
    George RUDEBUSCH; Theresa Chapas; James E. Bartell; Gary Bateman; Harvey Becher; John Bloom; Burton Brown; Craig Caldwell; Keith Cunningham; Randy Dillingham; Michael A. Falk; Jay Farness; Steve Funk; Wade Harrison; William Hildred; John Hill; Thomas Hoisch; Edward Hood; Guenther Huck; Stephen Jackson; Arnold Johnson; David Kitterman; Stephen D. Lapan; Eugene Loverich; Michael Malone; Andrew Odell; Richard Packard; Gilbert C. Pogany; Timothy L. Porter; Loren Reser; Adrian Riskin; Howard Salisbury; Michael Sanera; James D. Simmerman; Wayne Sjoberg; Michael Tanner; Charles T. Way; James Windes; Michael Wunsch; Robert Zoeliner; Ken Nicolls, Plaintiffs-Appellants, v. Eugene HUGHES, Individually and as President of Northern Arizona University; Margaret Hughes; State of Arizona; Northern Arizona University; Board of Arizona Regents, Defendants-Appellees.
    No. 01-15287.
    United States Court of Appeals, Ninth Circuit.
    Argued and Submitted March 13, 2002.
    Filed Dec. 9, 2002.
    
      Thomas C. Horne, Horne, Ducar, Loro-na & Slaton, L.L.P., Phoenix, AZ, for the plaintiffs-appellants.
    Janet Napolitano, Arizona Attorney General, and Lisa K. Hudson, Assistant Attorney General, Office of the Arizona Attorney General, Phoenix, AZ, for the defendants-appellees.
    Before: RYMER, KLEINFELD, and McKEOWN, Circuit Judges.
   Opinion by Judge McKEOWN; Partial Concurrence and Partial Dissent by Judge KLEINFELD.

McKEOWN, Circuit Judge:

We address here a challenge to the onetime base pay adjustments given to certain women and minority faculty by Northern Arizona University in an effort to achieve pay equity mandated by federal regulations. The appeal presents claims under both the Equal Protection Clause as against the university president and under Title VII as against the University. We affirm the finding of qualified immunity for the university president. We analyze the Title VII claim in accordance with the Supreme Court’s framework in Johnson v. Transportation Agency, 480 U.S. 616, 107 S.Ct. 1442, 94 L.Ed.2d 615 (1987). Because the aggrieved professors did not challenge the jury’s determination that a manifest imbalance justified the pay equity plan, we do not disturb this finding on appeal. Although we hold that the plan did not unnecessarily trammel the rights of the professors who brought suit, we nonetheless reverse and remand because the question whether the adjustments were more than remedial raises a factual issue that cannot, as occurred here, be decided on summary judgment.

Background

This lawsuit stems from events that took place almost a decade ago. At the time of this action, Northern Arizona University (“NAU” or “the University”) was a recipient of significant federal funding and thus subject to federal regulations requiring it to implement an affirmative action plan. The plan adopted by the University and approved by the federal government’s Office of Federal Contract Compliance Programs broadly mandated an increase in the recruitment and retention of minority faculty as well as an assurance of parity between men and women in all areas of employment. In terms of pay equity, the plan required the University to evaluate all employees’ compensation annually for purposes of gender equity and minority integration, and at least with respect to salary inequities attributable to gender, the University was required to remedy such disparities within one year of their identification. The ultimate responsibility for assessment of disparities fell to Dr. Eugene Hughes, NAU’s president.

Evidence of Discrimination and Pay Disparity

By 1989, six of 133 fall professors were women (up from three in 1985), and thirty-four of 188 associate professors were women (up from eighteen in 1985). The majority of female faculty occupied the lowest ranks of assistant professors, and even there they were far out-numbered by male faculty.

Five out of 53 faculty openings during this same time period were filled by minorities. And despite recruitment goals set for minority hiring in later years, NAU reported to the federal government in 1993 that it had lost twice as many minority faculty as it had hired during the 1991-1992 academic year. In fact, the University had lost over a quarter of its minority faculty in the two years preceding the pay adjustments — despite new hires.

Upon review of available statistics, Hughes concluded not only that there was a hiring disparity, but that overall pay inequity was also apparent. In 1989, female faculty were making on average over $8,000 a year less than male faculty. Minority faculty did not fare much better. The University’s 1988 annual study noted that their mean salary was over $6,700 less than that of non-minority faculty.

These disparities prompted Hughes to conclude that some form of corrective action was necessary as early as 1990. That same year, the Arizona legislature allocated funds to NAU for general “market adjustments” to faculty salaries (i.e., adjustments ostensibly intended to make the University’s salaries competitive with those of other schools). Department heads at the University were entrusted with making recommendations for individual adjustments. Hughes observed that these adjustments did not alleviate existing sex and race-based pay disparities, an observation that was confirmed by subsequent annual pay studies.

Hughes and NAU were not the only ones with concerns about pay disparity. Around the same time, the Arizona Board of Regents established the Commission on the Status of Women to report on this issue with regard to female faculty at the State’s three universities. In 1991, the Commission published a study that included many of the above findings about female faculty employment between 1985 and 1989.

The Commission concluded that the absolute differences in pay “were quite large.” Although some disparity could be attributed to “the clustering of women at the lower professional ranks and their overrepresentation within disciplines that have lower salaries on the national market,” the Commission concluded that even “[w]hen rank was controlled, the differences were still substantial.” Additionally, the Commission noted that making adjustments for rank may be problematic since “rank is itself affected by a faculty member’s sex. If it were the case that male faculty are more likely to be promoted than female, controlling for rank in the analysis would result in underestimating salary inequities.”

Chambers’ 1993 Annual Equity Report

Close on the heels of the Commission’s study was NAU’s own 1993 annual equity report, authored by the head of its office of institutional research, Dr. Stephen Chambers. Chambers had been producing these reports for the University since 1986. As he explained at trial, the regression analysis Chambers employed was similar to the model used by hundreds of institutions across the United States. In this context, regression analysis is a statistical application used to predict how salary (the dependent variable) should vary based on rank, years of service, discipline, and the like (considered independent variables). The regression model isolates the likelihood that factors other than legitimate differences such as rank, i.e., factors such as discrimination, play a role in the salary disparities. The likelihood is determined by predicting what the salary should be given the legitimate factors, and measuring the difference to the actual salary (in standard deviations).

Based on this time-tested analysis, the Chambers’ report concluded that there were “statistical differences in gender and ethnic equity” which could be removed with $278,966 in adjustments. The report ultimately recommended various adjustments for 72% of the female faculty. A majority of the adjustments were in the $1,001 to $3,000 per year range. The amount of each adjustment depended on how far an individual’s salary fell below the predicted salary of a similarly situated white male professor. Those women who were at or above this predicted salary received no adjustment.

Using the same benchmark as that used for female faculty adjustments — the predicted salary of a similarly situated white male professor — the report recommended adjustments ranging from $250 to $6,945 for about half of the minority male faculty. The majority of the adjustments were in the $2,001 to 3,000 range.

Considering the findings of the 1993 equity report and the 1991 study on the status of women, as well as the requirements of the University’s affirmative action plan, Hughes testified that he felt compelled to take remedial action in mid-1993. According to Hughes, the “usual process” of making salary adjustments involved recommendations and consultation with department chairs, deans, and the academic vice president, but because “that hadn’t worked on other occasions,” Hughes decided, with some modification, to adopt and implement the adjustments recommended in Chambers’ 1993 report. He did not simply accept the report as prepared. Rather, Hughes undertook an administrative review of the proposed adjustments and asked Chambers to run additional regression analyses before settling on the final adjustments. In order to achieve the goal of attaining pay equity, Hughes used $207,613 of unappropriated funds (from among other sources, salaries appropriated for vacant faculty positions) in the school’s existing budget to make the necessary adjustments.

Salary adjustments were awarded to female and minority male faculty whose actual salary fell below the predicted salary of a similarly situation non-minority male. Women and minority men who were already earning their predicted salary or more did not receive any adjustments, nor did any non-minority men receive adjustments, even those whose earnings were below the predicted salary.

The Gantz/Miller Study

Sometime after Hughes instituted the salary adjustments, and also after he had left his post at the University, NAU hired two outside consultants, Donald Gantz and John Miller, to do a study on the adjustments. The Gantz/Miller study criticized several aspects of Chambers’ methodology. Nevertheless, even Gantz/Miller’s preferred method of analysis would have led to adjustments for 93 male minority and female professors totaling $164,410. The only question for Gantz/Miller was whether such adjustments would be “required.” The study concluded that they were not. This finding resulted not because Gantz/Miller were unable to ascertain any unexplainable differences in pay — they in fact found a disparity for both women and for minorities — but because they concluded that these disparities were not statistically significant enough (that is, large enough) to prove that the “inequity [was] due to either gender or minority status.”

PROCEDURAL HISTORY

George Rudebusch, an NAU professor, along with a class of female and non-minority male professors (collectively “Rude-busch”) sued Hughes in his individual capacity under 42 U.S.C. §§ 1981 and 1983 for equal protection violations resulting from his decision to implement the pay adjustments. Rudebusch and a class of white male plaintiffs also sued the University and the Arizona Board of Regents (collectively “NAU” or “the University”) under Title VII.

Hughes responded to the equal protection claims by moving for summary judgment on qualified immunity grounds. The district court granted this motion in part, concluding that the law was clearly established and that Hughes was reasonable in concluding that a compelling interest justified his actions. But the district court reserved for trial the ultimate issue of qualified immunity because of factual issues surrounding the remedy imposed. On interlocutory appeal, a panel of our court affirmed. Rudebusch v. Hughes, 2000 WL 222598, at *2 (9th Cir.2000) (unpublished disposition). (These decisions were issued before the Supreme Court’s recent qualified immunity decision, Saucier v. Katz, 533 U.S. 194, 121 S.Ct. 2151, 150 L.Ed.2d 272 (2001).) At trial, the jury reached a verdict in favor of Hughes on both the sex and race-based claims.

During a second round of summary judgment motions, both sides moved for judgment as a matter of law on all other issues. The district court granted partial judgment to the University on the Title VII claim by concluding, as a matter of law, that the pay adjustments did not “unnecessarily trammel” Rudebusch’s rights. That ruling left for trial the question whether Rudebusch could prove that there was no “manifest imbalance” justifying the salary adjustments. The jury returned a verdict in favor of the University on the Title VII claim. Accordingly, judgment was entered in favor of Hughes and the University, and Rudebusch’s claims were dismissed.

DISCUSSION

We first address the propriety of NAU’s pay adjustments in the context of the equal protection framework and Hughes’ individual liability, and then turn to an analysis of Title VII as it relates to the liability of the University and the Arizona Board of Regents. Finally, we address Rudebusch’s evidentiary concerns regarding the admission of a Department of Labor letter.

I. Equal Protection Claims ajnd Qualified Immunity Under Saucier v. Katz

The equal protection claims asserted under §§ 1981 and 1983 against Hughes in his individual capacity were brought by two classes of plaintiffs — a class of white male faculty and a class of female plaintiffs comprised of both white and minority women. On appeal, Rudebusch argues that all along “[b]oth the subclass of non-minority males, and the subclass of females, brought ... equal protection claims, based on the racial discrimination in the salary increase.” Reply Br. at 17. Thus, for purposes of the constitutional claims, Rudebusch would have us focus solely on the pay adjustments made to minority male faculty, not to female faculty. Because the outcome is ultimately unaffected, for analytical simplicity we take Rudebusch at his word and consider these claims under the framework of racial classifications in reaching our conclusion that Hughes is entitled to immunity.

Hughes asserted the defense of qualified immunity as to all claims against him. As the Supreme Court reminds us, qualified immunity is “an entitlement not to stand trial,” that is “an immunity from suit rather than a mere defense to liability.” Mitchell v. Forsyth, 472 U.S., 511, 526, 105 S.Ct. 2806, 86 L.Ed.2d 411 (1985) (emphasis in original). As a consequence, qualified immunity “safeguards ‘all but the plainly incompetent or those who knowingly violate the law.’” Brewster v. Bd. of Educ. of the Lynwood Unified Sch. Dist., 149 F.3d 971, 977 (9th Cir.1998) (quoting Malley v. Briggs, 475 U.S. 335, 341, 106 S.Ct. 1092, 89 L.Ed.2d 271 (1986)). This standard “allows ample room for reasonable error on the part of the [official].” Knox v. Southwest Airlines, 124 F.3d 1103, 1107 (9th Cir.1997). It encompasses both mistakes of fact and mistakes of law. Butz v. Economou, 438 U.S. 478, 507, 98 S.Ct. 2894, 57 L.Ed.2d 895 (1978).

The district court here proceeded without the benefit of the Supreme Court’s recent teaching in Saucier v. Katz, which clarified the proper paradigm for assessing a qualified immunity claim. After Saucier, we ask a threshold question: “Taken in the light most favorable to the party asserting injury, do the facts alleged show the officer’s conduct violated a constitutional right?” 533 U.S. at 201, 121 S.Ct. 2151. Only after determining whether the right was violated do we proceed to the next step of this two-part inquiry: whether the law was so clearly established that “a reasonable official would understand that what he is doing violates that right.” Id. at 202, 121 S.Ct. 2151 (quoting Anderson v. Creighton, 483 U.S. 635, 640, 107 S.Ct. 3034, 97 L.Ed.2d 523 (1987)). “The concern of the immunity inquiry is to acknowledge that reasonable mistakes can be made as to the legal constraints on particular [official] conduct.” Id. at 205, 121 S.Ct. 2151. Central to our inquiry here, this analysis occurs in the specific context of “the situation ... confronted” by the official. Id. at 202, 107 S.Ct. 3034.

A. Violation op a Constitutional Right

Before turning to the heart of the qualified immunity inquiry, we must first determine whether Rudebusch has established an equal protection violation; “[i]f no constitutional right would have been violated were [Rudebusch’s] allegations established, there is no necessity for further inquiries concerning qualified immunity.” Id. at 201, 107 S.Ct. 3034. Rudebusch has overcome this first hurdle of the Saucier inquiry not only because of his rebanee on the after-the-fact Gantz/Miller study, but also because the Chambers study relied upon by Hughes raises serious concerns about permissible inferences of discrimination.

We begin the initial step of the Saucier analysis by noting that courts have yet to assess the constitutional limitations inherent in decisions to rectify pay inequity based on race. Nevertheless, the general rule is well enough established that race-based classifications must withstand strict scrutiny under the Fourteenth Amendment. See City of Richmond v. J.A. Croson Co., 488 U.S. 469, 493-94, 109 S.Ct. 706, 102 L.Ed.2d 854 (1989). Thus, for a state-sponsored program to survive strict scrutiny, there must be a compelling governmental interest in employing a racial classification, and the classification must be narrowly tailored to achieve that interest. See id.; see also Coral Constr. Co. v. King County, 941 F.2d 910, 916 (9th Cir.1991).

A governmental interest is sufficiently compelling to justify racial classifications “only if actual, identifiable discrimination has occurred.” Coral, 941 F.2d at 916. We have recognized that statistical comparisons represent an “invaluable tool” in evaluating the extent of discrimination warranting a response. Id. at 918. Looking to the Supreme Court’s jurisprudence in the Title VII disparate impact area, we have concluded for purposes of equal protection, “[wjhere gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination.” Id. (quoting Hazelwood Sch. Dist. v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977)).

Hughes supported his motion for summary judgment with two types of statistical evidence: (1) the 1993 Chambers study; and (2) the 1993 affirmative action summary report.

Chambers Study

In critique of the Chambers study, Ru-debusch relies primarily on the after-the-fact Gantz/Miller study. Although the Gantz/Miller study found pay disparities for more than half of NAU’s minority faculty, it expressly found them to be statistically insignificant, thus rejecting any notions that adjustments were necessary to remedy actual racial discrimination. In other words, Gantz/Miller concluded as a matter of statistical analysis that any differences were not sufficiently “gross” as to reliably prove that “inequity [was] due to ... minority status.” Quite simply, taking the Gantz/Miller study and its critique of the Chambers report as true, there was no evidence of actual discrimination.

In keeping with Saucier’s suggestion, we find it important to emphasize several aspects of the Chambers analysis that would make future rebanee upon such a study problematic as a matter of law. See Saucier, 533 U.S. at 201, 121 S.Ct. 2151 (“In the course of determining whether a constitutional right was violated on the premises alleged, a court might find it necessary to set forth principles which will become the basis for a holding that a right is clearly established. This is the process for the law’s elaboration from case to case.... ”).

First, we express concern about inferring discrimination from a study in which the highest single pay disparity for ethnic minorities fell 2.0 standard deviations away from predicted salary — but produced a lowest statistically unexplainable difference of $87 between ethnic minorities and their Anglo counterparts. In addition, this was even less than the $296 difference measured the previous academic year.

As the executive summary of the Chambers study itself indicated, “[t]he threshold for evidence of salary inequity’s generally considered 2.0 standard deviations,” but at least in the Title VII context, we rejected the proposition that standard deviations of 1.3 and 2.46 were sufficiently representative, at least on their own, to make an inference of discrimination. Gay v. Waiters’ & Dairy Lunchmen’s Union, 694 F.2d 531, 551 (9th Cir.1982). We came to this conclusion in the same breath as saying that “[i]t would be improper to posit a quantitative threshold above which statistical evidence ofidiscrimination] is sufficient as a matter of law to infer discriminatory intent, and below which it is insufficient as a matter of law,” id., while also recognizing the Supreme Court’s admonition that the usefulness of statistical evidence “depends on all of the surrounding facts and circumstances.” Int’l Bhd. of Teamsters v. United States, 431 U.S. 324, 340, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977) (quoted in Gay, 694 F.2d at 553). Consequently, we need not decide whether discrimination may ever be inferred from a probability that is this low to hold that, absent other evidence, a statistical difference of this order of magnitude does not, and by itself cannot, show a conspicuous imbalance in salaries such as to justify the salary adjustments here.

Heeding the Supreme Court’s directive to look at the “surrounding facts and circumstances” of the Chambers study, we discover further reason to discount permissible inferences of discrimination, namely the fact that while over half the minority faculty were making less than predicted salary, a significant percentage of white male faculty were also making less than predicted. There were 493 faculty members included in the 1993 regression. If the University discriminated, we would expect minorities (or women) to be paid less than the amount predicted while non-minority males would be paid more. In fact, eighty-five female and minority male faculty members out of the 493 were below predicted salary, but so were 192 non-minority males as well. Though this may show that almost everyone at NAU was being underpaid, the existence of across-the-board disparities would seem to undercut the study’s ability to demonstrate that minorities were discriminated against simply because their salaries fell below predicted. This evidence falls far short of showing conspicuous imbalance along ethnic or gender lines.

As the Gantz/Miller report on equity pay adjustments notes, neither before nor after the 1993 adjustment was there a statistically significant difference in salaries between males and females or between majority and minority members of the faculty. While this suggests that the adjustments themselves did not create a conspicuous imbalance to Rudebusch’s disadvantage, it also shows that adjusting salaries in the first place was not “urgently necessary” to correct a conspicuous imbalance.

As a final point, we have concerns about the way in which Hughes calculated and made the adjustments in this case. Particularly when, as was the case here, adjustments depend upon a regression analysis that does not account for performance factors such as academic credentials, performance, merit, teaching, research, or service — factors that are the major criteria for faculty compensation on campuses across the country — the failure to make some sort of more individualized determination of what sort of adjustments are warranted in any given case will not satisfy strict scrutiny.

This is not to say, however, that we dictate which factors must be included in regression studies. As the Supreme Court reminds us, the propriety of controlling for particular variables in a regression analysis goes to weight rather than admissibility. See Bazemore v. Friday, 478 U.S. 385, 400, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986); see also Maitland, 155 F.3d at 1017 (for finder of fact “to consider the variables that have been left out of an analysis, and the reasons given for the omissions, and then to determine the weigh to accord to the study’s results”). Rather, we emphasize that when adjustments are warranted by permissible inferences of discrimination, the school must at some point ensure that the adjustments given are somehow correlated to individual merit. As Hughes himself acknowledged, Arizona State University (under the same impetus to integrate its faculty as NAU) managed to provide such a individualized claim process for all faculty below predicted salary. So, too, did the University of Minnesota when faced with a similar problem. See Maitland, 155 F.3d at 1015.

Affirmative Action Report

We recognize that Hughes did not rely solely on the Chambers study when inferring discrimination. In particular, he also justifies his salary decisions by pointing to the disproportionate flight of minority faculty that became apparent upon his review of the federal affirmative action report. See Gay, 694 F.2d at 553 (circumstantial evidence of discrimination can be used to bolster otherwise inconclusive statistical proof by bringing “the cold numbers convincingly to life”) (quoting Teamsters, 431 U.S. at 339, 97 S.Ct. 1843). But as reasonable as it may have been to infer discrimination from these figures, the fact remains that the report itself did not attempt to isolate the reasons for the University’s failure to retain these faculty. Making all inferences in Rudebusch’s favor, as we must at this stage, Saucier, 533 U.S. at 201, 121 S.Ct. 2151, there could be numerous nondiscriminatory reasons for the minority faculty’s flight. Thus, this additional evidence cannot save Hughes from our conclusion that at least as matter of law that is now clearly established, Hughes’ actions would not survive strict judicial scrutiny.

We conclude that Rudebusch established an equal protection violation. There can be no compelling government interest in adjusting salaries on the basis of race when the differences in pay are neither statistically significant nor conspicuously out of balance overall; there is little or no evidence of de jure discrimination; and no anecdotal examples of discriminatory treatment are offered. For sure there was evidence that NAU was subject to a federally mandated affirmative action plan that, among other things, required it to ensure pay equity to integrate minority faculty into the University, and that some minority members of the faculty had left (although there is no indication why). However, the main evidence of pay inequity, and the study upon which the University acted in making the 1993 pay adjustments, was the flawed Chambers study.

B. Reasonableness of Conduct

Although Rudebusch has established an equal protection violation, we must still ask whether a “reasonable official” in Hughes’ position “would understand that what he is doing violates that right,” Saucier, 533 U.S. at 201, 121 S.Ct. 2151, keeping in mind that “officials will not be liable for mere mistakes in judgment, whether the mistake is one of fact or one of law.” Butz, 438 U.S. at 507, 98 S.Ct. 2894. With this perspective in mind, we conclude that. Hughes is entitled to qualified immunity. Our conclusion rests on a single factor — timing. The law in this area was not clearly established at the time Hughes made his decision nor did Hughes have the benefit of post-decision analyses and information.

We start with the proposition that at the time of the decision, the general rules were well enough established, for example, that the Fourteenth Amendment requires all racial classifications to survive strict scrutiny. See City of Richmond, 488 U.S. 469, 109 S.Ct. 706, 102 L.Ed.2d 854; Coral Constr. Co., 941 F.2d at 915-16 (applying strict scrutiny to county minority set-aside program). This is what we held on Hughes’s interlocutory appeal. But the specific contours of the law pertaining to pay equity were not well developed or sufficiently clear at the time. See Anderson, 488 U.S. at 640, 107 S.Ct. 3034 (no qualified immunity only if “contours of the right” are “sufficiently clear that a reasonable official would understand that what he is doing violates that right”). Saucier makes it clear that this is the level at which we are to measure Hughes’s response, because determining whether the law was clearly established “must be undertaken in light of the specific context of the case, not as a broad general proposition.” 533 U.S. at 201, 121 S.Ct. 2151.

Although there are numerous cases involving salary discrimination, many of them in educational institutions, most arise in the context of Title VII. These cases shed a fair amount of light on the persuasiveness of various regression analyses, but not much on applicable constitutional constraints. While these cases (and others) point up the serious weaknesses in NAU’s approach, they do not necessarily indicate that the Constitution was implicated. One need only look at the complexity of the models at issue in reported cases, and the discussion on statistics and multiple regression in the Federal Judicial Center’s Reference Manual on Scientific Evidence, to realize how tricky it is to measure whether sex and ethnicity are a significant determinant of salary. Two more recent opinions, Maitland, 155 F.3d 1013, and Smith, 84 F.3d 672 (4th Cir.1996), refine the parameters, but neither was around to guide Hughes’s decision.

Rudebusch suggests that the law clearly prohibits adjustments to minority salaries without also giving consideration to non-minority faculty whose compensation falls below their predicted salaries for reasons wholly unrelated to racial discrimination. To begin, as a matter of law, courts have yet to consider for purposes of equal protection whether pay adjustments focused solely on disparities stemming from perceived discrimination in minority salaries violate the rights of those individuals whose salaries are not considered for adjustment. Thus, it cannot be said that the law was clearly established on this nuance of pay equity at the time Hughes implemented these adjustments.

It should now be clear, however, that a conspicuous imbalance in salaries is not manifest by a salary disparity which is not statistically significant and that, absent other evidence, it will not be objectively reasonable for a university official to approve a salary plan based on a flawed multiple regression analysis which shows no statistically significant salary discrimination. However, because qualified immunity is to protect “ ‘all but the plainly incompetent,’ ” Saucier, 533 U.S. at 202, 121 S.Ct. 2151 (quoting Malley v. Briggs, 475 U.S. 335, 341, 106 S.Ct. 1092, 89 L.Ed.2d 271 (1986)), Hughes should not be denied his right to seek it on account of the statistical infirmities alone.

Our conclusion with respect to qualified immunity also rests on identifying what information was available to Hughes at the time he made his decision, as distinguished from analyses and information brought to light after the fact and in litigation. Rude-busch makes much of the district court’s conclusion that the “correct regression analysis” of the Gantz/ Miller follow-up reveals that “there is no statistically significant disparity between the salaries of males and females,” but he fails to recognize — as the district court did not — that the relevant inquiry is not whether, in hindsight, Hughes acted unreasonably, but instead whether his decision was reasonable in light of the information that he possessed at the time of implementation. See Anderson, 483 U.S. at 641, 107 S.Ct. 3034; cf. Brewster, 149 F.3d at 977 (“in order to ensure that government officials receive necessary guidance, courts should focus the qualified immunity inquiry at the level of implementation”).

At the time Hughes made his decision, he was faced with a federally mandated and approved affirmative action plan that required him to increase the retention of minority faculty and to ensure pay equity as a means of integrating minority faculty into the University’s community. He was faced with a situation where, despite a significant number of new hires, NAU still lost over a quarter of its minority faculty in the two years preceding the adjustments. Against this backdrop, Hughes was presented with the University’s annual equity analysis. But in making his decision, Hughes did not have the Gantz/Miller report or any of its related analysis.

Because we recognize that the overriding purpose of the qualified immunity defense is “the need to protect officials who are required to exercise their discretion,” Butz, 438 U.S. at 506, 98 S.Ct. 2894, in light of the undeveloped state of the law at the time and the lack of the more compelling Gantz/Miller study, we are hesitant to second-guess Hughes’ judgment, much less play the role of über-statistician only after all the results are in. Therefore, whether Hughes could have been legally mistaken as to the degree of statistical certainty required to demonstrate actual discrimination or whether he could have been factually mistaken as to the true extent of disparity justifying his decision, neither the law nor the facts were so clearly established at the time of his decision that Hughes reasonably should have known he was violating Rudebusch’s constitutional rights.

Likewise, we conclude that Hughes reasonably exercised his discretion in tailoring the adjustments to address the perceived disparities. As a preliminary matter, we recognize that the district court allowed the issue of narrow tailoring to go to the jury, despite the Supreme Court’s repeated efforts to stress “the importance of resolving immunity questions at the earliest possible stage in litigation.” Hunter v. Bryant, 502 U.S. 224, 227, 112 S.Ct. 534, 116 L.Ed.2d 589 (1991) (per curiam). Nevertheless, because the issue was resolved by the jury, under Federal Rule of Civil Procedure 50, we review the evidence in the light most favorable to Hughes and reverse only if the evidence permits but one reasonable conclusion, one that is contrary to the jury’s finding. Monroe v. City of Phoenix, 248 F.3d 851, 861 (9th Cir.2001). Given the standard, reversal is not justified on this score.

II. Title Vii

Turning to Title VII, Rudebusch and a class of forty white male professors claim that the University impermissibly failed to consider their eligibility for pay adjustments that were intended to correct overall disparities in pay between white male faculty and faculty of other races and female faculty.

Rudebusch’s characterization of the pay equity plan ignores the significant differences between a Title VII challenge and a constitutional challenge to the plan. Neither the Supreme Court nor our Circuit has examined the Title VII parameters for analysis of adjustments made to achieve pay equity. We therefore turn to the Supreme Court’s discussion of affirmative action hiring and promotion plans in the context of Title VII to provide the baseline for our analysis.

We note at the outset, however, that such hiring and promotion plans are not wholly analogous to pay equity plans. Often, affirmative action plans are viewed as providing preferential treatment for women or minorities. Although sometimes labeled as affirmative action, a pay equity plan such as that implemented by NAU does not provide an ultimate advantage but instead seeks to eliminate existing salary disparities for those particular individuals due to race and sex. The premise is that the salary is skewed due to discrimination on account of factors prohibited under Title VII — race and sex- — -and that, in fact, equalization results in elimination of any preference. Significantly, pay equity adjustments are often undertaken by an institution to avoid Title VII claims by women and minorities. The irony here is that such an effort resulted in this Title VII suit. But to assess whether this suit has wings, we look to the Supreme Court’s guidance in this arena.

Although Title VII prohibits employers from discriminating on the basis of race or sex, 42 U.S.C. § 2000e 2(a)(1), the Supreme Court has held that sex and race can be considered for purposes of hiring and promotion of women and minorities when such affirmative action is “justified by the existence of a ‘manifest imbalance.’ ” Johnson v. Transp. Agency, 480 U.S. 616, 631, 107 S.Ct. 1442, 94 L.Ed.2d 615 (1987) (upholding preferences for women for job promotions) (quoting Steelworkers v. Weber, 448 U.S. 193, 197, 99 S.Ct. 2721, 61 L.Ed.2d 480 (1979) (upholding preferences for minorities for admittance to training programs for skilled labor)); cf. Higgins v. City of Vallejo, 823 F.2d 351, 356 (9th Cir.1987). Significantly, the Court held that “[a] manifest imbalance need not be such that it would support a prima facie case against the employer ... since we do not regard as identical the constraints of Title VII and the Federal Constitution on voluntarily adopted affirmative action plans.” Johnson, 480 U.S. at 632, 107 S.Ct. 1442. Thus, the Court distinguished cases under Equal Protection, which require evidence of actual discrimination, and affirmative action cases under Title VII, which do not require the same degree of proof.

In addition, Johnson provides that hir-ings and promotions will not survive Title VII scrutiny if they would “unnecessarily trammel[ ] the rights of male employees or create[ ] an absolute bar to their advancement.” Johnson, 480 U.S. at 637-38, 107 S.Ct. 1442. Nor can remedial action be designed to do more than “attain a balance.” Id. at 639, 107 S.Ct. 1442.

Both the Fourth and Eighth Circuits have adopted the Johnson approach in their analysis of pay equity claims. See Maitland v. Univ. of Minn., 155 F.3d 1013 (8th Cir.1998); Smith v. Va. Commonwealth Univ., 84 F.3d 672 (4th Cir.1996). We agree that Johnson provides the proper framework, but not without noting that there are some significant conceptual differences between affirmative action in the promotional context and remedial measures used to cure pay inequity. Thus, we examine the three factors laid out by the Supreme Court in the context of our case: manifest imbalance, unnecessary trammeling, and adjustments necessary to obtain a balance.

A. Manifest Imbalance

After four days of trial testimony, the jury concluded that a manifest imbalance existed with respect to the pay of minority and women faculty. Consequently, in contrast to both Maitland and Smith, which addressed this issue on summary judgment, we have the benefit of a jury determination, which in the normal course would result in reversal only if no reasonable jury could have come to the same conclusion. Monroe, 248 F.3d at 861. But we need not make the assessment here because Rudebusch made no argument with respect to the jury’s determination in his opening brief. See, e.g., Int’l Union of Bricklayers v. Martin Jaska, Inc., 752 F.2d 1401, 1404 (9th Cir.1985) (holding to be inappropriate consideration of “matters on appeal that are not specifically and distinctly raised and argued in appellant’s opening brief’). With respect to Title VII and the University’s liability, Rudebusch challenged only the unnecessarily trammeling determination. Consequently, we assume that NAU addressed a manifest imbalance and turn to the next prong of the Johnson analysis.

B. UNNECESSARY TRAMMELING

Just as Johnson articulated the “unnecessarily trammeled” requirement in the context of affirmative action promotion, both the Fourth and the Eight Circuits in the pay equity context also adopted a requirement that efforts to remedy a manifest imbalance in race and sex-based pay disparities cannot survive Title VII scrutiny if they “unnecessarily tram-melt 1 the rights of [white] male employees.” Maitland, 155 F.3d at 1016 (quoting Johnson, 480 U.S. at 637, 639, 107 S.Ct. 1442); Smith, 84 F.3d at 676 (same). We agree, but note that neither Maitland nor Smith reached this issue or otherwise determined whether targeted pay adjustments would so trammel the rights of white male faculty. We review de novo the district court’s grant of summary judgment in favor of the University on this issue. Balint v. Carson City, 180 F.3d 1047, 1050 (9th Cir.1999) (en banc).

In the traditional settings of Title VII jurisprudence — hirings, promotions, and set-aside programs — courts have made the obvious point that whatever right is at stake, it is not some “absolute entitlement” to the position or contract; in other words, denial of the benefit would not unsettle any “firmly rooted expectation” of promotion. Johnson, 480 U.S. at 638, 107 S.Ct. 1442; Higgins, 823 F.2d at 357. Rather, what is at stake is the opportunity to compete for an otherwise available employment opportunity. Thus, Johnson’s approval of a hiring plan that “merely authorizes that consideration be given to affirmative action concerns when evaluating qualified applicants.” 480 U.S. at 638, 107 S.Ct. 1442; see also Gilligan v. Dep’t of Labor, 81 F.3d 835, 839 (9th Cir.1996) (noting in promotion context that “[i]f ... gender was the exclusive factor and that the position ... was, in fact, unavailable to [the plaintiff] because he was male, then the Department would be guilty of illegal discrimination”).

Citing this authority, Rudebusch argues that the University discriminated against him when it did not take into consideration the pay concerns of white male faculty during the remedial adjustment process. Cf. Maitland, 155 F.3d at 1015 (noting, without attaching any legal significance to the fact, that a similar adjustment scheme allowed any academic employee to file a claim seeking a salary increase under a “manifest inequity” provision of a court-ordered settlement). To begin, neither Rudebusch nor the class of plaintiffs have suggested that they either requested or were in fact denied a request for consideration of separate adjustments. But, to the extent that they claim their injury arose from the University’s failure to consider them for adjustments in the first instance, we recognize the need to explain how the pay equity situation presented here is fundamentally different from the promotional context upon which their argument is premised.

In the circumstance of a promotion, where there is competition for a finite position or where the benefits of promotion will have lasting employment consequences, appropriating the opportunity exclusively for purposes of alleviating racial or gender-based disparities may trammel upon the excluded employee’s legitimate expectation to compete equally for the position. See Johnson, 480 U.S. at 640, 107 S.Ct. 1442 (plan should visit “minimal intrusion on the legitimate expectations of other employees”). This same result might even be the case if, for instance, a legislature appropriated funds for across-the-board or merit-based raises which a state employer then distributed exclusively to minority or women employees. But none of these concerns are presented in this case.

Here, there would have been no opportunity or funds available for any pay adjustments but for the University’s decision to address the manifest imbalance between the salaries of white male professors and their female and minority counterparts in the first instance. In other words, the University’s decision to scrounge its budget for unused funds and make adjustments to women and minorities’ salaries was driven solely by the perceived need to make such adjustments. Allowing Rude-busch and the white male plaintiffs to claim that their exclusion from consideration “absolutely barred their advancement” would permit them to recharacterize NAU’s situation as an “opportunity for advancement” when, in fact, such an opportunity never existed in the first instance. Cf. Ende v. Bd. of Regents, 757 F.2d 176, 181 (7th Cir.1985) (endorsing a similar adjustment scheme for purposes of an Equal Pay Act claim brought by male faculty, concluding that “it determines the incremental adjustment to females’ salaries necessary to remedy the effects of past sex discrimination and eliminate sex as a determiner of salary. The formula merely [brings] the women to a salary level they would have reached in ordinary course if they had been men and not subjected to sex discrimination. It makes no sense to apply the formula to men in this context.”).

The effort here was a one-time adjustment. It was separate from the previous across-the-board raise and it was separate from ongoing evaluation and promotion. The plan presented “no absolute bar to [the] advancement” of the white male plaintiffs, Johnson, 480 U.S. at 637-38, 107 S.Ct. 1442, and, as in Johnson, the male faculty retained their positions at the same salary and were eligible for future promotions. No quotas were involved and the plan cannot be viewed as an effort to maintain a certain equilibrium in the workforce.

One thing is clear in this case: Whatever the reason, white male faculty who were earning less than their predicted salaries were not doing so because of their race or sex, or at least they have not demonstrated as much. Despite this reality, Rude-busch would have us hold that anytime an employer attempts to address a manifest imbalance in the pay equity context, it must simultaneously consider the unrelated concerns of those employees who have not demonstrated such a legally cognizable imbalance. Such logic would all but eliminate employer efforts to attain pay equity as required by law. Under Rudebusch’s analysis, there could never be any “catch up” adjustments without a concomitant adjustment or consideration of the entire employee pool. The result would be perpetuation, not elimination, of pay disparity. Rather, under the circumstances of this case, we conclude that Rudebusch’s concern is better characterized as a potential problem with the nature of the remedial measures themselves than whether the rights of white male faculty were unnecessarily trammeled.

C. Eliminating Imbalance

To the extent there is a problem in this case, it does not lie in the University’s failure to include white male faculty in its adjustment pool. Rather, it centers on the scope of the adjustments that were actually made to minority and female faculty salaries, not, as Rudebusch argues, those that should have been made to the salaries of non-minority males.

Remedial action is valid under Title VII only if it is designed “to eliminate a manifest racial [or gender-based] imbalance.” Weber, 443 U.S. at 208, 99 S.Ct. 2721. Implicit in this requirement is an inquiry whether the University may have impermissibly gone beyond “attainting] a balance” in making its adjustments. See Johnson, 480 U.S. at 639, 107 S.Ct. 1442. Because the district court did not distinguish this factor from its general analysis of the “unnecessary trammels” prong in its grant of partial summary judgment, we address it here separately.

The University does not dispute Rude-busch’s assertion that over half of its white male faculty were making less than the predicted salary of a similarly situated white male as calculated by the 1993 Chambers study. As the district court noted, the predicted salary represented the mean salary of white male professors in any given grouping. Such is the law of averages: some will be above the mean and some will be below. Such is also the reality of the teaching profession: even those faculty with the same rank, experience, and discipline will often find themselves being compensated at different levels.

Just as these realities of averages and the profession would not necessarily justify pay adjustments for those white male faculty falling below predicted levels, the use of the mean predicted salary as a baseline for the pay adjustments given to minority and female faculty — even when a manifest imbalance otherwise exists — raises legitimate questions about the scope of the adjustments made.

Thus, the real question is not whether Rudebusch should have been brought up to the mean, but whether using the predicted salary of similarly situated white male faculty for the minority and female adjustments somehow overcompensated these minority and women faculty members, i.e., whether the adjustments were more than remedial. This is a question the jury did not answer but instead was subsumed in the summary judgment ruhng on the “unnecessarily trammeled” issue.

It could be argued, as Rudebusch does, that the adjustments were more than remedial because the Chambers study was based on disparities as measured by the mean salary of comparable white male faculty. On the other hand, there was evidence of overall disparities of over $8,000 for women and $6,700 for minorities. Looking at these figures, the adjustments actually made — which were much lower— could arguably represent “a moderate, gradual approach to eliminating the imbalance. ...” Johnson, 480 U.S. at 640, 107 S.Ct. 1442. Indeed, the Gantz/Miller study upon which Rudebusch so heavily relies suggests that the adjustments which were actually made were so small as to be statistically insignificant — even when rank, experience, and discipline are taken into account. Then again, it is not clear whether the jury relied upon figures of overall disparity or some lesser figure when concluding that a manifest imbalance existed. Which is all to say that we cannot determine as a matter of law whether the range of adjustments made, however crude they may have been, fall within the range of moderate increases necessary to eliminate the imbalance. Because this is ultimately a disputed factual issue, it cannot be resolved on summary judgment, and we remand to the district court with instructions that a fact finder determine whether these adjustments were designed to attain a balance.

III. Department of Labor Letter

Finally, Rudebusch challenges the admission into evidence of a letter written to the University by the regional director of the Department of Labor’s Office of Federal Contract Compliance Programs, Joseph Franco. We review for an abuse of discretion the district court’s decision to admit this evidence at trial. United States v. Hankey, 203 F.3d 1160, 1166 (9th Cir.2000).

The OFCCP letter explains the Office’s continuing obligation to ensure that the University comply with its preapproved affirmative action policy in order to remain eligible for federal funding as a federal contractor. The letter specifically iterates OFCCP’s conclusion that Hughes’ actions in March 1993 were in compliance with the university’s affirmative action program and its obligations as a recipient of federal funding. Rudebusch objected to its admission at trial on hearsay and relevance grounds. The court admitted the letter over these objections; however, immediately after the letter was read into evidence, the court provided the following instruction to the jury:

Ladies and gentlemen, now is the appropriate time for me to make a comment about the evidence. This evidence goes to one of the issues that you’ll have to decide....
Mr. Franco’s statement or comment in the letter is simply some evidence which you may consider along with all the other evidence in the case in deciding ... the claim to which the letter relates. Mr. Franco — you cannot use his judgment to substitute for your judgment in making the ultimate determination in this case.
If he were a witness here, and he is not, I may or may not have allowed him to make the statement he includes in his letter in that direct fashion. He is not, therefore, subject to cross-examination because he is not here, so you must take the letter in that context and consider it as some evidence, but not the ultimate evidence on this issue....

Hughes argues that the letter should be admitted as a hearsay exception either as a business record under Fed.R.Evid. 803(6) or as a public record under Fed. R.Evid. 803(8). Neither exception appears to offer him a safe harbor because the letter does not establish a sufficient foundation, but even if the letter was erroneously admitted, “evidentiary error does not require reversal of a jury verdict unless a party’s substantial rights were affected.” Gilchrist v. Jim Slemons Imports, Inc., 803 F.2d 1488, 1500 (9th Cir.1986). Therefore, we must determine whether the verdict was “more probably than not” tainted by the error. Id. (citations omitted). Because this case is indistinguishable from Gilchrist, any error in admitting the OFCCP compliance letter was harmless.

In Gilchñst, we held that the district court erroneously admitted into evidence an EEOC “letter of violation” for an age discrimination action which had “a great[ ] possibility of unfair prejudice.” Id. As we noted, “[a] jury may find it difficult to evaluate independently evidence of age discrimination after being informed that the EEOC has already examined the evidence and found a violation.” Id. Nonetheless, we concluded that the error was harmless in light of a limiting instruction that mirrors the one given here. Id. at 1500-01 (the instruction read: “The letter need be given no greater weight than any other evidence in deciding the age discrimination claim.... You the jury, and not the EEOC are the sole judges of whether or not there was a violation of the Age Discrimination Employment Act.”). Coupled with the other evidence presented to the jury, Rudebusch’s effort to distinguish Gilchrist is unpersuasive. Any error was harmless.

Conclusion

Even if racial disparities in compensation at NAU were not so gross as to establish legally cognizable discrimination, we conclude that Hughes is nonetheless entitled to qualified immunity under the standard established in Saucier v. Katz. As for the Title VII claim, we cannot agree that summary judgment was appropriate for all aspects of this claim because a material dispute of fact prevents us from determining whether the adjustments did more than attain a balance. We therefore remand for further consideration. Finally, with respect to the Franco letter, we conclude that any error was harmless.

AFFIRMED IN PART; REVERSED AND REMANDED IN PART. Each party to bear its own costs on appeal.

KLEINFELD, Circuit Judge,

concurring in part and dissenting in part:

I.

I concur in the majority’s conclusion that President Hughes, acting on behalf of the State of Arizona, denied equal protection of the law to whites by categorically excluding them on account of their race from pay raises given to minorities. Appellants’ brief puts at issue whether female professors were denied equal protection with respect to minority males based on gender. Though the arguments relating to race and sex are commingled, appellants’s brief puts at issue whether white males were denied equal protection with respect to females as well as minorities. The first and second issues presented for review address “non-minority males” and “the non-minority male Class Action Plaintiffs.” I understand the majority decision to imply that, if the majority so read the briefs, then we would also be in agreement that President Hughes denied equal protection of the law to males on the basis of sex and white females on the basis of race.

I also concur in the majority’s conclusion that pay raises limited to minorities and females would not deny equal protection of the law, if they were narrowly tailored to remedy past discrimination and bring their salaries into parity with comparable persons of previously favored classes. I agree that a university president could (and should) identify and remedy any past discrimination based on race or sex by bringing the victims’s salaries into line with what they would have been in the absence of past discrimination. Such “catch-up” raises would properly be limited to individuals in the classes that had been discriminated against.

But, as the majority correctly concludes, the raises here weren’t just for parity or a “catch-up.” The Chambers study, on which President Hughes relied, said that females made, on average, $751 less than males, and minorities made, on average, $87 less than whites. But President Hughes didn’t raise average female and minority salaries by $751 and $87 respectively. Instead he raised female and minority salaries by averages of approximately $2400 and $3000 respectively. Thus, being female was worth an average of about $1,649 more than being white male as a university instructor (a $2,400 raise less a $751 catch-up yields about $1,649 excess value of females over males in an average case). Likewise, being a male member of an ethnic minority group was worth an average of approximately $2,913 more than being a white male. That’s not “parity” or “equity” or a “catchup.” Plain as day, it’s just paying minority males more than whites and females and females more than white males based on their race and sex.

Though I have put it more starkly, so far the majority opinion and I agree. President Hughes did indeed violate the constitutional rights of those disfavored on account of their sex and race. I respectfully dissent, however, from the majority’s holding that President Hughes is entitled to qualified immunity. The question on qualified immunity is “whether it would be clear to a reasonable officer that his conduct was unlawful in the situation he confronted.” In my opinion, it would. Any competent university president would know that he can’t pay people more or less than others based on their sex and race. The scheme here was straightforward: minorities are gold, women are silver, white men are bronze. It’s been a long time in America since anyone thought the Constitution allowed governmental discrimination based on sex and race. The law has been clearly established on this point for many years. President Hughes wasn’t entitled to pretend ignorance on this point because there was no case directly on point specifically on pay raises to “predicted” salaries based on regression analyses with the peculiar flaws of the Chambers study.

The majority justifies qualified immunity by saying “how tricky it is to measure whether sex and ethnicity are a significant determinant of salary.” Sometimes it is. But here, it wasn’t tricky. President Hughes’s own Chambers study said that minorities made an average of $87 less than whites and females made an average of $751 less than males. Moreover, it conceded that the disparities were not statistically significant between minority males and white males and that the largest individual case of disparity for a female professor and a predicted salary for a similarly situated white male was 1.77 standard deviations. But it wasn’t just that Hughes awarded differential pay raises based on the statistically insignificant pay disparity. Instead he instituted raises for females and minorities to levels much higher than the average amounts of $87 and $751 necessary to achieve parity.

This was because the stated theory of the Chambers study was to award raises to females and minorities to a “predicted” salary level based on rank, experience and tenure. This was mere obscurantism, but it was obvious which shell covered the pea. The “predicted” salaries aren’t “parity,” as they don’t bring women’s and minorities’s salaries up to the salary levels of similarly situated males and whites. Because of some crudities in Chambers’s analysis, such as assuming that the' difference in pay between assistant and associate professors would be the same as between associate and full professors, the “predicted” salaries were a theoretically ideal — not an empirically derived — number. That is what accounts for the resulting raises being far in excess of what was needed to achieve parity. Over half of the white males, about seventy percent of the females, and over half of the minority males were paid less than their “predicted” salaries, but Hughes only raised the females and minorities to the “predicted” levels, while white males under the predicted level got no raise. White males were not even allowed to apply for raises to bring their salaries up to “predicted” levels.

Arguably, a layman like President Hughes might not know that a statistically insignificant disparity did not mean anything, because he might not know what statistical significance means. A statistically significant difference is one “too large to be plausibly attributed to chance alone” and recognizing such a difference filters out variations due to chance. Thus, if you spin a roulette wheel (with no zero or double zero) twice and it comes out red both times that doesn’t mean it is rigged. On two spins it could come out Red-Red, Red-Black, Black-Red, or Black-Black, so a perfect wheel would come out Red-Red 25% of the time by chance. On two spins, Red-Red means nothing; it doesn’t show any “disparity” that needs correcting.

A common convention among statisticians is to use 0.05 as the measure of statistical significance, so that a result is treated as significant, where the number of cases is sufficient, if it would occur by chance no more than one timé in twenty. Analogously, a result is commonly treated as statistically significant when one can be 95% confident that it didn’t occur by chance. The majority’s reference to “two standard deviations” means the same thing: 95.4% of the cases are within two standard deviations above or below the mean of a normal distribution or curve if the number of cases is sufficiently high and the curve is of a normal shape.

A statistically insignificant difference is one where chance cannot be ruled out as explaining the result, like Red-Red in two spins of a roulette wheel. Chambers admitted that ethnicity was not a statistically significant variable and his study found the largest disparity for a female professor was 1.77 standard deviations from the predicted mean salary. In the case at bar, chance could explain differences in pay between candidates if, for example, one instructor joined the faculty in a fat year for faculty salaries and another in a lean year. “Correcting” a statistically insignificant disparity is like rigging a roulette wheel that came out red twice in a row so that it comes out black more often. A competent university president relying on a statistical study to award raises only to those persons with favored ethnic and sex characteristics would know what “statistically insignificant” meant or would find out. President Hughes claimed to rely on the Chambers study, so he was obligated to read and understand it.

Even if we couldn’t expect this level of statistical understanding from a university president, the Chambers study had another serious failing obvious to anyone affiliated with a university, which no university president could have missed. On the first page of the executive summary of Chambers’s study, which Hughes relied on to award the raises, in conspicuous type set off from the rest, Chambers stated that he did not control for “other factors influencing salary levels, including doctorate and performance.” There is not a university president, or even a university student, who wouldn’t know that a doctorate is the sine qua non for advancement on a university faculty. No competent university president could take seriously a study of pay discrimination among instructors that did not control for whether they had doctorates.

Indeed, in Bazemore v. Friday, the Supreme Court noted that “some regressions may be so incomplete as to be inadmissible” and irrelevant. Although incomplete regressions that leave out some factor will often be admitted and accorded less probative weight, Bazemore plainly states that a regression’s failure to include certain critical variables could lead to its complete irrelevance and inadmissability. A regression of salaries in a university setting that doesn’t include doctorate, merit, or performance as variables is like a regression study that predicts shoe size from weight without considering foot size. Had Chambers included doctorate, performance, and merit ratings (or even just doctorate) it may have even eliminated the statistically insignificant salary disparity.

Finally, even if President Hughes didn’t understand statistical significance, he would have had to see from the practical effect of the raises that he was causing rather than remedying sex and race discrimination. Here are a couple of typical examples. Two Assistant Professors of Criminal Justice, one minority and one “Anglo” (as the study put it) held the identical position, rank, title and duties. Before President Hughes’s raises, both were paid the identical amount, $33,000 per year. Pursuant to the Chambers study President Hughes gave the minority Assistant Professor a raise of $3,353. As Chambers admitted, he hadn’t controlled for “performance,” and this case, like others, highlights the significance of that failure. The Anglo professor had several more publications than the minority professor, including several books, and brought in more money in grants than the minority candidate. President Hughes testified that he was not concerned about merit or performance in awarding the raises. It shows. The additional $3,353 for the minority professor was because of his ethnicity and nothing else. And only ethnicity explains why President Hughes paid the Anglo nine percent less than the minority after the raise.

Since females were silver and minorities were gold, injustice prevailed even among those receiving raises. Two assistant professors of criminal justice both made $33,000 before the raises, one an Anglo female, the other a minority male. The female got a $2,146 raise, the minority male $3,353. Like the previous pair, they were both paid equally before the so-called “equity” raises. The only basis for why the minority male got $1,207 more than the Anglo woman, and she got three percent less than the minority after the raise, was his ethnicity. And all that explained why President Hughes paid the white male six percent less than the female was his sex. As in the previous example, considering performance dramatizes the kind of “equity” at play. Here, just like her white male counterpart, the female professor had more publications and brought in more grant money than the minority professor. But even disregarding performance, the female Anglo was paid less than the minority male because of her ethnicity, and the Anglo male less than her because of his sex.

The table showing these comparisons is in Chambers’s own executive summary. It includes names, so it would be easy for President Hughes' to make the comparisons, and it’s likely that he knew something about these individuals. There is no way to mistake these raises for “equity” raises bringing minorities and females into parity with white males. The record is replete with similar comparisons. And it is perfectly plain, and uncontradicted, that the raises were awarded purely for being of the preferred sex and the preferred ethnicity.

True, the Gantz-Miller study showing precisely why the Chambers study didn’t prove race or sex discrimination or justify the raises wasn’t prepared until after Hughes awarded the raises. But it didn’t rely on new data, it just penetrated the obscurantism and flaws in the Chambers study. And even without it, President Hughes could easily see . what he was doing, even if he couldn’t be expected to see exactly why the Chambers study didn’t justify doing it.

Though the facts were unmistakably obvious, President Hughes would still enjoy qualified immunity if the law were insufficiently clear. The right at issue has to have been “sufficiently clear that a reasonable official would understand that what he is doing violates that right.” Sometimes sufficient specificity requires a fair amount of development of the case law to inform the reasonable officer. For example, a policeman should know that he can’t use excessive force to arrest a suspect, but may need a case to tell him whether hurrying a suspect away from a location where the Vice President was speaking and shoving him into a van was excessive. But in this case, the law was clearly established at a sufficient level of specificity.

At the general level, everyone in America knows that the constitution prohibits the government from treating some people better than others because they are of a preferred sex or ethnicity. True, no case at the time specifically outlawed what Hughes did under the circumstances. But, we don’t require a case on point at that level of specificity in order to “clearly establish” the law. The qualified immunity standard of clarity is met provided that the “unlawfulness is apparent in light of preexisting law....” Even in the absence of an analogous case a right can be clearly established “on the basis of common sense.” Numerous cases detail the limitations on government to distribute a variety of benefits where the criteria considered for distributing those benefits is being the governmentally preferred race or sex. From these cases, a reasonable university president should have been able to conclude that awarding raises to individuals beyond what was necessary for parity because of their race or sex alone was unconstitutional. Even without cases on point, a reasonable university president would know that he could not constitutionally pay some people more than others based on a preference for their ethnicity or sex.

II.

As for the Title VII claim, I concur in the majority’s remand to determine whether the pay raises were “designed to attain a balance.” With the record as it stands now, there seems to me to be only one correct answer to that question. Chambers himself said that when he controlled for experience, rank, discipline and tenure status (not doctorate or performance), males made $751 more than females and “Anglos” made $87 more than ethnic minorities. I cannot see how, even if, disregarding statistical significance, raises of $751 and $87 could be “designed to attain balance,” that the female and minority raises averaging approximately $2400 and $3000 could be to “attain balance.”

The University admits, and the majority notes, that “over half of its white male faculty were making less than the predicted salary of a similarly situated white male” under the Chambers study, but answers their demand that solicitude be nondiscriminatory by saying, “[s]uch is the law of averages: some will be above the mean and some will be below. Such is also the reality of the teaching profession ....” The law of the Constitution requires that people not be discriminated against because they are the wrong color or the wrong sex. Though the law of averages ordinarily leaves some people below average, the government can’t constitutionally bring only some employees up, above average — to “predicted” levels— based on whether they have the right sex and ethnicity. But there’s no harm in leaving this to be fleshed out on remand.

III.

Finally, I dissent from the majority opinion’s holding that admitting the letter from Joseph Franco, the Regional Director of the Department of Labor’s Office of Contract Compliance, was harmless error.

President Hughes did not call Director Franco as a witness, so the evidence came in without any opportunity for plaintiffs to cross examine him, and see what he meant by the letter, whether it was an official position of his office, what Director Franco or his staff had examined prior to taking the position, whether the position was taken as a friendly accommodation to President Hughes rather than as an evaluation of the legal obligations of the university, and so forth. Plaintiffs’ hearsay objection was overruled. As the majority opinion correctly notes, the business and public records exceptions to the hearsay rule do not appear to allow admission of the letter.

The significance of the letter was to show the jury that President Hughes had no choice, the federal government required him to do what he did. The letter says that it is the position of the federal Contract Compliance Office that the female and minority raises at issue were a legal “obligation” of the university under a federal executive order and under the affirmative action plan that the university had an “obligation” to maintain. That is tremendously powerful evidence. A fair jury could hardly impose personal liability on a college president for doing what he was obligated to do by federal law. In the eyes of the jury, the handcuffs on the president were especially tight, because the Office of Contract Compliance could affect the university’s revenue stream.

Consequently, I respectfully dissent from the majority’s conclusion that the error was harmless. The test for harmlessness is whether “the jury more probably than not would have reached the same result absent the error.” Considering how weak the Chambers study was and the egregiousness of the sex and race discrimination, I question whether it would have, but for this letter.

Nor does the case the majority opinion relies on, Gilchrist v. Jim Slemons Imports, Inc., save the verdict from this devastating letter. The letter in Gilchrist was an agency determination that the employer had discriminated. We held that the district court should have exercised its discretion whether to admit it and erroneously admitted it as a matter of right. However, we held that the admission was harmless (though a “close call”) because it was only introduced on damages, not liability, and the district court told the jury that the jury and not the EEOC was the sole judge of whether there was a violation.

There are several differences between the Gilchrist letter and the letter in the case at bar. First, Gilchrist had been fired about two years before the letter, and a month after the letter, he was offered a position. The employer claimed he had failed to mitigate his damages by refusing the offer, and Gilchrist introduced the letter to show that the offer of a job was part of a package to make him waive damages the EEOC had already determined he was entitled to. In the case at bar, however, the letter did not affect any decision President Hughes made. President Hughes requested it from Director Franco after he awarded the raises, probably after the white males complained. And Hughes introduced it to show absence of liability — the core issue for the jury— not merely on a point of mitigation of damages. Second, the Gilchrist letter was relevant to whether Gilchrist ought to have taken the job offer, but the Franco letter, because it was subsequent to all of the relevant conduct, was irrelevant to any conduct at issue. It is impossible that a letter written after Hughes gave the pay raises was something that he relied on or obeyed. Because of this temporal impossibility, the letter can’t be probative on the qualified immunity issue, and can’t establish that President Hughes was merely obeying a government directive in the letter.

Finally, it is also less likely that cross examination would have mattered in Gilchrist, because of the nature of the letter there. The Gilchrist letter was an agency determination resulting from an adversarial proceeding before an administrative law judge, who reached a conclusion based on admitted evidence and produced a record to evaluate this decision. In contrast, the Franco letter said that it was “to confirm conversations and understandings” between Franco and someone on President Hughes’s staff, based on unspecified “information furnished to this office.” The letter does not even say whether Franco ever saw the Chambers report or any other data, or just had it described to him over the phone by someone on President Hughes’s staff. The indeterminateness of Director Franco’s basis for the letter and the one-sidedness of the process that led to its issuance magnifies the risk of unfair prejudice here.

Because Gilchrist was, as that decision said, “admittedly a close call” as to whether the erroneously admitted evidence was harmless, and the letter in this case was both much more prejudicial and much less relevant, extension of Gilchrist is not justifiable. Admission of the letter alone would be ground for reversal even if the case were not otherwise reversible, as it is. 
      
      . See Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977); Hazelwood, 433 U.S. at 309-12, 97 S.Ct. 2736 (1977); Palmer v. Shultz, 815 F.2d 84, 96 n. 9 (D.C.Cir.1987) (noting that based on Castaneda and Hazelwood court could not allow the threshold at which an inference of discrimination is raised to be lower than 1.96 standard deviations); Maitland v. Univ. of Minn., 155 F.3d 1013, 1016 (8th Cir.1998) (noting that prior study showed a statistically insignificant difference in pay (2%)).
     
      
      . See, e.g., Penk v. Oregon State Bd. of Higher Educ., 816 F.2d 458, 465 (9th Cir.1987) (upholding conclusion that plaintiffs failed to establish existence of actionable discrimination, noting that “such highly determinative quality and productivity factors as teaching quality, community and institutional service, and quality of research and scholarship” were missing from multiple regression evidence); Smith v. Virginia Commonwealth Univ., 84 F.3d 672, 676-77 (4th Cir.1996) (observing that “Bazemore and common sense require that any multiple regression analysis used to determine pay disparity must include all the major factors on which pay is determined,” and holding that whether the Virginia study had adequate proxies for performance, productivity and merit was question of fact).
     
      
      . David H. Kaye and David A. Freedman, Reference Guide on Statistics in REFERENCE MANUAL ON SCIENTIFIC EVIDENCE 83, 145-50 (2d ed.2000); Daniel L. Rubinfeld, Reference Guide on Multiple Regression, id. at 179-221.
     
      
      . Although some minority male and female faculty members received far less than these average values, I note, as the majority does, that most salary adjustments were between $1,001 to $3,000 for the female professors and between $2,001 to $3,000 for minority males. Majority Op. at 511-512.
     
      
      . Saucier v. Katz, 533 U.S. 194, 202, 121 S.Ct. 2151, 150 L.Ed.2d 272 (2001).
     
      
      . See, e.g., Richmond v. J.A. Croson Co., 488 U.S. 469, 109 S.Ct. 706, 102 L.Ed.2d 854 (1989) (striking down a city’s minority set aside plan in the contracting context); Regents of Univ. of Cal. v. Bakke, 438 U.S. 265, 98 S.Ct. 2733, 57 L.Ed.2d 750 (1978) (striking down a rigid set aside plan for allocating student spots in state-supported universities as violated the Equal Protection Clause); Mississippi Univ. for Women v. Hogan, 458 U.S. 718, 102 S.Ct. 3331, 73 L.Ed.2d 1090 (1982) (holding that a policy of a state-supported university, limiting its enrollment to women, of denying otherwise qualified males right to enroll for credit in its nursing school violated Equal Protection Clause); Reed v. Reed, 404 U.S. 71, 92 S.Ct. 251, 30 L.Ed.2d 225 (1971) (holding a provision of the Idaho probate code that gives a preference to men over similarly situated women violates the Equal Protection Clause); McLaurin v. Oklahoma State Regents for Higher Ed., 339 U.S. 637, 70 S.Ct. 851, 94 L.Ed. 1149 (1950) (holding that a state sponsored graduate school’s disparate treatment of an admitted black student based on his race violated the Equal Protection Clause).
     
      
      . Majority Op. at 518.
     
      
      . It may be that the Chambers study should have been excluded under Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), but that argument is not raised on the appeal, so we do not rule on it. The majority opinion states that the propriety of controlling for particular variables goes to the weight and not the admissibility of a study, but this is dicta, because we are not faced with a dispute about admissibility.
     
      
      . Gary Smith, Statistical Reasoning § 10.3 at 362 (2nd ed.1988).
     
      
      . Id. at 397-98.
     
      
      . Chambers Study, Executive Summary at 1.
     
      
      . 478 U.S. 385, 400-01 & n. 10, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986) (Brennan, J„ concurring, in a portion of his concurrence joined by the majority).
     
      
      . Id.
      
     
      
      . Similarly, the female professor received a $2146 raise over the white male from the prior example.
     
      
      . Saucier v. Katz, 533 U.S. 194, 202, 121 S.Ct. 2151, 150 L.Ed.2d 272 (2001).
     
      
      . See id. at 208-09, 121 S.Ct. 2151 (discussing whether this constituted excessive force under the conditions).
     
      
      . See Giebel v. Sylvester, 244 F.3d 1182, 1189 (9th Cir.2001) ("Precedent directly on point is not necessary to demonstrate that a right is clearly established.").
     
      
      . See id.
      
     
      
      . Id.
      
     
      
      . See supra note 2.
     
      
      . Majority Op. at 524.
     
      
      . Id. at 523.
     
      
      . Id.
      
     
      
      . Beachy v. Boise Cascade Corp., 191 F.3d 1010, 1016 (9th Cir.1999).
     
      
      . Gilchrist v. Jim Slemons Imports, Inc., 803 F.2d 1488 (9th Cir.1986).
     
      
      
        .Id. at 1500.
     
      
      . See 29 U.S.C. §§ 211, 626.; 29 C.F.R. § 1626.15(a) & (b).
     
      
      . Gilchrist, 803 F.2d at 1500.
     