
566 F.Supp. 1166 (1983)
Edna H. SOBEL, M.D., and Bella C. Clutario, M.D., on behalf of themselves and other professional faculty members employed by the Defendant, Yeshiva University, similarly situated, Plaintiffs,
and
Equal Employment Opportunity Commission, Plaintiff-Intervenor,
v.
YESHIVA UNIVERSITY, Defendant.
No. 75 Civ. 2232 (GLG).
United States District Court, S.D. New York.
June 24, 1983.
*1167 Specter & Buchwach, P.C., Pittsburgh, Pa., for plaintiffs and the class; Howard A. Specter, Michael D. Buchwach, Pittsburgh, Pa., of counsel.
E.E.O.C., David L. Slate, Gen. Counsel, James N. Finney, Associate Gen. Counsel, Jane L. Dolkart, Asst. Gen. Counsel, Estelle D. Franklin, Acting Supervisory Trial Atty., Washington, D.C., for plaintiff-intervenor; Richard P. Theis, Gary T. Brown, Washington, D.C., of counsel.
Sidney Schutz and Winer, Neuburger & Sive, P.C., New York City, for defendant; Daniel Riesel, Mark A. Chertok, Lawrence R. Sandak, New York City, of counsel.

AMENDED OPINION[*]
GOETTEL, District Judge:
Mark Twain supposedly once said that there are three kinds of lies: lies, damned *1168 lies, and statistics. Though perhaps hyperbolic, this declaration of distrust aptly warns that any conclusion based on statistics may be unsound. It is most unfortunate, therefore, that the evidence in this case is almost completely statistical.
From December 20, 1974, to October 15, 1979 (the "relevant time period"), the named plaintiffs in this class action, Edna H. Sobel and Bella C. Clutario, were medical doctors employed by defendant Yeshiva University ("Yeshiva") as full-time faculty members of its medical school, the Albert Einstein College of Medicine ("Einstein"), which is located in New York City. The class which Sobel and Clutario represent consists of all female physicians who, at some point during the relevant time period, were employed as full-time members of Einstein's faculty.[1] At trial, the plaintiffs claimed that during the relevant time period the defendant discriminated against them with respect to both salaries and pensions. For reasons discussed below, however, the Court has concluded that the plaintiffs have failed to prove both of these claims, except to the extent that they have established that Yeshiva's pension plan is illegally premised upon gender-based actuarial tables.

I. PROCEDURAL BACKGROUND
In their original complaint, filed on May 9, 1975, Sobel and Clutario claimed that Yeshiva, through Einstein, was intentionally discriminating, with regard to salaries and other terms of employment, against female faculty members who held M.D. degrees and worked in the Pediatrics Department. Believing themselves to be the victims of illegal sexual discrimination, the plaintiffs sought back pay[2] and other forms of relief authorized under Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq. (1976 & Supp. V 1981).[3]
On June 18, 1975, plaintiff Sobel filed her charge of discrimination with the Equal Employment Opportunity Commission (the "EEOC"), alleging gender-based discrimination in pay and in the amount of Yeshiva's contributions to her pension plan due to such lower pay. On the same date, plaintiff Clutario filed a similar charge with the EEOC.
After June 1975, the plaintiffs' claims in this action were substantially altered by a number of events. The EEOC issued "right to sue" letters to the plaintiffs on March 19, 1976. The plaintiffs amended their complaint on June 16, 1976, to include as defendants the chairpersons of certain departments at Einstein. Also, by virtue of that amended complaint, the class grew to include all female physicians who were employed by Yeshiva at any time during the relevant time period and who held the rank of instructor, assistant professor, associate professor, or full professor, whether in a full-time or part-time capacity.[4] Claims of gender-based discrimination in pay, promotion, and other terms and conditions of employment were alleged on behalf of the class. Later, on May 31, 1977, the Court *1169 granted the EEOC's motion to intervene as plaintiff, in the belief that the EEOC might be more experienced than the individual plaintiffs in the use of statistics to prove gender-based discrimination in a professional education setting.
Although these events bespoke a general tendency to add, or attempt to add,[5] issues and parties, the case was ultimately greatly simplified before trial. The group to be analyzed was limited to full-time faculty members of Einstein.[6] The claims against all individual department heads were dropped and Yeshiva became the sole defendant. The claims of discrimination in promotion and tenure were withdrawn and those concerning other more amorphous conditions of employment were not pursued. Thus, the case was ultimately reduced to the relatively narrow issue of whether, with respect to pay and pension benefits, Yeshiva had discriminated against the full-time female doctor-professors of Einstein.
Despite the narrowness of the issue and the fact that only the question of liability was tried (the question of damages having been reserved for the second part of these bifurcated proceedings), the trial lasted approximately three weeks and involved voluminous submissions by both parties. Throughout most of the trial, the plaintiffs continued their long-held strategy of trying to prove their pay claims under the theory of "disparate treatment." Thus, they attempted to show that Yeshiva and Einstein (hereinafter used somewhat interchangeably) intentionally engaged in a pattern or practice of discriminatory treatment during the relevant time period and that such treatment constituted the standard operating procedure at the college. As the trial continued and the evidence developed, however, the plaintiffs felt compelled to resort to a theory of "disparate impact" as well. Under this second theory, they attempted to prove that, while the procedure at Einstein might appear neutral on its face, it in fact had an unjustifiably harsh and discriminatory impact on the plaintiffs. See Teamsters v. United States, 431 U.S. 324, 335-36 n. 15, 97 S.Ct. 1843, 1854-55 n. 15, 52 L.Ed.2d 396 (1977) (contrasting disparate treatment and disparate impact). The procedural propriety of this shift in theories, as well as the merits of the plaintiffs' claims, cannot be discussed, however, until after a few basic facts have been set forth.

II. THE FACTS

A. The Organization of the College

The complex nature of Einstein's organization made statistical analysis of its employment practices difficult. Einstein's faculty during the relevant time period was extremely large and included approximately 1330 individuals with M.D. degrees[7]. Many of them either worked part-time or were actually staff members of affiliated hospitals and were therefore designated as part of Einstein's faculty even though the college did not pay them. Those faculty members who were paid by the defendant included 626 physicians. Of this latter group, 316 men and 95 women were full-time faculty members.[8] However, these *1170 numbers included everyone who worked at any time during the relevant time period.[9] The number of full-time faculty members with M.D. degrees in any given year ranged between 204 and 295, of whom 49 to 60 were women.
Even more impressive than the size of Einstein's faculty, however, was the complexity of its finances. From the date of its founding in 1955, Einstein received numerous public and private grants for its extensive scientific research. It also entered into affiliation contracts to provide patient care at, inter alia, the Bronx Municipal Hospital Center and the Lincoln Hospital. In 1966, Einstein also opened its own hospital. In addition to practicing medicine, conducting research, and teaching students at all of these institutions, Einstein's faculty provided similar services to eight other institutions in the New York Metropolitan area.[10] Einstein's income came primarily from payments for the patient care that Einstein's faculty provided at these institutions and from research grants. Only a very small portion of its total income came from the tuition paid by its students.
The activities and responsibilities of Einstein's professors varied enormously. Some were involved primarily in classroom teaching, others in research, and still others in the clinical instruction of students. Of course, many of the professors were involved in two or three of these activities.
A particular professor's responsibilities also depended in great part upon his or her particular department, specialty, and subspecialty. Einstein had twenty-eight primary departments, each headed by a chairperson who had overall responsibility for running the department, including making budgetary and salary recommendations.[11] These departments typically fell into one of two categories: preclinical and clinical.[12] The faculty members in the preclinical departments were primarily responsible for classroom instruction and laboratory research, while the faculty members in clinical departments had substantial responsibility for the administration of services and the instruction of students, interns, and residents in the hospital settings.
Not surprisingly, the economic rewards tended to vary with the lucrativeness of the activities the professors pursued. For example, those individuals who devoted substantial time to private practice would see this reflected in the amount of their total pay.[13] Also, as a general proposition, those physicians who engaged primarily in research were compensated at rates lower than those who engaged in clinical activities.[14] Those who were primarily classroom teachers received the least income. Moreover, *1171 within the group of professors who were primarily clinicians, their total income varied according to their specialties and sub-specialties. Typically, those in specialties which were hospital oriented and "essential," such as surgeons, anesthesiologists, and radiologists, were the most highly compensated.[15]
Finally, of greatest importance to this case, it appears that the women professors tended to specialize more in the non-clinical fields, and even those in clinical fields were typically in non-hospital related specialties such as pediatrics.[16] These tendencies and the other factors described above make it extremely difficult to treat all doctor-professors equally for statistical purposes, even if allowance is made for age and experience. The number of variables reveals, in fact, that the various positions were simply not fungible.

B. Initial Salaries

Throughout the period in question, Einstein followed a fairly standard procedure for determining initial salaries. The chairperson of a department would recommend the initial salary for a new faculty member, who was usually to be hired as either an instructor or assistant professor. In formulating this recommendation, the chairperson would consider several factors, including: the person's prior salary, specialty, sub-specialty, and clinical research; the needs of the college; and the demand for such a person in the open market. Also, for anyone who had already held a faculty position, the chairperson would look for such indications of productivity as faculty rank, the quantity and quality of publications, and the winning of any grants.
Each year, only a handful of outside scholars would be hired at the more senior ranks of associate professor and full professor. In particular, this might be done when a new departmental chairperson was to be appointed. The chairperson would be selected by the Dean upon the recommendation of a faculty search committee. Anyone appointed chairperson would receive additional compensation for the extensive administrative responsibilities that accompanied such a position. Each chairperson was the one member of his or her department who was to report directly and regularly to the Dean.[17]
The Dean was responsible for the establishment of salary scales, or "ranges," for both the preclinical and clinical departments. These ranges were determined in part by gathering comparable information from other medical schools. While the ranges of both the preclinical and clinical departments were calibrated to reflect faculty rank and the number of years within a particular rank, only the clinical departments' ranges also took into account individuals' specialties.[18]

C. Salary Increases

Salary increases for Einstein's professors were generally based on a "guideline increment" *1172 system. This system took into account annual increases in the cost of living as well as Einstein's financial resources and had been implemented to control faculty salary expenditures and to assure a balanced budget. The guideline increases took one of three forms: either a percentage of present salary, a fixed amount, or a combination of a salary percentage and a fixed amount. The guideline increases were determined annually by the Dean in consultation with his staff and the departmental chairpersons. During most of the relevant time period, the guideline increases merely approximated the annual increases in the cost of living, but in some years even fell short of the change in that indicator. As a result, those receiving a guideline increase typically received no increase in real earning power. Only someone who was promoted in faculty rank, and was thereby awarded an additional increment of five percent would see such an increase in real income.
After the guideline increases were determined, each department submitted to the Dean a budget, which included the various increases that the department recommended for its members. Any recommendation for an increase equivalent to the guideline increase was routinely approved, while a recommendation for a non-guideline increase was carefully reviewed and had to be justified.[19]
An above-guideline increase might be granted to reward an individual for outstanding production or exceptional achievement, or to compensate a person for assuming additional duties or administrative responsibilities, or to correct what was thought to be an unduly low salary. An increase made for the last purpose was sometimes referred to as an "inequity" increase. Such an increase would be granted, for example, when there was a need to equalize the lower salaries of long-appointed faculty members and the higher salary of someone recently hired.
Below-guideline increases were also made. For example, a faculty member who gave up either administrative responsibilities or activities that had generated income for the college, might receive a below-guideline increase. Also, on occasion, severe budgetary constraints within a department might compel below-guideline increases for some or all of its members.
In sum, although the majority of faculty members received guideline increases each year, departmental chairpersons possessed discretion to recommend non-guideline increases. These discretionary increases were carefully scrutinized by the Dean's office, which would approve, disapprove or modify them. Whatever increases the Dean finally endorsed became the actual increases that the faculty members received.[20]

D. Promotions in Rank

As mentioned earlier, the only way to receive an increase in real income was to be promoted. Promotions, however, were handled in a totally different manner than were salary increases. Appointments and promotions to senior ranks were recommended by one of two standing faculty committees which were independent of the Dean.[21] In each case, an ad hoc committee comprised of faculty members would be formed to determine whether a candidate had satisfied the criteria for promotion and to issue a nonbinding recommendation and report to the relevant standing committee. The criteria for promotion included creative scholarship, the quality of research, the *1173 quality of teaching, the extent and quality of clinical and administrative service, and the national or international reputation of the candidate. Thus, in contrast to the factors which were determinative of salary increases (the generation of revenue from private practice, one's specialty and sub-specialty, competing job offers, and the availability of funds), the primary consideration in a promotions decision was the quality of the candidate's work. The type of work done and the financial rewards adhering to it were of little or no importance.
Five years in a given rank was typically the minimum period spent before consideration for promotion to the next senior rank was given. Of course, after a faculty member had reached the highest rank, that of professor, no further promotions were available, and creative scholarship and scholastic achievement could be rewarded only by above-guideline pay increases or by appointment to an administrative position with its attendant increase in compensation.

III. DISCUSSION

A. Statistical Proof Generally

As noted earlier, the plaintiffs relied extensively upon statistics in their attempt to prove their case. Such a heavy reliance upon statistical evidence in employment discrimination cases has, of course, been widely accepted by the courts and even received the imprimatur of the Supreme Court. See Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741-42, 53 L.Ed.2d 768 (1977). In such a case, the court's task is to determine whether the plaintiff's statistics make out a prima facie case of a practice or pattern of discrimination, and, if so, whether that case is fatally undercut by a showing that the plaintiff's "proof is either inaccurate or insignificant." Teamsters v. United States, supra, 431 U.S. at 360, 97 S.Ct. at 1867. Of course, in determining whether the plaintiff has established a prima facie case, the court should not ignore the defendant's relevant evidence of nondisparate treatment. "Prima facie evidence means the `net of the evidence;' that is, the court must consider the evidence presented by both parties." Underwood v. Jefferson Memorial Hospital, 639 F.2d 455, 457 (8th Cir.1981); see also Equal-Employment Opportunity Commission v. E.I. Dupont de Nemours & Co., 445 F.Supp. 223, 232, 243 (D.Del.1978). Thus, this Court has carefully weighed both the plaintiffs' and the defendant's statistical proof before deciding whether a prima facie case of discrimination has been presented.
Here, the plaintiffs' experts designed a multiple regression model to estimate the effects that various independent variables had upon the single, dependent variablesalary level. When properly used in a Title VII case, this "methodology provides the ability to determine how much influence factors such as sex, experience, and education each have had on determining the value of a variable such as salary level." Coble v. Hot Springs School District No. 6, 682 F.2d 721, 731 (8th Cir.1982).
Significantly, the courts have generally accepted the idea that the plaintiff, to establish a prima facie case by statistical evidence, is required to demonstrate a difference of more than two or three standard deviations between the expected incidence of a particular type of event (or, as in this case, the expected level of salary for the minority in question) and the actual incidence of such events (or actual level of the minority's salary).[22]See, e.g., Hazelwood, supra, 433 U.S. at 308-09 n. 14, 97 S.Ct. at 2742 n. 14; Castaneda v. Partida, 430 U.S. 482, 496-97 n. 17, 97 S.Ct. 1272, 1281-82 n. 17, 51 L.Ed.2d 498 (1977); Board of Education of the City of New York v. Califano, *1174 584 F.2d 576, 584 n. 29 (2d Cir.1978), aff'd, 444 U.S. 130, 100 S.Ct. 363, 62 L.Ed.2d 275 (1979). Although some have suggested that such an absolute requirement should not be imposed in all cases, see, e.g., Hilton v. Wyman-Gordan Co., 624 F.2d 379, 381 (1st Cir.1980), few would disagree that where, as here, the fungibility of the faculty of a medical college is considerably in question and the number of independent variables so great, one can have little confidence in drawing inferences from statistics that reveal a disparity that is significant at a level of less than two standard deviations.[23]

B. Plaintiffs' Statistical Analysis

In attempting to analyze Einstein's unique and complex pay structure, the EEOC retained two outstanding economists and statisticians, Dr. Orley Ashenfelter of Princeton University and Dr. Donald E. Wise of the New Jersey consulting firm of Mathtech, Inc. Despite their being specialists in econometrics (the application of statistics and mathematical modeling to economic problems), this was their first experience with pay and promotions at a medical college.
Their initial problem was to construct a valid data base. They encountered numerous difficulties,[24] and their various proposals were repeatedly challenged by the defendant's experts, who began to construct their own data base. As the months progressed and the parties tried to resolve their disagreements about the data, the plaintiffs' experts issued a number of versions of what they thought the data base should be. Ultimately, however, they adopted the defendant's proposal almost in toto.[25] The two exceptions to this strategy were (1) the inclusion of a few faculty members who had been excluded by the defendant's experts,[26] and the substitution of their own data for the years preceding the academic year 1974-75.
Difficult as the data base problem was, it was insignificant in comparison to the problem of identifying the appropriate variables to be included in the regression analysis. The plaintiffs' experts were using a multiple linear regression to explain the variation between male and female salaries in terms of two components: an explanatory component (a linear function of a set of available, observable explanatory factors, called "variables") and an error component, which represented departures from the explanatory component due to unknown causes or random disturbances. The sex coefficient in the plaintiffs' multiple linear regression model purportedly reflected the differences in the annual average base salaries of male and female faculty members, while holding constant certain independent variables. The multiple linear regression model was intended to mimic, by statistical formula, the variety of factors which determined salary at Einstein. According to the plaintiffs' theory of labor markets (a general theory about the relationship between pay, the productivity characteristics of employees, and the nonpecuniary characteristics of particular jobs), any differences between the salaries of men and women that were not explained by the pertinent variables to be used in the model had to be the result of sex discrimination. Unfortunately, however, their theory of labor markets did not identify which variables had to be used in the model if it were to accurately and reliably explain the causes of any discovered salary differentials.[27]
*1175 The defendant's equally prominent experts, three of whom were associated with Columbia University, used a number of variables different from those originally used by the plaintiffs' experts. Interestingly, when the latter received the defendant's initial report, they decided to add to their rebuttal report some, but by no means all, of the defendant's data and variables.[28] Much later, in the plaintiffs' experts' fourth and final report (the only one offered in evidence), they presented two sets of tables, one of which omitted four variables that the defendant's experts considered critical and the other of which included those variables.[29] In the opinion of the defendant's experts, however, even this second table omitted several relevant variables and included other variables which were unnecessary and, in some cases, misleading.[30]
In their multiple linear regressions, the plaintiffs' experts analyzed the salaries of class members and of their male colleagues for the years 1969 to 1979 (and thus covered several years prior to the relevant time period). After determining for each year the raw difference between the average salary of female faculty members and that of male faculty members, the experts calculated an annual adjusted salary coefficient, or "sex coefficient." This sex coefficient represented that part of the total difference in salaries which, because it was not attributable to any of the explanatory variables, might be attributable to sexual discrimination. By means of these calculations the plaintiffs' experts determined to their satisfaction that the salary differences disfavoring women were statistically significant (at the 0.05, or two standard deviation, level) for the year 1970 and the years 1973 through 1978.[31] The plaintiffs also separately analyzed the differences between the salaries of full-time faculty members hired prior to March 24, 1972 (when Title VII became applicable to universities) and those hired thereafter. The overall conclusion of the plaintiffs' experts was that, at least with respect to faculty members hired before March 24, 1972, the average salary of the class members during the relevant time period was discriminatorily lower than that of their male colleagues and that the gross disparity in salaries increased with the passage of time.

C. Defendant's Statistical Analysis and Critique of Plaintiffs' Statistics

For a number of reasons, the defendant's experts did not agree with the conclusions of the plaintiffs' experts. First, from the broadest perspective, the defendant's experts noted that a multiple linear regression is best used where there is experimental control of the explanatory factors, replicability of observations, and randomization of experimental material of close comparison groups to eliminate systematic bias. The model must be properly specified, and the errors must be random and statistically independent of each other and of any explanatory *1176 variables. Moreover, the errors must be normally distributed with a zero mean and constant variance. The defendant noted that most of these requirements were not met by the plaintiffs' model.
Second, as indicated earlier, the defendant disputed some aspects of the data base used by the plaintiffs. The defendant concluded that if one used an accurate data base, such as that which the defendant eventually adopted, but still retained the plaintiffs' variables, salary discrimination at a statistically significant level could be shown in only three years  1974, 1975, and 1978.
Third, the defendant argued that the use of a logarithmic form of salary as the dependent variable would stabilize the scatter of residuals and provide a more accurate approximation for the assumptions underlying the multiple linear regression model. The defendant pointed out that when this was done and the appropriate data base was used, the disparity in salaries was statistically significant in only one year, 1975. Furthermore, if just some of the defendant's disputed variables were also added, the level of significance for that year decreased to exactly two standard deviations. Finally, the defendant contended when all of its variables and none of the plaintiffs' disputed variables were used, there was no year for which salary discrimination at a statistically significant level could be demonstrated.
A summary of the defendant's major points is amply illustrated by the six tables below, which are drawn from exhibit 752 L-1 and which cover only those years that are relevant to this action, 1974 through 1979. The defendant has incorporated the plaintiffs' idea of comparing figures for all faculty hired, regardless of the date of employment (Tables 1 and 2), with those of faculty hired prior to 1972 (Tables 3 and 4) and those of faculty hired thereafter (Tables 5 and 6). Within each of these three pairs of tables, the first (or odd-numbered) table uses only the plaintiffs' variables and the second (or even-numbered) table uses certain of the defendant's variables, see supra note 29 and accompanying text, as well as those of the plaintiff.
Each of the six tables gives, first, results based upon the plaintiffs' data base and, then, results based on the agreed upon corrected data base. The columns in each table delineate: (1) the year, (2) the sexual coefficient of salary in dollars, (3) the sexual coefficient of the logarithim of salary, (4) a student "t" level of significance for each coefficient,[32] and (5) the number ("n") of persons included in each year for each data base. In addition, an asterisk is used to highlight any salary disparity of statistical significance at or above the level of two standard deviations.


                                            HIRED ANYTIME
                                                Table 1
                                       (Only Plaintiffs' Variables)
                  Plaintiff's Data                                     Agreed Data
                               Log                                               Log
        Sex                    Sex                        Sex                    Sex
Year    Coef       t           Coef      t          n     Coef       t           Coef       t            n
1974    -2378    -2.13[*]   -.07    -2.12[*]   282    -2073    -1.98         -.057    -1.89         287
1975    -2586    -2.26[*]   -.07    -2.27[*]   300    -2588    -2.38[*]    -.070    -2.46[*]    295
1976    -2532    -2.15[*]   -.06    -2.15[*]   261    -2070    -1.80         -.048    -1.53         252
1977    -2999    -2.12[*]   -.06    -1.70        223    -2226    -1.65         -.044    -1.32         207
1978    -3145    -2.18[*]   -.05    -1.47        220    -2965    -2.14[*]    -.053    -1.59         204
1979    -2422    -1.81        -.04    -1.23        216    -2410    -1.89         -.041    -1.60         209



*1177
                                          Table 2
                       (Plaintiffs' and Some of Defendant's Variables)
                  Plaintiffs' Data                                     Agreed Data
                               Log                                           Log
        Sex                    Sex                         Sex               Sex
Year    Coef       t           Coef      t           n     Coef       t      Coef       t            n
1974    -1284    -1.32         -.04    -1.38        282    -1105    -1.20    -.033    -1.22         287
1975    -1549    -1.54         -.04    -1.54        300    -1723    -1.83    -.050    -2.00[*]    295
1976    -1814    -1.88         -.04    -1.91        261    -1750    -1.80    -.042    -1.54         252
1977    -2620    -2.22[*]    -0.05   -1.63        223    -2129    -1.90    -.042    -1.50         207
1978    -2402    -1.96         -.03    -1.10        220    -2210    -1.92    -.038    -1.39         204
1979    -1783    -1.55         -.02    -0.93        216    -1861    -1.64    -.033    -1.45         209



                                    HIRED PRIOR TO 1972
                                           Table 3
                               (Only Plaintiffs' Variables)
                  Plaintiffs' Data                                     Agreed Data
                               Log                                                Log
        Sex                    Sex                         Sex                    Sex
Year    Coef       t           Coef      t           n     Coef       t           Coef       t          n
1974    -4295    -2.77[*]    -.12    -2.93[*]   192    -4166    -2.74[*]   -.114    -2.89[*]   189
1975    -3742    -2.11[*]    -.10    -2.50[*]   187    -3706    -2.17[*]   -.105    -2.54[*]   179
1976    -4000    -1.98         -.10    -2.24[*]   155    -4179    -2.31[*]   -.110    -2.58[*]   143
1977    -5916    -2.39[*]    -.14    -2.57[*]   128    -5291    -2.24[*]   -.132    -2.47[*]   119
1978    -7077    -2.83[*]    -.14    -2.84[*]   111    -6450    -2.64[*]   -.134    -2.61[*]   104
1979    -8686    -2.79[*]    -.18    -3.21[*]   100    -6528    -2.27[*]   -.135    -2.60[*]   100
                                              Table 4
                             (Plaintiffs' and Some of Defendant's Variables)
                  Plaintiffs' Data                                     Agreed Data
                               Log                                               Log
        Sex                    Sex                         Sex                   Sex
Year    Coef       t           Coef      t           n     Coef       t          Coef       t           n
1974    -2338    -1.73         -.06    -1.87        192    -2054    -1.59        -.059    -1.75        189
1975    -2445    -1.53         -.07    -1.87        187    -2252    -1.51        -.067    -1.87        179
1976    -2666    -1.58         -.07    -1.81        155    -3026    -2.01[*]   -.079    -2.28[*]   143
1977    -4302    -2.14[*]    -.10    -2.33[*]   128    -4068    -2.06[*]   -.101    -2.34[*]   119
1978    -4597    -2.08[*]    -.09    -2.03[*]   111    -4117    -1.86        -.082    -1.77        104
1979    -6288    -2.09[*]    -.13    -2.40[*]   100    -5000    -1.68        -.101    -1.89        100



*1178
                                     HIRED SUBSEQUENT TO 1972
                                             Table 5
                                    (Only Plaintiffs' Variables)
                  Plaintiff's Data                                     Agreed Data
                              Log                                               Log
        Sex                   Sex                         Sex                   Sex
Year    Coef       t          Coef      t           n     Coef       t          Coef       t           n
1974    -2796    -1.54        -.12    -1.75         90    -1382    -1.00        -.059    -1.06         98
1975    -3614    -2.63[*]   -.12    -2.49[*]   113    -2416    -2.07[*]   -.085    -2.07[*]   116
1976    -2767    -2.15[*]   -.08    -2.12[*]   106    -1228    -0.89        -.035    -0.71        109
1977    -1124    -0.68        -.02    -0.41         95    - 164    -0.10        +.005    +0.09         88
1978    - 203    -0.12        +.00    +0.09        109    - 817    -0.49        -.025    -0.52        100
1979    +  70    +0.05        +.02    +0.44        116    -1053    -0.82        -.017    -0.54        109



                                                   Table 6
                                (Plaintiffs' and Some of Defendant's Variables)
                  Plaintiff's Data                                     Agreed Data
                              Log                                               Log
        Sex                   Sex                         Sex                    Sex
Year    Coef       t          Coef      t          n      Coef       t           Coef       t          n
1974    -2497    -1.60        -.10    -1.69        90     -1395    -1.02        -.058    -1.05        98
1975    -2605    -2.02[*]   -.09    -1.88       113     -2150    -1.98        -.073    -1.94       116
1976    -1424    -1.23        -.04    -1.25       106     -1246    -0.91        -.036    -0.72       109
1977    - 451    -.029        +.00    +0.00        95     + 352    +0.23        +.019    +0.41        88
1978    + 181    +0.12        +.01    +0.20       109     -  31    -0.02        -.012    -0.29       100
1979    -  41    -0.04        +.01    +0.43       116     -1250    -1.18        -.023    -0.87       109


D. Problems With the Plaintiffs' Proof

The Court concludes that there is substantial merit to the defendant's criticism of the plaintiffs' analyses. The discussion that follows is a detailed outline of the major shortcomings in the plaintiffs' proof.
1. Unmeasured differences that exist between the various faculty positions that were analyzed. Initially, it is clear that there was a disparity between the salaries of those in clinical departments and those in pre-clinical departments. The clinicians, who were more directly responsible for the receipt of income through affiliation contracts and from private patients and who, because of their occupations, had greater career opportunities, were clearly favored over the preclinical instructors, whose positions more nearly approximated those of traditional university professors. The higher representation of females in the preclinical fields, thus, was a distorting factor that was not adequately dealt with in the plaintiffs' studies. Moreover, even within the clinical departments, the distinction between those who were primarily researchers and those who primarily engaged in the practice of medicine was not adequately accounted for by the plaintiffs' variables. Nor was the inherent departmental stratification, with its attendant differences in salaries.[33]*1179 This alone has been cited as enough to defeat a plaintiff's attempt to establish a prima facie case through statistical evidence. Keyes v. Lenoir Rhyne College, 552 F.2d 579, 580 (4th Cir.) (failure to analyze salaries department by department or discipline by discipline invalidated plaintiff's proof), cert. denied, 434 U.S. 904, 98 S.Ct. 300, 54 L.Ed.2d 190 (1977).
Moreover, although the plaintiffs' regression model attempted to account for specialties, the advanced nature of the faculty at Einstein had resulted in most faculty members being Board-certified not only in a specialty but also in a sub-specialty.[34] The evidence indicates that the sub-specialties were a determinant of salary at Einstein because the limited number of persons in some sub-specialties made their services more valuable than the services of those in other sub-specialties.
2. Unmeasured effect of individual productivity on salary. Although the parties disagreed somewhat about which variables adequately reflected the major factors influencing hiring decisions, their major dispute concerned which variables, if any, should be included to measure productivity during the term of employment. The parties agreed that once faculty members were hired, their progress thereafter was largely determined by their productivity as faculty members. They also agreed that productivity was typically measured by considering such factors as quality of research, quality of teaching, quality and quantity of clinical work, number and significance of publications, reputation, generation of private practice, development of an important clinical process, procurement or administration of a major grant, any offer of employment from a competing college, mobility, significance of any contributions to science, and, more generally, the manner in which a faculty member spent his or her time.
Unquestionably, these are difficult considerations to quantify and include in the form of one or more variables. Only one of these factors, a faculty member's rate of publication, was easily measurable;[35] yet, this variable is a flawed indicator of productivity for several reasons. First, researchers had greater opportunity to publish than did clinicians. Second, the data base was not complete for this purpose because it was based on faculty members' resumes which were not always current and in some instances included only those works that had been published before the date of initial employment. (As a consequence of this second problem, the publication variable reflected a "rate" of publication rather than an absolute number of publications.) Finally, as the defendant contended, the publication variable did not take into account the difference between significant and insignificant publications.
In light of these limitations, the plaintiffs' experts attempted to account for productivity by using proxies. The defendant, however, convincingly argued that the proxies failed to adequately account for the true productivity differences and that the consequential underadjustment for these differences resulted in an overestimate of the sex coefficients.
*1180 The evidence was clear that certain types of productivity, such as the procurement and management of large research grants, clinical expertise, the generation of revenue through private practice and affiliation practice, and a significant clinical work load, had a direct affect upon compensation and should have been accounted for as significant sources of productivity differences. In addition, it was necessary to take account of the less tangible but highly important factor of the quality of performance in the areas of research, teaching, and clinical practice. Although these factors were not easily quantifiable, we cannot conclude that their omission had no effect on the results of the multiple linear regression study. On the contrary, the fact that male faculty members scored higher on sixteen of the plaintiffs' twenty proxies strongly suggests that the omission of the less tangible factors distorted the results in favor of the plaintiffs. The Court agrees, therefore, with the defendant's conclusion that the failure to adequately account for productivity resulted in an underadjustment bias and plaintiffs' overstatement of the sex coefficients.
To avoid this inadequacy in the plaintiffs' analysis, the defendant turned to faculty rank as a more appropriate indicator of productivity differences. The defendant believed that rank was one of the most important explanatory factors and that it played a role in the determination of salary beyond that of the promotion increase itself.
The plaintiffs, however, objected to the use of rank as a surrogate for productivity on two grounds. First, they argued that rank was not a truly independent variable. While this contention is partially true in that some of the factors considered in determining salary increases are the same factors that are considered in the determination of promotions, it ignores the more important point that promotion is based largely on the more intangible and less quantifiable indicators of productivity that are not factors affecting the annual salary increases.
Second, the plaintiffs argued that because the same sort of bias that might affect salary decisions might also affect the subjective evaluations preceding a faculty member's promotion, academic rank should have been included as an explanatory variable only where there was clear evidence that neutral and objective standards had consistently been followed and there was no chance that the decisions regarding rank had been affected by sexual discrimination. See, Finkelstein, The Judicial Reception of Multiple Regression Studies in Race and Sex Discrimination Cases, 80 Colum.L.Rev. 737, 741-42 (1980). Having heard substantial evidence on this very point, the Court, however, is convinced that promotions in rank, which were handled by independent faculty committees, were in fact based on merit and were not contaminated by elements of sexual discrimination.[36] Moreover, rank appears to be the only available surrogate for the productivity variables that cannot be quantified in any other manner. Although rank does not completely reflect such amorphous considerations as the quality of research and teaching, clinical expertise, and reputation, it is the only available variable that seems to give any weight to these important factors.[37]
Because variations in promotions in rank contributed substantially to salary differences, the exclusion of rank as a variable could easily result in statistically significant sex coefficients even in the absence of discriminatory salary and promotion decisions. Thus, a statistical study that omitted this most important determinant of differences in salaries would be insufficient to support a finding of discrimination. See, e.g., Presseisen v. Swarthmore College, 442 F.Supp. *1181 593, 614 (E.D.Pa.1977), aff'd mem., 582 F.2d 1275 (3d Cir.1978). Such an omission is more likely to lead to erroneous findings of discrimination in professional settings, where women are quite recent entrants into the field and the criteria for pay and promotion are more complex and less readily quantifiable, than it is in industrial settings, where productivity is more easily measured and women have worked for years. The Court concludes, therefore, that rank is an appropriate variable to be used in a multiple regression study.
When the defendant introduced rank into the plaintiffs' studies, the degree of apparent sex discrimination diminished substantially. Indeed, when faculty rank was added to the plaintiffs' preferred model, the sex coefficient and student t values diminished so much that statistically significant salary disparities appeared in only one year, 1975.
3. Other technical shortcomings in the plaintiffs' analysis. In addition to not adequately accounting for certain differences in faculty position and productivity,[38] the plaintiffs' study suffered from other technical difficulties. First, the study included some variables which were of no particular relevance, for example, whether or not someone had obtained an advanced degree other than an M.D. Obviously, some types of additional education might have been valuable to Einstein, but this would not have been the case if the degree earned were in classical Italian architecture; nor could the holder of such a degree have expected it to prompt the college to award a salary increase.
Second, the plaintiffs' attempt to control for experience through the use of approximately fourteen variables was not at all effective. Many of the variables  the total of prior experience squared, age, age squared, total medical experience, job tenure at Einstein, and job tenure squared  were patently collinear, which simply means they tended to measure the same thing. The absence of proper measures of experience and the presence of multi-collinearity created a multiple linear regression that was misspecified and unreliable. See Wilkins v. University of Houston, 654 F.2d 388, 404-05 & n. 21 (5th Cir.1981), cert. denied, ___ U.S. ___, 103 S.Ct. 51, 74 L.Ed.2d 57 (1982). This was demonstrated by the susceptibility of the sex coefficients to large variations when only small changes in data were made, such as the addition or exclusion of a single person. In one instance, the removal of a single faculty member from the data base lowered the relevant sex coefficient from $2,378 to $1,957, and the corresponding level of statistical significance from 2.13 to 1.77.
A third technical problem was that three widely used indicators of the accuracy of statistical models strongly suggested that the plaintiffs' model was unreliable. One, the adjusted R2,[39] measures the accuracy of a multiple linear regression. The R2 values, in this case, were better when the defendant's variables were used in the model than when the plaintiffs' preferred variables were used. The second indicator, the standard error of the regression, was employed to evaluate the accuracy with which the multiple linear regression model estimated the differences in salary attributable to differences in sex. (With this indicator, the smaller the standard error, the more reliable the conclusions.) The standard errors in the plaintiffs' tables for all employees, regardless of when hired, were unacceptably large. Finally, the unreliability of the model was also indicated by the fact that the random changes in the signs and amounts of the coefficients from year to year could not be explained by any changes in Einstein's policies.
*1182 The last technical flaw that must be noted is the plaintiffs' failure to validate their model. They demonstrated neither that their variables were entered in the correct functional form nor that the assumptions necessary for the model's use had been satisfied, particularly the assumption of an additive relationship between the effects of independent variables. Furthermore, the plaintiffs provided insufficient evidence that the errors in their model were not correlated with the explanatory variables, were independent of one another or had a zero expectation, and had a constant variance or normal distribution.
Faced with these many shortcomings, the Court has no alternative but to find the plaintiffs' model technically inadequate. Although the plaintiffs correctly argued that, in order to make out a prima facie case, they were not required to produce a perfectly designed or specified model, but rather one that only roughly controlled for the necessary considerations, the plaintiffs failed to produce a model that met even this lesser standard. For example, residual plots of the plaintiffs' model revealed an unacceptable increase in the scatter as the salaries increased, yet the plaintiffs' experts failed to control this problem by using the logarithmic form of salary, as the defendant's experts recommended. Such a failure is hard to accept. So too is it difficult to accept the failure to account for the underadjustment bias in the plaintiffs' model, which, as was discussed earlier, resulted from the plaintiffs' use of inadequate proxies for productivity. As the defendant later demonstrated, almost the entire average sex coefficient in the plaintiffs' preferred model could have been explained by the underadjustment bias attributable to the use of those proxies. The serious doubts that are raised by this flaw and the others already discussed convince the Court that the plaintiffs have failed to sustain their burden of proof by producing a valid and reliable model.[40]
4. Failure to consider the effect of pre-Act discrimination on later salaries. In the initial stages of litigation, the plaintiffs' regression study was not designed to analyze the extent to which salary differentials may have been the consequence of discriminatory acts that occurred prior to the date that Title VII became applicable to universities. When the plaintiffs' experts later performed such an analysis, they acknowledged that it revealed no statistically significant proof of sexual discrimination during the relevant time period. Nor was there any statistically significant evidence of discrimination in salary increases on a year-to-year basis. Indeed, the plaintiffs' expert, Dr. Ashenfelter, testified that both the plaintiffs' and defendant's statistical studies indicated that men and women have generally been treated the same during the relevant time period. Dr. Ashenfelter concluded that, under his theory of labor markets, the appearance of discrimination in salaries during the relevant time period resulted from lower salaries paid to female faculty members who had been hired prior to 1972. He added that with respect to female faculty members hired after March 24, 1972 (the effective date of Title VII), there was an absence of any statistical significance in salary differences. This situation is similar to that found in Gilinsky v. Columbia University, 488 F.Supp. 1309 (S.D. N.Y.1980), aff'd, 652 F.2d 53 (2d Cir.1981), where Judge Lasker, after noting that prior to 1972 Columbia University "`was free, as far as Title VII was concerned, to discriminate in its employment practices,'" determined that "the probative value of pre-1972 statistics is at best minimal" and, accordingly, dismissed the action because it was *1183 based largely on such cumulative statistics. Id. at 1313 (quoting Weise v. Syracuse University, 522 F.2d 397, 410 (2d Cir.1975)).
The absence of discriminatory treatment during the relevant time period was suggested by the defendant's study as well.[41] The defendant employed an "urn" model, believing it to be more appropriate than the standard multiple regression model.[42] In addition, the defendant separately analyzed initial salaries and each year's salary increases.[43] It also separately studied seven large departments and added a factor to differentiate between clinical and preclinical departments.[44] By these methods, the defendant was able to avoid some of the problems inherent in the plaintiffs' model.[45]
The defendant's studies of initial salaries for those hired during the relevant time period and for pay increases during that period showed no pattern or practice of male-female salary differentials. The defendant's studies stratified departments where possible, took into account sub-specialties as well as rank, time in rank, major administrative responsibilities, clinical research emphasis, and other factors which, this Court believes, were determinants of salary at Einstein and, thus, proper variables. With the incorporation of these variables, the analyses indicated that the proportion of male faculty members receiving more than the expected initial salary was slightly greater than the proportion of female faculty members receiving that level of compensation. The difference, however, was less than one standard deviation and, thus, of no legal significance.
The study of the yearly pay increases under the guidelines was particularly persuasive. The defendant's study first took the salary of each faculty member for a given year and then added to it that year's guideline increment to obtain a projected salary. The projected salary for each faculty member was then deducted from his or her actual salary to determine a salary residual for that year. This was done for each year during the relevant time period and for each faculty member. The difference between the average residual of men and the average residual of women was considered the unexplained portion of the gross disparity. The size and statistical significance of this difference was used as a test for the presence of discrimination in yearly pay increases.[46] The analysis of average *1184 salary residuals (without adjustment for promotions) showed that in three out of the five years during the relevant time period, the difference favored women. In none of the years were the differences statistically significant at the .05 level. Indeed, the proportion of women who received above-guideline increases was higher than that of men (though not at a level of statistical significance). Even when an adjustment for promotions was made, women appeared to be favored in three of the five relevant years and, again, no statistically significant differences were revealed.[47]
Average summary residuals were also calculated. These represented the difference between a faculty member's actual average yearly salary and the average yearly amount projected for that faculty member. Again, no statistically significant difference was shown. Indeed, a woman's average yearly earnings tended to be slightly larger than those of a man who started at the same initial salary and in the same academic year.
5. Absence of anecdotal evidence of any probative value. The anecdotal evidence, or, more accurately, the lack thereof, reflected the same absence of sexual discrimination that was suggested by the defendant's statistical evidence. The only general evidence of an anecdotal nature that had any significance was the fact that during 1972, the year that Title VII became applicable to universities, a faculty senate committee at Einstein appointed a sub-committee to investigate the existence of sex discrimination in pay.[48] The sub-committee prepared a report which included a review of the gross salary levels of male and female faculty members. The sub-committee, which was known as the Senate Committee on Women's Rights, after reviewing limited and incomplete salary information, wrote a report which, among other things, suggested that the mean salary of Einstein's female faculty members was approximately fifteen percent lower than that of their male colleagues. This report was distributed to members of the faculty senate. Some faculty members were of the personal belief that female professors at Einstein (as well as at other institutions and in society in general) were being paid lower salaries because of their sex.
Although the evidence of subsequent actions was somewhat vague, it suggested that some efforts were made, starting in 1972, to compensate female faculty for prior inadequate salaries. In fact, prior to the 1974-75 academic year (the first year of the relevant time period), a task force on fiscal stability, while recommending to the Dean that inequities in salary, particularly those between males and females, continue to be reduced, noted that much had already been accomplished in the prior year's budget. The Court finds it reasonable to conclude from this evidence that the consequence of the faculty senate report and the new applicability of Title VII to universities was that a conscious effort was made after 1972 to avoid any sex discrimination in salaries.[49]
*1185 The anecdotal testimony relating to individual female faculty members was also sparse, and most of it concerned matters predating the statute of limitations date of December 20, 1974. Such evidence is, thus, entitled to little weight and constitutes only relevant background evidence. United Air Lines, Inc. v. Evans, 431 U.S. 553, 558, 97 S.Ct. 1885, 1889, 52 L.Ed.2d 571 (1977).
The only individual class member who testified concerning alleged pay discrimination against her was the first named plaintiff, Edna H. Sobel. She is a full-time faculty member in the Department of Pediatrics who was hired long before March 24, 1972. Indeed, she has been a member of the faculty at Einstein since 1956. She is a Board-certified pediatrician with a sub-specialty in pediatric endocrinology.[50] Dr. Sobel has been responsible for a relatively small division of pediatric endocrinology at one of Einstein's campuses since she joined the faculty and has been a recognized authority in her field for some years.
When Dr. Sobel joined Einstein's faculty in 1956, she started as an assistant professor. In 1960, she was promoted to the rank of associate professor and in 1968, to the rank of full professor. Throughout her career she has had a broad range of responsibilities in teaching, research, and patient care. During the late 1960's and early 1970's, she received some research funds; however, she has not received any grant money since 1976.
In 1970, Dr. Sobel complained to her department chairperson, Dr. Lewis Fraad, that her salary was too low. He was inclined to agree with her and knew that other professors in the department believed that her low salary at that time may have been related to her sex. In 1972, she was recommended for and received an above-guideline salary increase. In 1973, she sought another above-guideline salary increase. Dr. Fraad noted that she had earned $7,000 of private practice income at the college hospital which was not being included in her base salary. Nonetheless, although he did not necessarily believe that she was underpaid at that time, he again recommended her for an above-guideline increase for the 1973-74 academic year. She again received one, although it was less than that which was requested.
In the following academic year, Einstein appointed a new department chairperson, Dr. Chester Edelmann, who remained the chairperson throughout the relevant time period. Dr. Sobel received no above-guideline increases thereafter, though she did receive the guideline increase every year. The defendant attributed Dr. Sobel's failure to garner larger increases to two factors. First, Dr. Edelmann was not completely satisfied with Dr. Sobel's teaching methods in small groups. (There were also overtones of a personality conflict between Dr. Sobel and Dr. Edelmann.) Second, she was hurt by her failure to generate much additional revenue for Einstein either from research grants or patient treatment. In fact, her laboratory research program had to be discontinued because of her inability to secure research grant support.[51]
Dr. Sobel, thus, failed to establish that she had been discriminated against on the basis of sex during the relevant time period. She did not even introduce any evidence of the compensation of similarly situated male faculty. In essence, her case reduced to the claim that her salary had been discriminatorily low prior to 1974 and that she should have been granted additional above-guideline increases to remedy the earlier discrimination.
The other named plaintiff, Dr. Bella C. Clutario, did not take the stand at trial. In *1186 fact, no evidence whatsoever was offered concerning her claim of discrimination.[52]
There was, therefore, none of the direct evidence of discrimination with respect to any particular class member that might have provided an acceptable means of proving discrimination in a case of this nature.[53]Cf. McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973) (where plaintiff did present the type of evidence needed to establish a prima facie case of discriminatory hiring). It seems reasonable to assume that, if there had been classwide discrimination, the plaintiffs should have been able to demonstrate some instances of discrimination against individuals. The absence of any such anecdotal evidence casts considerable doubt on the plaintiffs' claims. This is particularly true in a case such as this where discovery was undertaken over a seven-year period, with all of the resources of the EEOC available for the last several years.
Indeed, given the available evidence, the Court finds it extremely unlikely that the defendant would have even tried to discriminate against the class during the relevant time period. Title VII had been passed and made applicable to the university. The faculty senate committee had indicated an awareness of a prior problem. The social trend of the times was strongly contrary to employment discrimination against females. The metropolitan area in which Einstein is located provided a substantial market for physicians who were unhappy with their college salary. In addition, there were five other medical schools in the area and 125 medical schools in the country. Having highly marketable skills, these women were not at the mercy of the employer in the manner that an untrained person might be. Finally, since salary increases were largely the product of the recommendations of departmental chairpersons, any instance of sex discrimination would almost certainly have been the product of a particular chairperson's bias rather than that of any university or college policy.
The Court concludes, therefore, that the plaintiffs have failed to prove a prima facie case of disparate treatment with respect to salary. They have failed to carry their burden of persuasion for both the individual and the class claims.
6. Untimeliness and inadequacy of plaintiffs' disparate impact claim. When the plaintiffs recognized the factual weakness of their disparate treatment case midway through the trial, they switched, in part, to a claim of disparate impact. They argued that there was sufficient evidence from which to conclude that, largely because of the guideline increment system, the salaries of at least those female faculty members who were hired before March 24, 1972, were discriminatorily lower than those of male faculty members hired before that date, when Title VII first became applicable to universities. Although the plaintiffs conceded that the annual guideline increment system was neutral on its face, they claimed that it was discriminatory in operation, at least to the extent that it perpetuated the effects of pre-Act discrimination.[54]
Unfortunately for the plaintiffs, their disparate impact claim fails on two completely independent grounds. First, the plaintiffs' last-minute, mid-trial switch to *1187 an alternate theory must be rejected on the procedural ground of unfairness to the defendant. For seven years prior to the trial and throughout much of the trial itself, the defendant was confronted solely with a claim of disparate treatment. Much of the Court's purpose in permitting the parties so much time to prepare this case was to ensure full and fair discovery and complete development of all the legal issues that might arise at trial. Thus, to allow the plaintiffs to adopt a completely different theory of liability at such a late date, particularly when in the years preceding the trial they gave little if any indication that they were claiming disparate impact, would be to work a gross injustice on the defendant.[55]See Presseisen v. Swarthmore College, supra, 442 F.Supp. at 598, 603 (court refused to consider disparate impact claim first raised late in the trial); cf. Ste. Marie v. Eastern Railroad Ass'n, 650 F.2d 395, 399 n. 2 (2d Cir.1981) (Friendly, J.) (trial court's imposition of "the more stringent burden applicable in a disparate impact case" implicitly found to be unfair to defendant where both parties had consented to trial on disparate treatment theory and case was, in fact, tried on that theory).
Furthermore, even without such a procedural bar, the plaintiffs' claim of disparate impact must fail on its merits. In the seminal decision concerning disparate impact theory, Griggs v. Duke Power Co., 401 U.S. 424, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971), the Supreme Court held that "practices, procedures, or tests neutral on their face, and even neutral in terms of intent, cannot be maintained if they operate to "freeze" the status quo of prior discriminatory employment practices." Id. at 430, 91 S.Ct. at 853. Since Griggs, however, the Court has carefully circumscribed what it meant when it originally made this very broad statement of law. Most significantly for our purposes, the Court held in United Air Lines, Inc. v. Evans, 431 U.S. 553, 97 S.Ct. 1885, 52 L.Ed.2d 571 (1977), that any discriminatory act which occurs before the onset of the relevant limitations period cannot be considered an illegal act.
A discriminatory act which is not made the basis for a timely charge is the legal equivalent of a discriminatory act which occurred before the statute was passed. It may constitute relevant background evidence in a proceeding in which the status of a current practice is at issue, but separately considered, it is merely an unfortunate event in history which has no present legal consequences.
Id. at 558, 97 S.Ct. at 1889. Continuing, the Court emphasized the point that a plaintiff must prove a present violation, one that occurs within the relevant limitations period, not simply a past violation with ongoing effect. "Respondent emphasizes the fact that she has alleged a continuing violation. United's seniority system does indeed have a continuing impact on her pay and fringe benefits. But the emphasis should not be placed on mere continuity; the critical question is whether any present violation exists." Id.
Under the reasoning of Evans, the critical question here is whether the defendant has committed any act of illegal discrimination since the commencement of the limitations period on December 24, 1974. Particularly instructive in answering this question is a close comparison of the facts of Evans with those in this case.
*1188 In that case, respondent Evans sought credit for seniority that she had lost in February of 1968 when United terminated her as an employee under its then existing policy of not permitting female flight attendants to be married. Although Evans had been rehired in February of 1972, long after that policy had been discontinued and held illegal (in a case not involving Evans), United treated her for seniority purposes as if she were a new employee, rather than someone who had accrued more than a year of active service before her termination and four years of what was essentially an involuntary leave of absence. Having had informal requests for additional seniority denied, Evans filed a charge with the EEOC in February of 1973, one year after she was rehired. In the action that ensued, she argued that, although it was too late to obtain relief based on the 1968 violation, United had continued to violate her civil rights after the commencement of the 90-day limitations period by repeatedly denying her requests for additional seniority. Id. at 554-57, 97 S.Ct. at 1887-88.
The Supreme Court, however, disagreed. It observed that United's policy of not crediting rehirees with seniority for previous years of service had been applied fairly and uniformly to all individuals in Evans's situation, regardless of their sex and regardless of the reasons for their initial departures from United.
Nothing alleged in the complaint indicates that United's seniority system treats existing female employees differently from existing male employees, or that the failure to credit prior service differentiates in any way between prior service by males and prior service by females. Respondent has failed to allege that United's seniority system differentiates between similarly situated males and females on the basis of sex.
Id. at 557-58, 97 S.Ct. at 1888-89. What the Court perceived was an initial illegal act of discrimination in 1968 and an ongoing, impartially administered seniority system that was in no way discriminatory. Once Evans failed to file a timely charge in 1968, the initial discrimination forever lost whatever legal consequence it might have had, even though it was given "present effect" by the ongoing seniority rules. Id. at 558, 97 S.Ct. at 1889.
In the instant case we find a similar situation except for the fact that the alleged "initial discrimination" here was never illegal in the first place. The original salaries of those hired before March 24, 1972, did not have to meet the standards established under Title VII. Thereafter, increases in salary were determined under the guideline increment system, which, as we have already seen, was neutral both in principal and in operation.[56] Hence, the plaintiffs are placed in the awkward position of arguing that past initial salaries which were allegedly discriminatory but certainly legal, and present annual increases that have been shown to be fair and non-discriminatory somehow add up to a "present violation" of Title VII. Surely, the facts of this case are even more compelling than those of Evans, and the reasoning of that case must apply here as well.[57]
*1189 Consequently, the Court finds that the plaintiffs' claim of disparate impact fails on the merits, as well as on procedural grounds.

E. The Pension

All that remains, therefore, is the plaintiffs' claim that under Yeshiva's pension plan female pensioners received discriminatorily lower monthly payments than did male pensioners. Although this particular claim was not expressly raised in their original EEOC complaints, the Court has concluded that this omission or oversight does not bar the claim at this time. Sobel's and Clutario's original claims were quite broad in scope, covering all the peripheral aspects of their employment. The pension plan has always been considered an integral part of the employment compensation package: it was described as such in the literature provided to new employees and has been treated accordingly by all of the parties throughout the many years of this litigation. It would, therefore, be both unfair and unwarranted to bar the claim at this late date on the procedural ground that the plaintiffs never specifically alleged the claim in their complaint.[58]
The facts relevant to this issue, as adapted from the plaintiffs' unchallenged proposed findings of fact, can be summarized as follows:
(1) Prior to March 24, 1972, Yeshiva entered into a contract with the Prudential Life Insurance Company of America ("Prudential"), which obligated Prudential to provide certain of Yeshiva's employees, including the full-time faculty of Einstein, with a program for deferring a limited portion of their compensation until after their retirement, when the deferred amount would be repaid in the form of an annuity.
(2) The contract between Yeshiva and Prudential provided a method for the purchase, maintenance and distribution of annuities for the individual benefit of participants, and it controlled the operation of the pension benefits program.
(3) Those of Einstein's full-time faculty members who held M.D. degrees were given the option of participating in the pension benefits program.
(4) Approximately eighty percent of Einstein's eligible faculty members chose to participate.
(5) The annual contribution to the pension program for each full-time participant consisted of two parts: first, the participant's contribution, a seven percent deduction from his or her gross salary; and second, Yeshiva's contribution, the equivalent of ten percent of the participant's gross salary. Only Yeshiva's contribution actually constituted additional compensation to the participant.
(6) At all times after March 24, 1972, contributions by Yeshiva and faculty participants were used to purchase annuities at a rate determined by the contract between Yeshiva and Prudential.
(7) All rates that were used in the contract for the determination of the amount of annuities to be purchased on behalf of participants were based on sex-segregated mortality tables.
(8) The amount of annuities that would be purchased for the benefit of each participant was calculated on the employee characteristic *1190 of life expectancy which, in turn, was based solely on age and sex.
(9) All factors being equal but for sex, a female participant upon retiring received a lower monthly annuity payment than a similarly situated male.
(10) The pension benefits plan was a "defined contribution" plan.[59]
With these facts in mind, it is worth making a few points very clearly. First, Prudential's actuarial tables were based on the undeniable fact that women, as a group, live longer than men. Second, no one has seriously challenged the proposition that in any computation of either premiums or benefits for a large group, sex and age are the only factors that can readily be relied upon to reflect real differences in the costs that an insurer must bear. Third, Prudential, in recognition of its real costs, determined years ago that the most reasonable step it could take was to make the monthly payments to females less than those to males. Finally, Prudential took this step because it was prevented from doing otherwise by the constraints that are placed upon defined contribution plans, namely: both the employee's and the employer's contributions must be the same for women as they are for men, and the time an individual is vested in the plan also must be the same for men and women. Thus, Prudential determined that, since both sexes were entitled to equal amounts of total benefits at retirement, even though one sex on the average lived longer, the fair way to ensure that equal contributions yielded equal benefits was to award lower monthly benefit payments to that group with the greater longevity.
Despite the factual reasonableness of Prudential's solution to this real problem of how to achieve equal sharing of costs and benefits, the Supreme Court, in City of Los Angeles Dep't of Water & Power v. Manhart, 435 U.S. 702, 709-10, 98 S.Ct. 1370, 1375-76, 55 L.Ed.2d 657 (1978), held, in effect, that such a solution is unconstitutional. The defendant, realizing the impact of Manhart, attempted to negotiate with the EEOC a plan that would be both legal and economically viable. The EEOC, however, has been unwilling to render an opinion as to the propriety of any of the defendant's proposed plans. Its reluctance to take a stand on the issue stems partly from the fact that it is in litigation with the defendant and partly from the fact that none of the defendant's proposed plans makes adjustments for persons who are currently retired and receiving annuities under the challenged plan.
Not surprisingly, the courts have been baffled by the problem that Manhart has presented. On the one hand, private insurance companies are not willing to pay to women the same monthly benefits for the same premiums that they pay to men, because they know that sound actuarial principles require a real and substantial distinction. On the other hand, Manhart held that insurers may not employ group annuity plans that are based on such actuarial assumptions.[60]Id. One of the consequences of this conundrum is that, in applying the Manhart doctrine, two courts of appeals have recently reached completely different results.
*1191 In Peters v. Wayne State University, 691 F.2d 235 (6th Cir.1982), petition for cert. filed, ___ U.S. ___, 103 S.Ct. 442, 74 L.Ed.2d 599 (1982), the Sixth Circuit distinguished Manhart on the basis of two factual differences:
In Manhart the employer deducted retirement contributions at different rates from employees' paychecks. Because women were required to contribute more than men, women effectively earned less money than men for the same jobs. Women and men employees at Wayne State contribute the same amount to the retirement plan. Consequently they receive equal compensation. Furthermore, in Manhart the employer operated the pension fund. The city collected the contributions, managed the accumulated money, and calculated the disbursement rates. Wayne State does not operate the pension fund for its employees. Rather Teachers Annuity, an independent insurance company, manages the accumulated money in the individual accounts and calculates the disbursement rates.
Id. at 240. The Sixth Circuit reasoned that these factual differences[61] were significant because the Supreme Court's "primary concern, that women received smaller pay checks for the same work," was simply not a factor at Wayne State University. Id.
The Sixth Circuit continued by rejecting an argument that has also been made by the plaintiffs in the instant action.
Plaintiffs point out that individual women may not live to the predicted statistical age of death and, therefore, may not recover the full actuarial value of their retirement packages. This argument is equally true for men. After death the total benefits received could be calculated to determine whether a man or a woman has received more money. But because annuity payments must be calculated prior to death, insurers and employers must use the only tools available to calculate payments, mortality tables. Both women and men may not live to the predicted statistical age but both women and men have the same probability of living to the predicted statistical age.
Id. at 241. This analysis led the Court of Appeals to the conclusion that, in order to "equalize" the treatment of men and women, as the plaintiffs requested, Wayne State would have to contribute more to a woman's retirement fund than to a man's so that the man would, in effect, receive less, immediate compensation. The court simply could not accept such a result. Id.
In contrast, in Spirt v. Teachers Insurance & Annuity Ass'n, 691 F.2d 1054 (2d Cir.1982), petition for cert. filed, ___ U.S. ___, 103 S.Ct. 371, 74 L.Ed.2d 506 (1982), which involved a mandatory college pension plan,[62] the Second Circuit held that it could "discern no meaningful distinction between the disparate treatment accorded the female employees in Manhart, who were required to contribute" more than male employees in order to receive equivalent benefits, and the treatment accorded the female employees involved in Spirt, whose contributions equaled those of their male colleagues but whose monthly benefits were smaller. Id. at 1061.
Obviously, this Court is compelled to follow Spirt, which was decided in this Circuit, rather than Wayne State. This is true even though the defendants argue that Spirt is twice distinguishable on its facts. The first purported distinction is that Yeshiva's pension plan was optional, while the one involved in Spirt was mandatory. Unfortunately, we do not see this as being a meaningful distinction. Yeshiva contributed an amount equal to ten percent of a *1192 faculty member's gross salary to the pension plan. To pass up this opportunity was simply not a desirable or sensible alternative for most members of the faculty.
The defendant's second point is that while the insurers involved in Spirt were sued and eventually ordered to provide retroactive monetary relief (and the university was merely enjoined from contributing to such a plan), here Prudential was not sued and cannot be considered an employer under Title VII.[63] The problem with this argument, however, is that it appears to go only to the issue of remedies and not to that of liability.
Thus, we are compelled to follow Spirt, even though we have two strong reservations in doing so. Our first reservation arises from the fact that, read literally, Spirt bars employers from making any sex-based distinctions in any group policies for their employees. For example, any sex-based difference in either the contributions or the benefits specified under an employer's group life insurance program necessarily constitutes a Title VII violation, though in such a case the discrimination is against males.
Our second reservation has to do with the Second Circuit's rather puzzling treatment of the fact that under the remedy adopted in Spirt men as a group received less compensation under the merged gender table than did women. The court disposed of this problem in part by noting that the difference was not significant. Id. at 1069 & n. 12. However, it follows that if this difference was not significant then the original discrimination, which constituted the subject of the suit, was also insignificant.
More important than this Court's doubts about the long-term validity of the Spirt decision, however, is the fact that the Supreme Court has recently granted certiorari in a case involving these very issues, Norris v. Arizona Governing Committee for Tax Deferred Annuity, 671 F.2d 330 (9th Cir. 1982), cert. granted, ___ U.S. ___, 103 S.Ct. 205, 74 L.Ed.2d 164 (1982), and certiorari has been applied for in Spirt. Whether the Supreme Court will retreat from its Manhart holding or offer some reasonable means of applying it in a nondiscriminatory fashion remains to be seen. In any case, the Court is almost certain to comment upon several types of distribution options which have been offered to avoid a Manhart problem.[64] Thus, because the matter of a proper solution to the pension issue in light of Manhart has been a continually troubling one, and because the damage issues have not yet been tried, this Court will defer deciding upon the appropriate remedy in this case until such time as the Supreme Court has decided Norris, and, if certiorari is granted, Spirt.

IV. CONCLUSION
In accordance with the discussion above, the plaintiffs' claims of pay discrimination are dismissed and final decision is reserved on their pension benefit claims pending further ruling by the Supreme Court.
SO ORDERED.
NOTES
[33]   This amended opinion supersedes and replaces the opinion filed by this Court on May 25, 1983.
[33]   This amended opinion supersedes and replaces the opinion filed by this Court on May 25, 1983.
[33]   This amended opinion supersedes and replaces the opinion filed by this Court on May 25, 1983.
[33]   This amended opinion supersedes and replaces the opinion filed by this Court on May 25, 1983.
[34]  From the outset, it has been conceded that the defendant is an "employer," as that term is defined under 42 U.S.C. § 2000e(b) (1976), and that the Court has jurisdiction over the parties and the subject matter of this action.
[35]  The plaintiffs have since acknowledged that, pursuant to 42 U.S.C. § 2000e-5(g) (1976), any liability for back pay accrued only from June 18, 1973, or two years prior to the filing of their charges with the Equal Employment Opportunity Commission (the "EEOC").
[36]  The plaintiffs also alleged violations of section 1 of the Equal Pay Act of 1963, 29 U.S.C. § 206(d) (1976), and violations of various sections of the Civil Rights Acts, 42 U.S.C. §§ 1981, 1983 & 1985 (1976). The claims under sections 1981, 1983, and 1985 were withdrawn by the plaintiffs not long before the trial commenced.
[37]  A sub-class was created as well. It consisted of all female physicians who, during the relevant time period, were classified as full-time or part-time faculty members of Einstein in the above-stated ranks and who received salaries from affiliated institutions such as Montefiore Hospital and Medical Center, Bronx Lebanon Hospital, Bronx State Psychiatric Hospital, and Bronx Children's Psychiatric Center. Claims alleged on behalf of this sub-class concerned discriminatory promotions only and were withdrawn before trial along with all other claims involving promotions. See infra.
[38]  For example, an unsuccessful attempt was made to add those female professors who did not hold M.D. degrees.
[39]  Full-time faculty members are defined as those who gave their total professional commitment to Einstein and who, therefore, received all of their compensation from Yeshiva.
[40]  There were some faculty members who held degrees other than an M.D. However, they were not made a part of the class in this action.
[41]  At the time of trial, twenty-eight percent of Einstein's faculty members were women. This figure represented one of the five or six highest percentages for all of the medical schools in the country and compared very favorably to the national mean of sixteen percent. Furthermore, although the average age and experience of Einstein's female faculty members was less than the average age and experience of its male faculty members (apparently reflecting the increased entrance of women into the medical profession in recent years), two of the seven departmental chairpersons who were appointed during the period in question were women. Female faculty members also served on the Committee on Appointments and Promotions and the Associate Professors Committee, the two faculty committees responsible for determining appointments and promotions to the higher ranks.
[42]  For example, at the beginning of the relevant period, there were 54 women employed. Although some of them later left, 42 more became faculty members as the years progressed. Consequently, a total of 96 women were employed as full-time faculty members at one time or another during the relevant time period.
[43]  Those institutions were the Bronx Lebanon Hospital, the Bronx Psychiatric Center, the Bronx Children's Psychiatric Center, the North Central Bronx Hospital, the Beth Abraham Hospital, the Morrisania Hospital, the Sound View-Throgs Neck Community Mental Health Center, and the Bronx Developmental Services.
[44]  During this period, five of the chairpersons were women. One of these, Dr. Lucille Shapiro, has been promoted from Chairperson of the Department of Molecular Biology to Director of the Division of Biological Sciences, in which capacity she supervises and coordinates the activities of six departments.
[45]  To a great extent, a student's medical education consists of an initial two years of primarily preclinical instruction in the classroom and a final two years of predominantly clinical instruction in various hospital settings.
[46]  The handling of income from private practice varied from department to department. Although all payments were initially collected by the college, physicians in some departments were allowed to receive a portion of their private practice income, while those in other departments were paid a base salary that reflected the amount that their private practice contributed to meeting the departments' expenses.
[47]  An exception to this was the researcher who was able to attract a major grant, primarily because the holder of such a grant received additional compensation for the administrative responsibilities that were attached to the grant. Interestingly, during the relevant time period, about five times as many men as women held large research grants from such major sources as the National Institutes of Health.
[48]  Why the hospital oriented specialties were favored was not explored in any detail at trial, but the higher rate of compensation might have been related to the coverage provided by medical insurance, which was generally more comprehensive for hospital related expenses than for those expenses incurred during office visits.
[49]  There is no evidence to suggest that the women professors were coerced or compelled in any way in their selection of specialties and activities.
[50]  Responsible for the development and implementation of policies in the college of medicine, the Dean maintained a substantial professional staff (with titles such as "Associate Dean" and "Assistant Dean"), whose duties were primarily administrative in nature and thus not comparable to those of the other faculty members. The Dean's office had little involvement in the determination of salaries initially paid to younger professors, whose appointments were usually for only a year or two.
[51]  Of course, as has already been mentioned, other factors also influenced faculty salaries. Not only did those in clinical departments tend to make more than those in preclinical departments but also those who actively practiced medicine tended to make more than those who primarily did research. The latter factor presented an additional problem for plaintiffs' experts, whose initial analyses did not account for the fact that only those holding New York licenses are able to practice medicine in that state and that some of Einstein's faculty did not hold such licenses.
[52]  Because of their stronger economic position, the Departments of Radiology and Anesthesiology were permitted to develop their own guidelines for some of the years in question.
[53]  Almost all increases took effect on July 1st. However, on a rare occasion, such as when a faculty member was burdened with a great increase in duties or received an outstanding offer from another institution, a midyear adjustment would be approved and implemented.
[54]  The Committee on Appointments and Promotions, comprised of faculty members of the rank of full professor, considered appointments and promotions to that rank and, prior to the 1976-1977 academic year, to the rank of associate professor. After 1977, the Associate Professors Committee was formed to consider appointments to the rank of associate professor. This latter committee consisted of associate and full professors.
[55]  A proven disparity of 2.0 standard deviations enables one to conclude that a larger disparity than that which was actually observed would occur as a result of chance only one out of twenty times. Expressed differently, such a disparity would be significant at approximately the 0.05 level of probability. Similarly, a proven disparity of 3.0 standard deviations enables one to conclude that a larger disparity would occur as a result of chance approximately one out of a hundred times and that such a disparity would, therefore, be significant at approximately the 0.01 level of probability. "Thus, for large samples, the `2 or 3 standard [deviation]' rule is essentially equivalent to a rule requiring significance at a level in the range below 0.05 and 0.01." D. Baldus & J. Cole, Statistical Proof of Discrimination § 9.03, at 297 (1980).
[56]  Indeed, in the social sciences the two standard deviation test is viewed as the minimum test that must be met to show statistical significance, and there are many who contend that the three standard deviation test is more appropriate.
[57]  It should be noted that not only the salary figures of each faculty member but also the size and composition of the faculty changed every year. Moreover, the faculty salaries that were used were base salaries and did not include monies paid as supplements for the generation of private practice by the members of some departments.
[58]  Unfortunately, despite the parties' apparent pretrial resolution of their differences, the Court was nevertheless called upon during the trial to decide several issues concerning which data should be used.
[59]  The plaintiffs' report ultimately included three chairpersons and a number of deans whom the plaintiffs had intended to exclude.
[60]  The inclusion of proper variables and the exclusion of improper variables is referred to as the proper specification of the model.
[61]  Indeed, Dr. Ashenfelter later testified that certain of the variables that were employed by the defendant's experts and originally omitted from his reports are widely used in the theory of labor markets that he adopted.
[62]  The variables which were included in the second set of tables but not in the first were: 1) major administrative responsibilities which were undertaken prior to the relevant time period but performed during that period; 2) a faculty member's clinical or research emphasis; 3) faculty rank; and 4) time in faculty rank.
[63]  For example, one of the variables included by the plaintiffs was whether a medical degree was earned from a domestic or foreign medical school. As the defendant pointed out, the range in the quality and reputation of various foreign medical schools is tremendous. Some of these schools, such as McGill University in Canada, the University of Edinburgh in Scotland, and the University of Dublin in Ireland, are considered to be at least the equals of American medical schools. Other schools, including those found in non-English speaking countries and particularly those in developing nations, are not considered comparable. Consequently, the differentiation between domestic and foreign medical schools is not in itself meaningful.
[64]  It should be noted at this point that a similarity of results over a number of years adds little to the significance of any one year's results where, as here, the persons under consideration, the system of guideline increments, and the salaries change relatively little from year to year and any changes are for the most part symmetrical. Indeed, as the defendant noted, the comparative differentiation from year to year in the plaintiffs' results, if anything, indicated a lack of consistency and verifiability in the plaintiffs' model.
[*]  A student t is a statistic concerning the sample standard deviation, as opposed to the population standard deviation. It is a test of the validity of statistics that are drawn from a limited sample. P. Hoel & R. Jessen, Basic Statistics for Business and Economics, 187-90 (2d ed. 1977).
[*]  Although it is true that many of the departments would have been difficult to study separately because they were not large enough, certain of the large departments could have been stratified to eliminate intradepartmental differences, as was done by the defendant's experts in their studies.
[*]  To explain their exclusion of sub-specialties, the plaintiffs noted the restriction on the number of variables that could be included in their model and, in addition, argued that the great number of sub-specialties that are not Board-certified offset the value of accounting for any of the sub-specialties.
[*]  With respect to other factors which might have been easily measurable at another college, only limited information about the procurement of grants was available here (only data concerning grants of more than $100,000 from the National Institutes of Health and the American Cancer Society), and whatever data regarding private practice that was collectible would have had little value because of the already noted differences in how the various departments treated such service, see supra note 13.
[*]  Indeed, although the plaintiffs initially alleged that the promotion process itself was sexually discriminatory, they eventually abandoned that claim.
[*]  Faculty rank can act as a surrogate only for persons who have not become full professors. For those who have reached that highest level, the possibility of increasing faculty rank does not exist.
[*]  A similar, albeit lesser, shortcoming was plaintiffs' exclusion of the factors of time in faculty rank and level of administrative responsibility, which also had a substantial bearing upon salary.
[*]  R2 is the coefficient of determination: it "indicates the proportion of total variance in the dependent variable that is explained by or associated with the group of independent variables in the [regression] equation." D. Baldus & J. Cole, Statistical Proof of Discrimination, § 8.123[1], at 259 (1980).
[*]  At the very conclusion of the plaintiffs' rebuttal, they attempted to introduce still another study to deal with some of the problems of their earlier models. This study contained inaccurate data, was cumulative of their earlier submissions, and did not affect their experts' opinions. Moreover, in the opinion of the Court, the study did not address the major criticisms raised by the defendant's experts. The Court declined to accept this rebuttal report because of its untimely submission to the defendant's experts, who requested two additional weeks of trial in order to study and respond to it, and because of its almost complete lack of probative value.
[*]  The defendant presented a total of four experts: (1) Dr. Herbert Robbins, former chairperson of the Department of Mathematical Statistics at Columbia University; (2) Dr. Bruce Levin, a statistician with expertise in the application of multiple linear regression to categorical data; (3) Dr. Frank Sloan, an econometrician specializing in public health, particularly the compensation of physicians; and (4) Dr. Frederick Putney, principle administrator of the Columbia University School of Public Health, including the College of Physicians and Surgeons. The Court found Dr. Putney to be particularly knowledgeable and persuasive.
[*]  The urn model allowed the defendants to test for the significance of any difference in the average salaries of males and females by comparing that difference with the difference obtained by randomly dividing all the salaries into two groups (and thus simulating a clearly non-discriminatory distribution of salaries). The advantage of the urn model was that the validity of its use did not depend on the same underlying assumptions upon which the plaintiffs' model rested, and which were so much in doubt. Hence, although perhaps not as statistically powerful as the multiple linear regression model, the urn model provided a very appropriate test given Einstein's complex organization and the diffuse factors affecting salaries.
[*]  It should be noted that proceeding on the separate year basis avoided the distorting effect of interdependent variables which resulted from analyzing total salary in consecutive years as plaintiffs' experts did. The defendant's experts used the urn model tests in their study of initial salaries and an analysis of residuals in their study of subsequent annual pay increases.
[*]  As indicated earlier, it was impossible to study all departments separately since some were not large enough. In addition, the number of women present in certain departments was so small that no valuable comparison could be made.
[*]  Nonetheless, certain of the difficulties in making a complete study remained.
[]  For these purposes a "z score" was used rather than a student t value, see supra n. 32. These two statistics, however, serve the same functions, and a z score of less than 2.0, for example, denotes the same low level of statistical significance that a similar t value indicates.
[]  In each year in the relevant time period, between half and two-thirds of all faculty members received the guideline increment or within $100 of that amount.
[]  The Senate at Einstein was comprised of elected faculty representatives of all departments, several student representatives, all departmental chairpersons as statutory members, the Dean and certain associate deans. The Dean also chaired the Senate Council, which was elected by the Senate.
[]  Little evidence was offered to establish how women were discriminated against in the years prior to 1972. However, a few facts emerged from which some tentative conclusions can be drawn. During the late 1960's and early 1970's, Einstein was in difficult financial straits caused, at least in part, by the opening of its own hospital in the Bronx at a time when the need for a new hospital was not economically apparent. Consequently, it appears that most of Einstein's faculty members were not paid what they were worth. Raises tended to go only to those who made a great fuss about the failure to receive an adequate salary. In most instances, those who protested were men who were the sole sources of income for their families. (Although no statistics were presented on this matter, we take it as an accepted sociological fact that the percentage of men who were the sole wage earners for families with children exceeded the percentage of married women who were such.) This tendency to favor the sole working members of families appears to have disappeared in the 1970's as circumstances changed.
[]  She is not Board-certified in her sub-specialty, but the boards for that sub-specialty have only been in existence for a few years.
[]  During this period, she did not receive encouraging comments about her research proposals from the National Institutes of Health and others who might have provided grants.
[]  Although the issues of liability and damages were bifurcated, the Court's order of March 4, 1982 directed that the named plaintiffs would be required to testify and prove their particular damage claims during the liability portion of the trial. This requirement was imposed to give both parties the opportunity to prove the existence or nonexistence of individual damages at least to the extent that such evidence might prove or disprove any liability for sex discrimination in salaries.
[]  Although the plaintiffs did note that four of the class members had requested above-guideline increases during the relevant time period, no evidence was offered to establish that previous discriminatory treatment on the part of the defendant caused a need for such increases.
[]  It is still not clear that the plaintiffs have any real objection to the guideline system itself: if they were simply granted a one-time adjustment to make the average of their salaries equal to that of their male counterparts, they would be perfectly content to let the guideline system continue operating just as it has for years.
[]  If the defendant had been given adequate notice, it undoubtedly would have offered additional evidence to support its contention that the guideline system was justified as a "business necessity," see, e.g., Teamsters v. United States, 431 U.S. 324, 336 n. 15, 97 S.Ct. 1843, 1855 n. 15, 52 L.Ed.2d 396 (1977). What proof the defendant did offer tended to show that the system was designed to strike a reasonable balance between two conflicting needs: one for a balanced budget and the other for adequate and equitable salary incentives. That the defendant was thus effectively denied a full opportunity to justify its system, and thereby meet its burden of production and compel the plaintiffs to come up with another, less discriminatory system which also served the apparently legitimate "business" needs already served by the existing system, see, e.g., Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 2726, 53 L.Ed.2d 786 (1977), demonstrates rather clearly the degree of unfairness the plaintiffs have asked this Court to condone.
[]  In fact, as was noted earlier, the proof tends to show that efforts were made, as in the case of Dr. Sobel, to correct for past discrimination by making special "inequity" increases. Also, the statistics themselves suggest that the guideline system favored female faculty, if it favored anyone, though not to a statistically significant degree.
[]  Although the plaintiffs rely upon a number of cases which attempt to distinguish Evans on the ground that a present violation occurs each time an employer issues paychecks that reflect disparate salaries for men and women, e.g., Kim v. Coppin State College, 662 F.2d 1055, 1060-61 (4th Cir.1981); Satz v. ITT Financial Corp., 619 F.2d 738, 743 (8th Cir.1980), this Court questions the validity of such a distinction. Evans itself involved a claim of disparate pay brought by a present employee, Evans, supra, 431 U.S. at 555-56 & nn. 5 & 7, 97 S.Ct. at 1887-88 & nn. 5 & 7; yet, that fact did not lead the Supreme Court to conclude that a present violation had been alleged. Rather, it noted a present effect, looked for a present discriminatory practice that might be perpetuating that effect, and found instead a fair and neutral seniority system. Upon that basis, it concluded that Evans had not proven a present violation. That analysis yielded a similar result in Farris v. Board of Education of St. Louis, 576 F.2d 765, 767-68 (8th Cir.1978) (no violation where there was no suggestion that incremental raises were "in any way dependent upon sex"), and must lead to the same conclusion here as well. After all, as Judge Friendly has noted, an employer's obligation is "to eliminate any current discriminatory practices," not "all vestiges of ... former gender-based discrimination." Ste. Marie v. Eastern Railroad Ass'n, 650 F.2d 395, 404 (2d Cir.1981).
[]  Moreover, City of Los Angeles Dep't of Water & Power v. Manhart, 435 U.S. 702, 98 S.Ct. 1370, 55 L.Ed.2d 657 (1978), which not only held that pension contributions constitute compensation but also declared that use of sex segregated mortality tables to determine such contributions constitutes a prima facie case of disparate impact, id. at 710-18, 98 S.Ct. at 1376-80, was not decided until three years after the plaintiffs brought this action. They can hardly be faulted for not specifically alleging what, at the time, they had no clearly established legal right to claim.
[]  A "defined contribution" plan is one for which the formula for the employer's contribution is fixed at the outset (e.g., 10% of an employee's salary), so that the exact amount that the employer must contribute in any given year is defined as soon as the employee's salary for that year is established. Such a plan is somewhat different from a "defined benefit" plan, in which the formula for the employee's benefits is fixed at the outset (e.g., 3% of the employee's average monthly salary during the last year of employment times the number of years employed), so that the exact amount of the employer's contribution for any given year cannot be calculated until the date of the employee's retirement is known.
[]  The Court has concluded that no legal significance should be attached to two of the distinguishing characteristics of Manhart which some might find important, namely: (1) the fact that Manhart involved a government annuity program, and (2) the fact that the plan in that case was a "defined benefit" plan rather than a "defined contribution" plan. See supra note 59. No persuasive reason has been given for limiting the holding in Manhart on the basis of these rather technical distinctions.
[]  The court also pointed out that at Wayne State, as is true at Einstein, the faculty are not required to participate in the pension plan.
[]  Because the insurers in Spirt were organizations created solely for the purpose of assisting teaching institutions to provide retirement benefits and because the university shared in the administrative responsibilities of participation in the fund, the court held that the insurers themselves were "employers" for purposes of Title VII. Spirt, supra, 691 F.2d at 1063.
[]  See supra note 62.
[]  In Norris, supra, 671 F.2d at 332, one of the three benefit options is a lump sum payout at retirement. This was also one of the options that Einstein proposed to the EEOC. As noted earlier, the EEOC refused to take a position on whether such a plan would be a viable solution to the Manhart problem.
