#### EQUAL EMPLOYMENT OPPORTUNITY COMMISSION, Plaintiff-Appellant-Cross-Appellee, v. JOINT APPRENTICESHIP COMMITTEE OF THE JOINT INDUSTRY BOARD OF THE ELECTRICAL INDUSTRY, Defendant-Appellee-Cross-Appellant.

Docket Nos. 97-6193(L), 97-6203(XAP)

United States Court of Appeals, Second Circuit.

Argued March 30, 1998.

Decided Dec. 18, 1998.

Amended July 9, 1999.

*114C. Gregory Stewart, J. Ray Terry, Jr., Vincent J. Blackwood, Carolyn L. Wheeler, John F. Suhre, Equal Employment Opportunity Commission, Washington, D.C., for Plaintiff-AppellanNCross-Appellee.

Norman Rothfeld, New York, NY, for Defendanfi-Appellee-Cross-Appellant.

Before: PARKER, Circuit Judge, EGINTON,* and GLASSER,** Senior District Judges ***

*

The Honorable Warren W. Eginton, of the United States District Court for the District of Connecticut, sitting by designation.

**

 The Honorable I. Leo Glasser, of the United States District Court for the Eastern District of New York, sitting by designation.

***

 Chief Judge Ralph K. Winter certified a Judicial Emergency pursuant to 28 U.S.C. § 46(b) permitting the panel to include two district judges and one *circuit*judge.

EGINTON, Senior District Judge:

Plaintiff Equal Employment Opportunity Commission (“EEOC”) appeals from an order of the district court (Knapp, *Senior District*Judge) denying EEOC’s motion to enjoin defendant Joint Apprenticeship Committee of the Joint Industry Board of the Electrical Industry (“JAC”) from requiring applicants to its apprentice training program to possess a high school diploma or General Equivalency Diploma (“GED”), and denying back pay to certain individual claimants. JAC cross-appeals from the district court’s decision granting EEOC’s motion for partial summary judgment as to liability and from the district court’s award of back pay to individual claimant Beverly Mundle. We vacate the judgment and remand for further proceedings.

*I. BACKGROUND*

*A. The JAC Apprentice Training Program*

JAC, a committee of the Joint Industry Board of the Electrical Industry, administers a four-year electrician apprentice training program. At the time this action was commenced in 1984, JAC required applicants to its apprentice training program to be between the ages of 19 and 22 and to possess a high school diploma or GED. JAC eliminated the age requirement in 1985 pursuant to N.Y. Exec. Law § 296(l)(a) and (b), a state law prohibiting upper age limits for admission to apprenticeship programs. JAC continues to implement the education requirement.

JAC Recruitment announcements issued in 1981 and 1993 bore the caveat that “[ajnyone who does not meet the age, educational or any other requirement outlined in the notice should not request an application.” The recruitment announcements also stated in bold capital letters that “[A]LL APPLICANTS MUST MEET THE FOLLOWING MINIMUM QUALIFICATIONS IN ORDER TO QUALIFY,” with age and education being the first two qualifications listed.

Applicants meeting these and other preliminary criteria were interviewed and given an aptitude test.1 JAC would then offer apprenticeships to those applicants achieving the highest scores on the test and interview. Individuals failing to meet these preliminary criteria who nonetheless applied to the program were subject to rejection solely based on their age or edu*115cational status, and were not afforded the opportunity to interview or take the aptitude test.

JAC apprenticeships were and are paid positions, with compensation increasing as an apprentice garners skills and experience. For instance, from June 13, 1985 to June 12, 1986, a first-year apprentice earned $6.55 per hour, a second-year apprentice earned $7.60 per hour, a third-year apprentice earned $8.55 per hour, and a fourth-year apprentice earned $9.50 per hour. Upon successful completion of his or her apprenticeship, an individual is deemed an intermediate journey worker for a period of 18 months, and thereafter becomes a full journey worker. Between 1985 and 1986, an intermediate journey worker earned $11.50 per hour, and a full journey worker earned $23.50 per hour.

Successful completion of JAC’s apprentice training program also entitles an individual to membership in the International Brotherhood of Electrical Workers, Local 3, which is an electrical workers union (the “IBEW”). Most, but not all, IBEW members have gained admission to the union through JAC’s apprentice training program. A person need not possess a high school diploma or GED, however, to become an IBEW member.

*B. The Proceedings Below*

EEOC brought this action in 1984 pursuant to Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C. § 2000e *et seq.,*alleging that JAC’s education requirement had a disparate impact on Blacks and that its age requirement had a disparate impact on women. EEOC relied heavily on statistical evidence to support its claims.

On March 16, 1988, EEOC moved for partial summary judgment as to liability. Faced with this motion, JAC’s counsel made the strategic choice to attack the validity of EEOC’s prima facie case without making any timely showing of business justifications for the age and education requirements. After oral argument on EEOC’s motion for partial summary judgment, however, JAC attempted to proffer an affidavit which JAC claimed showed business justifications for the challenged requirements. The district court struck the affidavit as untimely. On May 1, 1989, the district court granted summary judgment as to liability in favor of EEOC, finding that EEOC had established a pri-ma facie case and that JAC had failed to show any business justification for the challenged requirements.

JAC appealed. This Court vacated the district court’s May 1, 1989 decision and remanded on the grounds that the district court had failed to find, as required by *Wards Cove Packing Co. v. Atonio,*490 U.S. 642, 109 S.Ct. 2115, 104 L.Ed.2d 733 (1989), that the challenged requirements had caused the statistical disparities. In that opinion, this Court expressed no view as to the sufficiency of EEOC’s statistics. *EEOC v. Joint Apprenticeship Committee of the Joint Industry Board of the Electrical Industry,*895 F.2d 86, 91 (2d Cir.1990).

On remand, the district court made the requisite finding of causation, and once again entered summary judgment in favor of EEOC. In so doing, the district court refused to reconsider JAC’s previously stricken affidavit or to allow the introduction of new evidence of business justification. Consequently, the district court’s decision rested entirely on its conclusion that EEOC had successfully established each prima facie case of Title VII discrimination. *EEOC v. Joint Apprenticeship Committee of the Joint Board of the Electrical Industry,*828 F.Supp. 264, 266-67 (S.D.N.Y.1993).

The case was thereafter referred to Magistrate Judge Naomi Reice Buchwald for consideration of whether eight female individual claimants who had been denied entrance to the JAC apprentice training program solely on the basis of age should be awarded back pay. After hearing three days of testimony, the Magistrate Judge recommended that the district court not *116award back pay to any of the individual claimants. On May 29,1996, Judge Knapp adopted the Magistrate Judge’s recommendations as to all claimants except for Beverly Mundle, to whom the district court awarded back pay for the years 1983-1985.

On June 4,1997, the district court granted EEOC’s application for an injunction prohibiting JAC from implementing its age requirement, but declined, without explanation, to enjoin JAC from utilizing its education requirement. This appeal followed.

*II. DISCUSSION*

EEOC’s primary basis for appeal is that the district court erred when it refused to enjoin JAC from continuing to implement its education requirement. EEOC argues that because the district court found JAC liable for race discrimination in violation of Title VII, the court was under a duty to grant the injunction. *See, e.g., United States v. Gregory, 871 F.2d*1239, 1246 (4th Cir.1989)(when a plaintiff establishes a defendant’s liability under Title VII, there is no discretion to deny injunctive relief completely). At first blush, this situation might appear to require a fairly straightforward and facile analysis, with the likely outcome being a mandate directing the district court to enter the sought-after injunction.

JAC, however, cross-appeals from the underlying grant of partial summary judgment as to the race claim, urging that because judgment for EEOC was made in error, no injunction should issue. Moreover, JAC counters EEOC’s second basis for appeal — the denial of back pay — by, cross-appealing from the judgment entered in favor of EEOC as to the sex discrimination claim.

For the reasons discussed below, we find that the district court erred in not allowing JAC to present any evidence of business justification on remand. We therefore vacate judgment in favor of EEOC as to both Title VII claims, and once again remand the case to the district court, this time for consideration of the business justification issue. We reach this conclusion not because we believe that the district court abused its discretion in striking JAC’s late-filed affidavit. Rather, we conclude that this court’s somewhat ambiguous January 31,1990 opinion was intended to have the effect of re-opening the business justification inquiry. We stress that although we are troubled by the longevity of this litigation, we are loathe to hold the education requirement invalid absent the full hearing on the merits that was this Court’s intention. We further emphasize that we do not fault Judge Knapp for misreading this Court’s imprecise 1990 ruling.

*A. The Statistical Evidence*

Before reaching the business justification analysis, however, we address JAC’s assertion that the district court erroneously granted summary judgment as to liability in favor of EEOC because, according to JAC, EEOC’s statistical evidence is spurious and, therefore, insufficient to support a prima facie case of Title VII discrimination. Upon *de novo*review, we find that EEOC’s statistics, while not flawless, are nonetheless sufficient to establish a prima facie case for each claim. *See Eagleston v. Guido,*41 F.3d 865, 870 (2d Cir.1994) (grants of summary judgment are reviewed *de*novo).

*1. Legal Standards*

Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e *et seq.,*prohibits employers from discriminating on the basis of an individual’s race, color, religion, sex, or national origin. This mandate encompasses more than just overt and intentional discrimination. It also proscribes facially neutral employment practices which result in discrimination because they fall more harshly on a protected group than on other groups, and cannot be justified. *Waisome v. Port Authority of New York and New Jersey,*948 F.2d 1370, *1171374 (2d Cir.1991). EEOC’s claims fall within this latter category, the so-called “disparate impact” theory of employment discrimination, the archetype of which involves a facially-neutral hiring or promotion policy which disproportionately impacts a protected group. *Sobel v. Yeshiva University,*839 F.2d 18, 28-29 (2d Cir. 1988).

In order to prevail on a disparate impact claim, a plaintiff must initially establish a prima facie case of discrimination. A plaintiff makes such a showing by first pointing out the specific employment practice it is challenging and then demonstrating that the challenged employment practice caused a significant disparate impact on a protected group. A plaintiff may rely solely on statistical evidence to establish a prima facie case of disparate impact. *Wards Cove Packing Co. v. Atonio,*490 U.S. 642, 656-57, 109 S.Ct. 2115, 104 L.Ed.2d 733 (1989). In this case, it is undisputed that EEOC has met the first prong of the *Wards Cove*analysis by identifying the education and age requirements as the challenged employment practices. This debate thus focuses on whether EEOC’s statistics establish that the education and age requirements caused a significant disparate impact on Blacks and women, respectively.

Because statistical analysis, by its very nature, can never scientifically prove discrimination, a disparate impact plaintiff need not prove causation to a scientific degree of certainty. *Bazemore v. Friday,*478 U.S. 385, 400, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986); Ramona L. Paetzold and Steven L. Willborn, *The Statistics of Discrimination,*§ 2.05 (1996) (hereinafter “Paetzold and Willborn”). Accordingly, this Court has held that a plaintiff may establish a prima facie case of disparate impact discrimination by proffering statistical evidence which reveals a disparity substantial enough to raise an inference of causation. That is, a plaintiffs statistical evidence must reflect a disparity so great that it cannot be accounted for by chance. *Waisome*at 1375; *Bridgeport Guardians, Inc. v. City of Bridgeport,*933 F.2d 1140, 1146 (2d Cir.1991).

*2. EEOC’s Statistics*

EEOC tendered the following statistical evidence with respect to the challenged education requirement: (1) For counties from which JAC received five or more applications, 89.2% of Whites and 68.3% of Blacks between the ages of 18 and 22 possessed a high school diploma or GED. According to EEOC, this statistical disparity exceeds 220 standard deviation units.2 (2) Blacks comprised 18.3% of the potential applicant pool for JAC’s apprentice training program but made up 12.2% of actual applicants to the program. EEOC defined the potential applicant pool as comprising of operatives and laborers in the geographical regions from which JAC drew its applicants. According to EEOC, the likelihood of this disparity occurring by chance is less than 1 in 10,000. (3) Of the actual applicants to three successive apprentice training programs numbered 10, 11, and 12, Blacks failed to meet the education requirement at a higher rate than did Whites. For instance, in program 10, 2.27% of Black applicants did not possess a high school diploma or GED, whereas 1.07% of White applicants did not. In programs 11 and 12, the percentages were, respectively, 3.97 for Blacks and 0.87 for Whites, and 5.01 for Blacks and 1.28 for Whites. According to EEOC, the likelihood of these disparities occurring by chance is less than 1 in 10,000. [See EEOC’s Reply Brief at 6]

*118As to the age requirement, EEOC submitted the following statistics: (1) Women comprised 28.8% of the potential applicant pool for the apprentice training program, but made up 2.5% of actual applicants to the program. EEOC defined the potential applicant pool as consisting of operatives and laborers in the geographical regions from which JAC drew its applicants. According to EEOC, this disparity is significant at the 0.0000 level. (2) Of the actual applicants to JAC programs 10,11; and 12, women applicants were overage at a higher rate than were male applicants. For instance, in program 10, 20.31% of female applicants were overage, whereas 2.61% of male applicants failed to meet the age requirement. In programs 11 and 12, the percentages were, respectively, 14.29% for women and 1.80% for men, and *5.43% for*women and 2.00% for men. According to EEOC, the likelihood of these disparities occurring by chance is 1 in 10,000. [See *Id.*at 21]

The district court found these statistics to be significant, and concluded that “the educational requirement and the age maximum had a chilling effect on black and women applicants, which caused the ... statistical disparities.” *EEOC v. JAC, 828*F.Supp. at 266. The district court also found that no other explanation existed for the disparities which, in its view, were directly attributable to JAC’s recruitment announcements which stated that “[a]ny-one who does not meet the age, educational or any other requirement outlined in the notice should not request an application” and warned, in bold capital letters, that all applicants must meet the age and education requirements in order to qualify for the program. *Id.*

*3. JAC’s Contentions*

On appeal, JAC criticizes the district court’s reliance on the statistics comparing the characteristics of actual applicants who failed to meet the challenged requirements. *See EEOC v. JAC,*828 F.Supp. at 265-66. JAC contends that if this Court were to disregard those statistics, EEOC would be unable to establish a prima facie case for either of its claims. Moreover, JAC urges us to heed JAC’s own statistical analysis, which according to JAC, demonstrates a lack of disparate impact. We conclude that although certain of JAC’s criticisms are well-founded, EEOC’s evidence, on the whole, suffices to support a prima facie case for each Title VII claim. In addition, we find JAC’s proposed statistical approach to be inapposite.

JAC’s chief argument focuses on the district court’s application of the so-called four-fifths or 80% rule to those statistics which compare the characteristics of actual applicants who failed to meet the education and age requirements. The four-fifths rule derives from the EEOC Uniform Guidelines on Employment Selection Procedures, 29 C.F.R. § 1607.4 D, and has been looked to by this Court for guidance in gauging the significance of statistical evidence of discrimination. *See, Waisome,*948 F.2d at 1375-76; *Bridgeport Guardians,*933 F.2d at 1146-47. This rule is not binding on courts, and is merely a “rule of thumb” to be considered in appropriate circumstances. *Waisome*at 1375-76. The rule states in pertinent part:

> A selection rate for any race, sex, or ethnic group which is less than four-fifths *{%)*(or eighty percent) of the rate for the group with the highest rate will generally be regarded by the Federal enforcement agencies as evidence of adverse impact, while a greater than four-fifths rate will generally not be regarded by Federal enforcement agencies as evidence of adverse impact. Smaller differences in selection rate may nonetheless constitute adverse impact, where they are significant in both statistical and practical terms....

29 C.F.R. § 1607.4D.

JAC asserts that the district court erroneously endorsed the application of the four-fifths rule to what JAC calls a “fail *119ratio.”3 JAC argues that the four-fifths rule was not designed for use with fail ratios because often, as in this case, the amount of people who apply but fail to meet challenged criteria are few in number, and therefore, random differences in the sample could cause significant differences in the resulting statistics. *See Guinyard v. City of New York,*800 F.Supp. 1083, 1089 (E.D.N.Y.1992) (with a small sample size, slight variations in data can lead to large differences in the result). JAC also points out that the plain language of the EEOC Uniform Guidelines, which refers to the “selection rate,” seems to presuppose the use of a ratio consisting of those individuals who were selected for the at-issue position — that is, JAC argues that the Guidelines presume the use of a “pass ratio.”

We agree with JAC that the district court inappropriately sanctioned the application of the four-fifths rule to the fail ratio. In this case, the vast majority of actual applicants, including Blacks and women, met the challenged requirements. For instance, 96.3% of Black and 98.6% of White applicants possessed a high school diploma or GED. This means that the fail ratio sample consisted of the very small number of applicants who did not meet the challenged requirements. Under these circumstances, we find that the application of the four-fifths rule to this particular fail ratio was inappropriate, because such a small sample would tend to produce inherently unreliable results. *Guinyard*at 1089 (statistics of disparate impact must be scrutinized, especially when the sampling size is small); Paetzold *&*Willborn at § 5.06 (noting that the four-fifths rule “simply cannot” be applied based on rejection rates alone and criticizing courts which so apply the rule).

We do not agree with JAC, however, on its contention that once the fail ratio statistics are eliminated, EEOC is rendered bereft of evidence supporting a prima facie case for each of its Title VII claims. This position disregards the fact that the district court properly based its conclusion on an array of well-crafted and highly significant statistics, including studies based on general population data and potential applicant pool data. *EEOC v. JAC,*828 F.Supp. at 265-66. Indeed, these types of data often form the initial basis of a disparate impact claim, especially in cases such as this one in which the actual applicant pool might not reflect the potential applicant pool, due to a self-recognized inability on the part of potential applicants to meet the very standards challenged as being discriminatory. *See, Dothard v. Rawlinson,*433 U.S. 321, 329-30, 97 S.Ct. 2720, 53 L.Ed.2d 786 (1977) (allowing use of general population data to show disparate impact of height and weight requirement on women); *Griggs v. Duke Power Co.,*401 U.S. 424, 430, 91 S.Ct. 849, 28 L.Ed.2d 158 (relying on general population data in finding disparate impact of diploma requirement on Blacks); *EEOC v. Local 638,*532 F.2d 821, 825 (2d Cir.1976); Wards *Cove, supra,*490 U.S. at 650-51, 109 S.Ct. 2115 (recognizing that a comparison of the characteristics of “otherwise-qualified applicants” for at-issue jobs and the characteristics of the persons actually holding at-issue jobs can form the basis for the initial inquiry in a disparate impact case); *Banks v. City of Albany,*953 F.Supp. 28, 34 (N.D.N.Y.1997); Paetzold *&*Willborn at §§ 4.03, 5.04.

Moreover, like the district court, we are not persuaded by JAC’s largely unsupported and peripheral challenges to these statistics. For instance, JAC argues that EEOC’s statistics are based on stale census data, but makes no *120showing that more recent census data would produce significantly different results. JAC also posits, without support, that the disparity between the characteristics of the potential applicants and the actual applicants can be attributed to a general lack of interest on the part of Blacks and women in becoming electricians. This position appears to be derived in large part from stereotypes, and at any rate, begs the question. A lack of interest, if any, on the part of Blacks and women might equally be attributable to a cognizance of the barriers which may impact the chances of Blacks and women entering the trade. *See, e.g., Sobel, supra,*839 F.2d at 33 (refusing to credit “accepted sociological fact”, or “stereotype”, that men are more often sole wage earners as a viable explanation for why lower salaries were paid to female faculty members). JAC’s unsupported conjectures and assertions that these missing factors would explain the disparities revealed by EEOC’s statistical evidence cannot operate to debunk those statistics. In order to prevail in discrediting EEOC’s statistics, JAC was obliged to demonstrate that when the alleged missing factors are organized and accounted for, no significant disparity exists. *Id.*at 43. JAC has made no such showing.

Finally, we reject JAC’s contention that the appropriate statistical inquiry would have focused on a “pass ratio,” which JAC defines as a comparison between the percentages of Black and female applicants who met the challenged requirements and were subsequently offered apprenticeships and the percentages of other similarly-qualified applicants who received apprenticeship offers. According to JAC, such an approach would demonstrate that the challenged requirements had no disparate impact whatsoever on Blacks and women. We agree with the district court’s assessment that “[t]his calculation ... assumes that the number of applicants to the programs is random, when, in fact, the EEOC’s claim is precisely that the number of applicants was itself affected by the educational requirements.” Indeed, JAC’s position ignores the well-established principle that a statistical showing of disparate impact need not, and in instances such as this should not, be premised on an analysis of the characteristics of actual applicants. *Dothard,*433 U.S. at 330, 97 S.Ct. 2720.

We therefore agree with the district court that EEOC’s general population and potential applicant pool studies reveal disparities so great that they could not have occurred by chance. *See, e.g., Bridgeport Guardians, supra,*933 F.2d at 1147 (occurrence rates of 1 in 10,000 and 1 in 5,000 had statistical significance); *Ottaviani v. State University of New York at New Paltz,*875 F.2d 365, 371-72 (2d Cir.1989) (statistical analysis yielding level of significance at or below .05 is suspect, and a disparity of 2 standard deviation units establishes threshold level of statistical significance). Accordingly, we conclude that EEOC’s statistical evidence reveals that the challenged education and age requirements caused a significant disparate impact on Blacks and women, respectively. *See Wards Cove*at 656-57, 109 S.Ct. 2115.

*B. Business Justification*

Normally, the disparate impact analysis does not end once the plaintiff has established a prima facie case. Instead, the case shifts to the defendant to show a business justification for the challenged employment practice. At this phase, the defendant carries the burden of production. The ultimate burden of persuasion, however, remains at all times with the plaintiff. *Wards Cove,*490 U.S. at 658-59, 109 S.Ct. 2115; *Watson v. Fort Worth Bank and Trust,*487 U.S. 977, 997, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988).

If the defendant succeeds in producing evidence showing a business justification for the challenged employment practice, then the plaintiff must persuade the fact finder that other tests or selection devices would also serve the defendant’s legitimate employment goals without producing a similarly undesirable disparate *121effect. *Wards Cove*at 658-59, 109 S.Ct. 2115; *Watson*at 998, 108 S.Ct. 2777.

This case is unusual in that it never reached the business justification inquiry. It was instead truncated and decided at the conclusion of EEOC’s prima facie case. This procedural irregularity was caused by JAC’s unconventional and somewhat myopic litigation strategy: JAC focused its entire defense on undermining EEOC’s prima facie case, and thus made no timely attempt to produce evidence of business justification. When JAC realized that its strategy might not succeed, it attempted, very late in the proceedings, to introduce an affidavit which it claimed showed JAC’s business justifications for the age and education requirements. Judge Knapp, acting within his discretion, struck the affidavit as untimely. The case was then, as Judge Knapp put it, “in the same posture as it would be at a trial of the liability phase of the case if, after losing their motion to dismiss at the close of the plaintiffs case, defendants rested without calling any witnesses.” *EEOC v. International Brotherhood of Electrical Workers, Local 3,*No. 84 Civ. 3373(WK), slip op. at 7-8 (S.D.N.Y. May 1, 1989). The district court thus only needed to conclude, which it did, that EEOC had established a prima facie case in order to grant EEOC’s motion for partial summary judgment as to liability. *Id.*

As previously noted, this Court thereafter vacated the district court’s grant of partial summary judgment, and remanded for consideration of whether EEOC had established, as required by *Wards Cove,*490 U.S. at 657, 109 S.Ct. 2115, a causal nexus between the challenged requirements and the statistical disparities. *EEOC v. JAC,*895 F.2d at 91. That opinion also stated:

> If it is determined that EEOC has advanced a prima facie case of disparate impact, the burden of production shifts to JAC to produce evidence rebutting the prima facie case. Thus, JAC would then bear the burden of showing that there are “legitimate, nondiscriminatory reasons” for the specific employment practices in question.

*Id.*at 91.

In our view, the above-quoted language was meant to set forth the path that this case was to take on remand, and as such, authorized the district court to reopen the record and allow JAC to introduce evidence of business justification in the event that causation was found. On remand, however, the district court apparently believed that it was bound by its earlier decision to disallow JAC to introduce evidence of business justification.4 It therefore refused to allow JAC to introduce either the previously stricken affidavit or any new, additional evidence of business justification. *EEOC v. JAC,*828 F.Supp. at 267, n.3.

The conundrum thereafter faced by the district court became evident when EEOC moved, in 1997, to enjoin JAC from future implementation of its education requirement. Although we may never know why the district court refused to enter the injunction, we can infer that the court was reluctant to enjoin an admission requirement which may have had a legitimate business justification.

We believe that this Court intended to avoid this type of situation when it provided the above-quoted road map for the proceedings on remand. Accordingly, we are obliged to once again remand the case for the full and fair hearing on the business justification issue that was this Court’s intention. We stress, however, that today’s opinion should not be interpreted as condoning JAC’s litigation tactics, or as encouraging the admission of late-filed documents. We make this decision based solely on our reading of this Court’s 1990 ruling in this matter, to which we are *122bound. *See generally, Sobel v. Yeshiva University,*839 F.2d at 23-24 (absence of procedural bar in Title VII case entitled plaintiff to full and fair hearing on the merits).

Finally, in order to guide the district court on remand, we feel compelled to address certain statements made by the district court in *dicta.*Referring to JAC’s business justification evidence, the district court stated:

> even if we were to allow the affidavits, neither refers to any study or scholarly work (or indeed work of any kind) to support its conclusions. We thus see no reason to believe that a person with a diploma would be capable of making mathematical computations, but, for example, a person with only three years of high school study would not, or that a mentor-mentee relationship can only be created if an apprentice is 22 years old or younger, rather than, for example, 25 or younger. As such, the affidavits appear to be entirely unpersuasive.

*EEOC v. JAG,*828 F.Supp. at 267, n. 3.

We believe that this approach, if it were to be adopted on remand, would be improper. First, it places too high a burden on the defendant, which bears only the burden of production, not of proof, at the business justification phase of a disparate impact case. *Wards Cove*at 658-59, 109 S.Ct. 2115; *Watson,*487 U.S. at 997-98, 108 S.Ct. 2777. This being the case, defendant’s business justification evidence need not include studies or scholarly work. *Watson*at 998, 108 S.Ct. 2777 (employers are not required to introduce formal “validation studies” showing that particular criteria predict actual on-thé-job performance). Second, this approach infringes upon the province of the fact-finder, whose job it is to weigh the persuasiveness of defendant’s evidence. In our view, a reasonable fact-finder could find that business justifications exist for JAC’s education and age requirements. Accordingly, this question should be presented to the fact-finder on remand.

*C. Back Pay*

Today’s decision to vacate the judgment entered in favor of EEOC moots the district court’s order concerning individual claims for back pay and the parties’ appeals therefrom. Because the back pay inquiry may be revisited on remand, we take this opportunity to clarify a few key issues raised by the parties on appeal. We stress that the fact that we opt here to discuss damages does not in any way indicate our views on the merits of the underlying Title VII claims.

An applicant denied employment in violation of Title VII is ordinarily entitled to an award of back pay from the date of the discriminatory action to the date of judgment. *Sands v. Runyon,*28 F.3d 1323, 1327 (2d Cir.1994); *EEOC v. Local 638,*532 F.2d at 832 (back pay is the rule rather than the exception under Title VII). When, as here, there has been an allegation of an unlawful refusal to hire, a plaintiff establishes a prima facie case of entitlement to back pay simply by showing that she applied for the position at issue and was not hired. The burden then shifts on the defendant to show that the plaintiff would not have been hired even absent discrimination. Any uncertainty as to whether the plaintiff would have been hired is resolved against the defendant, since it is the defendant’s discriminatory employment practices which are the source of the uncertainty. *Cohen v. West Haven Board of Police Commissioners,*638 F.2d 496, 502 (2d Cir.1980); *Association Against Discrimination in Employment, Inc. v. City of Bridgeport,*647 F.2d 256, 289 (2d Cir.1981).

In this case, the district court, applying *Cohen*and *City of Bridgeport,*found that, with one exception, each individual claimant had established a prima facie ease of entitlement to back pay because each had applied to the apprentice training program and was rejected. The district court went on to find that JAC had failed to show that *123those individual claimants would not have been hired absent discrimination.

JAC contends on appeal that the district court erred in applying *Cohen*and *City of*Bridgeport—cases which JAC argues were abrogated by the Supreme Court’s decision in *Wards Cove v. Atonto,*490 U.S. at 659, 109 S.Ct. 2115. Specifically, JAC asserts that *Wards*Cove’s holding that the ultimate burden of proof remains at all times with the plaintiff applies not only to the liability phase of a Title VII claim, but also to the determination of back pay. JAC thus posits that in order to receive back pay, a plaintiff must prove that she would have been hired but for the unlawful discrimination.

We do not think that this is a permissible reading of *Wards*Cove—a case which deals exclusively with the standards for establishing liability in a Title VII claim, and never intimates that its holding was meant to extend beyond that context. First, we note that as a practical matter, the employer is ordinarily in a better position than the plaintiff to offer evidence of its hiring and decision-making processes. *See EEOC v. New York State,*No. 92 Civ. 2789, 1996 WL 384926 at *6 (S.D.N.Y. July 10, 1996). Second and more important, however, is the fact that JAC’s reading of *Wards Cove*would tend to undermine one of the fundamental purposes of the Title VII back pay provision, which is to deter discriminatory conduct and to spur employers to evaluate their employment practices. 42 U.S.C. § 2000e 5(g); *Local 638*at 832; *Albemarle Paper Co. v. Moody,*422 U.S. 405, 418-19, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975). In this regard, it is essential to keep in mind that by the time that a case reaches a back pay inquiry, it is beyond question that the employer has engaged in discriminatory conduct viola-tive of Title VII. In our view, therefore, to relieve an employer of the burden to show that it would not have hired the plaintiff absent discrimination would contravene part of Congress’s intent in enacting Title VII, in that an employer would be less likely to avoid or eliminate discriminatory employment practices if it knew in advance that it would never have to answer for those practices when faced with a claim for back pay. *See Albemarle*at 421, 95 S.Ct. 2362 (central statutory purpose of Title VII is to eradicate discrimination throughout the economy). Accordingly, we find the district court properly applied *Cohen*and *City of Bridgeport*in its back pay analysis.

We turn next to EEOC’s contention that the district court abused its discretion when setting the parameters for the back pay period. In this regard, the district court found that certain individual claimants were not entitled to back pay because, immediately after being rejected by JAC, they obtained jobs which initially paid more than a first-year apprenticeship, but which did not increase in pay at the same rate as the JAC program. EEOC argues that this approach defeats the purpose of make-whole relief. We agree. *See Sands v. Runyon,*28 F.3d at 1327 (the district court’s fashioning of remedial relief is reviewed for abuse of discretion); *Cohen*at 504 (although the fashioning of a back pay award falls within the trial court’s sound discretion, that discretion should be exercised with a view toward fashioning the most complete relief possible); *Albemarle,*422 U.S. at 416, 95 S.Ct. 2362 (a court must exercise its discretionary power to award back pay in light of the large objectives of Title VII).

The purpose of back pay is to *“completely redress*the economic injury the plaintiff has suffered as a result of discrimination.” *Saulpaugh v. Monroe Community Hospital,*4 F.3d at 145 (quoting *Gutzwiller v. Fenik,*860 F.2d 1317, 1333 (6th Cir.1988)) (emphasis added). In this sense, when awarding back pay, a court should attempt to place a victim of unlawful discrimination in as near a position as she would have been in absent the discrimination. *Ford Motor Co. v. EEOC,*458 U.S. 219, 230, 102 S.Ct. 3057, 73 *124L.Ed.2d 721 (1982). An award of back pay, therefore, should ordinarily consist of lost salary, including anticipated raises, and fringe benefits. *Saulpaugh*at 145; *Sands*at 1328 (district court properly included step increases, cost of living increases, and other increases in back pay award).

The district court was of the belief that its approach would “end any detrimental economic effects of defendant’s discrimination.” Given the nature of the JAC program and its pay structure, we find this view to be unfounded. This is because JAC’s apprentice training program was somewhat low paying at the beginning, but culminated in the obtainment of union membership and the entitlement to excellent wages. It seems to us that the goal of one applying to such a program would not be to earn the low hourly wage initially paid to first-year apprentices, but rather, to obtain the skills and credentials necessary to earn a full journey worker’s wages. The bite of the alleged discrimination, therefore, was not that it may have denied the claimants low paying apprenticeships. Rather, the real harm is that the alleged discrimination may have operated to deprive the claimants of the opportunity to train for a highly skilled and compensated trade.

We note that although we can imagine a situation in which the obtainment of a higher-paying position would completely mitigate a plaintiffs damages, and therefore, justify cutting off the back pay period before the date of judgment, for the reasons just stated, this is not such a case. The ordinary rule of this Circuit is that the back pay award runs from the date of the discriminatory action to the date of judgment, and should include any anticipated raises, step increases, cost of living increases, and other increases necessary to make the plaintiff whole. *Sands*at 1328. However, this analysis should not be applied to the present case, as such could result in highly speculative awards. The Supreme Court has stated that “it remains a cardinal, albeit frequently unar-ticulated assumption, that a back pay remedy must be sufficiently tailored to expunge only the actual, and not merely speculative, consequences of the unfair labor practices.” *Sure-Tan, Inc. v. NLRB,*467 U.S. 883, 900, 104 S.Ct. 2803, 81 L.Ed.2d 732 (1984). Thus, the district court must perform fact-finding as to each plaintiff in order to determine whether such plaintiff would have been likely to have proceeded all the way through the apprenticeship program — four years as an apprentice, two years as an intermediate journey worker and then on to full journey worker. The district court may determine that each plaintiff would have gone through the apprenticeship program, or it may determine that on these facts it cannot speculate as to what might have occurred.

It would be helpful to ascertain, for example, what percentage of successful applicants became full journey workers. We leave the methodology of such fact-finding to the District Court.

*III. CONCLUSION*

For the reasons stated in this opinion, the judgment of the district court is reversed, and the case is remanded for consideration of the whether JAC can show business justifications for the age and education requirements. The appeals taken from the district court’s order concerning individual claims for back pay are moot.

1

. Other requirements for entry into the JAC apprentice training program were residency in the Greater New York Metropolitan Area for the two years immediately prior to receiving an application, and the physical* ability to perform the work required by the apprenticeship.

2

. A standard deviation analysis measures the probability that a result occurred randomly— the more standard deviations, the lower the probability that the result is random. *Waisome*at 1376. The standard deviation is obtained by computing the square root of the variance, which is the sum of the squared deviations around the mean. Paetzold & Willborn at § 2.02, Table 2.1.

3

. The district court stated in a footnote that it saw "no reason to adopt ... the use of a pass ratio rather than a fail ratio when calculating the so-called 80% rule.” In this case, the fail ratio consisted of the comparison between those Black and female actual applicants who failed to meet, respectively, the education and age requirements, and other actual applicants who also failed to meet the challenged requirements.

4

. Referring to its earlier decision not to admit JAC's affidavit supporting its assertion of business justification, the district court noted that it “believe[d] this decision to be the law of the case and adhere[d] to it.” *EEOC v. JAC,*828 F.Supp. at 267, n.3.

GLASSER, J., District Judge

Dissenting:

I would affirm the decision of the district court and therefore respectfully dissent from the conclusion reached by the majority. The facts and background of this appeal have been fully and clearly stated. My disagreement with the conclusion reached is based upon my reading of Judge Knapp’s decisions of May 1, 1989 and August 31,1993.

*125In my view, Judge Knapp’s decision of May 1, 1989 reflects a studied analysis of the relevant statistics upon which the EEOC relied and which the defendant failed to challenge. That opinion, in my view, also reflects a consideration of the causal connection between the offending employment practice and its resulting disparate impact. In that opinion Judge Knapp wrote:

> The EEOC has conducted exhaustive discovery and analysis of JAC’s applicant records for the years 1980-rl984, covering three successive apprenticeship programs ... The EEOC has presented statistical data, gleaned from these records as well as from outside sources such as census data, revealing disparity between blacks and whites and between women and men in several categories.

Joint Appendix (“JA”), Vol. I at 346. Further on in that opinion, Judge Knapp found that “[d]efendants have failed to cast doubt on the validity of EEOC proffered statistics.” *Id.*at 348. His decisions based upon those findings are related in the majority opinion.

On appeal, this Court vacated Judge Knapp’s May 1, 1989 decision concluding that a remand was warranted for the reason that his decision *“appears*not to conform to the applicable legal standard” (emphasis mine) announced in *Wards Cove Packing Co. v. Atonio,*490 U.S. 642, 109 S.Ct. 2115, 104 L.Ed.2d 733 (1989). *See EEOC v. Joint Apprenticeship Committee,*895 F.2d 86, 91 (2d Cir.1990). That standard, simply put, requires the plaintiff, in establishing a prima facie case, to show that there is a causal connection between the employment practice and the disparate impact. *See,*490 U.S. at 656, 109 S.Ct. 2115. I would suggest that the requisite causal connection appeared in that decision and its appearance inadvertently overlooked. Thus, in discussing the high school diploma requirement, Judge Knapp wrote: “[T]he EEOC has presented statistics showing a significant disparity between the percentages of blacks with high school diplomas and whites with high school diplomas in the geographical area from which JAC draws its applicants .... ” JA, Vol. I at 346. After citing the relevant statistics, Judge Knapp continued:

> This disparity may explain the under-representation of blacks in the applicant pool during the year's in question: blacks made up 12.2% of the applicants to the three programs, but comprise 18.3% of the available pool of “operatives” and “laborers” in the relevant geographical area, based on 1980 Census data. *Yet it is not even necessary to speculate on the degree to which the high school requirement deters blacks without high [school] diplomas from applying, because the data concerning actual applicants to the three programs show that blacks without high school diplomas apply, and are turned away, at a higher rate than whites without high school diplomas.*For example, with respect to Program 12, 6.2% of the black applicants lacked high school diplomas, as compared with 2.13% of white applicants.... According to the EEOC’s statistical analysis, *all of the above-listed disparities are statistically significant well beyond the two to three standard deviations suggested by the Supreme Court as determinative of whether a legally significant disparate impact has been shown. Castaneda v. Partida,*430 U.S. 482 n. 17, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977).

JA Vol. I, at 347 (emphasis added).

That Judge Knapp was aware of and found the requisite causal connection is perhaps most clearly manifest from this portion of his opinion:

> *Second, [defendants] argue that an insufficient “nexus”*has been shown between the age maximum and the disparity between the percentages of male and female applicants, suggesting that other factors, such as gender stereotyping in education, may be responsible. *The main flaw in this argument is that it**126*ignores the import of the bare numbers:*there were consistently higher percentages of overage female applicants than male applicants, and thus the age maximum had a disparate impact on female applicants. It is not necessary for plaintiffs to explain the disparity on which their prima facie case rests; they must only show that its existence is more probable than not. *Eldredge v. Carpenters 46 Northern California Counties Joint Apprenticeship and Training Committee,*833 F.2d 1334, 1340 n. 8 (9th Cir.1987) *cert, denied*487 U.S. 1210, 108 S.Ct. 2857, 101 L.Ed.2d 894 (1988) *(“For purposes of [plaintiffs] prima facie case,*... *the issue is not why the [requirement] has a discriminatory impact, rather the issue is simply whether it had such an impact.”)*

JA Vol. I at 350-51 (emphasis added).

The “appearance” of a causal connection between the offending employment practice and the disparate impact to which it gave rise is, I suggest, readily found and not made invisible by the absence of words such as “causal connection” an insistence upon which would be to exalt form over substance and to require a mantra-like recitation of a formula to express a finding otherwise made.

In his second opinion dated August 31, 1993, following the remand, Judge Knapp wrote:

> Turning to the key question on remand, whether the EEOC has demonstrated a causal nexus between the challenged practices and the statistical disparities, we are persuaded by a careful consideration of the record that the educational

> requirement and age maximum had a chilling effect on potential black and women applicants, which caused the above-described statistical disparities. Thus we conclude that the EEOC has carried its burden and made out a prima facie case of disparate impact with respect to both requirements. 828 F.Supp. at 266 (S.D.N.Y.1993)

Two conclusions follow inevitably from the foregoing. First, Judge Knapp initially found the requisite causation because its absence was specifically argued by the defendant and rejected by him. Second, the defendant deliberately calculated not to pursue a business necessity justification but elected instead, to disparage, albeit unsuccessfully, the statistical data upon which the EEOC relied. Their awakening to the realization that they blundered strategically1 and then belatedly (after the record was closed and oral argument concluded) attempted to correct it by submitting affidavits, which Judge Knapp quite properly foreclosed,2 does not entitle them to revisit that issue nor did this Court invite the issue to be revisited on remand. In remanding to the district court, this Court wrote: “In doing so, we express no view as to the sufficiency of EEOC’s statistics to establish the requisite disparities, or as to whether summary judgment is appropriate with respect to the issue of causation.... If it is determined that EEOC has advanced a prima facie case of disparate impact, the burden of production shifts to JAC to produce evidence rebutting the prima facie case. Thus, JAC would then bear the burden of showing that there are ‘legitimate nondiscriminato*127ry reasons’ for the specific employment practice in question.” 895 F.2d at 91.

The direction to remand does not require the district court to revisit the issue of business necessity. Rather, it is a direction to remand solely for the purpose of determining whether the plaintiff has indeed set forth a prima facie case, given that Wards *Case*requires a showing of a causal connection between the statistics presented and the practices being challenged. Whether a plaintiff can establish a prima facie case of disparate impact and whether a defendant can show business necessity are two separate inquiries. The fact that plaintiffs prima facie case was revisited and reaffirmed on remand should in no way obligate the district court to again address the issue of business necessity which the defendant elected to forego. To do so would simply permit the defendants two bites at the apple. This litigation, commenced fourteen years ago, should not be further prolonged.

Judge Knapp’s musings in a footnote, 828 F.Supp. at 267 n.3, gives the majority some pause, namely “even if we were to allow affidavits, neither refers to any study or scholarly work (or *indeed ivork of any*kind) to support its conclusions .... ” (emphasis added). First, it is dicta and second, the phrase “or indeed work of any kind” I construe as a muted echo of *Matsushita Electric Industrial Co. v. Zenith Radio Corp.*475 U.S. 574, 586-87, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986) where the Court wrote that in opposing a motion for summary judgment the “opponent must do more than simply show that there is some metaphysical doubt as to the material facts.... In the language of the Rule, the nonmoving party must come forward with ‘specific facts showing that there is a *genuine issue for trial.’*” Judge Knapp considered “the record taken as a whole” and found in essence that it “could not lead a rational trier of fact to find for the nonmoving party, there is no genuine issue for trial.” *Id.*at 587, 106 S.Ct. 1348. Coming forward with no “work of any kind” is not even to raise a metaphysical doubt.

As regards the issue of back pay, I would also affirm the judgment of the district court.

1

. As Judge Knapp expressed it in his order of May 1, 1989 at JA 352:[A]l oral argument [defendants] admitted that a strategic decision had been made to proceed in this manner, placing all of their chips on their (now failed) effort to undercut the EEOC's prima facie case. See also 828 F.Supp. 264, 267 n. 3 (S.D.N.Y.1993)

2

. Although in theory, a motion may be amended at any time before the Judge has acted upon it, "it is particularly inappropriate after briefs have been interposed by the opposing parties and oral argument heard ...” Wright & Miller, Federal Practice and Procedure: Civil 2d § 1194, cited with approval in *Select Creations, Inc. v. Paliafito America, Inc.,*828 F.Supp. 1301, 1357 (E.D.Wis.1992). It is important to note that this Court made no finding that Judge Knapp abused his discretion in foreclosing the submission of affidavits after briefs were submitted and oral argument heard.