#### Brenda S. GRIFFIN and Margaret Waimon, Plaintiffs-Appellants, v. BOARD OF REGENTS OF REGENCY UNIVERSITIES, a public corporation, et al., Defendants-Appellees.

No. 84-2981.

United States Court of Appeals, Seventh Circuit.

Argued Nov. 1, 1985.

Decided June 18, 1986.

*1282Robert J. Lenz, Bloomington, 111., for plaintiffs-appellants.

John L. Swart, Giffin, Winning, Lindner, Newkirk, Cohen & Bodewes, P.C., Springfield, Ill., for defendants-appellees.

Before CUMMINGS, Chief Judge, CUDAHY, Circuit Judge and CAMPBELL, Senior District Judge.*

*

 The Honorable William J. Campbell, Senior District Judge for the Northern District of Illinois, is sitting by designation.

CUDAHY, Circuit Judge.

Plaintiffs, who were faculty members at Illinois State University, brought this employment discrimination claim, as individuals and as representatives of a class, against the defendants1 under section 701 *1283et seq. of Title VII, 42 U.S.C. § 2000e et seq., the Equal Pay Act, 29 U.S.C. § 206 and 42 U.S.C. §§ 1983, 1985.2 The district court found for the defendants on all claims. We affirm.

I.

Faculty positions at Illinois State University (the “University” or “ISU”) are divided into two categories, regular positions and temporary positions. Regular positions are ones that might lead to a grant of tenure. University departments must conduct national searches for regular faculty hiring. Regular faculty are employed under one-year contracts, renewable for up to seven years. In the sixth year a teacher on the regular faculty is notified whether or not tenure will be granted (although tenure may be awarded earlier). Tenured employees must have a doctorate, although such a degree is not required for a candidate to be hired to a regular position. If tenure is not awarded the teacher serves one additional year on a terminal contract. At ISU approximately two-thirds of the teaching positions are tenured.

Temporary faculty are also employed under one-year contracts, renewable for up to seven years.3 Temporary faculty, however, are not eligible for tenure. One must apply for a regular position in order to be considered for it. Temporary faculty earn less money and enjoy fewer benefits than regular faculty but are not required to have a doctorate. The district court found that the responsibilities and skills of temporary and regular faculty differ. Dist.Ct. Order at 20.

Plaintiff Brenda Griffin4 was first hired as a temporary employee in the Department of Sociology and Anthropology (the “Sociology Department”) in the fall of 1974. She did not receive her doctorate until 1978. In 1976 she was demoted to part-time status; she resumed full-time work the following year. Griffin testified that Dr. Dorothy Lee, Department Chairperson, told her that a woman could not handle a family and a full-time job at the same time. Lee denied making the statement and the district court believed that Lee’s testimony was more credible. Dist. Ct-Order at 11.

A regular faculty position became available in the Sociology Department for 1977-78. A national advertisement for the position listed various specialties including theory, methodology, urban sociology, industrial sociology, demography and race relations, which would be useful for the position. Griffin applied for the position, but Dr. Roy Treadway was hired. Treadway had his Ph.D., while Griffin did not at this time. Further, he had taught at Yale and Princeton, and had experience with population institutes and' in applied research. Treadway possessed skills in demography and research methodology, which the Department was especially interested in because someone with these skills was needed to develop a community research center. Griffin’s .application indicated no expertise in these areas. Griffin claims that the. position requirements were changed to correspond with Treadway’s qualifications because no mention of community research was made in the position advertisement. However, Lee testified that at the time the position was advertised it. was uncertain whether a community research position would be available.

In June 1978 a tenured faculty member in the Department resigned. Under University regulations, the position that was vacated reverted to temporary status. Griffin apparently claims that she should have been hired as a regular faculty member to fill what she believed was a regular position. The district court, however, held *1284that there was no indication that a regular position was available.5 Dist.Ct. Order at 13.

Subsequently, Griffin was notified that she would be demoted to part-time status for 1979-80. Lee testified that this was necessary in order to comply with a Department rule adopted in 1975 that restricted to three the number of years a person could serve under a temporary full-time contract.6

In August 1979 Griffin filed a sex discrimination charge with the EEOC. Because of the constraints imposed on her with respect to discussion of the charges and because an adverse decision would require her to grant tenure to Griffin, the Department Chairperson, Lee, decided at that time not to request the creation of a new regular position. Subsequent to the filing, Lee assigned a juvenile delinquency course scheduled for 1980-81, which Griffin had previously taught, to Richard Stiv-ers. Stivers had also previously taught the course. He had practical experience working . with juvenile gangs and in juvenile court and had studied and published in the area of deviancy. Another course taught by Griffin, social stratification, was can-celled for 1980-81 after enrollment figures were calculated. Griffin was not offered a contract for 1980-81 in the Sociology Department because of the three-year rule. She was offered a part-time job in the Department of Corrections. Further, because of the pending charges, Lee did not feel she could talk with Griffin without a witness present.

In February 1980 a proposed settlement agreement was agreed to and signed by Griffin, the EEOC and an attorney for the University. The agreement was made expressly subject to the approval of the University Board. In May 1980 the Board rejected the agreement.

Griffin applied for a temporary position in the Sociology Department for 1981-82, but was not hired. She was reinstated in 1981 on a half-time basis pursuant to a preliminary injunction.

In December 1980 the district court certified the following class:

> All women academic non-student temporary employees who were employed at Illinois State University at any time after March 24, 1972 and who had not left the employ of the University more than 180 days prior to the filing of the EEOC complaint on August 31, 1979; and all women who may .in the future be employed in academic non-student temporary positions or who may in the future apply for regular line positions but be denied such employment.

II.

Griffin argues that her individual Title VII claim was erroneously denied because the evidence showed that she was performing the same work as regular male faculty members. As the district court held, the dual classification system, under which employees are classified as either temporary or regular, is illegal only if women are not treated the same as men. Dist.Ct. Order at 20, 26. Further, the district court held that the failure to hire Griffin for a regular position was not discriminatory because better candidates were available for the positions for which she applied. Dist.Ct. Order at 10-13. Griffin does not now contest this finding. The district court also declined to review the University’s decisions to classify some positions as temporary and others as regular. Dist.Ct. Order at 13. We agree with the court below that under Title VII the University has not discriminated against Griffin.

Title VII forbids an employer:

> *1285(1) to fail or refuse to hire or to discharge any individual, or otherwise to discriminate against any individual with respect to his compensation, terms, conditions, or privileges of employment, because of such individual’s race, color, religion, sex, or national origin; or

> (2) to limit, segregate, or classify his employees or applicants for employment in any way which would deprive or tend to deprive any individual of employment opportunities or otherwise adversely affect his status as an employee, because of such individual's race, color, religion, sex, or national origin.

42 U.S.C. § 2000e-2(a).

In a Title VII claim, the plaintiff bears the burden of proving a prima facie case of sex discrimination. The plaintiff must establish: 1) that she is a member of a protected class; 2) that the employer was seeking applicants for a job and that she qualified for and applied for the job; 3) that, despite her qualifications, she was rejected; and 4) that after rejecting the plaintiff the position remained open and the employer continued to seek applicants with plaintiff’s qualifications. *See McDonnell Douglas Corp. v. Green,*411 U.S. 792, 802, 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973). Once the plaintiff has established a prima facie case, the defendant has the burden of offering a legitimate, nondiscriminatory reason for rejecting her. *Id.*After the employer articulates such a nondiscriminatory reason, the plaintiff must demonstrate that the employer’s reason was pretextual or discriminatory in its application. *Texas Department of Community Affairs v. Burdine,*450 U.S. 248, 253, 101 S.Ct. 1089, 1093, 67 L.Ed.2d 207 (1981); *McDonnell Douglas,*411 U.S. at 804, 93 S.Ct. at 1825.

Plaintiffs argue that defendants’ system of dual classification was illegal because women classified as temporary faculty performed the same work as men classified as regular faculty, but received fewer benefits and less pay. We agree with the district court that the dual classification system at ISU is not illegal, however, when women are not treated differently from similarly situated men. Further, the district court found that temporary and regular faculty have different responsibilities.7 Although the evidence was mixed, the district court’s finding is. not clearly erroneous.

Dr. Warren Furness, former Director of the Office of Academic Affairs for the American Council on Education, testified that separate categories of faculty — regular a,nd temporary — are commonly employed in higher education in the United States. Tr. Vol. 8, at 897, 905-08. Temporary contracts for faculty provide flexibility in the face of changing enrollments, course demands and needs of departments. Temporary contracts can be especially important when, as in the case of ISU, the institution does not have a large graduate program that can supply teaching assistants. Tr. Vol. 8, at 914-15; Tr. Vol. 11, at 1336-37. The proportion of tenured faculty to total faculty at ISU is about average for institutions of its size. Tr. Vol. 8, at 906-08. Hence we do not believe that the University violated Title VII by maintaining a dual classification system for faculty.

Plaintiffs also argue that jobs held by women were “miselassified.” We think that the district court properly declined to review the University’s decisions with respect to classification of positions as temporary or regular. The district court did find that there was no evidence that the determination of how positions were to be classified was influenced by considerations of gender. Dist.Ct. Order at 13. This finding is not clearly erroneous. Plaintiffs argue that the “evidence shows that fewer regular jobs were made available in areas in *1286which women had expertise.” Plaintiffs’ Brief at 20. The district court did find that women are more likely to possess expertise in areas in which fewer regular positions are available. Dist.Ct. Order at 33. The district court relied upon Defendant’s Exhibit 34, which shows for the departments in which men were hired in any given academic year, regular positions as an average percentage of all new full-time positions, and the comparable average percentage for women.8 While this exhibit does show that fewer *new*regular positions were available in the departments in which women tended to work, it does not show — counting existing as well as new positions — that there was a lower ratio of regular to temporary posts in the departments in which women tended to work. And it certainly does not show that the University discriminated against women in determining which positions to classify as regular.9 In fact, there was testimony that the phenomenon involving the ratio of regular to temporary jobs occurs because women tend to chose to teach in areas in which there is less demand for new tenured faculty. Tr. Vol. 12, at 42. In other words, women tend to place themselves in the sectors of the academic labor market that are crowded. Plaintiffs’ Exhibit C-196 shows a negative correlation between defendants’ variable for availability of positions in specific departments and female sex. But this evidence does not show, as plaintiffs claim, that the University chose to make more “men’s jobs” than “women’s jobs” regular positions. We therefore agree with the district court that plaintiffs have failed to establish that they were discriminated against because the University “misclassified” positions.

The plaintiffs also object to the finding that Griffin was not discriminated against within the class of temporary faculty on tthe basis of her compensation.10 We, however, accept this finding for the reasons articulated, *infra,*in connection with the class claims. Plaintiffs challenge particularly the finding that the University could legitimately pay Terrance Russell, a male temporary employee, more than like female employees. The district court relied upon *Horner v. Mary Institute,*613 F.2d 706, 714 (8th Cir.1980), which held that under some circumstances an employer may pay an employee a salary higher than others when such a salary is required to secure his services. Here Russell rejected the first offer extended to him and demanded a higher salary. Tr. Vol. 9, at 1089. Plaintiffs try to distinguish *Horner*on the grounds that there the employee in question had turned down the first offer ostensibly because he was earning more elsewhere. But we do not think that this fact was essential to the holding. Further, the Eighth Circuit in *Heymann v. Tetra Plas**1287*tics Corp.,*640 F.2d 115, 122 (8th Cir.1980), noted that “a sample consisting of one male employee ... carries little evidentiary value, particularly when there exists other more reliable data, *i.e.,*the average wage.” 11 The court noted that a “comparison to a specifically chosen employee should be scrutinized closely to determine its usefulness.” *Id.*True, as the plaintiffs point out, the court in *Heymann*stated that “[i]f there was evidence indicating that appellant had the most operator experience and performed the best work, then a comparison to average wage might not accurately reflect appellant’s worth and might be less reliable than a comparison to the wage of an individual possessing similar experience and skill.” *Id.*But in *Hey-mann,*as in this case, there was no evidence that the appellant “performed the best work.” 12

III.

With respect to the class action claims, the district court analyzed these claims under a disparate treatment theory. Dist.Ct. Order at 27-28. The plaintiffs argue that the court erred in failing to rule on their disparate impact theory. In this connection, plaintiffs generally may pursue Title VII claims under either a disparate treatment or a disparate impact analysis. In a disparate treatment class claim, the plaintiff’s case generally combines two elements: a) an individual disparate treatment claim offering to prove that the defendant intentionally discriminated against her because of her sex; and b) a claim that the employer’s adverse treatment of the plaintiff is part of a “pattern and practice” of discriminatory treatment toward the protected class. *See International Brotherhood of Teamsters v. United States,*431 U.S. 324, 335, 97 S.Ct. 1843, 1854, 52 L.Ed.2d 396 (1977). The plaintiff must prove by a preponderance of the evidence that a pattern or practice exists and that it was the defendant’s regular operating procedure. *Id.*at 336, 97 S.Ct. at 1854. To show a pattern or practice of' disparate treatment, the plaintiff may rely upon meaningful statistics to create an inference of classwide discrimination. *Id.*at 339, 97 S.Ct. at 1856. The defendant can then rebut this inference of discrimination by demonstrating that the plaintiff’s statistics are flawed. *Id.*at 339-40 n. 20, 97 S.Ct. at 1856 n. 20.

In a disparate impact class claim, the plaintiff must prove that a facially neutral employment practice in fact impacts more harshly upon a protected group than upon others. *See Dothard v. Rawlinson,*433 U.S. 321, 329, 97 S.Ct. 2720, 2726, 53 L.Ed.2d 786 (1977); *United States v. Town of Cicero,*786 F.2d 331, 333 (7th Cir.1986). Unlike a disparate treatment case, proof of discriminatory intent is not required. To prove their claim here, the plaintiffs must show that the policies and practices at issue have a substantially disproportionate impact on the protected class. *See Albemarle Paper Co. v. Moody,*422 U.S. 405, 425, 95 S.Ct. at 2362, 2375, 45 L.Ed.2d 280 (1975). Once this is purportedly shown, the defendant' may, of course, demonstrate that there are deficiencies in the plaintiffs’ statistical evidence. *See Dothard,*433 U.S. at 330, 97 S.Ct. at 2727. Assuming proof of disparate impact, the defendant has the burden to show that its practice is manifestly related to the job in question or significantly serves some important business purpose. *See Cicero,*786 F.2d at 333. If the defendant meets this burden, the plaintiff may show that the employer was using the practice in question as a mere pretext for discrimination or that there are alternatives with a lesser discriminatory impact that would also serve the employer’s legitimate interest. *See Dothard,*433 *1288U.S. at 329, 97 S.Ct. at 2726; *Cicero,*786 F.2d at 333.

We think that plaintiffs have not adequately articulated a disparate impact theory. Plaintiffs argue that the dual classification system itself impacts disparately on women. However, the dual classification system in and of itself has no impact on women or men as such. Women are affected only when they are placed in one of the two categories. On the facts of this case, however, women cannot be said to be affected merely because the two categories exist. Women may complain only when they are actually assigned to a regular or to a temporary position. Then any discrimination in assignment might be addressed either by a treatment or by an impact rationale.

With respect to the disparate impact theory as applied to the class, plaintiffs must identify a facially neutral criterion or practice that causes women to be assigned disproportionately to temporary positions.13 Plaintiffs, however, have not articulated any such criterion or described any such practice.14 They cannot argue that the mere fact that a decision must be made *1289allocating temporary and regular positions has a disparate impact on women.

*Heagney v. University of Washington,*642 F.2d 1157 (9th Cir.1981), is especially instructive. In *Heagney*the plaintiff alleged that the University’s practice of categorizing certain employees as “exempt” was a neutral employment practice that had a disproportionate impact upon the salaries of female employees. The court reasoned that the creation of jobs that are exempt from a state personnel law “cannot be equated with such well-defined objective employment practices as personnel tests or minimal physical requirements.” *Heagney,*642 F.2d at 1163. The court held that impact analysis was inappropriate because the plaintiff’s real argument was “that the lack of well-defined employment criteria allowed a pattern or practice of discrimination to exist.” *Id.*The case before us is similar. A dual classification system at a University does not involve well-defined, objective employment criteria. Plaintiffs are really arguing that the dual classification system allows a pattern or practice of discrimination to exist by permitting the defendant to deliberately classify women as temporary and men as regular.

Even if we held that the plaintiffs have alleged an adequate disparate impact claim, the defendants probably have shown that the dual classification system serves an important business purpose. *See supra*at 1285. The district court noted that “ISU attempts to use temporary faculty positions the way a university with a more developed graduate program would use graduate assistants. In this way the University attempts to maintain adequate staffing without having a department become 100% tenured____ When the tenure track level is kept below 100%, it allows the University to adjust for changes and [sic] enrollment.” Dist.Ct. Order at 14. Plaintiffs have not shown that recourse to the use of temporary positions is a mere pretext for discrimination.

Going on to the disparate treatment branch of the class claim, we think that this is what plaintiffs have really articulated. But the district court held that they had not been able to prove it, and we agree. The district court’s finding that the plaintiffs’ statistics did not establish a disparate treatment claim is not clearly erroneous. 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.” *International Brotherhood of Teamsters v. United States,*431 U.S. 324, 340, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396 (1977). Mark Twain said the same thing perhaps more memorably: “There are three kinds of lies —lies, damned lies and statistics.” *See Wilkins v. University of Houston,*654 F.2d 388, 395 n. 6 (5th Cir.1981). This court has noted that, “especially where statistical evidence is involved, great deference is due the district court’s determination of whether the resultant numbers are sufficiently probative of the ultimate fact in issue.”15*Soria v. Ozinga Brothers, Inc.,*704 F.2d 990, 995 n. 6 (7th Cir.1983).

The district court did not err in its preference for statistics that control for the *1290possession of a doctorate and for the effects of pre-1972 decisions.16 Although a doctorate is not a prerequisite for appointment to a regular position, it is required for tenure. Obviously the University may reasonably prefer to hire individuals with doctorates for its regular positions, which anticipate tenure. Thus the statistics relied upon should control for the possession of a doctorate. *See Wilkins v. University of Houston,*654 F.2d 388, 397 (5th Cir.1981), *vacated on other grounds,*459 U.S. 809, 103 S.Ct. 34, 74 L.Ed.2d 47 (1982).

Title VII was first applied to public employers in 1972. Prior to 1972, the University was free to discriminate in employment without violating Title VII. Any pre-1972 discrimination in hiring would statistically affect the percentage of males currently in regular positions.17 This circuit has held that “data on employment practices that occurred prior to the liability period do have some probative value, *though less than data focusing on practices after the liability cut-off date.” Coates v. Johnson & Johnson,*756 F.2d 524, 540 (7th Cir.1985) (emphasis supplied); *see also Movement for Opportunity & Equality v. General Motors Corp.,*622 F.2d 1235, 1245 (7th Cir.1980) (an approach emphasizing the day-to-day decisions made during the relevant period is better than an approach that includes pre-statute of limitations actions by virtue of cumulative statistics).

The district court did examine the statistics that incorporate the effect of pre-Title VII decisions. Dist.Ct. Order at 28. Although the district court erred in holding that pre-1972 data has no probative value, we think it was permissible under the controlling cases to prefer statistics that excluded the effect of pre-Title VII decisions. Although a court may not always exclude evidence that contains the effects of pre-Ti-tle VII actions, it is certainly not required to rely on such evidence when more carefully focused evidence shows no discrimination.

Plaintiffs’ Exhibit C-58, a regression analysis for category of appointment for 1979-80, does control for the effect both of the subject’s possession of a doctorate and for pre-1972 appointments. The independent variables in this regression are sex, possession of a doctorate, date of initial appointment, year highest degree was received, age and department. The regression coefficient for sex is — .15 (t-test18 =— *12913.506; P19 < .0005). The coefficient of multiple determination (R2)20 for the regression is .45.

The district court held that this regression would not support an inference of discrimination because the R221 was low and because there was a lack of individual examples of discrimination. The district court appears to have made an informed decision about the probative value of plaintiffs’ statistics — in particular Exhibit C-58. The district court did not clearly err in regarding the plaintiffs’ statistics as insufficiently reliable. *See Soria v. Ozinga Brothers, Inc.,*704 F.2d 990, 994-97 (7th Cir.1983).

There seem to be adequate reasons for rejecting plaintiffs’ statistics as supporting an inference of discrimination. The model itself reflected in Exhibit C-58 may be flawed, thus making any inference of discrimination unreliable. First, the model explains only 45% of the variation in the dependent variable.22*Wilkins*questioned, but did not decide, whether a model that explained only 52-53% of the variation was inherently unreliable. 654 F.2d at 405. The court in *McCleskey v. Zant,*580 F.Supp. 338, 351 (N.D.Ga.1984), *rev’d en banc McCleskey v. Kemp,*753 F.2d 877 (11th Cir.1985), decided that “the validity of the model depends upon a showing that it predicts the variations in the dependent variable to some substantial degree.” *Id.; see*580 F.Supp. at 361. Other courts have also recognized that the R2 value is appropriately considered in assessing statistical models. *See Sobel v. Yeshiva University,*566 F.Supp. 1166, 1181 (S.D.N.Y.1983); *EEOC v. International Business Machines Corporation,*583 F.Supp. 875, 899 (D.Md.1984). We will not attempt to establish a particular predictive capability as a *1292*sine qua non*for a model to pass muster. Obviously, however, the explanatory power of a model is a factor that may legitimately be considered by the district court in deciding whether the model may be relied upon.23

In addition, there are no individual examples of proven discrimination to buttress a class claim of disparate treatment. Several individuals testified for the plaintiffs, but none of them established that they had suffered discrimination. The testimony of these witnesses could only show that some women who were temporary employees performed duties similar to those of regular faculty. An extensive effort was made to show that the individual plaintiffs, Griffin and Waimon, were victims of discrimination. The district court, however, found against them and we do not reject this finding. The Fifth Circuit has noted that “where the employer is engaged in widespread discrimination against a class of employees there should be many individual examples of such discrimination.” *Wilkins,*654 F.2d at 402 n. 18. Certainly, examples of individual discrimination are not always required, but we think that the lack of such proof reinforces the doubt arising from the questions about validity of the statistical evidence.24 Here, in light of the deficiencies of plaintiffs’ statistical evidence, they failed to establish discriminatory motive and to prove that there was a “pattern and practice” of discrimination.

The district court also held that the plaintiffs failed to prove that they were discriminated against in rank or salary because the plaintiffs’ evidence did not analyze separately temporary and regular employees. The district court noted that “there is no evidence that lower salary and rank are not attributable to the riondiscriminatory assignment as temporary or regular.” Dist.Ct. Order at 34. The plaintiffs argue that their Exhibit C-178, which compares the salaries of male and female temporary employees, was overlooked by the district court. But in any event Exhibit C-178 does not prove salary discrimination. It merely shows average salaries for full-time temporary faculty and does not account for the variables that clearly may affect salary, such as experience and degree held. Further, Defendants’ Exhibit 49, which accounts for factors such as these, provides no inference of discrimination. Therefore, the district court’s findings are not clearly erroneous.

IV.

Both Griffin and Waimon alleged under 42 U.S.C. § 1983 that they were deprived of property without due process of law. The district court denied both these claims. The plaintiffs now appeal Waimon’s section 1983 claim.25

*1293Waimon argues that a 1976 agreement with the University granted her a property interest in full-time continued employment. She claims that she was deprived of this property interest without due process when she was hired for only a part-time position for 1980-81.

Waimon was first employed by the University in 1962. She worked for eighteen years in the Department of Education and Psychology; eight of those years she was employed full-time. She was at all times employed as a temporary employee. Waimon testified that each of her one-year contracts was separate and without any additional promise of employment. In fact, she does not argue that these contracts (which she did not introduce into evidence) in any respect created a property interest. In 1973 Waimon enrolled in a doctoral program; in 1976 she had completed the course work for her Ph.D., but not her dissertation.

In 1976 Waimon was informed that she would not be hired as a regular faculty member even with a Ph.D. She agreed to have her rank changed from assistant professor to faculty associate. She continued to work full-time in temporary positions26 until 1980-81. In 1979 the University had drafted a rule that permitted temporary employees to be employed full time for no longer than six years. This six year rule became effective in 1980-81. Because of it Waimon was offered only a part-time position for 1980-81.

Waimon argued that she accepted the demotion in 1976 to faculty associate only because of a clear understanding that she could continue to work full-time indefinitely. The district court held that she had failed to prove such an agreement. This finding is not clearly erroneous.

The written policy of the University provides that an interest in tenure can be acquired only by express contract. Waimon does not even argue that her yearly employment contracts granted her an interest in continued employment. Further, a letter from the Department Chairperson, dated July 19, 1976, explained the reasons for her “demotion” to faculty associate.

> Because of the circumstances listed above we cannot at any time offer you full-time employment [as an assistant professor] because it would eventually place us in the position of denying you further employment because we could not recommend tenure____ If you become a faculty associate, and it is mutually desirable, full-time employment might be possible without the threat of a negative tenure decision since faculty associates are not on a tenure track.

The letter does not promise continued employment. Instead it suggests that continued employment “might be possible”- with the rank of faculty associate, whereas it would be impossible with the rank of assistant professor. To the extent that Waimon argues that an oral agreement more favorable to her was reached in 1976, there was sufficient evidence before the district court to finS .to the contrary.27

V.

Plaintiff Griffin contends that ISU’s refusal to renew her contract in 1980-81 and its decision not to rehire her in the Sociology Department for 1981-82 were both retaliatory actions. In this respect Title YII provides:

> It shall be an unlawful employment practice for an employer to discriminate against any of his employees ... because he has opposed any practice made an unlawful employment practice by this subchapter, or because he has made a *1294charge, testified, assisted, or participated in any manner in an investigation, proceeding, or hearing under this subchap-ter.

42 U.S.C. § 2000e-3(a). In a Title VII claim for retaliation, “the plaintiff must establish (1) statutorily protected expression, (2) an adverse employment action, and (3) a causal link between the protected expression and the adverse action.” *Smalley v. City of Eatonville,*640 F.2d 765, 769 (5th Cir.1981); *see Klein v. Trustees of Indiana University,*766 F.2d 275, 280 (7th Cir.1985). Once the plaintiff establishes her prima facie case, the burden shifts (as in the McDonnell-Douglas test) to the defendant to articulate a legitimate, nondiscriminatory reason for its actions. *See Texas Department of Community Affairs v. Burdine,*450 U.S. 248, 253, 101 S.Ct. 1089, 1093, 67 L.Ed.2d 207 (1981); *Payne v. McLemore’s Wholesale & Retail Stores,*654 F.2d 1130, 1141 (5th Cir.1981), *cert. denied,*455 U.S. 1000, 102 S.Ct. 1630, 71 L.Ed.2d 866 (1982). After the defendant has an opportunity to rebut the prima facie case, the plaintiff has a chance to show that the defendant’s reason is pretextual. *See Payne,*654 F.2d at 1142;

Plaintiff Griffiijj claims that the failure to. hire her in 1980-81 was a retaliatory response to her filing a claim with the EEOC. The district court, we think correctly, held that Griffin was not refused a contract for retaliatory reasons. Assuming Griffin established a prima facie case of retaliation, she failed to show that ISU’s proffered explanation was pretextual. The district court’s finding that the Sociology Department’s three-year rule28 was a legitimate, nondiscriminatory reason for its failure to rehire Griffin in 1980-81 and 1981-82 is not clearly erroneous.

By the 1980-81 year, plaintiff Griffin had taught for four years as a temporary faculty member.29 The Sociology Department’s three-year rule precluded ISU from offering Griffin continued employment.30 The plaintiff does not argue that the rule was applied to her but not to other employees or to women but not to men. She does contend that she could have been hired as a part-time temporary or a full-time regular faculty in the Sociology Department without violating the rule. She does not argue, however, that such positions were available or that she applied for them. Thus, the district court correctly held that the defendant had presented a legitimate, non-discriminatory explanation for its actions.

Plaintiff Griffin also argues that her salary was reduced in retaliation for her filing of a discrimination claim with the EEOC. The district court denied her claim on the theory that the change in her salary was a result of her shift between departments and was not a matter of retaliation for filing the EEOC charge. Griffin earned $1050.00 per month when employed part-time in the Department of Corrections in 1980-81 and $860.00 per month when employed part-time in the Sociology Department in 1981-82 pursuant to a preliminary injunction. Plaintiff’s Exhibit G-2. Salaries for assistant professors' in the Department of Corrections were generally higher than salaries for assistant professors in the Sociology Department. Dist.Ct. Order at 24-25; Plaintiff’s Exhibit W-22, pp. 88, 106. As a result, when plaintiff Griffin transferred from Corrections to So*1295ciology, her salary decreased in line with the compensation of other part-time assistant professors in the Sociology Department.31 Accordingly, the disposition below of the claim for a retaliatory decrease in salary must be sustained.

In addition, plaintiffs argue that certain actions taken against the class were retaliatory. They cite in particular the adoption of a University-wide three-year rule and a salary freeze. In 1982 the University adopted a rule similar to the one already in effect in the Sociology Department. Under the rule, one could be employed as full-time temporary faculty for only three years. Plaintiffs argue that the district court was required to rule in their favor in this matter because the Provost of the University “admitted that (1) he promulgated the rule; (2) he was aware of this suit at that time; (3) he knew that a class had been certified; and (4) the rule reduced the time persons could serve as full-time temporary faculty from six to three years.” Plaintiffs’ Brief at 42. Plaintiffs do not present any argument or authorities to demonstrate that these bare showings are sufficient to establish a causal link between the protected expression and the adverse action. Therefore the plaintiffs have not established a prima facie case of retaliation.

Further, the plaintiffs contend that the defendant in retaliation for the lawsuit limited the salary increase for the temporary class in 1981-82 and froze salaries for the temporary faculty in 1982-83. Dr. Boothe, Provost at the University, testified that funding for temporary faculty salaries increased by four percent in 1981-82, while funding for regular faculty increased by eight percent. Tr. Vol. 9, at 973-74. In 1982-83 there was no increase in the pool of money available for temporary contracts. Tr. Vol. 9, at 981. Funding for regular faculty, however, did increase.32 Tr. Vol. 9, at 981-82. Dr. Boothe testified that at this time the University was experiencing severe financial difficulties and that these decisions were dictated by tight budgets. Tr. Vol. 9, at 973, 975, 981. We do not believe that the plaintiffs in these matters have shown adverse employment actions and a causal link between their protected expression and those adverse actions. Plaintiffs, for example, do not direct us to any evidence that temporary faculty salaries were usually increased in line with regular faculty salary increases. Further, plaintiffs present no evidence, other than the timing of the decisions, to indicate that these changes were retaliatory. The evidence supports the University’s contention that it was experiencing financial difficulty and the plaintiffs have not shown this justification to be a pretext.

We can appreciate that widespread use of temporary positions for university teachers creates frustration and hardship. More of the same no doubt results from interruptions in employment and the impacts of budget deficiencies. All these factors and others played significant parts in the case before us. But we cannot say that any of the facts clearly establish any of the plaintiffs’ claims of discrimination or retaliation. Therefore, we believe that the district court correctly found for defendants on all claims and we affirm.

AFFIRMED.

1

. The defendants are the Board of Regents of Regency Universities, a public corporation, and various individuals acting individually and as agents for the Board. The defendants will be collectively referred to as the "University" or “ISU.”

2

. The section 1985 claims were later dropped.

3

. During 1975 the Sociology Department adopted a rule under which one could be employed as a full-time temporary employee for only three years. In 1982 the University adopted a similar rule for the entire University.

4

. The history of plaintiff Margaret Waimon’s relationship with the University is covered in the discussion of her section 1983 claim, the only individual claim that Waimon appeals.

5

. There was evidence that the Department Chairperson could have requested an additional regular position. But after the needs of the Department were assessed, the Department Chairperson, with the agreement of the tenured faculty members, decided not to ask for the creation of a regular position.

6

. Griffin was employed full-time in 1978-79 because Lee had exercised her option of allowing a fourth year of full-time employment under temporary contract because of a lack of personnel or for other reasons.

7

. This finding is not in conflict with the fact that Griffin performed tasks similar to those performed by regular faculty members. Dist.Ct. Order at 11. A teaching position, whether regular or temporary, involves teaching courses in the regular curriculum. Similarity of tasks, however, does not necessarily import similarity of responsibilities, educational background and experience. As noted by the district court, regular employees have more education, skills and experience and heavier responsibilities than temporary employees. Dist.Ct. Order at 20.

8

. For example, in 1978-80, the average female appointed to a full-time position at ISU entered a department in which 12! 1% of the new positions (in full time equivalent terms) were regular positions. For males this number is 15.5%. In 1980-81 the figure for females is 9.6% and for males 16%. In 1981-82 the figure for females is 17.6% and the figure for males is 21.1%.

9

. Plaintiffs argue that the Sociology Department’s staffing plan barred Griffin from being classified as regular after the resignation of a tenured professor in that Department. But a resignation of a regular employee causes his or her position to revert to a temporary position. Plaintiffs do not challenge this rule. Therefore, plaintiffs’ claim must be that the Department’s failure to create a regular position (for which Griffin could apply) was discriminatory. There is no evidence that the gender of potential applicants for a regular position influenced this procedure. Plaintiffs also argue that Griffin’s job continued to be classified as temporary even after the subjects she taught were identified as long-term needs of the Department. We do not think that this determination is sufficient to establish a prima facie case of discrimination. And defendants point out, "the evidence failed to show that her qualifications were unique and that none of the other faculty of the department were capable of meeting the long term needs of the department.” Defendants’ Brief at 39.

10

. Plaintiffs claim that she was discriminated against because she was not paid as much as regular faculty must fail. The dual classification system is not illegal and temporary employees may be paid less than regular employees. *See Wilkins v. Univ. of Houston,*654 F.2d 388, 405 (5th Cir.1981), *vacated on other grounds,*459 U.S. 809, 103 S.Ct. 34, 74 L.Ed.2d 47 (1982).

11

. Griffin was paid $1400 per month during 1977-78, the relevant time period, while the average wage for women was $1360 and the average wage for men $1313. Defendants’ Ex. Lee 60.

12

. It is obvious that Griffin had more seniority. But seniority alone does not entitle her to a higher wage. Plaintiffs do not argue that she had more teaching experience or that she did the best work.

13

. We express no opinion on whether plaintiffs could identify a combination of criteria or practices, the combined effect of which would cause an adverse impact; plaintiffs have not identified any such combination. *See Pouncy v. Prudential Ins. Co.,*668 F.2d 795, 800 (5th Cir.1982); *Griffin v. Carlin,*755 F.2d 1516, 1525 (11th Cir.1985).

14

. Further, a disparate impact analysis may not be appropriate for faculty hiring decisions because such decisions necessarily involve many subjective factors. Disparate impact claims generally involve facially neutral criteria, such as minimum height or weight requirements or a minimum score on an objective test. *See Regner v. City of Chicago,*789 F.2d 534, 538 (7th Cir.1986). We have previously noted, without deciding the issue, that a "disparate impact claim is more problematic when subjective factors are present in the decisionmaking process.” *Regner,*789 F.2d at 538; *see Moore v. Hughes Helicopters,*708 F.2d 475, 481 (9th Cir.1983); *Robinson v. Polaroid Corp.,*732 F.2d 1010, 1015 (1st Cir.1984). The circuits are split on the issue whether'a disparate impact analysis may be applied to subjective employee selection procedures. The Fourth, Eighth and Ninth Circuits will apply impact analysis only to specified objective employee selection practices. *See EEOC v. Fed. Reserve Bank,*698 F.2d 633, 638-39 (4th Cir.1983), *rev’d Cooper v. Fed. Reserve Bank,*467 U.S. 867, 104 S.Ct. 2794, 81 L.Ed.2d 718 (1984); *Harris v. Ford Motor Co.,*651 F.2d 609, 611 (8th Cir.1981); *Atonio v. Wards Cove Packing Co.,*768 F.2d 1120, 1131-33 (9th Cir. 1985); *Heagney v. Univ. of Washington,*642 F.2d 1157, 1163 (9th Cir.1981). The Sixth, Tenth, Eleventh and D.C. Circuits have allowed a disparate impact claim to proceed even with respect to a subjective employment practice. *See Rowe v. Cleveland Pneumatic Co., Numerical Control, Inc.,*690 F.2d 88, 94-95 (6th Cir.1982); *Hawkins v. Bounds,*752 F.2d 500, 503 (10th Cir.1985); *Bauer v. Bailar,*647 F.2d 1037, 1042-43 (10th Cir.1981); *Griffin v. Carlin,*755 F.2d 1516, 1522-25 (11th Cir.1985); *Segar v. Smith,*738 F.2d 1249, 1288 n. 34 (D.C.Cir.1984), *cert. denied sub nom. Meese v. Segar,*— U.S. —, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985). The Fifth Circuit has recently examined a subjective promotional system under a disparate impact analysis. *See Page v. U.S. Indus.,*726 F.2d 1038, 1045-46 (5th Cir.1984). The court in *Page,*however, failed to reconcile its holding with other Fifth Circuit cases that held that impact analysis should not be applied to subjective practices. *See Vuyanich v. Republic Nat’l Bank,*723 F.2d 1195, 1202 (5th Cir.), *cert. denied,*— U.S. —, 105 S.Ct. 567, 83 L.Ed.2d 507 (1984); *Carroll v. Sears, Roebuck & Co.,*708 F.2d 183, 188-89 (5th Cir.1983); *Pegues v. Mississippi State Employment Serv.,*699 F.2d 760, 765 (5th Cir.), *cert. denied,*464 U.S. 991, 104 S.Ct. 482, 78 L.Ed.2d 679 (1983); *Pouncy v. Prudential Ins. Co.,*668 F.2d 795, 800-01 (5th Cir.1982).

The Ninth Circuit has explained the rationale behind requiring challenges to subjective employment decisions to proceed under a disparate treatment analysis:

> Presumably, therefore, the disparate impact model was created to challenge those specific, facially-neutral practices that result in a discriminatory impact and that by their nature make intentional discrimination difficult or impossible to prove. Were the facial-neutrality threshold to disappear or be ignored, the distinction between disparate impact and disparate treatment would diminish and intent would become a largely discarded element. Rather than becoming an irrelevant factor as envisioned, race (or sex, etc.) could then become an overriding factor in employment decisions. Employers with work forces disproportionate to the minority representation in the labor force could then face the choice of either hiring by quota or defending their selection procedures against Title VII attack. We do not find such a result has been mandated by Congress or through Supreme Court interpretation of Title VII. Therefore, practices and policies such as a lack of well-defined criteria, subjective decision making, hiring from different sources or channels, word-of-*1289mouth recruitment, and segregated housing and messing, which are not facially neutral, lend themselves far better to scrutiny for intentional discrimination.

*Atonio v. Wards Cove Packing Co.,*768 F.2d 1120, 1133 (9th Cir.1985).

15

. The Fifth Circuit, recognizing that regression analysis ‘‘is subject to misuse and thus must be employed with great care," has observed:

> 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.

*Wilkins v. Univ. of Houston,*654 F.2d 388, 403 (5th Cir.1981), *vacated on other grounds,*459 U.S. 809, 103 S.Ct. 34, 74 L.Ed.2d 47 (1982). The district court in this case heard expert testimony from both sides and thus was able to make an informed decision as to the probative value of the statistical evidence. We will reverse the district court's conclusions on the value of this evidence only if they are clearly erroneous.

16

. Multiple regression analysis is likely to be inappropriate unless three major assumptions are satisfied:

> (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, on the "bell curve” generally characteristic of the distribution of the sum of independent random effects.

Fisher, *Multiple Regression in Legal Proceedings,*80 Colum.L.Rev. 702, 708 (1980). The first assumption will not be satisfied unless the model includes all of the major variables likely to have an effect on the dependent variable.

17

. Plaintiffs argue that we should consider statistics that include pre-1972 hiring decisions because the Supreme Court, in *International Brotherhood of Teamsters v. United States,*431 U.S. 324, 341, 97 S.Ct. 1843, 1857, 52 L.Ed.2d 396 (1977), considered statistics that did not segregate decisions made prior to the effective date of Title VII. The facts in *Teamsters,*however, were considerably different from those before us. In *Teamsters*both of the lower courts had found substantial evidence of post Title VII discrimination, including the testimony of many individuals about their personal experiences. The Supreme Court found that even after Title VII became effective, the company continued to hire whites almost exclusively. Further, in *Teamsters*the statistical evidence consisted of percentages of minority workers; a sophisticated regression that analyzed employees’ qualifications was not at issue.

18

. The t-statistic indicates standard deviations.

The “standard deviation” is a number that quantifies the degree to which disparities spread out above and below the mean of distribution, thus describing the probability that chance is responsible for any difference between an expected outcome and the observed outcome in a sample consisting of two groups (a binomial distribution). The greater the number of standard deviations, the less likely it is that chance is the cause of any difference between the expected and observed results. The Supreme Court noted in *Castaneda v. Partida,*430 U.S. 482, 97 S.Ct. 1272, 51 *1291L.Ed.2d 498 (1977), that under a "two-tail” test of statistical significance, “[a]s a general rule for ... large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that the [disparity] was random would be suspect to a social scientist.” *Id.*at 497 n. 17, 97 S.Ct. at 1281 n. 17. The general rule should be applied with caution, however, and its particular applicability may vary from case to case. *See*D. Baldus & J. Cole, Statistical Proof of Discrimination § 9.03, at 293-97 (1980), 108-12 (Supp.1984); *see also American National Bank,*652 F.2d at 1190-93.

*Coates*v. *Johnson & Johnson,*756 F.2d 524, 536 n. 11 (7th Cir.1985).

19

. In addition to describing statistical significance in terms of levels of standard deviation, statistical significance also may be expressed as a probability value (P) on a continuous or relative scale ranging from 0 to 1.0. The level of statistical significance rises as the value of the (P) level declines____ A (P) value below .05 is generally considered to be statistically significant, *i.e.,*when there is less than a 5% probability that the disparity was due to chance. For large samples, statistical significance at a level in the range below 0.05 or 0.01 is “essentially equivalent” to significance at the 2 or 3 standard deviation level.

*Coates v. Johnson & Johnson,*756 F.2d 524, 537 n. 13 (7th Cir.1985).

20

. The coefficient of multiple determination measures the portion of the variance in the dependent variable that is accounted for by the independent variables. A perfectly predictive model would have an R2 = 1. An R2 of zero would indicate that movements in the independent variable do not explain movements in the dependent variable at all. The R2 here indicates that the model explains forty-five percent of the hiring decision.

21

. The plaintiffs make much of the fact that the district court erroneously referred to the R2 statistic as a correlation coefficient. Clearly, however, the district court was not confused about what the R2 measures, for it gave the correct definition of this term in its opinion.

22

. As the district court noted, this relatively low level of predictability may occur because the independent variables are related. Dist.Ct. Order at 33. For example, there was evidence that male faculty members were more likely to possess a doctorate when hired. The closer the link between sex and possession of a doctorate, the less effective multiple regression will be in distinguishing between the effects of these two variables. Under these circumstances the sex coefficient has diminished probative value. *See Fisher, supra*note 16, at 713.

Further, the district court thought that plaintiffs’ model should have accounted for the availability of regular positions in the department of hire. Dist.Ct. Order at 33. Plaintiffs argue that they need not account for availability because their case involves only the classification of jobs already held by women rather than a hiring claim. We have previously discussed this mis-classification claim. *See supra*at 1285-86.

23

. The plaintiffs argue that use of R2 leads to gross errors. We agree that the R2 alone cannot determine the validity of a model. We recognize that sex discrimination may be present even though R2 is low. However, the explanatory power of a regression is clearly relevant to the validity of the model. Further, we are reluctant to rely on a single regression when other regressions could have been presented to aid our determination. We would have liked to examine regressions that corrected for the problems we have noted. Further, a regression similar to the one in Exhibit C-58, but omitting sex as an independent variable, would have permitted us to determine how much of the variation around the dependent variable was accounted for by sex. The difference between the R2 of the model with sex and the R2 of the model without sex would indicate *how much*more of the variation of the dependent variable was explained by the inclusion of sex in the model. *Wilkins,*654 F.2d at 403-04.

24

. In *Teamsters,*the court noted that the statistical demonstration was bolstered by evidence of more than forty specific instances of discrimination. 431 U.S. at 338, 97 S.Ct. at 1855. In *McCleskey*the court stated that of the six appellate decisions relying upon regression analysis that it had been able to locate, the party relying on that analysis prevailed in two cases and "in both cases their showings were supported by substantial anecdotal evidence.” 580 F.Supp. at 350.

Plaintiffs here point out that defendants objected to plaintiffs class witnesses at trial. Plaintiffs, however, were allowed to present the testimony of these class members.

25

. Plaintiffs do not appeal Griffin’s section 1983 claim. Further, they do not challenge the pretrial dismissal of the elements of Yiaimon’s section 1983 claim relating to compensation.

26

. Until 1978-79 Waimon was a faculty associate. In 1978-79 she was given the title of instructor. In 1979-80 she was an assistant professor.

27

. Plaintiffs argue that Waimon was employed full-time for an eighth year in 1979-80, thus violating the University’s Constitution, which limits full-time temporary employment to seven years, and thus indicating that there must have been an agreement for continued employment. We do not think that this extended employment proves such an agreement, especially in light of the weakness of Waimon’s other evidence.

28

. During 1975-76, the Sociology Department adopted a rule under which one could only be employed by the Department as a full-time temporary employee for three years. Tr. Vol. 9, at 990-94. This rule was adopted to prevent claims of de facto tenure. The three year rule was effective only for full-time temporary employees.

29

. Under the three-year rule, employment could be extended for an additional year if requested by the chair. Tr. Vol. 9, at 990-91. This option was exercised in favor of Griffin in the 1979-80 year.

30

. Plaintiff Griffin argues that according to *Flowers v. Crouch-Walker Corp.,*552 F.2d 1277 (7th Cir.1977), she could expect continued employment so long as she performed her job satisfactorily. However, *Flowers*is inapplicable because Griffin was employed under a one-year contract. She was not dismissed during the course of that contract. Rather, she was simply not offered a new contract.

31

. Griffin argues that the decrease in her salary was retaliatory because "Defendant did not ask where she wanted to work or at what salary.” Plaintiffs' Brief at 42. The preliminary injunction required that she be reinstated in "an area of her specialty.” Clearly sociology was an area of her specialty. We can draw no inference that the University acted in retaliation when it reinstated her in the very department in which she had spent most of her academic career. Further, we think it obvious that defendant was not required to ask Griffin what salary she would like to receive. The defendant was required only to pay her a salary comparable to those of similarly situated employees.

32

. But ISU gave regular employees only one-half of the salary increase they received the previous year. This increase was granted only in the spring because there was no money available for salary increases during the fall. Tr. Vol. 9, at 981-82.