to President, Vice President, Assistant Vice President, Assistant to Vice President, Dean, Associate Dean, and Assistant Dean) never comprised more than 4 per cent, of the total faculty during the relevant period. (In 1977-1978 there were 20 administrators and 502 faculty members.) Px. 44. The effect of the inclusion of such a small proportion of administrators is not obvious, and the defendants chose not to rework the multiple regression analyses on a corrected data base in order to demonstrate that the results would be more favorable to them. See Trout v. Lehman, 702 F.2d 1094, 1101-02 (D.C.Cir.), cert. granted, — U.S.-, 104 S.Ct. 1404, 79 L.Ed.2d 732 (1984).
Nor are we convinced that the plaintiffs were required to use the M.A. + 45 and M.A. + 90 categories. The defendants have not used these categories in making assignments or promotions to rank since 1971. DB. 35. At any rate, Px. 339 cured both of these objections, and it reflects a statistically significant differential in rank.
. The defendants argue that there were female exceptions in the early years. They point only to one example, however, and it reflects a hiring exception, not a promotion exception. Px. 258.
. Given the state of the record, it is appropriate to use studies based on this population. See note 7, supra.
. The defendants, relying on General Tel. Co. v. Falcon, 457 U.S. 147, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982), argue that there is no class representative for salary claims for 1975-1976 and previous years. In April 1976 Craik, Andrzejew-ski, and Goemer participated in a settlement of an Equal Pay Act suit against the defendants. The settlement agreement recited that it was "a full and final compromise and settlement of all matters and all causes of action arising out of the facts and claims set forth in the pleadings ... by ... plaintiffs and other persons who have filed a consent form with respect to this action.” Dx. 10 at 7. The magistrate held that the settlement agreement "settles all salary claims plaintiffs may have through 1975-1976 and the principles of res judicata preclude relitigation of those claims here.” M. 54 (citation omitted). Assuming that this means that the settlement barred only the claims of those named plaintiffs and unnamed class members who filed consent forms, we agree. Those individuals have been compensated for any salary discrimination they suffered through 1975-1976. Hemmer, the remaining named plaintiff, likewise has no claim for salary discrimination for 1975-1976 and before, because she did not begin work at SCSU until the summer of 1976. V.9.6.
Nevertheless, we do not believe that Falcon compels the conclusion that the named plaintiffs here cannot represent class members who have salary claims for the pre-suit period. In Falcon the Court held that a plaintiff who alleged that he had been discriminatorily denied a promotion was not a proper representative for a class claim of discriminatory hiring practices. Here, in contrast, we are not confronted with two such independent employment practices as hiring and promotion. The defendants’ practices regarding rank — both initial assignments and promotions — had a direct impact on salaries. Thus, any individual with a valid claim regarding discrimination with regard to rank during the pre-suit period can properly represent other individuals who have either rank or salary claims.
. Knutson testified that his report reflected the views of four of the six committee members: himself, Prochnow, Dwyer, and Redding. Knut-son at 83. Redding, however, testified that he did not agree with the statement quoted above. V.30.27. The magistrate made no finding on *483this point, but the discrepancy does not affect our analysis. We are not bound, in determining whether Craik was the victim of unlawful discrimination, by the vote of the committee.
. The magistrate appears to have rejected this allegation. M. 19. He inferred that Craik was not allowed to teach statistics because another faculty member had previously taught it and normally would be expected to continue to teach it. We find no indication in the record, however, that another faculty member had traditionally taught statistics. Thus, we need not defer to this finding.
. The court should require the parties to notify all class members so that they may come in and present their claims.
. The court should re-examine the record when considering the claims of the intervening plaintiffs, rather than taking new testimony.
. Our brother Swygert, who dissents in part, does not seem to disagree in any material respect with our discussion of the law. His opinion is directed rather to an examination of the particular facts of this case. We have stated and discussed the facts in what seems to us to be sufficient detail, and we therefore forego a point-by-point response to the dissenting opinion. We add only that all three members of the panel seem to agree that there is a great deal of smoke here, and that our own conviction that *485there is also some fire remains definite and firm.