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Jeanine W. WILKINS and Sharon D. Hill, Et Al., Plaintiffs-Appellants, v. the UNIVERSITY OF HOUSTON, Et Al., Defendants-Appellees
GEE, Circuit Judge:
Jeanine Wilkins and Sharon Hill, employees of the University of Houston, brought this Title VII 1 suit against the university and KUHT — TV on behalf of themselves and a class of women, alleging that the university discriminated against women in a variety of its employment practices. The class certified by the district court included all past, present, and future female employees on the faculty or in a professional or administrative staff position, as well as unsuccessful female applicants for such employment. 2 After a trial on the merits, the district court rendered judgment for the university on both the individual and class claims. As to the claim that the university discriminated against its women employees in the academic division of the professional and administrative staff with respect to compensation, we reverse the district court’s judgment for the defendants. 471 F.Supp. 1054. In all other respects, we affirm.
I. STANDARD OF REVIEW
The standard by which we review a factual finding of a district court depends upon whether the finding at issue is one of ultimate fact or subsidiary fact. The ultimate fact at issue in a Title VII action is whether the defendant unlawfully discriminated against the plaintiff. That finding is not subject to the clearly erroneous standard of review; rather, the reviewing court must make an independent determination of the ultimate fact issue of discrimination. In doing so, however, the appellate court is bound by the trial court’s findings of subsidiary facts that are not clearly erroneous. Danner v. United States Civil Service Commission, 635 F.2d 427 (5th Cir. 1981).
II. INDIVIDUAL CLAIMS A. Jeanine Wilkins.
Ms. Wilkins was employed by KUHT-TV (“KUHT”), an auxiliary enterprise of the University of Houston, in August of 1973. In April of 1974, Ms. Wilkins notified the university that she was terminating her employment effective July 31, 1974. Plaintiff Wilkins claims that she was constructively discharged by defendants in violation of her Title VII rights. As we recently reiterated, a “[cjonstructive discharge occurs when the employer deliberately makes an employee’s working conditions so intolerable that the employee is forced into an involuntary resignation.” Pittman v. Hattiesburg Municipal Separate School District, 644 F.2d 1071, 1077 (5th Cir. 1981). The question is not whether the employer’s purpose was to force the employee to resign; rather, the issue is whether “a reasonable person in the employee’s position and circumstances would have felt compelled to resign.” Id. It is clear from our review of the record that Ms. Wilkins was not constructively discharged by sexually discriminatory employment practices committed by defendants.
When Ms. Wilkins was hired, the film production unit at KUHT had been virtually shut down for more than a year, and efforts were underway to revitalize the department. This situation, and the small size of the station’s film operation, dictated that employees of the department perform a variety of tasks. While Ms. Wilkins replaced the station’s only film editor, it is *391 undisputed that there was not nearly enough film editing to be done, to justify the employment of a full-time film editor and that her duties were to extend considerably beyond merely editing films. In fact, both Jim Bauer, the station manager, and Bob Cousins, a producer-director at KUHT and Ms. Wilkins’ immediate supervisor, testified that Ms. Wilkins expressed a strong desire to engage in a wide variety of activities at the station and that their decision to hire her was based in part on that desire.
Shortly after Ms. Wilkins was hired, the film unit began working on a mass transit film with a rather short deadline entitled “Getting There.” While plaintiff testified that she did not edit the major portion of this film, the trial court found on the basis of substantial evidence that she edited some 97 percent of it. The remaining segment of the film was edited by a Mr. Brian Beasley, a film editor who had worked with Mr. Cousins on other films not related to KUHT. This 3 percent segment involved cutting the film to music, a process that is somewhat more difficult than the typical editing of film. Beasley, who had more than ten years’ experience as a film editor and who was then employed elsewhere, edited the film on a Saturday on a voluntary, noncompensatory basis apparently as a favor to Cousins.
The mass transit film was finished in late September or early October 1973. From that date until at least the following January, Beasley was completely uninvolved with KUHT. According to Ms. Wilkins, she learned in January 1974 that Beasley was going to be hired on a free-lance basis to edit a film the station was going to make for Rice University later in the spring. Plaintiff testified that the station’s decision to use Beasley on the Rice film — conceded by all to be the most important project that had come into the film production unit— was a major factor in her decision to terminate her employment at KUHT. Her Title VII claim is that Cousins could not accept women working with him in positions of authority; that this attitude was reflected not only in the decision to use Beasley on the Rice film but also in the fact that Cousins assigned various clerical, routine, and relatively menial tasks to Wilkins; and that this situation made working conditions so intolerable that Wilkins was forced into an involuntary resignation. We reject this argument for a number of reasons.
First, it is clear that Beasley had considerably more experience and skill as a film editor than did Wilkins. Cousins testified that Beasley had been editing films for some twenty to twenty-two years and that he (Cousins) considered Beasley “probably the best film editor in Houston and the southwest.” Cousins and Beasley had worked together on films for the National Aeronautic^ and Space Administration; from that experience Cousins had developed “every confidence” in Beasley as a film editor. Producing and directing films is a creative process the ultimate success of which is highly dependent upon the work of the film editor, with whom the producer-director must work closely. Cousins testified that his decision to hire Beasley to edit the Rice film was based on his belief that Beasley was an excellent editor and his desire to make certain that the very important Rice film was produced and edited properly. While Cousins stated that Wilkins had competently edited the other films to which she had been assigned, he also testified that her limited experience editing films — prior to coming to KUHT Wilkins had one year of film experience in which she had edited two films — was a factor in his decision to hire Beasley for the Rice film. Cousins’ decision to use the best possible people on the Rice film was also reflected in his hiring a freelance cameraman to shoot the film rather than using the station’s male staff cameraman. We agree with the district judge’s finding that Cousins’ decision to hire Beasley to edit the Rice film, rather than using Wilkins, was not sexually discriminatory.
Other factors supporting our decision that Wilkins was not constructively discharged include the following: Wilkins was hired to perform a variety of tasks other than editing films. While she testified that she edited, partially or wholly, at least sev *392 en films, the evidence also indicates that she was involved in researching film ideas, writing proposals, producing a film, and assisting in the production of several other films. At the time the Rice film was being produced, KUHT was involved in its annual auction from which it derived a major portion of its operating funds for the next year. Wilkins was assigned to produce and edit a number of short commercial films for the auction. While the Rice film may have been the station’s most important film project from a creative standpoint, the auction generated more than forty times as much revenue for the station than did the Rice film. Finally, we note that near the beginning of 1974 Ms. Wilkins told Cousins that her salary was too low; soon thereafter she began interviewing for other employment. As there is no serious contention that Wilkins was discriminated against with respect to pay, the effect of her dissatisfaction with her salary on her decision to resign indicates a reason other than sexual discrimination for that decision. Our review of the record indicates that Wilkins was assigned a variety of tasks of varying degrees of importance and difficulty at KUHT and that sexually discriminatory practices committed by the station, if any, did not make her working conditions so intolerable as to force her into an involuntary resignation.
B. Sharon Hill.
In late 1973, Ms. Hill worked for the university in a computer laboratory that serviced the College of Engineering by providing computer programming and access to computers primarily to faculty and students within the college. At that time David Lowell was the lab employee with technical proficiency in the computer services offered by the lab. Ms. Hill’s duties involved such tasks as scheduling users’ access to the computers, billing, budgeting, hiring and supervising student computer operators, |and ordering supplies; the extent of her supervisory authority over Lowell is the subject of some dispute and is discussed below. In late 1973, Ms. Hill formally requested that her job be reclassified and that she be given a raise. At that time her job title was research assistant, and she was earning $7,878 per year. Her application was approved: effective January 1, 1974, her annual salary was raised to $9,120, and she was given the title coordinator of operations. 3
In the fall of 1974, Lowell left the lab and was replaced on a temporary basis by David Killough, who was then a full-time employee of Exxon. Killough, on the verge of retirement and seeking part-time computer-related work, agreed to fill the vacancy left by Lowell on a voluntary, noncompensatory basis until a permanent replacement could be found and trained. That replacement was an electrical engineer named Lew Folkerth; he was hired by the university in November of 1974 at an annual salary of $14,500. Problems between Hill and Folkerth arose immediately; before Folkerth arrived for his first day at the lab, Hill notified the university’s equal employment officer that the situation with Folkerth created a “glaring inequity" because Folkerth, whom she assumed would be under her supervision, would be paid some $5,000 per year more than she was being paid. Shortly thereafter — before Hill’s complaint had been processed by the university — she filed a formal charge with the Equal Employment Opportunity Commission alleging that the salary differential was attributable to sex discrimination.
The university responded to Hill’s complaint by having a representative of the personnel office, Mr. Silber, investigate the charge by “auditing” Hill’s job. Silber vis *393 ited the lab, watched it in operation, and had a discussion with Hill concerning her duties. He concluded that her job was a relatively low level administrative position; that it could not be compared with managerial positions at the university’s other two computer facilities because those positions required technical skill and the administrative management of a much larger operation; that Folkerth’s technical computer competence justified his higher salary; but based on salaries being paid to other administrative personnel, Ms. Hill should be given a raise to $10,750 or $11,000 per year. While Hill testified that the dean refused to approve her raise, the district court found— consistent with computer printouts introduced by plaintiff listing employees and their salaries — that in February of 1975, just one month after Silber’s job audit and recommendation, Hill was being paid at an annual rate of more than $10,800.
Meanwhile, the working relationships between Hill on the one hand and Killough and Folkerth on the other were deteriorating. The prime sources of these problems were apparently a difference in opinion between the three concerning Hill’s supervisory authority over Folkerth and a personality conflict between Hill and Folkerth. On several occasions Hill’s attempts to exercise supervisory powers over Folkerth were ignored by him, exacerbating the problem. The situation continued to deteriorate until it became evident that Killough, and probably Folkerth, would quit if Hill was not fired. After discussing the problem with the lab personnel, Dean Kirkpatrick fired Hill; that decision resulted in this lawsuit. The district court found that sex was not a factor with respect to either Hill’s termination or her salary and that the university had not terminated her in retaliation for her filing a charge with the EEOC. We agree.
Hill’s salary claim is disposed of easily. Folkerth had a degree in electrical engineering and one or two years’ — the testimony was inconsistent — experience with computers in industry. Uncontroverted testimony established that his $14,500 annual salary was below market value for persons with his qualifications. Hill had taken one IBM course covering a wide range of topics relating to computers; while she apparently had some understanding of computer languages, it is undisputed that she lacked the technical competence to develop and maintain computer systems or to assist users in programming. Her duties were administrative in nature; on the basis of the personnel department’s job audit, a recommendation was made that Hill’s salary be raised to $10,750 or $11,000. The district court found on the basis of credible evidence that just one month after this recommendation Hill was making more than $10,800 per year.
The issues of whether Hill was terminated because of her sex or in retaliation for her having filed a charge with the EEOC will be considered together. Hill claims that after she filed the EEOC charge she was demoted and ultimately fired. While the university argues strenuously that Hill was not demoted, it is clear that her duties changed when Lowell was replaced by Killough and Folkerth. The issue, however, is whether her duties were curtailed because of her sex or in retaliation for her having filed the EEOC charge; we agree with the district judge that they were not.
The fundamental problem appears to have been a difference in opinion between Hill and the others involved with the lab about the extent of Hill’s supervisory authority. It is clear that Hill had supervisory authority over Lowell — Dr. Motard, the lab director, so testified, and an organizational chart for the lab and job descriptions for Hill’s and Lowell’s positions bear this out. When Lowell left and Killough and Folkerth arrived, Hill attempted to exercise supervisory authority over Folkerth; Dean Kirkpatrick responded to the resulting problem by issuing a new organizational chart that essentially provided that Killough was in charge of the technical side of the lab and thus was to be Folkerth’s supervisor. Hill argues that this action was made in retaliation for her having filed the EEOC charge; while the new chart was *394 issued only a month after Hill filed the charge, we find that the dean did not do so with a retaliatory motive.
Dr. Motard and Dean Kirkpatrick testified that Lowell, who was in the process of completing his degree requirements, needed supervision in scheduling projects, meeting deadlines, not taking on too many outside projects, and staying within the budget. To this extent Hill was Lowell’s supervisor; she did not supervise his systems development and programming work. Lowell’s replacement, Killough, had many years of experience at Exxon in both the technical and managerial aspects of a computer operation; that he required no supervision is not contested. Rather, Hill’s complaint goes to her position in the lab with respect to Folkerth. Defendants’ argument is that Killough was in charge of the technical aspects of the lab; that it was reasonable for Killough to supervise Folkerth, whom Killough essentially was training to take Lowell’s job; that Folkerth did not have the same difficulties as Lowell in administering his work load so that he simply did not need the kind of supervision that Hill exercised over Lowell; and that neither Hill’s sex nor the EEOC charge had anything to do with her “demotion.” We find this argument entirely reasonable, supported by the evidence, and in fact largely uncontroverted by any.
While the source of the problem that lead to Hill’s termination appears to have been her dissatisfaction with her salary relative to Folkerth’s and the misunderstanding as to her supervisory authority, the discontent in the lab manifested itself in a variety of ways. Communications between Folkerth and Hill apparently were strained from the date Folkerth was hired. While Killough apparently made efforts to mediate, his patience was limited; at a meeting between Dr. Motard, Hill, and Killough concerning Folkerth, Killough became very angry, stormed out of the meeting, and said that he had had enough and was quitting. At that point it was evident that a choice had to be made between Killough and perhaps Folkerth on the one hand and Hill on the other. For this and a number of other reasons, Dean Kirkpatrick decided to fire Hill. She spent inordinant amounts of time on the telephone for nonbusiness reasons; she had begun spending most of her time in her office with the door shut and often locked, making it difficult to communicate with her; she had become belligerent and hostile toward coworkers in the lab; and her position would be much easier to fill than would Killough’s or Folkerth’s. 4 In short, the trial court was correct in finding that “Ms. Hill was terminated for good cause . .. that sex was not a factor in said termination .... and [that she] was not a subject of .... retaliation because of the filing of an EEOC claim.” 471 F.Supp. at 1058.
III. CLASS CLAIMS
A. Introduction.
Plaintiffs Wilkins and Hill sued not only for themselves but also on behalf of a class consisting of all past, present, and future female employees on the faculty or in a professional or administrative staff position and unsuccessful female applications for such employment at the University of Houston. Initially, we note that, the class having been certified prior to trial, the district court’s dismissal of the named plaintiffs’ claims and our affirmance of that decision do not negate the need for consideration of the class claims. Thurston v. Dekle, 531 F.2d 1264, 1271 (5th Cir. 1976).
Plaintiffs essentially allege that the university treats women less favorably than men because of their sex; there is no claim *395 that employment practices of the university that are facially neutral in their treatment of male and female employees fall more harshly on females than on males. Accordingly, plaintiffs have stated a “disparate treatment,” as opposed to a “disparate impact,” claim and must therefore prove discriminatory motive. 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); Lee v. Conecuh County Board of Education, 634 F.2d 959, 961 n.3 (5th Cir. 1981). Furthermore, plaintiffs’ class claims, alleging that the university engaged in a systemwide pattern or practice of discriminating against women, cannot succeed on the basis of proof of “the mere occurrence of isolated or ‘accidental’ or sporadic discriminatory acts. [Rather, plaintiffs] had to establish by a preponderance of the evidence that [sex] discrimination was the [university’s] standard operating procedure — the regular rather than the unusual practice.” Teamsters, 431 U.S. at 336, 97 S.Ct. at 1855.
Plaintiffs introduced a substantial amount of statistical evidence in an attempt to meet their burden of proving that the university acted with a discriminatory motive and engaged in a pattern or practice of discriminating against women. 5 In Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977), also a Title VII disparate treatment class action, the Supreme Court did not discuss explicitly the discriminatory motive issue but stated that “[w]here gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination.” Accordingly, where the statistical showing is sufficiently strong in a disparate treatment action, plaintiffs’ prima facie case can be made without additional evidence establishing that defendant purposefully treated minorities protected under Title VII less favorably than other persons.
Because of the significant role that statistics can play in discrimination cases and of their inherently slippery nature, it is imperative that they be used properly. While gross statistical disparities may alone establish a prima facie case of employment discrimination in a proper case, the Supreme Court has cautioned “that statistics are not irrefutable; they come in infinite variety and, like any other kind of evidence, they may be rebutted. In short, their usefulness depends on all of the surrounding facts and circumstances.” Teamsters, 431 U.S. at 340, 97 S.Ct. at Í856-57. 6 (footnote omitted.)
B. Faculty.
The claims made on behalf of female faculty members challenge various employment practices engaged in by the university during the 1973 through 1978 school years. 7 In particular, plaintiffs allege that the university discriminated against women with respect to (1) hiring, (2) recruiting, (3) compensation, and (4) promotion. After full consideration of each claim, we conclude *396 that plaintiffs have failed to establish a prima facie case of unlawful discrimination in regard to the application of any of the challenged practices to women.
1. Hiring.
The statistical evidence in support of plaintiffs’ faculty hiring claim was introduced in an attempt to establish that from 1973 through 1978 a significantly smaller number of women were hired to faculty positions than were available for hire. 8 The key components in this showing obviously are the number of women faculty members hired in the relevant time period and the number of women available for hire to such positions. 9 The seemingly simple and straightforward task of comparing the number of women hired with the number of women available is complicated by the fact that the availability component is to a significant extent dependent upon the subject matter field in which the faculty person is hired. Further, the number of available women qualified to hold faculty instructor or assistant professor positions may be significantly different from the number qualified to hold positions as associate or full professors, as the latter positions generally require a number of years of experience in teaching or research in addition to an advanced degree.
Plaintiffs’ statistical evidence on the hiring claim does not reflect a consideration of the number of faculty persons hired by different colleges within the university. Similarly, with respect to the availability issue, no explicit attempt has been made t<p differentiate between the university’s hiring of instructors and assistant professors on the one hand and associate and full professors on the other. The importance of the college or departmental factor is demonstrated by the fact that the number of doctorates granted to men in the physical sciences, engineering, and life sciences fields in 1977 was somewhat more than 10,000, while the number of such degrees granted to women in that year was just under 1,500. In contrast, in the social sciences, humanities, and education fields, men were granted approximately 12,400 doctorates in 1977, while women were granted slightly over 8,000. 10 Obviously, if the bulk of the university’s faculty hiring during the years in question were concentrated in the former fields one would expect that the proportion of men hired would have been substantially higher than the proportion hired had the bulk of faculty hiring been in the latter fields.
Depending upon the needs of the college within the university doing the hiring, faculty persons are hired as either instructors, assistant professors, associate professors, or full professors. While evidence at trial in *397 dicated that the majority of instructors at the University of Houston are graduate students at the university who are not considered permanent faculty members but are teaching on a part-time basis pending receipt of their advanced degrees, a substantial number of instructors are persons who are close to receiving their doctorates from another university and who will be given the rank of assistant professor upon receipt of these degrees. Positions occupied by the latter group of instructors and by the assistant professors are generally entry level positions open to recent graduates from other universities. By contrast, associate and full professorships are available only to persons with a number of years experience — usually in the academic would — subsequent to their receipt of an advanced degree. As plaintiffs have demonstrated, recent years have seen a rise in the proportion of doctorate recipients who are women; accordingly, it is evident that for the years in question the number of women available for hiring as instructors or assistant professors will be greater than the number available for hiring as full or associate professors.
With these considerations in mind, we turn to the evidence introduced by plaintiffs on their faculty hiring claim. The availability data supplied by plaintiffs is a Department of Labor publication indicating that the percentage of teachers employed in colleges and universities who were women was 28.3 in 1970 and 31.3 in 1976. By interpolating and extrapolating, percentages were derived for each of the years covered by this lawsuit. The appropriate percentage was then applied to the total number of faculty members hired in each year to get the “expected” number of women hired in each year, which was then compared with the actual number “of women hired. From this analysis we learn that for the six years at issue the number of women we would expect to have been hired is 244, while the actual number of women hired was 164. A binomial distribution statistical analysis of this difference demonstrates that it is a statistically significant one. See Castaneda v. Partida, 430 U.S. 482, 496 n.17, 97 S.Ct. 1272, 1281 n.17, 51 L.Ed.2d 498 (1977).
For a number of reasons, we decline to accept this showing as sufficient to establish a prima facie case of sex discrimination in faculty hiring. First, the amount of hiring done by particular colleges within the university was not considered. Second, the instructor and assistant professor versus associate and full professor distinction was ignored even though new associate and full professors accounted for more than one-third of the new faculty members hired during the six-year period. Further, plaintiffs’ availability data includes all college and university teachers without regard to whether the teachers held doctoral degrees; as many junior colleges and community colleges employ teachers who do not have such advanced degrees, the data submitted by plaintiffs does not reflect the number of persons available for hire at the University of Houston, which requires an advanced degree of its faculty members. 11
*398 In addition, other evidence introduced by plaintiffs reveals that during the six-year period at issue, 26 percent of the 350 assistant professors and 37.5 percent of the 173 instructors hired by defendant were women. In light of the evidence that 30.4 percent of all doctorate recipients in 1977 who planned to teach were women, we do not find a gross statistical disparity sufficient to make a prima facie case between the number of women hired by the defendant and the number defendant would have hired had its hiring of instructors and assistant professors mirrored the availability of women for such positions. 12
Plaintiffs’ hiring statistics for associate and full professors are more compelling. During the six-year period at issue, of the 154 associate professors hired only 5 were women; similarly, of 111 full professors hired, 3 were women. The impact of these statistics is lessened considerably by plaintiffs’ failure to introduce data as to the availability of qualified women for these positions. As discussed, the only availability data presented by plaintiffs included teachers at junior colleges and community colleges, many of whom undoubtedly lacked doctorate degrees and the requisite experience and thus were not qualified for hire as an associate or full professor at the University of Houston. Further, the record does not reveal the extent of hiring within the various colleges of the university; as discussed, the availability of women for faculty positions is to a significant extent dependent upon whether the position is in a science-related field — where men currently predominate — or a humanities or social science field — in which qualified women are available in more proportionate numbers. 13
*399 Finally, we note that plaintiffs introduced evidence of only one specific instance in which a woman arguably was discriminated against with respect to a faculty position, and this instance was persuasively rebutted by defendants. While, as we have noted, gross statistical disparities may alone be sufficient to establish a prima facie case of discrimination in a proper case, the statistical disparities in this case, because of the problems with plaintiffs’ availability data, are not sufficiently “gross” to satisfy plaintiffs’ burden. The failure to introduce e\ idence of specific examples of discrimination in faculty hiring decisions is thus significant. Cf. Teamsters, 431 U.S. at 338-39, 97 S.Ct. at 1855-56 (evidence of 40 specific instances of discrimination introduced); Hazelwood, 433 U.S. at 304-06, 97 S.Ct. at 2739-41 (plaintiffs introduced evidence of 55 specific instances of discrimination, 16 of which were found by the court of appeals to be unrebutted by defendants). We conclude that plaintiffs have failed to establish a prima facie case of discrimination with respect to the faculty hiring decisions made by the university during the academic years from 1972-73 through 1977-78.
2. Recruiting.
As stated in footnote seven, plaintiffs introduced evidence that on a number of occasions the university selected new faculty members by informal means rather than by the formal procedures established under the university’s equal employment opportunity procedures. Plaintiffs’ claim that new faculty members often were selected through operation of an “old boy network” by which exclusively male or male-dominated recruitment committees discriminated against women. In addition to the evidence that a number of faculty positions were filled the day the vacancy was announced, plaintiffs introduced evidence that in four of the six years at issue 47.8 percent of the faculty positions for which equal employment opportunity compliance data information was available were filled by men with no women even being considered for the job.
It is clear that with respect to a number of faculty positions filled during the six-year period the university engaged in informal, subjective recruiting and hiring practices. While a number of witnesses testified as to the formal, objective procedures designed for filling faculty positions, Dr. Lawless, associate chancellor at the university, candidly admitted that “if you are really trying to build an outstanding program, [you] identify a top level individual and then try to recruit that top level individual.” Relying on United States v. Georgia Power Co., 474 F.2d 906 (5th Cir. 1973), plaintiffs argue that where word-of-mouth recruitment and preferential hiring of friends or relatives results in a disproportionate number of minorities being excluded from an employer’s work force, such practices cannot stand. Finding Georgia Power distinguishable from the instant case, we decline to reverse the district court’s judgment for defendants on the recruiting claim.
In Georgia Power substantially all of the employer’s recruiting was accomplished by word of mouth or by interviewing at all-white, or predominantly all-white, educational institutions. With respect to word-of-mouth recruiting, we stated that “[u]nder word-of-mouth hiring practices, friends of current employees admittedly received the first word about job openings. Since most current employees are white, word-of-mouth hiring alone would tend to isolate blacks from the ‘web of information’ which flows around opportunities at the company.” Id. at 925. Concluding that word-of-mouth recruiting and hiring operated as a “built-in headwind” to blacks and was not justified by business necessity, we nevertheless refused to enjoin such practices. Rather, we held that “[t]he built-in headwinds which the present Georgia Power system harbors must be offset by affirmative steps reasonably calculated to encour *400 age black employment and to break through the currently circumscribed web of information.” Id. at 926. While we declined to specify what affirmative steps the employer would have to take, we suggested that advertisements of openings in publications accessible to nearby black communities and public notice that the company was an equal opportunity employer be considered.
Here the university has an affirmative action plan; pursuant to that plan a substantial majority of vacancies for faculty positions are advertised nationally. That some faculty positions are filled by word-of-mouth recruiting and hiring practices does not negate the fact that the formal procedures of advertising vacancies and considering all applicants — employed for the substantial majority of faculty vacancies — constitute affirmative steps reasonably calculated to encourage the employment of women. Further, of the faculty positions filled on the same day the vacancy was announced or soon thereafter, we are not told the proportions of men and women hired. Thus, it is possible that substantial numbers of women were hired as a result of word-of-mouth recruiting. In addition, the same availability question discussed with respect to the hiring claim is present here: plaintiffs' evidence of jobs being filled by men when no women were considered does not indicate which jobs were filled in this manner or whether women were available for such positions. As there is no showing that these jobs were the same ones filled by word-of-mouth recruiting, the possibility that women were not considered for a number of jobs because they did not apply for them is a significant one.
Finally, we note that Georgia Power and its progeny were all racial discrimination cases. We find this significant because the obstacle of widespread segregation faced by potential black employees in those cases is not present for women seeking university faculty positions due to the fact that for the most part women are and have been educated at the same institutions and by the same professors as their male counterparts. In short, we decline to assume that word-of-mouth recruiting of faculty persons operates to isolate women from the web of information surrounding job opportunities at the University of Houston, and there has been no showing that it operates as a built-in headwind to women seeking faculty positions at the university.
3. Promotion.
Plaintiffs claim that the university discriminated against women in its promotion and tenure decisions. Evidence offered in support of this claim included testimony that one woman was granted tenure but denied the promotion to associate professor that usually accompanies the grant of tenure. In another instance, a woman was finally granted tenure after having been employed as an instructor “far beyond the time” at which she should either have been terminated or granted tenure. The only evidence offered of class-wide discrimination with respect to promotion and tenure were statistics comparing the percentage of instructors, assistant professors, associate professors, and full professors who were women over the six-year period at issue. Plaintiffs attempted to support this statistical showing with evidence that the university’s promotion procedures are based to a large extent on purely subjective considerations.
The district court’s finding on the promotion claim was as follows:
With regard to promotions, the court heard lengthy testimony as to the University’s practices in promoting faculty from an entry level position of an untenured assistant professor on up the academic hierarchy. The court finds that the decision making on tenure and promotion is indeed based on highly subjective qualifications, but cannot condemn the practice as discriminatory in result. The University is unlike an industrial plant where more precise qualifications for promotion can be distinguished, consolidated, and put into print. The court finds no such discrimination in the Defendants’ promotion practices and poli *401 cies, and finds that a subjective procedure for promotion is a necessary, indispensable, and bona fide means for determining promotion in the academic field. 450 F.Supp. at 1056.
Plaintiffs argue that our decision in Jepsen v. Florida Board of Regents, 610 F.2d 1379 (5th Cir. 1980), rejects the hands-off approach to the university’s promotion practices taken by the district court. In Jepsen a female associate professor brought a Title VII suit against her employer, alleging that it had discriminated against her by not promoting her to full professor. The district court, finding a qualitative difference similar to that enunciated by the district court in this case between discrimination claims made against universities and claims made against a factory or union, held for the defendant on the ground that plaintiff had failed to prove that the university had abused its discretion in failing to promote her. We reversed and remanded, holding that a plaintiff in a Title VII suit against a university need meet no higher standard than that imposed by McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1972), on other Title VII plaintiffs.
While it is clear that under Jepsen a university’s employment practices are not free from scrutiny under Title VII, we do not read that opinion to mean that- subjective factors cannot be considered by a university in making its promotion and tenure decisions. 14 Rather, the university is free to rely on such factors in rebutting a plaintiff’s McDonnell Douglas prima facie case, and the plaintiff must then prove by a preponderance of the evidence that the reasons advanced by the university for its decision were a pretext for-discrimination. Accordingly, we decline to impose a rigid, objective system for making promotion and tenure decisions on the university.
Under Teamsters, 431 U.S. at 336, 97 S.Ct. at 1855, plaintiffs’ burden with respect to the promotion claim was “to establish by a preponderance of the evidence that [sex] discrimination was the [university’s] standard operating procedure — the regular rather (han the unusual practice.” Plaintiffs’ scanty evidence of specific instances of discriminatory promotion decisions is not sufficient to meet this burden, nor is the statistical evidence that essentially demonstrates only that the percentage of assistant, associate, and full professors who were women remained relatively constant during the six-year period while the percentage of instructors who were women increased substantially. There is no evidence as to the number of men and women who were eligible for and denied tenure during the years in question and no evidence as to the average length of time men and women served in each rank before being promoted to the next one. Accordingly, we affirm the trial court’s judgment on the promotion claim.
4. Compensation.
Plaintiffs’ faculty compensation claim is based entirely on statistics. Through a series of analyses, plaintiffs established that with respect to the faculty: (1) men are paid more, on the average, than women; (2) with the college mean subtracted from each person’s salary, men are still paid more than women; (3) considering only faculty members hired since 1972, the year Title VII became applicable to the University of Houston, men are paid more than women; (4) male assistant, associate and full professors are paid more than women of the same rank; (5) given the same length of service at the university, men are paid more than women; (6) men are paid more than women of the same age; and (7) within each college, men are paid more than women. 15 These comparisons *402 were intended to demonstrate that the differential between men’s and women’s salaries was not caused by any of the lawful, nondiscriminatory factors (e. g., rank, college, length of service, and age) that might result in men earning more than women. We find this evidence insufficient to do so.
The fundamental flaw in plaintiffs’ statistical evidence is that it fails to take into account the fact that a number of factors operate simultaneously to influence the amount of salary a faculty member receives. It appears uncontroverted that the most important factor is the college in which a professor teaches — all other factors being equal, professors in colleges such as law and engineering are, because of market forces outside of the university, paid significantly more than professors in colleges such as humanities and social sciences. Accordingly, plaintiffs’ statistical evidence showing that men and women of the same age, 16 rank, or length of service are paid differently does not demonstrate discrimination because the college factor has not been considered. Similarly, plaintiffs’ attempt to filter out the college factor is insufficient because the effect of the other factors — e. g., age, rank, and length of service, etc.— has not been considered simultaneously. Thus, if most of the women faculty members of a given college have been hired in recent years — as is likely to be the case given that women have become available for professorships in increasing numbers over recent years — we would expect that men within that college would be paid more than women because of higher rank and length of service. In short, a faculty person’s salary is dependent upon a number of factors that operate simultaneously; plaintiffs’ attempt to prove that sex was one of them must fail because of their failure to filter out the combined effect of the others.
Had the university presented no evidence on the faculty compensation issue, our task would be completed by the finding that plaintiffs’ statistical evidence did not prove discrimination. The university, however, performed two multiple regression analyses 17 that plaintiffs contend independently prove their faculty compensation claim. We find defendant’s multiple regression analyses ambiguous and insufficient to prove plaintiffs’ compensation claim.
Multiple regression analysis is a relatively sophisticated means 18 of determining the *403 effects that any number of different factors have on a particular variable; while it may be the best, if not the only, means of proving classwide discrimination with respect to compensation in a case such as this — where a number of factors operate simultaneously to influence salary — it is subject to misuse and thus must be employed with great care. Ideally, when a multiple regression analysis is used, it will be the subject of expert testimony and knowledgeable cross examination from both sides. In this manner, the validity of the model and the significance of its results will be fully developed at trial, allowing the trial judge to make an informed decision as to the probative value of the analysis. In the instant case, the statistical evidence associated with the multiple regression analysis is inconclusive, raising more questions than it answers. The following discussion of some of our problems with the analysis is not intended to exhaust the considerations to be analyzed in evaluating a multiple regression analysis; that task will be accomplished by subsequent cases in which this statistical device is used.
The university’s expert performed two multiple regression analyses on the faculty salary data. In the first, salary was the independent variable with the dependent variables being (1) the mean salary of the department; (2) experience as an instructor at any university, including the University of Houston; (3) experience as a faculty member other than at the University of Houston; (4) experience as a full professor at the University of Houston; (5) experience as an associate professor at the University of Houston; (6) experience as an assistant professor at the University of Houston; (7) possession of a doctoral degree other than a Ph.D.; and (8) possession of a Ph.D. degree. Defendant’s second analysis is identical to the first except that sex is added as a ninth independent variable. Plaintiffs’ multiple regression argument relies on the fact that the coefficient for the sex variable in the university’s second analysis is $694 per year with that amount being subtracted if the faculty person is a woman and added for men, resulting in an alleged difference in salary of some $1,388 per year attributable solely to a faculty member’s sex. Plaintiffs’ argument that this evidence satisfies their burden of proving a pattern and practice of discrimination with respect to faculty compensation may be correct — a t-statistic test demonstrates that the coefficient for the sex variable is significant. See Fisher, supra n. 17 at 716-17. However, other aspects of the statistical evidence apparently are inconsistent with this conclusion, and there are a number of questions as to the validity of the multiple regression model as a whole. Moreover, the only expert to testify on the subject stated that in his opinion the multiple regression analysis did not establish that the university discriminated against women with respect to faculty compensation. Accordingly, we decline to reverse the trial court’s judgment on this claim.
As for the apparent inconsistencies in the results of the university’s multiple regression analyses, the first model (without sex as a factor) explained 52.4 percent of the variation around the average salary for faculty persons while the second model (with sex as a factor) explained 53.2 percent of the variation. According to the university’s expert, despite the $694 coefficient for sex in the second model, the multiple regression analysis do not indicate discrimination against women because the model with sex as a factor explained only .8 percent more of the total variation around the average salary than did the model without sex: “It is not the values of the coefficients themselves which matter so much in a statistical interpretation of two models, it is the difference in proportion of variation that is *404 explained.” Plaintiffs introduced no evidence that sex was not, in a statistical sense, independent of the other independent variables in the model (e. g., department, rank, experience, and degree); thus, there has been no showing that the incremental contribution of sex to the variation explained by the university’s models is understated because part of its influence erroneously had been attributed to the other independent variables. 19 Further, plaintiffs did not introduce evidence that the value of the coefficient for the sex variable is significant notwithstanding the fact that only .8 percent more of the total variation was explained when sex was added into the model. As we have no basis for rejecting the opinion of the university’s expert, we decline to do so.
A second inconsistency in the results of the university’s multiple regression analyses supports the conclusion that discrimination was not proven by the fact that the coefficient for the sex variable was $694. The university’s expert applied the first multiple regression model (without a sex variable) to each faculty member to get an estimate of the salary that each should be earning. That estimate was then compared to the faculty person’s actual salary. If the university discriminated against its faculty women, one would expect that women, in general, would be paid less than the amount predicted by the model while men would be paid more. In fact, 343 men were paid less, and 302 more, than the model predicted they would be paid, while 61 women were “underpaid” and 55 “overpaid”; the ratio of underpaid to overpaid is thus 1.136 for men and 1.109 for women, thus indicating that, if anything, a higher proportion of men are underpaid than are women. In an attempt to determine whether the amount a person was underpaid or overpaid depended on that person’s sex, the university’s expert made similar comparisons of the numbers of men and women overpaid or underpaid by as much as $1,500. The results of this test were that 227 men were underpaid by at least $1,500 while 186 were overpaid by at least that amount, while the respective numbers for women were 34 and 30. Thus, the ratio of underpaid by at least $1,500 to overpaid by at least $1,500 is 1.220 for men and 1.133 for women, again indicating no discrimination. 20 Plaintiffs made no attempt to show that men overpaid by more than $1,500 received a substantially greater amount over $1,500 than did women, or that women underpaid by more than $1,500 were paid substantially less than $1,500 below the expected salary while men were not; we, of course, cannot assume either to be the case.
In addition to the apparent inconsistencies in the results of the university’s multiple regression analyses, fundamental questions relating to the model itself are raised. Multiple regression analysis is based on three major assumptions 21 — where these *405 assumptions fail, “the use of multiple regression analysis is likely to be inappropriate,” Fisher, supra n. 17, at 708, though advanced tools of econometrics may allow such failure to be dealt with. Id. Whether these assumptions are valid in this case has not been addressed; neither have other questions such as those relating to the relationship among the independent variables, 22 whether a linear model is appropriate in this case, 23 whether variables have been erroneously included or excluded in the model, 24 and whether the fact that the model explains only 52 to 53 percent of the total variation in average salaries means that the model as a whole is not very reliable. 25
We conclude that plaintiffs have not proven that the university discriminated against its women faculty members with respect to compensation.
C. Professional and Administrative Staff.
The claims made on behalf of women in professional and administrative staff positions involve compensation and the failure of the university to hire or promote women into higher level jobs.
1. Compensation.
Most of the evidence plaintiffs introduced in support of their claim that the university discriminated against women in professional and administrative positions is statistical in nature. Further, most of it is similar to, and suffers from the same weakness as, the single factor analyses plaintiffs relied on in attempting to prove their faculty compensation claims. For example, plaintiffs demonstrated that among the professional and administrative staff, men were paid more than women of the same age; men with a given length of service were paid more than women with the same number of years of service; and men were paid more than women with the same amount of formal education. Among the factors omitted from each of these analyses is the job performed by the men and women. If men occupy the higher level, better paid positions at the university — as plaintiffs’ evidence on their hiring/promotion claim convincingly demonstrates — we would expect men to be paid more than women on that basis. Thus, we find that plaintiffs’ isolated factor analyses are of little, if any, probative value.
Plaintiffs introduced no evidence that women were paid less than men for equal work; that failure is not necessarily fatal, however, as the Supreme Court recently held in County of Washington v. Gunther, --U.S.--, 101 S.Ct. 2242, 68 L.Ed.2d 751 (1981), that a sex discrimination compensation claim can be brought under Title VII without regard to whether the equal work standard of the Equal Pay Act, 29 U.S.C. § 206(d), is met. In Gunther the women plaintiffs alleged that the county evaluated the worth of their jobs, determined that they should be paid 95 percent as much as men who held similar jobs, and yet paid them only 70 percent as much, while paying the men the full evaluated worth of their jobs. These allegations were held to state a claim under Title VII even though the men and women did not perform equal work under the Equal Pay Act standard; 26 the case was remanded to the district court for a determination of wheth *406 er part of the pay differential was attributable to sex discrimination.
Unlike the trial court in Gunther, in the instant case the trial judge allowed plaintiffs to present their compensation claim without a showing that women were paid less than men for equal work. A portion of plaintiffs’ evidence on this point was somewhat similar to the facts as alleged by the plaintiffs in Gunther. In 1975 the university formulated a pay plan for most of its professional and administrative staff employees. With the aid of an outside consulting firm, all of the jobs to be covered by the pay plan were evaluated and classified into one of nine levels, with the highest paying, most responsible jobs being those in level nine. Each level had a low and high figure associated with it representing the minimum and maximum pay a person whose job fell in that level should receive. The academic division of the professional and administrative staff employed some 68 persons when the pay plan was formulated — 35 men and 33 women. Plaintiffs introduced evidence that, of those 68 persons, 21 were paid less than the minimum for the level in which their job fell, and that 18 of those 21 were women; 27 according to plaintiffs’ expert, a binomial distribution statistical analysis of this data demonstrates that this allocation of men and women among the 20 underpaid employees did not occur by chance. 28 This showing is strengthened by evidence that all of the four employees in the academic division who were paid more than the maximum set for the job level of their position were men.
Furthermore, the jobs of five of the eighteen women who were paid less than the minimum for their job level and two of the women who were not paid less than the minimum were reclassified to a lower job level, while the jobs of none of the men in the academic division, including the three who were underpaid, were similarly reclassified. The significance of this conduct of the university is demonstrated by the fact that Mr. Silber, the university official in charge of formulating the pay plan, testified that it would be inappropriate to reclassify into a lower job level the job of an employee who was being paid less than the minimum for the level in which his job was originally classified because the basis upon which a pay plan is formulated is an objective analysis of jobs, not individuals. If a goal of a pay plan is to obtain uniformity and equity in pay based upon a comparative analysis of the jobs covered by the plan, that goal clearly is frustrated by reclassifying an employee’s job because the employee is being paid less than the minimum for the level in which his job originally was classified. 29
The final piece of plaintiffs’ evidence supporting their compensation claim is that the university’s equal opportunity officer testified that one of the reasons for developing the pay plan was to cure inequities in pay existing between men and women professional and administrative employees. Thus, plaintiffs’ evidence of discrimination in the compensation of professional and administrative employees consists of the facts that (1) a statistically significant, disproportionate number of women in the academic division were paid less than the minimum established by the pay plan for the level of their jobs; (2) all four of the *407 employees in the academic division who were being paid more than the maximum for their job level were men; (3) in the academic division, five of the eighteen women who were underpaid and two other women had their jobs reclassified into lower levels, while no jobs held by men were similarly reclassified; and (4) the university’s equal opportunity officer testified that a purpose of the pay plan was to remedy sexually discriminatory compensation practices of the university. The issue is whether this is sufficient to establish by a preponderance of the evidence that the university engaged in a pattern or practice of discriminating against its professional and administrative women employees in compensating them; i. e., whether this evidence established that sex discrimination was the university’s “standard operating procedure— the regular rather than the unusual practice.” Teamsters, 431 U.S. at 336, 97 S.Ct. at 1855.
With the exception of the testimony of the university’s equal opportunity officer, all of plaintiffs’ evidence on the compensation claim involves the academic division of the professional and administrative staff. While it is not entirely clear how many professional and administrative employees were covered by the pay plan at the time of the reclassification, the number was at least 350, and probably was in the 450 to 550 range, with 150 to 200 of them being women. 30 As mentioned above, the academic division consisted of 68 employees, 33 of whom were women. As to the remaining 280 to 480 employees, 120 to 170 of whom were women, plaintiffs must rely on the testimony of the equal opportunity officer and on the inference, if any, that can be drawn from the situation in the academic division. As to the latter, plaintiffs were, of course, free to present evidence on the other divisions within the professional and administrative staff. Their failure to do so arguably supports an inference that the evidence would have demonstrated no discrimination in those divisions; at any rate, we decline to supply by inference the showing plaintiffs should, if indeed they could, have made. As to the equal opportunity officer’s testimony, in our view her expression of her belief that the pay plan was needed to remedy inequities in pay between men and women professional and administrative employees 31 is not sufficient to establish, by a preponderance of the evidence, that sex discrimination was the university’s standard operating procedure for its professional and administrative employees employed in divisions other than the academic division.
We conclude that plaintiffs have not proved their compensation claim for the professional and administrative staff as a whole. That conclusion, however, does not negate the strong showing that plaintiffs made of discrimination in the academic division. As to that claim, we reverse the judgment of the district court and direct that judgment be rendered for that portion of the plaintiff class employed in the academic division of the professional and administrative staff.
2. Hiring and Promotion.
Plaintiffs allege that the university discriminated against its professional and administrative women employees by hiring them only for lower level positions and by not promoting them to the more responsi *408 ble, higher paying jobs. While plaintiffs convincingly demonstrated that women were absent from these top level jobs, they made no showing that women hired into the lower level positions were qualified for higher level jobs. Similarly, no evidence was introduced as to the university’s practices or policies with regard to promotions within the professional and administrative staff. Accordingly, the claim we address is that the university discriminated against women by not hiring them for high level professional and administrative positions.
As to that claim, plaintiffs introduced evidence that since at least as early as 1970 only one woman has ever served on a permanent basis in an administrative position at or above the level of dean. 32 The total number of these positions at the university is not in the record, though on the basis of an exhibit listing a total of fourteen colleges, it appears that there are at least twenty-one. 33 In addition, plaintiffs introduced evidence that during the 1976-77 academic year, there were no women employed in the fourteen jobs classified in levels 8 and 9 of the professional and administrative pay plan, 34 and that only one of fifteen level 7 jobs was held by a woman. 35 Thus, plaintiffs rely on evidence that of the top fifty professional and administrative positions (twenty-nine in levels 7, 8, and 9 of the pay plan and at least twenty-one not covered by the plan), only one was a woman in the 1976-77 academic year and that the numbers would not be significantly different from these for the years preceding the 1976-77 school year.
As discussed above with regard to the faculty hiring claim, where special qualifications are required for a particular job, plaintiffs asserting a discriminatory hiring claim must demonstrate an availability of qualified class members to give their statistical showing meaning. We find that requirement particularly significant with respect to the positions at and above the level of dean. As to those jobs, one of plaintiffs’ witnesses testified that the great majority of them are filled only after a nationwide search and that candidates for these positions must have some degree of academic excellence as well as prior administrative experience. There was no showing made as to the number of men and women with these qualifications available for such positions at the University of Houston. To the contrary, the university introduced evidence that it had recently taken applications for a new associate chancellor, a provost, and two associate provosts; for these four positions, 202 applications were received, only eleven of which were from women.
*409 Similarly, plaintiffs made no availability showing for the 29 jobs in levels 7, 8, and 9. While their brief states that “with the possible exception of the very highest level jobs, promotion is effected from within the ranks of current employees,” there is no record reference supporting that statement, and we have been unable to find evidence in the record on this point. If that statement were substantiated, plaintiffs might be correct in their assertion that the only necessary availability showing would be that of women in the ranks of current employees. Johnson v. Uncle Ben’s, Inc., 628 F.2d 419, 425 (5th Cir. 1980), vacated and remanded on other grounds,-U.S.-, 101 S.Ct. 1967, 68 L.Ed.2d 290 (1981). 36 As it has not been demonstrated that jobs in levels 7, 8, and 9 are filled by promoting employees in lower level jobs, we are left without availability data against which to view the university’s hiring practices. 37
Furthermore, the university introduced evidence that four of the six jobs in level 9 had been held by men for ten years or more so that no discriminatory hiring decision could have been made during the period covered by this lawsuit. One of the other two level 9 positions is director of the physical plant; while the record does not reveal how long the male currently in that position has held the job, it is clear from one of the exhibits that he has been employed in that capacity at least since 1974. The sixth level 9 job was filled by a man a year and a half or so before trial. Thus, only one or perhaps two of the six level 9 jobs were even possibly the subject of a discriminatory hiring decision made during the period at issue.
Finally, we note that at most plaintiffs established that the university had discriminated against only one individual woman in its hiring of professional and administrative employees. 38 Under Hazelwood, 433 U.S. at *410 307-08, 97 S.Ct. at 2741—42, evidence of individual instances of discrimination is not necessary where plaintiffs are able to show “gross statistical disparities”; in our view in light of (1) the relatively small number of positions in levels 7, 8, and 9; 39 (2) the diverse and specialized qualifications necessary for such positions; (3) the absence of an availability showing for these jobs; and (4) the university’s showing of a lack of turnover for level 9 positions, a showing of a sufficiently “gross statistical disparity” has not been made. Accordingly, a showing ir. addition to the statistics was required for plaintiffs to satisfy their burden of proving, by a preponderance of the evidence, that the university had engaged in a pattern or practice of discriminating against women with respect to hiring top level professional and administrative employees. As sufficient independent evidence of discrimination was not introduced, we affirm the district court’s judgment on this claim.
In closing, we add a note both rueful and cautionary. The bar is reminded that sound statistical analysis is a task both complex and arduous. Indeed, obtaining sound results by these means, results that can withstand informed testing and sifting both as to method and result, is a mission of comparable difficulty to arriving at a correct diagnosis of disease.
We are no more statisticians than we are physicians, and counsel who expect of us informed and consistent treatment of such proofs are well advised to proceed as do those who advance knotty medical problems for resolution. Our innate capacity in such matters extends to “the inexorable zero” 40 and perhaps, unevenly, somewhat beyond; but the day is long past — past at least since the Supreme Court’s sophisticated analysis in Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977) — when we proceed with any confidence toward broad conclusions from crude and incomplete statistics. That everyone who has eaten bread has died may tell us something about bread, but not very much.
CONCLUSION
The district court’s judgment for the university on the compensation claim for professional and administrative women employees in the academic division is reversed and the case remanded for further proceedings related to that claim. On remand, the question of individual relief for those academic division employees who were victims of the university’s discriminatory practices will arise. As plaintiffs have proven that the university engaged in a pattern or practice of discriminating against women em *411 ployees in the academic division of the professional and administrative staff, an inference arises that each of those women was discriminated against. Accordingly, each is “presumptively entitled to relief, subject to a showing by the [university] that its [compensation of the employee] was not based on its policy of discrimination.” Teamsters, 431 U.S. at 362, 97 S.Ct. at 1868. Of course, the showing required of the university to avoid liability to an individual employee will be substantially greater for those members of the class who were paid less than the minimum for their job level than for the other members who were not. For those individual members of the class found to be entitled to relief, the amount of damages will have to be ascertained.
The judgment is affirmed in all other respects.
AFFIRMED IN PART, REVERSED AND REMANDED IN PART.
Footnotes
[1] 42 U.S.C. § 2000e.
[2] Relying on East Texas Motor Freight System, Inc. v. Rodriguez, 431 U.S. 395, 97 S.Ct. 1891, 52 L.Ed.2d 453 (1977), the university argues that the class should not have been certified because the named plaintiffs were not qualified to hold the vast majority of faculty and administrative positions. In Falcon v. General Tel. Co., 626 F.2d 369, 375 (5th Cir. 1980), we rejected defendants’ argument that Rodriguez bars the kind of “across the board” attack on discriminatory employment practices plaintiffs have made in this case.
[3] In her application for reclassification Ms. Hill sought the title “manager of operations.” Her supervisor, Dr. Motard, approved her request though he expressed reservations regarding the title “manager of operations” as opposed to “operations supervisor,” apparently because she lacked familiarity with computer operating systems and programming languages. While the parties have disputed the issue of Ms. Hill’s appropriate title at some length, we find that issue largely irrelevant to the fundamental questions of whether her duties were discriminatorily curtailed and whether her termination was discriminatorily motivated.
[4] Killough was a well-trained engineer with a great deal of computer experience who was assisting in the lab on a voluntary basis. The evidence indicated that it took several months for the university to find Folkerth and that he had accepted the job for less than market value. In contrast, Hill was replaced by her assistant, Ms. Sandy White, who by all accounts performed admirably in that position and got along well with Killough and Folkerth. While the fact that Hill was replaced with a female substantially weakens — if indeed it does not defeat — her claim that she was terminated because of her sex, see Marks v. Prattco, Inc., 607 F.2d 1153, 1155 (5th Cir. 1979), it does not resolve the retaliatory discharge question.
[5] As discussed below, plaintiffs also introduced evidence of several specific instances of allegedly discriminatory employment decisions made by the university.
[6] That statistics can be, and often are, misused is nothing new. In his autobiography, Mark Twain observed that “[t]here are three kinds of lies — lies, damned lies and statistics.” While it may be that the numbers themselves do not lie, the meaning ascribed to the numbers certainly can be misleading. Plaintiffs’ single factor analyses supporting their compensation claims, discussed below, are good examples. Another is an argument made by the university that the percentage increase in the number of women faculty members hired over the six years at issue was greater than the corresponding percentage increase for men. That statement is true and at first glance seems significant; further reflection, however, demonstrates that it is not. If the university had one female faculty member and hired another, the number of female faculty members would have increased by 100%; if the university had 100 male faculty members and hired 50 more, the percentage increase would be only 50%. Thus, by hiring 1 woman and 50 men, the university would have increased the number of female faculty members at a rate twice as great as that for its male faculty.
[7] Effective March 24, 1972, application of Title VII was extended to include state and local governmental employers. Hazelwood, 433 U.S. at 304 n.7, 97 S.Ct. at 2740 n.7.
[8] Plaintiffs also introduced evidence tending to show that in a number of instances the university failed to comply with its own equal employment opportunity procedures. For instance, there was some indication that perhaps as many as 15 percent of faculty vacancies were filled on the same day the vacancy was announced, thus indicating that the person hired had been preselected rather than chosen as a result of compliance with procedures designed to insure that minorities were not discriminated against. Initially we note that there is no indication of the proportions of men and women who were hired under these circumstances. Further, while we find failure to comply with equal employment opportunity procedures significant, in the absence of stronger proof of discrimination than is present in this case we do not find that failure sufficiently probative to require a different result.
Data on the percentage of applicants for faculty positions who were women would be very relevant to the discriminatory hiring claim. The absence of such evidence, however, will not prevent plaintiffs from recovering. Hazel-wood, 433 U.S. at 308 n.13, 97 S.Ct. at 2742 n.13.
[9] It is clear that statistical challenges to a defendant’s hiring practices for positions requiring special qualifications must be based not on comparisons with the general population but on comparisons with “the smaller group of individuals who possess the necessary qualifications.” Hazelwood, 433 U.S. at 308 n.13, 97 S.Ct. at 2742 n.13. Mayor v. Educational Quality League, 415 U.S. 605, 620-21, 94 S.Ct. 1323, 1333, 39 L.Ed.2d 630 (1974).
[10] The National Research Council of the National Academy of Sciences, Summary Report 1977 Doctorate Recipients from United States Universities 8 (1978).
[11] That plaintiffs’ availability data are suspect is indicated by the fact that defendants introduced evidence that 30.4 percent of all 1977 doctorate degree recipients who planned to teach were women. As both parties agree that the trend of recent years is an increasing population of women receiving doctoral degrees, one would expect that the percentage of newly graduated doctorate recipients available for university teaching positions in 1977 who were women would be greater than the percentage of women holding such positions in that same year. As the great majority of faculty members with 10 to 20 or more years teaching experience in 1977 were undoubtedly men, we would expect to see a substantial difference between the percentage of newly graduated doctorate degree recipients who were women in 1977 and the percentage of all university faculty members with doctorate degrees who were women in that same year. Instead, the percentages are not only very close together, but in fact the percentage of women on college and university faculties in 1977 — 31.8 percent per plaintiffs’ availability data — is higher than the percentage of doctorate degree recipients in 1977 who were women — 30.4 percent per defendants’ availability data. Perhaps the explanation for this anomaly is the one suggested in the text: that a substantial proportion of the women included in plaintiffs’ availability data are junior college and community college teachers who do not hold doctorate degrees *398 and who are therefore not qualified for employment as faculty at the University of Houston.
[12] The record does not provide a basis for determining the percentage of doctorate recipients during the entire six-year period who were women; accordingly, we are unable to perform a precise binomial distribution statistical analysis of defendants’ hiring of instructors and assistant professors during the six-year period. See Castaneda v. Partida, 430 U.S. 482, 496 n.17, 97 S.Ct. 1272, 1281 n.17, 51 L.Ed.2d 498 (1977). However, even assuming that 30.4 percent of all doctorate recipients during the entire six years were women — due to the trend of an increasing proportion of women doctorate recipients in recent years, the 30.4 percent figure of 1977 is undoubtedly too high for the entire six-year period from 1973 to 1978 — the difference between the number of women hired as instructors (37.5% of 173 = 65) and assistant professors (26% of 350 = 91) and the number we would expect to have been hired (instructors, 30.4% of 173 = 53; assistant professors, 30.4% of 350 = 106) is not statistically significant under the analysis approved by the Supreme Court in Castaneda-. Id.
[13] It is clear that statistical evidence relating to claims of discrimination in hiring is of little probative value unless it is based on an analysis of those members of the population who possess the necessary special qualifications for the job at issue. Hazelwood, 433 U.S. at 308, 97 S.Ct. at 2741-42. However, the extent to which a plaintiff must tailor her availability data in a complex class action suit involving different categories of jobs among which there is reason to believe that the availability factor is significantly different is not clear. In Hazelwood plaintiffs challenged the hiring practices of a local school district, and the Supreme Court held that the proper statistical “comparison was between the racial composition of [the district’s] teaching staff and the racial composition of the qualified public school teacher population in the relevant labor market.” Id.
Arguably Hazelwood dictates that the proper comparison in this case is the one made by plaintiffs: between the sex composition of the university’s new faculty members hired during the six years at issue and the sex composition of all college and university teachers during that time period. In our view, however, there is a significant distinction between Hazelwood and the instant case. In Hazelwood there was no indication that blacks were any more or less available for any particular class of teaching position in the Hazelwood public schools than for all teaching positions within those schools. Here is it clear that women qualified for instructor and assistant professor positions were available in substantially greater numbers than for associate and full professorships. Further, the evidence is clear and undisputed that women were available in substantially greater numbers for faculty positions in fields such as humanities, social sciences, and education than they were in fields such as life sciences, physical sciences, and engineering. While we need not today decide whether in a case such as this plaintiffs must make a separate availability showing with respect to each department within the university, such a showing at least should have been made at the college level. As the Supreme Court noted in Teamsters, the “usefulness [of statistics] depends on all of the surrounding facts and circumstances.” 431 *399 U.S. at 340, 97 S.Ct. at 1856-57. Absent a more particularized availability showing, plaintiffs’ statistical evidence with respect to faculty hiring is of limited usefulness.
[14] Plaintiffs, in fact, do not even so contend: “Even though some subjective evaluation procedures may be necessitated by the complexity of positions in a university environment, university decisions in hiring, promotion, tenure and wages are as much subject to court review as those of other types of employers.” See Davis v. Board of School Comm’rs, 600 F.2d 470, 475 (5th Cir. 1979).
[15] For three of these seven categories, plaintiffs also introduced evidence that the statistical disparities between men’s and women’s salaries had statistical significance, i. e., that there was less than a 2% possibility that the discrep *402 ancies were attributable to chance. Because of our disposition of the compensation claim, we need not decide what effect the failure to demonstrate statistical significance with respect to the other four comparisons would have on plaintiffs’ showing.
[16] We need not and do not express an opinion on whether age alone is a valid basis for paying one faculty person more than another.
[17] For an explanation of the theory and the mechanics of multiple regression analysis and a description of its use in a number of other cases, see generally Fisher, Multiple Regression in Legal Proceedings, 80 Colum.L.Rev. 702 (1980); Finkelstein, The Judicial Reception of Multiple Regression Studies in Race and Sex Discrimination Cases, 80 Colum.L.Rev. 737 (1980).
[18] In Wade v. Mississippi Co-op. Extension Serv., 528 F.2d 508 (5th Cir. 1976), defendants challenged the probative value of plaintiffs’ multiple regression analysis because of its sophisticated nature. While acknowledging that “multi-variant regression analysis is indeed a sophisticated and difficult method of proof in an employment discrimination case,” id. at 517, we found that the statistical evidence had been supplemented by additional evidence of specific instances of discrimination and that the combination of these two forms of evidence was sufficient to establish an inference of discrimination.
We do not read Wade to mean that statistical evidence in the form of a multiple regression analysis, standing alone, can never satisfy plaintiffs burden of proving a pattern and practice of discrimination. As discussed earlier in this opinion, the Supreme Court has stated that “[w]here gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination.” Hazelwood, 433 U.S. at 307-08, 97 S.Ct. at 2741. While the gross statistical disparities described in Hazel-wood refer to differences between the number of minorities hired and the number available, we see no reason to require independent evidence of specific instances of discrimination for a compensation claim where a gross statistical disparity is established by a multiple regression analysis. While such an analysis is more complex than a comparison of the number of minorities hired with the number available, if properly used, multiple regression analysis is a *403 relatively reliable and accurate method of gauging classwide discrimination. Of course, where the employer is engaged in widespread discrimination against a class of employees, there should be many individual examples of such discrimination, and evidence of them would be admissible to support plaintiffs statistical showing. Thus, in Teamsters, 431 U.S. at 338, 97 S.Ct. at 1856, the Court noted that the statistical evidence was bolstered by evidence of over 40 specific instances of discrimination.
[19] For example, if plaintiffs had proven that women were discriminated against with respect to promotion, the independent variable for experience as an assistant professor would be related to sex because women, due to the discrimination, would have more experience at that rank than would men. In that event, part of the variation in average salary that should have been attributed to sex would not have been because it would have been “explained” by the experience-as-an-assistant-professor variable. As discussed above, plaintiffs did not prove discrimination with respect to promotion.
[20] While a higher proportion of men (186 -e 645 = 28.84%) than women (30 -*■ 116 = 25.86%) were “overpaid” by at least $1,500, men were also more frequently underpaid by at least $1,500 than were women (men, 227 — 645 = 35.19%; women, 34 - 116 = 29.31%).
[21] Each of the three assumptions involves those influences on the dependent variable, /. e., salary, that are not included in the model and that are collectively referred to as the “random disturbance term.” The three assumptions are;
(a) that the effects of the random disturbance term are independent of the effects of the independent variable; (b) that the values of the random term for different observations are not systematically related and that the average squared size of the random effect has no systematic tendency to change over observations; and (c) that the sum of random effects embodied in the disturbance term is distributed normally, in the “bell curve” generally characteristic of the distribution of the sum of independent random effects.
Fisher, supra n. 17, at 708.
[22] Id. at 713.
[23] Id. at 711-12 n. 20.
[24] Id. at 713-15.
[25] Id. at 720.
[26] In Gunther the Supreme Court was careful to note that the issue before it did not involve “the controversial concept of ‘comparable worth,’ under which plaintiffs might claim increased compensation on the basis of a comparison of the intrinsic worth or difficulty of their job with that of other jobs in the same organization or community.” -U.S. at-, 101 S.Ct. at 2246 (footnotes omitted). The Court found that that issue was not before it because plaintiffs alleged that the county itself had evaluated the worth of plaintiffs’ jobs and nevertheless chose to pay them less while not making a similar reduction in the wages paid to men. As discussed below, plaintiffs in the instant case introduced evidence of similar import — our decision is based on this evidence and bears no relation to the “comparable worth” concept.
[27] In their brief and statistical analysis, plaintiffs claim that 20 employees in the academic division were found to be underpaid and that 17 of them were women. The source of this information is also in the record, however, and it reveals that 21 employees were underpaid, 18 of whom were women.
[28] Such a distribution of men and women would, according to plaintiffs’ expert, occur by chance only four times in 10,000; that possibility is sufficiently minimal to be ignored.
[29] Plaintiffs introduced no evidence as to the reason for the reclassification; however, one woman who was paid less than the minimum for the level in which her job originally was classified and whose job subsequently was reclassified into a lower job level testified that her duties were not reduced when her job was reclassified. As the only positions reclassified into lower job levels were held by women and as the university introduced no evidence on that issue either, we find that the fact of the reclassification is probative as to the discriminatory compensation claim.
[30] Various charts comprising plaintiffs’ statistical evidence reveal different numbers of employees covered by the plan in the years 1976 and 1977, when the reclassifications apparently occurred.
[31] Relevant portions of the equal employment officer’s testimony follows:
There was no plan that included [the professional and administrative employees], and our hiring salary was not very systematic, it just depended on the amount in the budget.
I personally felt, and the personnel director agreed with me, that inequities had grown up in the professional plan, particularly since the earlier years when I was employment manager, there was a lot of individual departmental hiring and they just hired people in and set an arbitrary salary.
We felt that if there were inequities, particularly among or between men and women, that that is where they were.
So we made the commitment in the affirmative action plan that we would develop a professional pay plan.
[32] At the time of trial, the university apparently had just completed a reorganization of its top administrative positions. While it is not entirely clear from the record, it appears that from the departmental chairman, the hierarchy proceeds upward as follows: dean and assistant or associated deans; provost and associate provosts; chancellor and associate chancellors; and president. Shortly before trial a woman was named assistant provost; this action by the university, which occurred on the very eve of trial, is of minimal probative value.
[33] Fourteen deans, one provost, two assistant or associate provosts, one chancellor, two associate chancellors, and one president.
[34] In May of 1978 a woman’s job that apparently had been classified in level 7 was reclassified as a level 8 position. This conduct, like that described in footnote 32, occurred on the eve of the June 1978 trial and is of little probative value on the question of whether the university discriminated against women during the six academic years from 1972 to 1978.
[35] The positions of dean, provost, chancellor, president, and assistant or associate dean, provost and chancellor are not covered by the professional and administrative staff pay plan. The breakdown by sex of the employees in the nine levels established by the plan during the 1976-77 academic year was as follows:
[36] But even then questions would arise whether promotion is from level to level and, if so, whether discrimination would have been shown for hiring into levels 8 and 9 in light of the fact that only one woman held a level 7 job. Further, due to the nature of the jobs in levels 7, 8, and 9, it is not evident that promotions could routinely be effected from one level to the next. See n.37, infra.
[37] That special qualifications within the meaning of Hazelwood, 433 U.S. at 308 n.13, 97 S.Ct. at 2742 n.13, are required for these jobs is evident from their descriptive titles. The 14 jobs in levels 8 and 9 are: staff legal counsel, director of the physical plant, director of computer operations and educational systems, controller, director of counseling and testing, director of personnel services, director of architectural services, director of construction, director for research development, director of housing, director of internal auditing, director of facilities, director of administrative systems, and director of the university center. While some of these positions arguably require only a college degree and administrative experience, the majority appear to require a specialized education as well as technical and administrative work experience. We recognize that making the required availability showing in a case such as this is a difficult task; while we need not and do not decide the question, it may be that claims of discriminatory hiring with respect to a relatively small number of positions requiring diverse and specialized qualifications relating to education and work experience simply are inappropriate claims for class actions that rely on statistical proof.
[38] Plaintiffs attempted to demonstrate that three individual professional and administrative women employees were victims of discriminatory hiring practices. One witness testified that she and a number of other people applied for a position as a clerk manager in the College of Education; that the duties for that position were substantially similar to the duties she was then performing for the university in a lower paying job; and that a male got the job. The university did not rebut this evidence.
A second witness testified that she had participated in an administrative internship program designed to train women for high level administrative positions within the university but that when a vacancy occurred for the position of associate dean of faculty, a man was hired. However, this same witness responded to the question of whether she was interested in advancing into an academic administrative position as follows: “I had very mixed feelings about it. At the time I finished my internship, I was glad it was over, glad I was going back to the department, and felt, and didn’t hide the feeling, that I had mixed feelings on whether or not in the future I wanted an administrative job.” Under these circumstances, the university certainly had a valid reason for not offering her the associate dean of faculty position.
A third witness testified that she was not promoted to station manager of the university’s television station despite having been led to *410 believe that she would be when the present manager retired. Instead, a man with a high school education was hired — she had a master’s degree in radio-television — and she was told by the overall supervisor of the station that a man who could deal with the engineers was needed for the job. We have several problems with this evidence. First, the incident occurred around 1969, before Title VII became applicable to state-operated universities, thus limiting its probative value. See Hazelwood, 433 U.S. at 309 n.15, 97 S.Ct. at 2742 n.15. Second, the university’s evidence showed that the man hired had 10-15 years’ experience at the station covering all phases of its operations, with extensive experience in the broad field of public programming. By contrast, the woman not hired had only a few years’ experience that was concentrated in the more narrowly defined field of instructional programming.
[39] A review of the distribution of men and women in the nine pay levels, see n.35, supra, indicates that women held the following percentages of jobs in each level: level 1, 63.6%; level 2, 51.8%; level 3, 37.5%; level 4, 30.8%; level 5, 30%; level 6, 34.6%; level 7, 6.7%; level 8, 0%; and level 9, 0%. Plaintiffs argue that these percentages demonstrate that women were discriminatorily assigned to lower level jobs. As discussed, however, no showing was made that women qualified for positions in a given job level were not considered for such positions but were instead hired into lower level jobs. As for job levels 3, 4, 5, and 6, no showing was made that qualified women were available for these positions in greater proportions than 30-37.5%. As all of these positions, are by definition professional and administrative jobs, rather than clerical, ministerial positions, a general work force availability figure cannot be applied; rather, a Hazelwood showing of persons available possessing the necessary special qualifications is necessary.
[40] Then Chief Judge Brown, writing for the court in United States v. T.I.M.E. —D.C., 517 F.2d 299, 315 (5th Cir. 1975).