62 F.3d 659
68 Fair Empl.Prac.Cas. (BNA) 1062, 64 USLW 2192,102 Ed. Law Rep. 469
Ted J. SMITH, III;  Guy J. DeGenaro;  Frank Belloni;  GeorgeW. Rimler;  Allan Rosenbaum, on behalf ofthemselves and all others similarlysituated, Plaintiffs-Appellants,v.VIRGINIA COMMONWEALTH UNIVERSITY, Defendant-Appellee.American Association of University Professors, Amicus Curiae.
No. 94-2187.
United States Court of Appeals,Fourth Circuit.
Argued April 5, 1995.Decided Aug. 24, 1995.Rehearing En Banc Granted;  Opinion Vacated Oct. 13, 1995.

ARGUED:  Bradley Brent Cavedo, Shuford, Rubin & Gibney, P.C., Richmond, VA, for appellants.  Guy Winston Horsley, Jr., Sr. Asst. Atty. Gen., Office of the Atty. Gen., Richmond, VA, for appellee.  ON BRIEF:  Robert A. Dybing, Shuford, Rubin & Gibney, P.C., Richmond, VA;  Michael P. McDonald, Leonard A. Leo, Center for Individual Rights, Washington, DC, for appellants.  James S. Gilmore, III, Atty. Gen. of VA, Catherine C. Hammond, Deputy Atty. Gen., Neil A.G. McPhie, Sr. Asst. Atty. Gen., Office of the Atty. Gen., Richmond, VA;  David L. Ross, Sp. Asst. Atty. Gen., Jean F. Reed, Sp. Asst. Atty. Gen., Office of the Gen. Counsel, Virginia Commonwealth University, Richmond, VA, for appellee.  Darrel Long Tillar, Richmond, VA;  Michael A. Olivas, Gen. Counsel, Ann H. Franke, Helen D. Irvin, American Ass'n of University Professors, Washington, DC, for amicus curiae.
Before WIDENER and MICHAEL, Circuit Judges, and CHAPMAN, Senior Circuit Judge.
Reversed by published opinion.  Senior Judge CHAPMAN wrote the opinion, in which Judge WIDENER joined.  Judge MICHAEL wrote a dissenting opinion.
OPINION
CHAPMAN, Senior Circuit Judge:


1
Plaintiffs-appellants are five male professors at Virginia Commonwealth University ("VCU") who filed claims under the Equal Pay Act and Title VII of the Civil Rights Act of 1964 in the Eastern District of Virginia.  The appellants objected to pay raises that VCU gave to its female faculty in response to a salary equity study conducted at the university.  Both parties moved for summary judgment.  The district court denied the appellants' motion and granted VCU's motion.  The district court also denied the appellants' motion to alter or amend the judgment.  Because we find that there remains a genuine issue as to material fact, we reverse the district court's grant of summary judgment.

I.

2
VCU is a state institution of higher learning located in Richmond, Virginia.  In the spring of 1988, several groups called on VCU to evaluate its pay structure to determine whether female professors were victims of sex based discrimination in pay.  VCU appointed a Salary Equity Study Committee to investigate, and a Salary Equity Advisory Committee to review the findings of the Study Committee.


3
The Study Committee chose to employ a multiple regression analysis, which compares many characteristics within a particular set of data and enables the determination of how one set of factors is related to another, single factor.  The VCU study controlled for such differences as doctoral degree, academic rank, tenure status, number of years of VCU experience, and number of years of prior academic experience.  Any difference in salary after controlling for these factors was attributed to sex.  The study included only tenured or tenure-eligible instructional faculty at the rank of assistant professor or higher.  The first regression study in the summer of 1989 showed a $1,354 difference in salaries not attributable to permissible factors.  A second analysis run in the summer of 1991 showed a difference of $1,982.


4
Until the study, the compensation system at VCU had been based on merit alone.  A professor was awarded a pay increase after a detailed annual review, provided funds were available.  Merit factors considered in the annual review were teaching load, teaching quality, quantity and quality of publications, and service to the community (the "performance factors").  The department chair recommended a pay raise to the dean, and the dean awarded a pay raise, subject to approval from VCU's Board of Visitors.  Salaries vary widely from department to department.


5
The multiple regression analysis did not include the performance factors because VCU contended that these would be too difficult to quantify.  VCU maintained that indirect performance variables were already included in the study in the form of academic rank, status, and experience.  The study also did not take into account a faculty member's prior service as an administrator.  Administrators are paid higher wages, and faculty members retain this increase in salary when they return to teaching, thus inflating faculty salaries.  Most of the faculty that had previously served as administrators were men.  Furthermore, the study did not include career interruptions when measuring academic experience.  Finally, the Study Committee worked under the assumption that there was no reason to suspect that female faculty members were less productive on the average than male faculty members.


6
After the study was completed, VCU approved more than $440,000 in funding to increase female faculty salaries.  These funds were outside of the normal salary process.  The pay increases were implemented by the Salary Equity Implementation Committee made up of three women.  Female faculty members had to apply for a pay increase by submitting a curriculum vitae or a narrative statement and a vitae.  Of the 201 women eligible for salary review, 172 requested it.  All women who requested a review received an increase in salary.


7
After the district court's denial of the plaintiff's motion for summary judgment and the grant of VCU's motion, the plaintiffs filed a motion to alter or amend the judgment.  In this motion, the plaintiffs offered the affidavit of expert witness Dr. Fred McChesney.  McChesney contended that the performance factors VCU claimed it could not quantify had in fact been included in several studies of various faculty systems, and that the inclusion of the performance factors and other variables was necessary to ensure accurate statistical data.  McChesney also contended that there was data to dispute VCU's assumption that women were as equally productive as men.  In response, VCU's expert witness, Dr. Rebecca Klemm, stated that she ran several various statistical studies with VCU's raw data and found a salary gap to be consistent with that found in the study.  McChesney never conducted a pay study himself.  The district court denied the motion to alter or amend the judgment.

II.

8
We review for the district court's grant of summary judgment de novo.  Tuck v. Henkel Corp., 973 F.2d 371, 374 (4th Cir.1992).  The evidence must be viewed in the light most favorable to the nonmoving party.   Ross v. Communications Satellite Corp., 759 F.2d 355, 364 (4th Cir.1985).


9
Title VII of the Civil Rights Act prohibits employers from, among other things, discriminating on the basis of sex with respect to compensation.  42 U.S.C. Sec. 2000e-2(a)(1) (1992).  On its face, an affirmative action plan that provides for pay raises to only female faculty members violates this provision, but affirmative action plans are allowed in some instances.  A court may remedy a violation of Sec. 2000e-2(a)(1) by instituting an appropriate affirmative action plan.  42 U.S.C Sec. 2000e-5(g)(1).  The Supreme Court has determined that in certain circumstances, an employer may voluntarily establish an affirmative action plan without violating Title VII.   United Steelworkers v. Weber, 443 U.S. 193, 197, 99 S.Ct. 2721, 2724, 61 L.Ed.2d 480 (1979).


10
According to  Weber, an employer's voluntary affirmative action plan is not a violation of Title VII if (1) its purpose is similar to that of Title VII, namely to "break down old patterns" of discrimination;  (2) the plan does not "unnecessarily trammel" the rights of those outside the group that it is designed to protect;  and (3) it is designed to eliminate a manifest racial or sexual imbalance.   Id. at 208, 99 S.Ct. at 2729-30;   Johnson v. Transportation Agency, 480 U.S. 616, 628-31, 107 S.Ct. 1442, 1450-51, 94 L.Ed.2d 615 (1987).  The burden of establishing that an employer's voluntary affirmative action plan violates Title VII is on the plaintiff:


11
Once a plaintiff establishes a prima facie case that race or sex has been taken into account in an employer's employment decision, the burden shifts to the employer to articulate a nondiscriminatory rationale for its decision.  The existence of an affirmative action plan provides such a rationale.  If such a plan is articulated as the basis for the employer's decision, the burden shifts to the plaintiff to prove that the employer's justification is pretextual and the plan is invalid.


12
Johnson, 480 U.S. at 626, 107 S.Ct. at 1449.


13
A plan is invalid if it does not meet the  Weber  requirements as set forth above.  The appellants assert that there is a material question of fact as to whether there was a manifest imbalance in pay between male and female faculty members, and as to whether the plan instituted by VCU unnecessarily trammelled the rights of male faculty;  therefore, the appellants contend, the motion for summary judgment should not have been granted.  We agree that there is a material question of fact as to whether there was a manifest imbalance in compensation between the male and female faculty.  We do not reach the question of whether the plan unnecessarily trammelled the rights of the male faculty.


14
VCU relied on its multiple regression analysis in determining that there was a manifest imbalance and in instituting its affirmative action pay raises.  Therefore, the validity of the plan stands or falls on the soundness and accuracy of the regression study.  The appellants contend that the multiple regression study was flawed because of the inclusion of an inflated pool of faculty members, and the failure to account for significant variables that could have a bearing on wage differences between the male and female faculty members.


15
Statistics are often used to determine whether a manifest imbalance exists.  See Johnson, 480 U.S. at 631-2, 107 S.Ct. at 1451-52.   In  Johnson, the court stressed that valid statistical analyses must include logical comparisons.  The Court stated:


16
in determining whether an imbalance exists that would justify taking sex into account, a comparison of the percentage of minorities or women in the employer's work force with the percentage in the area labor market or general population is appropriate in analyzing jobs that require no special expertise....  Where a job requires special training, however, the comparison should be with those in the labor force who possess the relevant qualifications.


17
480 U.S. at 632, 107 S.Ct. at 1452.   Because the instant case does not involve a simple question of whether women are underrepresented as compared to the available labor pool in a particular job, a more sophisticated statistical analysis was necessary to determine if female faculty members were paid less than male faculty members based solely on their sex.  It is still necessary, however, to avoid illogical comparisons.


18
The appellants contend that the study used illogical comparisons by comparing an inflated pool of faculty members.  The study included male faculty members who had returned from higher paying positions in the VCU administration, but it did not account for this salary differential.*  An inflated pool can undermine the validity of a statistical study to determine imbalances.   Johnson, 480 U.S. at 636, 107 S.Ct. at 1454;  see E.E.O.C. v. Sears, Roebuck & Co., 839 F.2d 302, 322-24 (7th Cir.1988).  Appellants' expert, Dr. McChesney, stated that failure to include a faculty member's status as a former administrator could easily have caused a salary differential that was not attributable to sex.  Dr. Henry, the man who designed VCU's regression study, stated that inclusion of this factor in the study would have had an effect on the study, and that if he had had the information, he would have included it.  The appellants clearly produced evidence to support a finding that the pool was inflated.


19
More importantly, VCU did not include major factors that are legitimate reasons for wage disparity in its multiple regression analysis.  Although failure to include some factors affects a study's weight, not its admissibility, a study must include all major factors.   Bazemore v. Friday, 478 U.S. 385, 400, 106 S.Ct. 3000, 3009, 92 L.Ed.2d 315 (1986).  Not only did the study fail to account for a professor's status as a former administrator, but the study also failed to measure the amount of time actually spent in teaching as opposed to the lapse of time since the professor began teaching.


20
Most significantly, the study failed to include the performance factors.  VCU maintains that it could not have included the performance factors because, due to their subjective nature, they are not suitable for statistical analysis.  The appellants' expert, nevertheless, stated that the study was not valid without adding the performance factors, and that studies performed by disinterested outside researchers "have regularly included productivity measures such as teaching loads and publications," and these studies have shown that productivity has a positive effect on the level of faculty compensation.  Because VCU's pay system is based on merit, and the factors on which faculty pay scales are decided are the very performance factors left out of the regression analysis, it cannot be said that VCU's study included all major factors.  The inclusion of the performance factors could very well alter the results of the multiple regression analysis, and there is a dispute of material fact as to whether inclusion of these factors is feasible.


21
Given the number of important variables omitted from the multiple regression analysis, and the evidence presented by the appellants that these variables are crucial, a dispute of material fact remains as to the validity of the study.  Therefore, the decision of the district court granting VCU's motion for summary judgment is


22
REVERSED.

MICHAEL, Circuit Judge, dissenting:

23
Trying to avoid summary judgment, plaintiffs (five male professors) simply threw rocks at VCU's salary equity study, rocks that either missed or glanced off harmlessly.  On the record before us, VCU's multiple regression study establishes that there was a manifest imbalance in pay between men and women faculty members (women were underpaid) at that state university.  Plaintiffs argue that VCU's study should have included more variables, but they fail to demonstrate that the inclusion of those variables would have eliminated the statistically significant effect of gender on salaries.  Thus, plaintiffs' response does not satisfy either Supreme Court precedent (Bazemore ) or settled summary judgment principles.  With all respect for the majority, I therefore dissent because there is no material fact in dispute.

I.

24
VCU's study (a multiple regression analysis) mathematically estimated the effect of eight independent variables on salaries VCU paid to 770 tenured and tenure-track faculty members.  The eight independent variables were:  (1) national salary average (same discipline and rank), (2) doctorate or not, (3) tenure status, (4) quick tenure (within four years of appointment) or not, (5) years of experience at VCU, (6) academic experience before VCU, (7) service, if any, as department chair, and (8) gender.  When the effect of the seven variables other than gender was taken into account, the effect of gender on faculty salaries was a statistically significant $1,354 in 1989 and $1,982 in 1991.  Specifically, women faculty members, because they were women, on average were paid that much less than men.  These findings were confirmed by VCU's expert statistician, Dr. Rebecca Klemm.  Dr. Klemm testified (in deposition) that she took VCU's raw data and ran new regression studies using models different from the one used by VCU.  Dr. Klemm's new studies consistently showed a gender difference in salary at VCU of a magnitude "very similar" to that found by VCU's original model.  In moving for summary judgment, VCU relied on its original regression study and Dr. Klemm's testimony to establish the existence of a manifest imbalance in pay tied to the impermissible factor of gender.


25
Against this specific evidence, plaintiffs offered the deposition testimony and an affidavit (filed post-judgment) from Dr. Fred McChesney, an economics professor from Emory University.  Unlike VCU's expert, Dr. McChesney did not perform a statistical study in this case.  Indeed, he admitted that he had never performed a pay study such as the one at issue here.  Nevertheless, Dr. McChesney opined that VCU's model should have included additional independent variables, such as performance1 and any prior service as an administrator.  This omission was a fatal flaw, he said.  When pressed, however, Dr. McChesney agreed that gender could affect salary at VCU.  He also admitted that, even if the variables he suggested had been included, it was possible that the study results would have been essentially the same.  In short, Dr. McChesney could not say that adding his variables would have had a statistically significant effect on the results of the VCU study.


26
On this record the majority finds a genuine issue of material fact.  In doing so, the majority gives Dr. McChesney far too much credit.  Dr. McChesney's opinion does not justify the majority's conclusions that "failure to include a faculty member's status as a former administrator could easily have caused a salary differential that was not attributable to sex," ante at 663 (emphasis mine), and that "inclusion of the performance factors could very well alter the results of the multiple regression analysis," id. at 663 (emphasis mine).


27
Dr. McChesney's untested conjecture does not undermine the validity of VCU's multiple regression analysis.  To avoid summary judgment, plaintiffs must do more than list a few other variables that might have been included in the regression analysis.  Instead, plaintiffs must demonstrate that including an omitted variable would have eliminated any statistically significant disparity between the salaries of men and women.   Bazemore v. Friday, 478 U.S. 385, 399-403, 106 S.Ct. 3000, 3008-3010, 92 L.Ed.2d 315 (1986).


28
Bazemore is controlling here.  In  Bazemore, certain employees of the North Carolina Agricultural Extension Service sued various state and local officials, alleging that discriminatory differences in pay between black and white workers violated Title VII of the Civil Rights Act of 1964.  478 U.S. at 391, 106 S.Ct. at 3004.   To help prove discrimination, the plaintiff-employees offered multiple regression analyses, which both the district court and our court rejected.  The Supreme Court took the case and said that our court had erroneously concluded that " '[a]n appropriate regression analysis of salary should ... include all measurable variables thought to have an effect on salary level.' "   Id. at 399, 106 S.Ct. at 3008 (quoting  Bazemore v. Friday, 751 F.2d 662, 672 (4th Cir.1984) (alterations in original)).  After pointedly noting that the employees' expert testified that the disparities shown by the regressions were statistically significant, a unanimous Supreme Court said:


29
The [Fourth Circuit's] view of the evidentiary value of the regression analyses was plainly incorrect.  While the omission of variables from a regression analysis may render the analysis less probative than it otherwise might be, it can hardly be said, absent some other infirmity, that an analysis which accounts for the major factors "must be considered unacceptable as evidence of discrimination."   Normally, failure to include variables will affect the analysis' probativeness, not its admissibility.


30
Importantly, it is clear that a regression analysis that includes less than "all measurable variables" may serve to prove a plaintiff's case.  A plaintiff in a Title VII suit need not prove discrimination with scientific certainty;  rather his or her burden is to prove discrimination by a preponderance of the evidence.


31
Id. at 399-400, 106 S.Ct. at 3009 (internal citations and footnote omitted).


32
The majority cites this passage from  Bazemore  for the undisputed proposition that "a study must include all major factors."  Ante at 663.  The majority then goes on to conclude that the variables omitted here (such as performance) are "crucial" factors because it believes their "inclusion ... could very well alter the results of [VCU's] multiple regression analysis."   Id. at 663 (emphasis mine).  According to the majority, this creates a dispute of material fact "as to the validity of the study."   Id.  The record does not support this conclusion.


33
Plaintiffs never demonstrated the statistical significance of the omitted variables, and this is the fatal flaw in their response.  It is fatal because  Bazemore teaches that statistical significance must be the wedge that divides "major" (or "crucial") factors from other "measurable" factors.  The  Bazemore Court criticized the governmental respondents for a trial strategy that made no attempt "--statistical or otherwise--to demonstrate that when these [allegedly important] factors were properly organized and accounted for there was no significant disparity between the salaries of blacks and whites."  478 U.S. at 403 n. 14, 106 S.Ct. at 3010 n. 14.   In addition, the Court noted three times that the regression analyses in the  Bazemore record showed salary disparities that were "statistically significant."   Id. at 399 n. 9, 401, 404 n. 15, 106 S.Ct. at 3008 n. 9, 3009, 3010 n. 15.   Bazemore therefore sends a clear signal:  "major" factors are statistically significant factors.  In the case before us, the omitted variables cannot be characterized as "major" because plaintiffs did not demonstrate that their inclusion would eliminate the statistically significant disparity between the salaries of men and women at VCU.  Thus, under  Bazemore the district court was correct in rejecting plaintiffs' claim.

II.

34
Even without  Bazemore, VCU is entitled to summary judgment.  Under settled Rule 56 jurisprudence, a defendant is entitled to judgment as a matter of law when the plaintiff fails to adduce facts on an element of his case for which he bears the burden of proof.   Celotex Corp. v. Catrett, 477 U.S. 317, 322, 106 S.Ct. 2548, 2552, 91 L.Ed.2d 265 (1986);   Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248-49, 106 S.Ct. 2505, 2510, 91 L.Ed.2d 202 (1986).  In this case, the majority acknowledges that plaintiffs bear the burden of establishing that VCU's affirmative action plan was implemented in the absence of a manifest imbalance in salary between male and female faculty members.  Ante at 662.  To meet this burden, plaintiffs simply assert that VCU's multiple regression analysis failed to include enough factors.  But, as I have already pointed out, plaintiffs have not shown the statistical significance of even one of the factors they say was erroneously excluded from VCU's study.2  In fact, their expert, Dr. McChesney, indicated that he did not know whether including the factors he identified would change the result of VCU's studies in a statistically significant way.  To avoid summary judgment, plaintiffs must do more.  The complaining male professors must produce firm evidence showing that, after adjusting for an omitted factor, a statistically significant gender effect on salary no longer exists.  Nothing else can create a genuine issue of material fact concerning the study's validity.


35
* * *


36
This case should be decided on the record.  The record establishes that women faculty members at VCU were paid less because they were women.  VCU made adjustments for the disparity based on a study that has not been discredited.  The district court's award of summary judgment to VCU should be affirmed.



*
 Of the 82 faculty members considered in the pool who were paid more because they had held administrative positions, 71 were male


1
 VCU maintains that the variables in its study relating to tenure, experience and any service as a department chair are "broad measures of performance."


2
 The district court put it this way:  "no record evidence exists that including these additional variables would have altered the results of VCU's study."   Smith v. Virginia Commonwealth University, 856 F.Supp. 1088, 1093 n. 15 (1994)


