Circuit Judge:
Andra A. Capaci and the Equal Employment Opportunity Commission (EEOC) brought this Title VII sex discrimination suit against Katz & Besthoff, Inc. (K & B), a drugstore company based in New Orleans. With the exception of one minor aspect of Capaei’s individual disparate treatment case, the district court held for the defendant company after a bench trial. 525 F.Supp. 317 (E.D.La.1981). Numerous issues are raised on appeal, the most important of which concern the use and abuse of statistical techniques by the parties in the trial below. We hold that the district court was clearly erroneous in finding that the defendant had not discriminated against women in hiring manager trainees from 1965 through 1972. In all other respects we affirm.
I. CLASS CLAIMS
This suit began when Andra Capaci, then a pharmacist with K & B, filed a class action complaint under Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq., alleging gender discrimination by her employer. The EEOC intervened, alleging that the defendant had failed to promote and hire females into management positions on the same basis as males.
K & B operates a chain of drugstores in New Orleans and several other towns and cities in Louisiana, Mississippi and Alabama. Managers at the stores fall into four categories: manager, assistant manager, relief manager and manager trainee. In those stores where the manager is not a pharmacist, a chief pharmacist is appointed to supervise the pharmacy department; On appeal as at trial, the case centers on the employment practices of K & B with respect to manager trainees and pharmacists.
A. Statistical Evidence.
The EEOC relied primarily on a statistical case presented through exhibits and the testimony of its expert witness, Dr. Gast-wirth. K & B countered with testimony of its expert, Dr. Cranny. On appeal, the statistical methods used by the experts, rather than their raw data, are the major concern.
1. Manager Trainees
Manager trainees are hired both internally from the ranks of existing employees and externally from the civilian labor market. The only objective qualification is a high school diploma.
In our view the most important single fact presented to the district court is this: From July 1965, the effective date of Title VII, to January 1, 1973, the date just prior to Capaci’s filing of discrimination charges, K & B hired or promoted 267 individuals to the position of manager trainee, of which 267 were male. The days of testimony that followed were consumed in part in determining whether or not this fact could be said to constitute statistically significant evidence of discrimination.
Dr. Gastwirth performed some rather sophisticated statistical tests for discrimination. He first determined a relevant labor market with which he could compare the proportion of females in management. Using 1970 census data, he looked to all managers in Louisiana and refined the comparison further by looking to experienced wholesale and retail managers, general merchandise retail managers, and department and sales managers. He made further refinements by looking to the census data for these categories in three separate geographic locations — New Orleans, Baton Rouge, and the remainder of the state — and weighting the figures by the number of stores in each region. He then took the “lower bound” of these geographical weightings to be conservative,1 and excluded those trainees hired outside of Louisiana. He also looked to managers earning less than $7,000 in 1969, on the assumption that those earning more would not be interested in the manager trainee position paying between $5,980 and $6,500 at that time. In short, he arrived at a number of comparable *652segments of the labor force, which ranged from 16% to 29% female. With all of the manager categories, these percentage figures were conservative, since, as even Dr. Cranny admitted on cross-examination, they underestimated present female availability by reflecting past discriminatory employment decisions.
Using this data, Gastwirth computed the probability that K & B’s selections could have been made in an unbiased or random manner. Regardless of which “referent” group was used, for the period 1965-1972 the probability calculated was consistently far less than one in a billion.2 Indeed, the highest probability of unbiased hiring was 5.367 X 10-2°, less than one in a billion billions.
Gastwirth performed comparable tests for manager trainees hired from 1973 through 1977, a period between the filing of the charge and the trial. During this period some female manager trainees were hired, but the vast majority of trainees chosen were male. The results of the tests, though considerably less dramatic than those for the 1965-1972 period, consistently showed the probability of such disparate hiring occurring by chance to be less than one in 10,000.
The EEOC also relied on “applicant flow” data, that is, data on the number of men and women hired compared with the number who actually applied for the job. Only applications from July 1976 through 1977 were made available through discovery. This information indicated that 19.2% of the applicants for manager trainee were female, within the 16%-29% range Gastwirth predicted using census data. However, women made up only 9.2% of those chosen. Sixteen percent of the female applicants were successful, compared with 37% of the males. Using a chi-square test, Gastwirth determined that the probability of such hiring occurring by chance was less than one in a thousand.3
*653K & B attacked the EEOC statistical case in four ways. It argued that: (1) the government failed to consider that women might not want the job and through “self-selection” would not apply; (2) Dr. Gast-wirth failed to make various refinements in the census data necessary to make accurate comparisons; (3) the statistical tests looked only to external hiring of manager trainees and failed to consider internal promotions; (4) tests using data broken down by year and geographic location showed vastly reduced or no statistical significance. We find these objections less than convincing.
Certainly there is some merit to the self-selection argument. The district court found that “[t]he job requires the manager trainee to unload supply trucks, to put up stock, straighten up the store, and the work schedule includes night work, weekend and holiday work.” 525 F.Supp. at 325. The court credited the testimony of Dr. Cranny, an industrial psychologist and labor economist, that such job conditions “would substantially retard females from applying as compared to males.” Id. Several witnesses also testified that females had selected themselves out of the manager trainee job or applicant pool. This testimony emphasized in particular the unwillingness of women to work the hours required of manager trainees.
Despite this evidence, and deferring completely to the trial judge in weighing the credibility of these witnesses, we have great trouble accepting self-selection as an explanation for the complete absence of women in the manager trainee program for the seven and one-half year period preceding the discrimination charge. There is no reason to believe that the female witnesses called were representative of all women in the labor market or employed by the defendant. By looking to other merchandising, wholesale and retail, and department and sales managers, Gastwirth’s statistical tests were already corrected for self-selection to some extent, since all managers face hours and responsibilities that would not appeal to some women. Gastwirth testified that an applicant pool that was even 2% female would still have led to a finding of statistical significance for the 1965-1972 period. The applicant flow data indicated that 19.2% of manager trainee applicants were female, within the range found for other managers, and inconsistent with a theory of total self-selection. The defendant’s witnesses also made clear that non-management and non-professional employees, 79% of whom are women, also have weekend and night duties and perform physical labor. Dr. Cranny stated that management trainees and assistant managers “do much of the same work as the rest of the people in the organization do.”
K & B maintains that the census data used by Gastwirth was not sufficiently “refined” to make his tests meaningful. The district court found that “Dr. Gastwirth admitted that his groups include part time employees and the self employed, some of whom are not potential applicants for the manager trainee position, and that no data was available to him to make the refinements,” and that “[a]ll of the [Gastwirth comparison] groups included data on businesses not comparable to the K & B operation, such as boutiques and dress shops.” 525 F.Supp. at 325, 328.
The use of census data is an appropriate method of demonstrating discrimination. Hazelwood School District v. United States, 433 U.S. 299, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977). The defendant would require refinements beyond that available in published statistics. A perfect statistical model is not required. Phillips v. Joint Legislative Committee, 637 F.2d 1014, 1025 (5th Cir.1981), cert, denied, 456 U.S. 960,102 S.Ct. 2035, 72 L.Ed.2d 483 (1982); Vuyanich v. Republic National Bank of Dallas, 505 F.Supp. 224, 314 (N.D.Tex.1980). The de*654fendant must do more than raise theoretical objections to the data or statistical approach taken; instead, the defendant should demonstrate how the errors affect the results, Vuyanich, supra, at 255-56, 306-07, particularly in cases where the plaintiff has demonstrated gross disparities in employer practices, id. at 357; International Brotherhood of Teamsters v. United States, 431 U.S. 324, 342 n. 23, 97 S.Ct. 1843, 1858 n. 23, 52 L.Ed.2d 396, 419 n. 23 (1977). In this case, the EEOC demonstrated that inclusion of self-employed persons actually increased the female percentage in the retail trade manager group from 15.44% to 18.72%. The Commission also points out that the general merchandise retail manager group it used, composed of 23.96% women statewide, does not include dress shops. Furthermore, there is nothing in the record suggesting that the census statistics systematically included stores likely to be managed by women, while excluding stores likely to be managed by men, such as gun shops or adult bookstores. It bears repeating that any applicant group composed of more than 2% women would have produced statistically significant results for the 1965-1972 period.
K & B contends that Gastwirth’s statistics “are largely irrelevant because they ignore the established practice of K & B to look first to its existing work force for new manager trainee candidates before going outside.” 525 F.Supp. at 324. This argument is singularly unpersuasive for the 1965-72 period. In that period, 265 manager trainees, all male, were hired from the external labor force. Two manager trainees, both male, were promoted internally. Including internal availability and promotion would have only increased the statistical significance of the results for this period, particularly since women constituted 79% of the non-managerial and non-professional internal work force, a much higher percentage than that estimated for the relevant external labor force. Gastwirth also considered internal promotions along with external hiring for the 1973-1977 period in Manager Trainee Exhibits 12 and 13. Even without taking into account the higher proportion of females in the internal labor pool than in the external labor market, the probability of randomly selecting 20 females out of 365 persons hired directly or promoted from within was still less than 1 in 10,000.
Finally, K & B attempted to demonstrate that there was no statistically significant evidence of discrimination when the data was broken down by city or year or both. In our view, this was an unfair and obvious attempt to disaggregate that data to the point where it was difficult to demonstrate statistical significance. By fragmenting the data into small sample groups, the statistical tests became less probative. Wheeler v. City of Columbus, Mississippi, 686 F.2d 1144, 1151 (5th Cir.1982). Indeed, it became impossible to demonstrate significance with such small numbers in many instances, since even a record of hiring or promoting zero women would not yield statistically significant results.4 There was no *655reason to fragment the data geographically, since all hiring decisions regarding manager trainees are made at the firm’s New Orleans office, and liability is premised on “across-the-board” practices, id., occurring at all locations. Likewise, liability is S.R. stands for selection ratio: N.S. means not significant. Another example of the defendant’s fragmentation of data is found in the district court opinion, 525 F.Supp. at 326 n. 12. *656premised on actions taken within the entire 1965-1977 period, and there was no reason to fragment the data by year. Aggregating the data as the plaintiff did was a much more reasonable approach, since liability under Title VII depends on whether the EEOC demonstrated a “systemwide pattern or practice” of disparate treatment, rather than “the occurrence of isolated or ‘accidental’ or sporadic discriminatory acts. It had to establish ... [that] discrimination was the company’s standard operating procedure — the regular rather than the unusual practice.” International Brotherhood of Teamsters v. United States, 431 U.S. 324, 336, 97 S.Ct. 1843,1855, 52 L.Ed.2d 396, 416 (1977).
2. Pharmacist Promotions
The testimony and exhibits concerning pharmacist promotions were more complicated than those for manager trainees, for several reasons. First, the EEOC was trying to demonstrate not only disparate treatment in selection for promotion but •also in length of time to promotion. Second, the creation of the chief pharmacist position in 1967 had altered the chain of promotion and created two different lines of progression to storewide management. Third, K & B presented a strong statistical case of its own, rather than concentrating on refuting the EEOC statistics. The district court reported at length this aspect of the case. 525 F.Supp. at 328-334.
In light of the legal standards and the nonstatistical evidence discussed below, we have little trouble affirming the trial court’s finding that pharmacist promotions were not made in a discriminatory manner. We discuss here the statistical evidence only in sufficient detail to explain why we conclude that the findings are not clearly erroneous.
The EEOC’s statistical case was not nearly as strong as with manager trainees. Generally, the data base was smaller, and the probability of random occurrence much higher than with the manager trainee tests. Ostensibly to control for seniority, Gast-wirth had done tests for promotion during two different time periods. He compared the hiring and promotion of men and women in each period, but in so doing, disregarded women hired in period one and promoted in period two. Two of the original six chief pharmacists were women. The district court was suspicious of this “juggling of dates to eliminate from the data .. . female pharmacists who were promoted after the effective date of the Act and before the date of the filing of the Capaci charge, so that 0 females was the consistent data tested.” 525 F.Supp. at 334. With the help of 1973 Louisiana pharmacist data provided in an HEW Division of Manpower Intelligence report, Dr. Cranny demonstrated that 11% of the active pharmacists in Louisiana were female. The comparable figure was 9% for Louisiana community chain pharmacies and 13.3% for K & B. Of promotions to chief pharmacist from 1965 to 1973, 13.3% were women, the same percentage as for female pharmacists employed at K & B. The male and female selection ratios were also identical at 15%, indicating that the chances of promotion were the same for men and women.
B. Other Evidence
1. Employee Testimony
The defendant relied heavily on testimony of former and present employees to demonstrate that it did not discriminate against women. The district court was entirely correct in admitting and considering such testimony. While statistics alone may reveal a great deal, the testimony of employees “about their personal experiences with the company” are useful to bring “the cold numbers convincingly to life.” International Brotherhood of Teamsters v. United States, 431 U.S. 324, 339, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396, 417 (1977).
The Commission relied on the testimony of several women to demonstrate disparate treatment of female job applicants and employees. For various reasons the district court did not credit their testimony. 525 F.Supp. at 334-36. The defendant called numerous past and present employees concerning its hiring and promotion practices, including over a dozen women who had served in management and several key male executives who set corporate policy.
*657The trial was consumed in large part by the testimony of these and other fact witnesses. We do not attempt a comprehensive summary here. After reviewing the record with some care, we find that K & B made a sizable and respectable presentation of testimonial evidence that it did not discriminate against women after the Capaci charge was made. However, what little testimonial evidence was presented concerning practices prior to the charge does not support the same conclusion.
As with the statistical evidence, we concentrate our concern on the period from July 1965, the effective date of Title VII, to January 11, 1973, the date Capaci filed her charge with the EEOC. We cannot review the lay testimony without at least an occasional glance at the raw numbers. At oral argument, K & B asked us to consider its Exhibit 110, described by counsel as one “of critical significance.” The exhibit lists all females who ever entered management from 1947 through 1978. Of the fifty-one women, thirty-eight, or 75%, entered management after Capaci filed her charge. Twenty-one of those thirty-eight entered management only after the EEOC’s intervention into the case in January 1977. During the July 1965-January 1973 period, only four women are listed, three of whom assumed posts as “cosmetic supervisors,” an all-female position. The fourth, Josephine Liuzza, first hired by K & B in 1931, was promoted to chief pharmacist in 1968.
The district court opinion made specific reference to the testimony of four former female managers. “The testimony of Genevieve Ronquette, Lillian Hennessey, Blanche Callihan and Inez Nungesser is to the effect that they were not treated differently from males by K & B in promotion to management.” 525 F.Supp. at 337. We find their testimony unhelpful on the issue of discrimination against manager trainees in the 1965-1972 period. All four had entered management prior to the effective date of Title VII. Hennessey, Callihan and Nungesser all testified that men and women were treated equally at K & B, but indicated complete unfamiliarity with the manager trainee program. Ronquette testified primarily on advertising practices, discussed further below, but mentioned that she was familiar with the manager trainee program. She testified that she did nothing to discriminate against women, but did not discuss whether the firm as a whole had committed such acts.
Nearly all of the other female managers who testified — Johnson, Boudreaux, Bonvil-lain, Robottom, Falcon, Feigel, Lachaussee and Choate — were promoted after the charge was filed. There is no reference by name to any of these witnesses in the district court opinion indicating that their testimony was significantly relied upon by the trial judge in reaching his conclusions. The only female member of management promoted during the 1965-1972 period who was called to the stand was June Buras, a cosmetic supervisor. She testified about specific events involving Ms. Capaci and Louise Oregon, another witness who had claimed disparate treatment and had testified for the EEOC. Buras was not asked and offered no opinion of storewide practices and policies regarding women.
The male executives of the company who testified indicated that K & B did not discriminate against women. However, if carefully examined their testimony does not support a finding of nondiscriminatory treatment in the 1965-1972 period.
Sidney J. Besthoff, III, the president of K & B, testified that “the early thrust of the Civil Rights Act was to prevent discrimination by race,” and that upon its passage, the firm took active steps to set up a “complete program” in regards to racial aspects of the Act. Noting that “[t]he sex aspect of the discrimination was passed as a part of the Civil Rights Act as an afterthought,” he stated that the firm’s initial concern was with racial minorities and that “for various reasons, we did not have any real interest in the 1950’s or the 1960’s in women in management.” At another stage of the trial he stated: “So when we had fairly well gotten into the racial problem and we thought that we had handled that problem adequately, racial discrimination in employment, we *658then went on to the other aspects of the Act, the sex aspect of the Act and beginning in the early 1970’s we began a program of bringing women into our management at that time.” He admitted in deposition testimony read at trial that the Capaci charge had “spurred us to review more carefully the use of females in management and to encourage the hiring and promotion of females within the company.”
Walter Feltman, vice president and operations director of the company, testified at length about many aspects of the case. He stated that K & B tried to recruit actively females for management, some as early as 1968. When asked to describe the company’s experience since 1970 regarding the active recruiting of women, he stated that “once we gained some success, in ’73 or ’74, we gained a little success in recruiting some of the females, it then started to accelerate and it started, you could use the word ‘snowball,’ I guess, and it’s continuing that way .... ”
The earliest printed statement of K & B policy not to discriminate in the record is an Employee Handbook dated May 1973. Felt-man also indicated that the firm had adopted an “affirmative action plan,” set out in a short booklet dated January 1976. The booklet states in substance that “Katz & Besthoff, Inc. is committed to providing equal opportunity to all,” that “[tjraining programs at K & B are available on a non-discriminatory basis” and that while promotions are “made on the basis of an individual’s demonstrated performance and qualifications” managers should look for qualified people “with special emphasis for women and members of minority groups.”
The district court reached the following findings based on the oral testimony:
William Serda became personnel director in March 1971, and at that time there were still only four females in management, — one manager, one assistant manager, one chief pharmacist, one cosmetics supervisor. He realized that this situation made the company vulnerable to charges of violation of the federal law against discrimination, and for that reason and the additional reason that the company had an urgent need for manager trainees in the expansion program, which was within his area of responsibility, he made the recommendation to his superior Walter Feltman in 1971 or 1972 that females be encouraged to apply for managerial positions. The recommendation for affirmative action was taken under advisement, but was Ultimately approved.
The promotion record does not indicate that the implementation of Serda’s recommendations was immediate, and the written affirmative action policy was not published until 1976. Besthoff agreed that the Capaci charge was the impetus for the implementation of Serda’s affirmative action recommendation.
525 F.Supp. at 338.
K & B presented an impressive group of fact witnesses at trial. The district court was entitled to rely on them as it saw fit. However, there is little if any testimonial evidence to counter the strong statistical case concerning manager trainees chosen before the Capaci charge.
2. Advertising Evidence
The EEOC relied at trial on the content and placement of job vacancy advertisements in newspaper classified sections from 1965 to 1971. Again, the evidence here concerns the period about which we are most concerned, namely, the period after the effective date of Title VII and before the Capaci charge.
The Commission argued that the advertisements were discriminatory for two reasons. First, the content of several advertisements indicated a preference for males in management openings and a preference for females in non-management positions. A series of advertisements run in the Baton Rouge Morning Advocate expressed an interest in “qualified young men” to train for store management positions.5 A 1965 ad*659vertisement placed in the New Orleans Times Picayune sought “Local Men 23 to 45 to train as assistant to ice cream plant manager,” and a 1971 advertisement in the Times Picayune for a personnel director stated: “We are seeking a vital, aggressive man who is ready to realize his potential.” See 525 F.Supp. at 339 n. 29. In contrast, a number of other advertisements sought “counter girls” and “salesladies” for non-management positions.
The Commission also pointed out that the advertisements for manager trainees, even when gender-neutral in content, were routinely placed in the newspapers’ “Help Wanted-Male” or “Male Help Wanted” columns. At the time, the Times Picayune had columns designated “Help Wanted-Male,” “Help Wanted-Female” and “Help Wanted-Male or Female.” The Morning Advocate had columns designated “Male Help Wanted,” “Female Help Wanted” and “Help Wanted.” Frequently, advertisements for secretaries, salesladies, counter girls, counter clerks and cashiers — all non-management positions' — were placed in the female columns, while advertisements for a manager trainee, “career in management,” fountain manager trainee and personnel director were found in the male columns.
We find that the advertising evidence is evidence of discrimination. While not determinative by itself, it should have weighed in the EEOC’s favor. None of the reasons given by the district court and by the defendant for disregarding this evidence are persuasive.
The district court noted that EEOC regulations prior to 1969 did not prohibit neutral advertising under male or female newspaper headings.6 However, this circuit has held that placing advertisements for flight attendants in female columns without corresponding advertisements in male columns is an unlawful employment practice under section 704(b) of Title VII, 42 U.S.C. § 2000e-3(b), since sex is not a bona fide occupational qualification for that position. Hailes v. United Air Lines, 464 F.2d 1006 (5th Cir.1972). The advertisement in question in that case was placed in a New Orleans newspaper in 1967, contemporaneously with the K & B advertisements at issue here. While administrative interpretations of statutory meaning are entitled to deference, Batterton v. Francis, 432 U.S. 416, 424, 97 S.Ct. 2399, 2405, 53 L.Ed.2d 448, 456 (1977), a prior panel decision of the circuit is entitled to more than deference, and cannot be overruled by a later panel, Gates v. Collier, 616 F.2d 1268, 1272 (5th Cir.1980). Were it simply a matter of choosing an authority to follow, we would adhere to the law of our circuit. This entire argument, however, is somewhat off the mark. K & B was not sued for discriminatory advertising. While such practices are expressly prohibited by Title VII, 42 U.S.C. § 2000e-3(b), the class aspect of this suit was brought for discrimi*660natory treatment of female employees under 42 U.S.C. § 2000e-2(a). The plaintiff claiming disparate treatment of women as a class must establish a pattern and practice of gender-based discrimination by the employer, and must also establish discriminatory motivation. Wheeler v. City of Columbus, Mississippi, 686 F.2d 1144, 1150 (5th Cir.1982). Especially since the defendant has never claimed that it actually relied upon or was even aware of the then-existing EEOC guidelines, the advertising evidence is useful and probative insofar as it goes to establish motivation and hiring policies.
At trial, retired employment manager Genevieve Ronquette took responsibility for the placement and wording of some of the advertisements. She was the first woman ever appointed to a management position at K & B. The district court and the defendant apparently rely on two arguments concerning Ronquette’s actions. One argument is that Ronquette “had no instructions [from higher management] as to the column in which the ads should be placed ....” 525 F.Supp. at 339. We fail to see why this fact matters. Ronquette held a position in storewide management and was touted by K & B as living proof that it does not discriminate against women and does promote them to important management posts. She acted for management and the defendant is responsible for those actions. Liability under Title VII is not limited to acts of the chairman of the board or other males at the very top of the corporate pyramid.
The district court, impressed with Ronquette as a truthful witness, also relied on the finding that “her practices in composing and placing ads were not to carry out any policy of discrimination against women, but to achieve the best results from the ads in light of her experience as to the gender which would be more interested in the job vacancy being advertised.” 525 F.Supp. at 340. We find little if any testimony in the record to support this conclusion with respect to management positions. When counsel pointed out that advertisements for manager trainees usually ran in the male columns, her response was: “Well, that was because managers were always males. So, I put it in the male column.” Furthermore, even if the advertisements were placed out of a sincere belief that females would not be interested in the job, such a belief is precisely the kind of stereotyped assumption that Title VII is aimed at eliminating.
Before the Civil Rights Act of 1964 was enacted, an employer could fashion his personnel policies on the basis of assumptions about the differences between men and women, whether or not the assumptions were valid.
It is now well recognized that employment decisions cannot be predicated on mere “stereotyped” impressions about the characteristics of males or females.... The statute makes it unlawful “to discriminate against any individual with respect to his compensation, terms, conditions, or privileges of employment, because of such individual’s race, color, religion, sex, or national origin.” 42 U.S.C. § 2000e-2(a)(l) (emphasis added). The statute’s focus on the individual is unambiguous. It precludes treatment of individuals as simply components of a racial, religious, sexual, or national class.... Even a true generalization about the class is an insufficient reason for disqualifying an individual to whom the generalization does not apply.
City of Los Angeles, Department of Water and Power v. Manhart, 435 U.S. 702, 707-OS, 98 S.Ct. 1370, 1375, 55 L.Ed.2d 657, 664-65 (1978).
K & B points out that other advertisements it introduced were neutral as to gender. This argument goes to the weight of the EEOC evidence, but does not completely eliminate its importance. Finally, we note that K & B faces a dilemma. If the advertising did in fact deter women from applying for management positions, then its effect was discriminatory. On the other hand, if there were no adverse effects on women, then Dr. Gastwirth’s statistical case is strengthened, and the defendant faces a *661great, and in our view insurmountable, challenge to explain why all 265 manager trainees hired from the external labor force in the 1965-1972 period were men.7
C. Disposition on Appeal
The scope of review in this case is a narrow one. We are confined to asking whether the district court was clearly erroneous in finding that K & B did not discriminate in hiring manager trainees and promoting pharmacists. Fed.R.Civ.P. 52(a); Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982); Chaline v. KCOH, Inc., 693 F.2d 477, 480 (5th Cir.1982). We cannot hold a factual conclusion clearly erroneous unless it “is so against the great preponderance of the credible testimony that it does not reflect the truth of the case,” Merchants National Bank of Mobile v. Dredge General G.L. Gillespie, 663 F.2d 1338,1341 (5th Cir.1981), cert, dismissed, 456 U.S. 966,102 S.Ct. 2263, 72 L.Ed.2d 865 (1982), or unless we are “left with the definite and firm conviction that a mistake has been committed,” United States v. United Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746, 766 (1948).
Statistics play an important and often controversial role in cases of this type. In a proper case, gross statistical disparities may alone constitute prima facie proof of a pattern or practice of discrimination. Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741, 52 L.Ed.2d 768, 777 (1977). Likewise, statistical evidence may be used to establish discriminatory motive, a necessary element of a Title VII disparate treatment claim. Pouncy v. Prudential Insurance Co. of America, 668 F.2d 795, 802 (5th Cir.1982). Of course, numerical data is not irrefutable and must be used properly.8 Id.
This court and this panel take the clearly erroneous standard seriously, particularly in light of recent admonishment by the Supreme Court that we properly defer to district court fact findings in discrimination *662cases as we would in any other case. With this standard firmly in mind, we have little trouble affirming the district court on the issue of discrimination in promoting pharmacists, for the reasons described above. We also affirm the findings with regard to manager trainee hiring after the Capaci charge was filed. The statistical evidence was relatively weak, the testimonial evidence strong and there was no questionable advertising during this period.
We hold that the court erred, however, in not finding discrimination in the manager trainee program during the 1965— 72 period. Summarizing the discussion of this period given above, there was: (1) an overwhelmingly strong statistical case; (2) a dearth of meaningful testimony by employees to rebut the numbers; (3) newspaper advertising which, while not determinative in itself, must be viewed as some evidence of discrimination.
We cannot escape the fact that during these seven and one-half years, there were hundreds of male manager trainees chosen and not a single woman. The hiring record demonstrates not just disparities in hiring, but total exclusion of women from the entry level management position. We differ with the defendant’s suggestion that “zero is just a number.” To the noble theoretician predicting the collisions of weightless elephants on frictionless roller skates, zero may be just another integer, but to us it carries special significance in discerning firm policies and attitudes. Evidence of two or three acts of hiring women as manager trainees during this period might not have affected the statistical significance of the tests performed by the experts, but it would indicate at least some willingness to consider women as equals in firm management. Perhaps for this reason, the courts have been particularly dubious of attempts by employers to explain away “the inexorable zero” when the hiring columns are to-talled. International Brotherhood of Teamsters v. United States, 431 U.S. 324, 342 n. 23, 97 S.Ct. 1843,1858 n. 23, 52 L.Ed.2d 396, 419 n. 23 (1977), vacating United States v. T.I.M.E.-D.C., Inc., 517 F.2d 299, 315 (5th Cir.1975); Wilkins v. University of Houston, 654 F.2d 388, 410 (5th Cir.1981), cert. denied, — U.S. —, 103 S.Ct. 51, 74 L.Ed.2d 57 (1982).
II. CAPACES INDIVIDUAL CLAIM
In her individual claim Andra Capaci asserted that K & B had discriminated against her by denying her promotion into management, subjecting her to sexual harassment, and harassing and discharging her in retaliation for filing discrimination charges. In a careful and thorough discussion the trial court rejected most of the allegations, but agreed with Capaci that K & B had deliberately built up her personnel file with disciplinary matters after the charge was filed, with the purpose and effect of imparting to Capaci a sense of harassment. 525 F.Supp. at 342-50.
Capaci rested her case on March 5, 1979, after many days of trial. On March 26, 1979, during the defendant’s case in chief, Capaci’s attorney was removed from the case, held in contempt and suspended from practice in the trial judge’s court for his behavior during the period of the trial. Her case was severed from the EEOC case and trial proceeded for five days, during which Capaci had no legal representation. More than a year later, on April 14, 1980, Capaci’s rebuttal case was presented by a new attorney and the trial came to an end. Several arguments on appeal concern the individual claim.
A. The Refusal to Receive Personnel Files During Rebuttal
On the last day of trial the plaintiff’s new attorney attempted to introduce into evidence the personnel files of 123 males. The purpose of this evidence was to demonstrate that men who committed acts similar to those allegedly committed by Capaci were treated more leniently than she, and that the reasons offered to explain her treatment were hence pretextual. The trial judge refused to allow the evidence to be introduced in rebuttal, because he found that the files should have been introduced *663during the case in chief, if at all, under the circumstances of the case.
The plaintiff asserts that this evidence was legitimate proof of pretext, and as such was properly offered in rebuttal under the three-step approach for deciding Title VII cases set out in McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). That case established that once a plaintiff has made a prima facie showing of discrimination, the defendant must “articulate some legitimate, nondiscriminatory reason for the employee’s rejection.” 411 U.S. at 802, 93 S.Ct. at 1824, 36 L.Ed.2d at 678. Once this second step has been met, the plaintiff “must ... be afforded a fair opportunity to show that [defendant’s] stated reason for [plaintiff’s] rejection was in fact pretext.” 411 U.S. at 804, 93 S.Ct. at 1825, 36 L.Ed.2d at 679. Capaci sees these three steps in McDonnell Douglas as corresponding to the three major stages of the traditional trial: plaintiff’s case in chief, defendant’s case in chief, and plaintiff’s rebuttal. She argues, therefore, that the trial judge was incorrect in viewing the offered evidence of pretext as inappropriate at the rebuttal stage.
We do not believe that McDonnell Douglas requires presentation of proof in a strictly ordered fashion corresponding to the three traditional stages of trial. “The tripartite arrangement is a useful tool in analyzing these controversies, but it should not be construed so as to divide a single cause of action into three different cases.” Whack v. Peabody & Wind Engineering Co., 595 F.2d 190,193 (3rd Cir.1979). “Although cases are analyzed in terms of these three phases, there is no requirement that the evidence be introduced in such compartmentalized form.” Worthy v. United States Steel Corp., 616 F.2d 698, 701 (3d Cir.1980). The McDonnell Douglas decision, “did not purport to create an inflexible formulation,” International Brotherhood of Teamsters v. United States, 431 U.S. 324, 358, 97 S.Ct. 1843,1866, 52 L.Ed.2d 396, 429 (1977), and sets out a method that “was never intended to be rigid, mechanized, or ritualistic,” but instead “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, 967 (1978). Most trials would be lopsided indeed if plaintiffs were confined to making the usually simple presentation of proof required to establish a prima facie case9 in their case in chief, leaving all other complex questions of pretext, disparate treatment, legitimate grounds for rejection of the plaintiff, prior history of discrimination, etc.,, to be litigated in later stages of the trial.
In short, McDonnell Douglas did not radically alter the ordinary rules of evidence, procedure and practice followed by the courts in all trials. The trial court may, subject to review only for abuse of discretion, maintain the pace of the trial, Moore v. United States, 598 F.2d 439, 442 (5th Cir.1979), determine the relevancy and materiality of evidence, United States v. Ashley, 555 F.2d 462,465 (5th Cir.), cert, denied, 434 U.S. 869, 98 S.Ct. 210, 54 L.Ed.2d 147 (1977); United States v. Calles, 482 F.2d 1155, 1160 (5th Cir.1973), and decide generally whether or not to admit evidence, Miller v. Universal City Studios, Inc., 650 F.2d 1365, 1374 (5th Cir.1981).
For several reasons we do not find that the trial judge abused his discretion in refusing to admit the personnel files. Based on the extensive discovery and pretrial order, the plaintiff’s attorney was fully aware of the defendant’s proffered reasons for failing to promote and discharging her. The questions of disparate treatment and *664pretext were intertwined under the facts of this case, and were extensively litigated in the plaintiff’s case in chief. Employee files and the testimony of many witnesses were introduced at that time. The court made specific findings on issues of pretext in lack of promotion and discharge. 525 F.Supp. at 345, 350. All of the files the plaintiff’s attorney wished to introduce were in the courtroom throughout the trial. The trial judge felt that the new attorney, with a complete transcript of the thirty-four days of trial that had transpired a year earlier, was simply attempting to retry the case, as he made clear on the last day of trial:
I know, but you reviewed the record, and you’re second guessing Mr. Schumacher. You are saying now, well he didn’t try the case right. He didn’t try the case so we could win it, so I’m going to try it over again. And that we cannot do. If Mr. Schumacher hadn’t been an able lawyer I might, well, I might have to do it anyhow, but I would be more inclined, but Mr. Schumacher exhausted all this. I was leaning over backwards during that trial to give this plaintiff every opportunity to get her case before me. If you read that record, you could see that I did.
We agree that the plaintiff was given ample opportunity to prove her case.
Numerous concerns faced the trial judge. He was no doubt concerned that the plaintiff should not benefit from the sins of her previous attorney, to the unfair detriment of the defendant, by having a new attorney with an unusual opportunity to carefully and leisurely review the transcript and to offer a new approach to trying the case. He was faced with legitimate concerns of the defendant and other litigants on his docket to see this case end. The defendant also argued that the files were cumulative, and that they were offered “in a vacuum” without any testimony that would make for meaningful comparisons or tell the whole story of what happened to the employees reviewed in the files. Under these circumstances we find no error.
B. Evidence of Pretext
Capaci argues on appeal that, even without the introduction of the 123 employee files, there was overwhelming evidence that K & B’s reasons for her treatment as a pharmacist were pretextual.
The reasons given by the defendant for not promoting Capaci were numerous, based in large part on alleged lack of concentration and disorganization, and inability to work well with others. The specific complaints against her included “tardiness, excessive time on the telephone, too frequent and prolonged absences from the prescription department for talks with customers, visits to the cosmetic department to assist customers, attention to personal matters and application of makeup while on duty.” 525 F.Supp. at 343.
Capaci was allegedly fired because of the “Lambremont” incident one evening in which she: (1) created customer dissatisfaction by taking an inordinate amount of time to fill prescriptions; (2) invited a customer into the prescription department against company policy; (3) offered medication to a customer who was not the person for whom the prescription was made.
Capaci argues that males who committed similar acts, such as giving pills to customers, shaving on duty and talking excessively on the phone, had not been disciplined and in some cases had been promoted, and that the two major reasons given by one official for discharge were gross dishonesty and irregularity in dispensing drugs.
These comparisons do not render the trial court’s findings on pretext clearly erroneous. The plaintiff was portrayed as a singularly inefficient and contentious employee. One executive described her as unstable and immature; another “described her attitude after she filed her charge as having placed herself in a protective cocoon.” 525 F.Supp. at 350. She was unable to work well with any of her managers or chief pharmacists, and they consistently sought to have her fired or transferred to other stores. Six of these transfers between 1970 and 1973 are chronicled in the district court opinion. 525 F.Supp. at 344-345. One manager described her as “proba*665bly the worst pharmacist that I ever had working for me.” A co-worker stated that “I have never worked with another pharmacist who was as disorganized .... she, in comparing her with other pharmacists that I have worked with, had no awareness of trying to fill prescriptions or trying to get the work out.” On four occasions prior to filing the charge her superiors endeavored to have her fired. On the last occasion, vice president Feltman, personnel manager Ser-da, and supervisors LeBlanc and Levet all agreed that she should be terminated, but Sydney Besthoff, III, the president, decided to give her another chance, out of an interest in reducing turnover in the professional staff and a hope that the problems could be overcome. K & B has maintained that the Lambremont incident was the last straw. Under these facts, the court’s findings are amply supported.
C. The Severance
As explained above, Capaci’s claim was severed from the EEOC case and the trial proceeded for five days after her attorney was suspended. She now complains that during those five days evidence prejudicial to her case was admitted, and that her due process rights were thus violated. She argues that the trial should have been continued to allow her to seek new counsel, rather than allowing it to proceed without legal representation for her.
Decisions regarding continuances and severances of actions are left to the trial court’s discretion and will not be disturbed absent an abuse of discretion. American Lease Plans, Inc. v. Silver Sand Co. of Leesburg, 637 F.2d 311, 318 (5th Cir.1981) (continuance); United States v. Swanson, 572 F.2d 523, 528 (5th Cir.), cert, denied, 439 U.S. 849, 99 S.Ct. 152, 58 L.Ed.2d 152 (1978) (severance); Hertz Corp. v. Cox, 430 F.2d 1365, 1372 (5th Cir.1970) (severance). The trial judge endeavored to protect Ms. Capaci’s rights, while letting the other parties continue to litigate their claims. As he stated in court after suspending her attorney:
So there will be no misunderstanding, the case of Ms. Capaci is suspended as of now, as of this morning. I will disregard any evidence that has any direct effect upon her case unless it also affects the EEOC’s case. As far as her case is concerned, though, I will disregard it until she has her lawyer and her trial is resumed and if necessary we will call back the same witnesses that we are calling now which you think you may need to defend yourself in her case. I am doing this, stating that so that she will have a chance to fully cross-examine any witness which might affect her case.
Months later, Capaci had a new attorney, and with the benefit of a transcript of the entire trial to that point, she was allowed to present rebuttal testimony. On appeal, Ca-paci does not clearly specify any evidence relied upon by the district court in reaching its decision that was introduced during the five days she was without an attorney and that she was not allowed to refute during her rebuttal on the last day of trial. We find no abuse of discretion.
D. The Cross-Appeal
After the discrimination charge was filed in 1973 Mr. Feltman issued instructions that unusual occurrences involving Ms. Capaci should be documented in her personnel file. He testified that this effort was not to harass her but to “correct the error K & B had made in not having her performance documented previous to the charge.” 525 F.Supp. at 347. The court found that “[t]he result of his instructions, however, was the building of a file which included reports of trivial, petty, insignificant events involving Capaci, which would never have appeared in the file of another employee. These could serve no purpose other than to impart to Capaci a sense of harassment.” Id. K & B argues that it was reasonably justified in documenting unusual occurrences based on its prior experiences with Capaci. While such an argument is plausible, the trial court’s finding is not clearly erroneous. Before the charge was filed the plaintiff’s file contained only a few complimentary letters from customers and Mr. Besthoff. Two years after the *666charge the file contained approximately 100 discipline slips.
III. CONCLUSION
We reverse the finding of nondiscrimination in the selection of manager trainees for the period July 1965-December 1972, and remand for determination of appropriate remedies. In all other respects we affirm.
AFFIRMED IN PART, REVERSED AND REMANDED IN PART.
. The lower bound was derived by choosing the smallest percentage female figure found in the geographic regions for each occupational category.
. Manager Trainee Exhibit 3 is typical of several EEOC exhibits presented at trial:
Statistical Tests Comparing Manager Trainee Hires With The Lower Bound for Various Labor Market Referents For The Period July 1, 1965 to January 1, 1973
The exhibit reports the probability of observing 0 females out of the 265 persons hired directly as manager trainees from the inception of the Civil Rights Act until January 1, 1973 just prior to the charge. The results are given for the lower bound for any geographical weighting of the various external labor market referents.
Referent Probability Theoretical of Observed Fraction Data_
Civilian Labor Force .3431 4.338x10-4®
Managers Earning Less than $7000 (in 1969) .2899 3.978x10-4»
Experienced Wholesale & Retail Managers Earning Less than $7000 (in 1969) .2507 6.078x10-34
General Merchandise Retail Store Managers .2364 9.109x10-32
Department and Sales Manager (Retail Trade) .2207 2.003xl0-29
Probability Theoretical of Observed Referent Fraction Data
All Managers .1607 6.888xl0-21
Note: All probabilities are far less than one in a billion. The two and three standard deviations tests described by the Supreme Court in Castanada v. Partida, 430 U.S. 482, 97 S.ct. 1272, 51 L.Ed.2d 498 (1977), correspond to probabilities of 1 in 20 (.05) and 1 in 100 (.01).
The probabilities in the last column are all less than one billionth of the probability levels used in Castanada.
. Manager Trainee Exhibit 17 gives Dr. Gast-wirth’s test of the applicant flow data:
Statistical Comparison of the Difference in the Proportion of Male and Female Applicants for the Manager Trainee Position Who Were Hired as Manager Trainees
This exhibit calculates the chi-square test to determine whether the difference between the proportion of male applicants (37.37%) for the manager trainee position, during 1976 and 1977, who were actually hired as manager trainees, and the corresponding proportion of female applicants (15.96%) is statistically significant.
Hired Not Hired Total
Males 148 248 396
Female 15 79 94
Total 163 327 490
*653The value of the chi-square statistic is 14.-75, which indicates that the probability of the observed data, under the hypothesis of equal hiring probabilities for applicants of each sex, is ¡ess than one in a thousand. This result is statistically significant and we conclude that the success rate of male applicants in the period (37.37%) is significantly greater than that of females (15.96%).
. K & B Exhibit 119 is an example of the defendant’s “divide and conquer” technique:
GEOGRAPHICAL ANALYSIS AND STATISTICAL TEST UTILIZING CORRECTED 1977 APPLICATION FORM DATA AND HIRING DATA REFERRED TO IN EEOC MT EXHIBIT 16 & 17
LOCATION SEX APPLICANTS HIRES STAT. TEST S.R.
_
Alexandria M 26 1 N.S. 3.8%
F 4 0 0.0%
Baton Rouge M 25 14 56.0% N.S.
F 11 4 36.4%
Bogalusa M 5 2 40.0% N.S.
F 1 0 0.0%
Gulfport M 7 0 0.0% N.S.
F 3 0 0.0%
*655GEOGRAPHICAL ANALYSIS AND STATISTICAL TEST UTILIZING CORRECTED 1977 APPLICATION FORM DATA AND HIRING DATA REFERRED TO IN EEOC MT EXHIBIT 16 & 17
LOCATION SEX APPLICANTS HIRES S.R, STAT, TEST
Gonzales M 1 1 100.0% N.S.
F 0 0 N/A
Hattiesburg M 22 . 1 4.5% N.S.
F 5 1 20.0%
Houma M 8 3 37.5% N.S.
F 1 1 100.0%
Lafayette M 33 2 6.1% N.S.
F 3 0 0.0%
Lake Charles M 12 3 25.0% N.S.
F 7 0 0.0%
Long Beach M 5 3 60.0% N.S.
F 2 0 0.0%
Laurel M 1 0 0.0% N.S.
F 0 0 N/A
Mobile M 25 3 12.0% N.S.
F 11 0 0.0%
Monroe M 1 1 100.0% N.S.
F 1 0 o,.o%
McComb M 1 1 100.0% N.S.
F 0 0 N/A
Morgan City M 5 1 20.0% N.S.
F 1 0 0.0%
Natchez M 2 1 50.0% N.S.
F 0 0 N/A
New Orleans M 51 39 76.5% .01
F 6 0 0.0%
Opelousas M 2 2 100.0% N.S.
F 0 0 N/A
Pascagoula M 8 1 12.5% N.S.
F 9 0 0.0%
Ruston M 2 1 50.0% N.S.
F 0 0 N/A
Shreveport M 50 3 6.0% N.S.
F 15 1 6.7%
Thibodaux M 3 1 33.3% N.S.
F 0 0 N/A
Sulphur M 1 0 0.0% N.S.
F 0 0 N/A
Slidell M 0 0 N/A N.S.
F 1 1 100.0%
Vicksburg M 2 2 100.0% N.S.
F 0 0 N/A
No Area M 3 0 0.0% N.S.
F 1 0 0.0%
. An example is a September 22, 1968 want ad:
KATZ & BESTHOFF
*659OPENING 3 COMPLETE DRUG STORES IN THE BATON ROUGE AREA AND IS LOOKING FOR QUALIFIED YOUNG MEN TO TRAIN FOR STORE MANAGEMENT
Locations of the Stores
7543 Jefferson Hwy. 5840 Plank Road 11288 Florida Blvd.
EXCELLENT FUTURE
Starting Salary $455 PER MONTH 48 Hour Week
FRINGE BENEFITS INCLUDE:
Hospitalization
Life Insurance
Disability Insurance
Excellent Retirement Plan
Paid Vacations
Discounts
For Further Information Call Collect To
Mr. Henry Gabb
523-1234
New Orleans, La.
. The 1966 version of 29 C.F.R. § 1604.4(b) read:
Advertisers covered by the Civil Rights Act of 1964 may place advertisements for jobs open to both sexes in columns classified by the publishers under “Male” or “Female” headings to indicate that some occupations are considered more attractive to persons of one sex than the other. In such cases, the Commission will consider only the advertising of the covered employer and not headings used by publishers.
Later regulations disapproved of such advertising.
. As a final argument, the EEOC maintains that K & B violated the record-keeping provisions set out in 29 C.F.R. § 1602.14 by destroying applications for the manager trainee position. The regulation requires preservation of personnel records for six months from the date of the making of the record or the personnel action, and continued preservation of all relevant records once a charge of discrimination has been filed. The Commission argues that violating this regulation should raise a presumption that the applicant flow data would have confirmed its case, citing Anderson v. Mt. Clemens Pottery Co., 328 U.S. 680, 66 S.Ct. 1187, 90 L.Ed. 1515 (1946); United States v. County of Fair-fax, Virginia, 629 F.2d 932 (4th Cir.1980), cert, denied, 449 U.S. 1078, 101 S.Ct. 858, 66 L.Ed.2d 801 (1981). K & B argues, and the district court agreed, that no violation occurred because applicant flow data was made available for the period dating from six months before the EEOC moved for intervention on January 4, 1977, arguably the first date that an issue regarding discrimination in initial hiring (as opposed to promotion) was raised.
We find the Commission’s allegation important and troubling. Curiously, the district court refused to allow any inquiries during discovery and trial into when and why earlier records were destroyed, and went on to hold that “[t]he EEOC has presented a less than impressive statistical case” because “[a]s the defense unfolded, it became obvious that the EEOC needed applicant flow data to make a strong statistical case as to the manager trainee job.” 525 F.Supp. at 341. Nevertheless, even if we agree with the Commission that under the law and the facts of this case it was entitled to a presumption that the missing data would have bolstered its statistical case for the period after the charge was filed, we find that the defendant presented sufficient evidence to overcome any such presumption.
. To quote one skeptic:
In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aider-men.
M. Twain, Life on the Mississippi, quoted in D. Huff, How to Lie with Statistics 142 (1954).
. Establishing a prima facie case of racial discrimination under McDonnell Douglas requires only that the plaintiff show:
(i) that he belongs to a racial minority; (ii) that he applied and was qualified for a job for which the employer was seeking applicants; (iii) that, despite his qualifications, he was rejected; and (iv) that, after his rejection, the position remained open and the employer continued to seek applicants from persons of complainant’s qualifications.
411 U.S. at 802, 93 S.Ct. at 1824, 36 L.Ed.2d at 677.