This constitutes the second appeal arising from a class suit brought under title VII of the Civil Rights Act of 1964, §§ 701-718, 42 U.S.C. §§ 2000e to 2000e-17, and 42 U.S.C. § 1981 alleging racial discrimination by the International Association of Bridge, Structural and Ornamental Iron Workers, Local No. 396 (Union) in training opportunities, referral methods and wage rates.
Rule filed a complaint in March 1973, naming as defendants the Union, the Iron-workers Joint Apprenticeship Committee of St. Louis, Missouri (JAC), and National Ironworkers and Employer Training Program (MTP). The Union, JAC, and MTP effectively controlled training opportunities in the ironworkers trade in the St. Louis, Missouri, area. Before 1964, all ironworkers in St. Louis were white. In 1964, the federal government and area civil rights organizations began to pressure unions and contractors to increase minority employment opportunities in the construction industry. Increasingly, blacks sought admission to the ironworkers trade. In 1964, the JAC first required a high school diploma, or its equivalent, as a prerequisite for entry into the apprentice program. In 1965, JAC introduced aptitude tests to aid in the selection of apprentices. During the times relevant to this litigation, applicants to the apprentice program had to satisfy four prerequisites: (1) be between 18-30 years of age, (2) present a doctor’s certificate of fitness, (3) be a United States citizen, and (4) have a high school diploma or its equivalent. Applicants who satisfied these prerequisites, were then rated on the basis of eight selection criteria: (1) physical ability, (2) past experience, (3) references, (4) written examinations, (5) residence, (6) military service, (7) oral interview, and (8) education. Applicants were admitted to the apprentice program on the basis of their score on these selection criteria. The four prerequisites should be distinguished from the eight selection criteria because the plaintiffs allege that the effect of the high school diploma prerequisite is discriminatory by itself, the impact of the eight criteria is discriminatory by themselves, and the overall impact of the selection process is discriminatory.
*510In 1970, the Union introduced the minority training program for the purposes of facilitating the entrance of blacks and other minorities into the ironworkers trade. The MTP was established for persons over the apprenticeable age (usually 30), regardless whether the candidate had a high school diploma. Trainees during the years 1970-1973 received slightly less pay than apprentices. The plaintiffs alleged that the separate maintenance of the MTP and apprentice programs and their differential wage rates discriminated against blacks.
Rule and the class also alleged that the work referral system maintained by the Union discriminated against blacks.1
On remand from the first appeal, the district court enjoined the requirement of a high school diploma as a condition for admission to the Ironworkers Apprentice Program. See Rule v. International Association of Bridge, Structural and Ornamental Iron Workers, Local Union No. 396, 471 F.Supp. 1335, 1343 (E.D.Mo.1979). The court also awarded back pay to those individuals in the MTP from 1970 to 1973 who would have, except for the lack of a high school diploma, been qualified to be selected as an apprentice by the JAC.2 The defendants have appealed those rulings. With minor exceptions, the district court rejected all other class and individual claims. The plaintiffs have appealed, alleging the trial court erred by (1) failing to find a broad pattern of racial discrimination in the JAC selection criteria, (2) applying incorrect legal standards to assess the JAC admission standards, (3) upholding the referral system, (4) failing to provide an adequate remedy, and (5) denying attorney’s fees.3 Although we find the district court was correct in enjoining the use of the high school diploma as a condition of eligibility for selection into the apprentice program, we vacate the judgment below and remand to the district court on the ground that the relief granted is too narrow; we likewise find the district court erred in failing to accord relief to the victims of the discriminatory apprenticeship criteria and failing to award attorney’s fees.
A. Diploma Requirement.
We turn first to the defendants’ appeal concerning the district court’s enjoining the use of the high school diploma as a condition of eligibility for selection to the apprentice program.
In Donnell v. General Motors Corporation, 576 F.2d 1292 (8th Cir. 1978), this court held that the requirement of a high school education, or its equivalent, as a prerequisite to admission to a skilled trades apprentice program, had a disproportionate impact upon blacks in the St. Louis area. Id. at 1296-97. Both Donnell and this case involved a high school diploma prerequisite for a skilled trades apprentice program in an area which includes the St. Louis labor market during the late 1960’s and 1970’s. The statistics that were found sufficient to establish a prima facie case in Donnell were introduced in this case. This evidence showed that 27.9% of the black males over fourteen and 49.1% of white males over fourteen had completed four years of high school in the St. Louis, Missouri-Illinois, *511Standard Metropolitan Statistical Area (SMSA).4
In the proceeding on remand in the district court the defendant made no attempt to dispute the plaintiffs’ statistics or to show a business necessity for the diploma requirement. The district court’s finding that the high school diploma requirement had a significant disproportionate impact on black applicants to the apprentice program is not clearly erroneous. See Griggs v. Duke Power Co., 401 U.S. 424, 430 n.6, 91 S.Ct. 849, 853, 28 L.Ed.2d 158 (1971); Donnell, 576 F.2d at 1296-97; Pettway v. American Cast Iron Pipe Co., 494 F.2d 211, 237 n.60 (5th Cir. 1974), cert. denied, 439 U.S. 1115, 99 S.Ct. 1020, 59 L.Ed.2d 74 (1979); Johnson v. Goodyear Tire & Rubber Co., 491 F.2d 1364, 1370-72 (5th Cir. 1974); United States v. Georgia Power Co., 474 F.2d 906, 918-19 (5th Cir. 1973); Carter v. Gallagher, 3 FEP Cases 692, 700 (D.Minn.), aff’d in part, rev’d in part, 452 F.2d 315 (8th Cir. 1971), rehearing en banc, 452 F.2d 327, cert. denied, 406 U.S. 950, 92 S.Ct. 2045, 32 L.Ed.2d 338 (1972); United States v. Inspiration Consolidated Copper Co., 6 FEP Cases 939, 948-49, 957 (D.Ariz.1973); United States v. Ironworkers, Local 10, 6 FEP Cases 59, 67 (W.D.Mo.1973) (The same iron-worker apprenticeship diploma requirement at issue in this case was found to have a disproportionate impact in the Kansas City area).
The district court also held that the difference in wage rates paid to trainees in the MTP and apprentices in the JAC program was discriminatory. This holding was premised on a finding that the segregation of blacks into the MTP and whites into the JAC program was due in part to the racially discriminatory diploma requirement for the JAC program. Rule III, 471 F.Supp. at 1343. The district court found that plaintiffs had established a prima facie violation of title VII and that defendants had failed to rebut this showing. These findings are not clearly erroneous.5
We turn now to the plaintiffs’ appeal.
B. Apprenticeship Selection Criteria.
Applicants who met the apprenticeship eligibility requirements were then rated on the basis of eight criteria: (1) physical ability, (2). past experience, (3) references, (4) written examinations, (5) residence within the geographic jurisdiction of Local No. 396, (6) military service, (7) oral interview, and (8) education. Applicants whose composite score on these selection criteria was less than 70 were rejected. Applicants whose composite score was above 70 were eligible for admission. The JAC would then determine the number of positions for each year’s apprenticeship class and fill these positions with applicants who had the highest composite scores. Plaintiffs contend that the selection criteria had a disproportionate impact upon minorities. In our previous remand, we directed that “[t]he apprentice selection process must be viewed as a whole to discover whether there is a disparate racial impact.” 568 F.2d at 565 n.10.
This directive was evidently misunderstood by the district court. First, the district court found that the defendants’ use of the diploma eligibility requirement so tainted apprenticeship selection that the overall impact of the selection process was discriminatory. The district court, however, failed to give any effect to this finding beyond enjoining the diploma requirement. 471 F.Supp. at 1340-41. The district court then considered whether a single selection criterion-the written aptitude test-had a disproportionate impact on blacks. Finding that the aptitude tests had no such impact, and ignoring its finding that the eight criteria as a whole had such *512an impact, the district court denied all class and individual claims for relief based on the overall impact of the discriminatory selection criteria. The district court’s failure to give proper effect to its finding of an overall discriminatory impact requires this court to review plaintiffs’ statistical evidence and consider its effect. The record demonstrates unequivocally that the selection criteria had a disproportionate impact on black applicants who had a high school diploma or its equivalent.
The following data on applicants 6 to the apprentice program were admitted by the defendant during discovery or unchallenged at trial:
White Black
Number of applicants 1965 - April 1974 7 978 202
Number of applicants completing the application process 542 77
Number of applicants whose composite score was over 70 530 65
Number of applicants accepted into apprentice program 375 22
Title VII permits employment criteria to be administered to applicants provided that the tests are not “used” to discriminate against a group protected by the Act. Civil Rights Act of 1964, § 703(h), 42 U.S.C. § 2000e-2(h). Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 2726, 53 L.Ed.2d 786 (1977); Albemarle Paper Co. v. Moody, 422 U.S. 405, 425, 95 S.Ct. 2362, 2375, 45 L.Ed.2d 280 (1975); Griggs v. Duke Power Co., 401 U.S. at 431-32, 91 S.Ct. at 853-854 (1971). Criteria which disproportionately exclude one racial group are “used” to discriminate within the meaning of the Act unless the user can show a business necessity for their use. Griggs, 401 U.S. at 433-36, 91 S.Ct. at 854-856; Kirby v. Colony Furniture Co., 613 F.2d 696, 702-03 (8th Cir. 1980); Donnell, 576 F.2d at 1299.
If the use of selection criteria or tests results in differential pass rates for whites and blacks, the difference could be due to legitimate selection criteria, racially discriminatory selection criteria, or chance. See, generally D. Baldus & J. Cole, Statistical Proof of Discrimination 288-92 (1980). If tests of statistical significance eliminate *513chance as a likely explanation for the differential pass rates, courts will presume that the disparate pass rates are attributable to racially discriminatory selection criteria. Castaneda v. Partida, 430 U.S. 482, 496-97, 97 S.Ct. 1272, 1281-1282, 51 L.Ed.2d 498 (1977); Hazelwood School District v. United States, 433 U.S. 299, 308-09 n.14, 97 S.Ct. 2736, 2741-2742, 53 L.Ed.2d 768 (1977). The defendant can avoid liability under title VII by showing that the differential pass rates were caused by legitimate selection criteria which are justified by business necessity. Griggs, 401 U.S. at 431, 91 S.Ct. at 853; Kirby v. Colony Furniture Co., 613 F.2d 696, 703-04 (8th Cir. 1980). If the defendant fails to make such a showing, its selection criteria violate title VII.
In this ease, the actual applicant data shows that the defendants’ selection criteria result in disproportionate pass rates. Ninety-eight per cent of the whites completing the application process scored over 70 on the selection criteria. Eighty-four per cent of the blacks completing the process scored over 70 on the selection criteria. The pass rate for whites is computed as follows:
No. of whites with composite score over 70 No. of whites who completed the application process _ 530 542 _ 9g _ gg^
The pass rate for blacks is computed as follows:
No. of Blacks with composite score over 70 No. of Blacks who completed the application process _ _65 77 _ g^ _ g^
The probability that this disproportionate pass rate (.98 of whites v. .84 of blacks) is a result of chance is very small. The data shows that the defendants’ cutoff score of 70 has a statistically significant disproportionate impact on blacks and a prima facie violation of title VII has been made out.8 *514The disproportionate impact of the selection criteria is also evident when the proportions of blacks and whites admitted to the apprentice program is considered. The difference between the number of blacks expected to be accepted as apprentices and the observed number of black admittees is 5.5 standard deviations.9 A difference of two or three standard deviations is statistically significant at the five per cent significance level. See Shoben, Differential Pass-Fail Rates In Employment Testing: Statistical Proof Under Title VII, 91 Harv.L.Rev. 793, 800 (1978). This significance level has been adopted in Equal Employment Opportunity Commission (EEOC) guidelines for test validation. See 29 C.F.R. § 1607.14(B)(5). The difference in this case of 5.5 standard deviations means that it is highly unlikely that the disproportionate apprentice admission rates are due to chance. Because 69% of the whites (375 of 542) completing the application process were admitted to the apprentice program and only 29% of the blacks (22 of 77), we find that the difference in admission rates is significant in both statistical and practical terms. See 29 C.F.R. § 1607.4(D). The plaintiff has shown, therefore a prima facie violation of title VII. Once the disproportionate impact was shown, the burden shifted to the defendants to prove the job relatedness of their criteria. Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 2726, 53 L.Ed.2d 786 (1977); Kirby, 613 F.2d at 703; Firefighters Institute For Racial Equality v. City of St. Louis, 549 F.2d 506, 510 (8th Cir. 1977).
The defendants’ only attempt to show the job relatedness of its selection criteria was testimony that the criteria had been approved by the Bureau of Apprenticeship and Training, Department of Labor, in 1964 and by the EEOC in 1973. This testimony *515is at best inconclusive as to whether either agency seriously evaluated the eight selection criteria. One of the criteria-the written aptitude test-was submitted to the EEOC and the agency failed to object to its use. The defendants claim this acquiescence amounts to a prima facie showing of job relatedness. Administrative inaction, however, seems to be a poor basis for presuming job relatedness of selection criteria. Nor did the defendant present any evidence as to the standards by which the Bureau of Apprenticeship and Training evaluated the written aptitude test or other selection criteria. There is no evidence that the Bureau of Apprenticeship and Training considered the racial impact or job relatedness of the selection criteria.
The reliance of Ironworkers Local 396 on the alleged administrative approval in this case seems particularly curious in light of Judge Hunter’s rejection of such a defense in United States v. Ironworkers, Local 10, 6 FEP Cases 59, 67 (W.D.Mo.1973). In that case, the court rejected the union’s argument that administrative approval was tantamount to a showing of job relatedness. Additionally, between the time this case was first tried (April 1975) and the remand (1979), this court established guidelines for validation of employment criteria in Firefighters Institute v. City of St. Louis, 549 F.2d at 509-13. The defendants failed to conform their proof to any of the validation methods recognized in Firefighters.
At the original trial and on remand the defendants moved to dismiss at the close of the plaintiffs’ evidence. The district court reserved ruling on both motions. The defendants should have been made aware of their need to present any of their defenses to plaintiffs’ claims at those trials. Nevertheless, they made no attempt to validate the selection criteria.
To allow the defendants another opportunity to present evidence to validate its selection criteria would drag out an already protracted case, unnecessarily burden the district court and encourage defendants in subsequent cases to refuse to present their title VII defenses in the original trial. See Hazelwood, 433 U.S. 318-19, 97 S.Ct. 2747 (Stevens, J., dissenting).10
For these reasons, there is no need to remand this case to the district court in order to allow the defendants to attempt to validate their selection criteria. We find the use of the selection criteria and the requirement of a high school diploma as a condition of eligibility were discriminatory and violated title VII for the period from July 2, 1965 to April 1974.
C. The Referral System and Letter Agreement.
Plaintiffs also allege that the district, court erred in finding a Letter Agreement signed in 1972 did not create a disproportionate impact on blacks. We find no error in the court’s holding. In 1972, the Union struck to obtain greater control over refer*516rals of ironworkers to the contractors. The subsequently negotiated collective bargaining agreement contained a clause, known as the “Letter Agreement,” which, for the first time, created a system of priorities for employment referrals. Rule II, 568 F.2d at 563. The Letter Agreement gave first preference in referral to “qualified journeymen,” defined as union members who had worked at least 6,000 hours in the trade in the Union’s territorial jurisdiction. This policy took effect in August 1972 and continued until November 1973, when the consent decree barred the Union and JAC from applying the 6,000-hour policy to blacks. Rule III, 471 F.Supp. at 1341-42. The priority accorded journeymen in referral is alleged to have had the effect of freezing the status quo of discriminatory employment practices on the theory that blacks admitted to the Union had not had sufficient opportunity to accumulate 6,000 working hours by 1972. Id. at 1342. The district court held that the evidence put forth by plaintiffs in support of this theory is insufficient to establish a prima facie case as to the effect of the Letter Agreement for the one year. Id. We agree.'
This court has recognized that referral systems based on the amount of time employees have worked are seniority systems. United States v. Sheet Metal Workers International Association, Local Union No. 36, 416 F.2d 123, 133 n.20 (8th Cir. 1969). Seniority systems must be judged under the principles of International Brotherhood of Teamsters v. United States, 431 U.S. 324 (1977) and United Air Lines, Inc. v. Evans, 431 U.S. 553 (1977). Teamsters and Evans immunize bona fide seniority systems which have a disproportionate impact on blacks or other minorities, provided that any disparity is not the result of intentional discrimination.11 Teamsters, 431 U.S. at 353; Evans, 431 U.S. at 560.
For plaintiffs to prevail on their claim that the referral system violated title VII, proof of discriminatory motive is critical. The issue in regard to the Letter Agreement is whether plaintiffs have shown facts sufficient to establish an inference of defendants’ discriminatory animus in the creation or maintenance of the seniority system in 1972. The plaintiffs’ evidence shows the number of hours of work time accumulated by ironworkers of different races for times after August 1, 1973. The court is asked to interpolate from this evidence that in 1972, a year for which no evidence was made available, only one black had accumulated the 6,000 work hours necessary to qualify for referral priority and over 200 whites had accumulated the requisite 6,000 hours. The plaintiffs contend that once this fact is established the plaintiffs have borne their burden of establishing a prima facie showing of defendants’ discriminatory intent.
A myriad of factors determine how many hours any single ironworker has accumulated and whether an ironworker is even eligible for referral priority. Rule III, 471 F.Supp. at 1342 n.5. Some of these factors include date of entry into the trade, regular work in particular years, willingness to work, aggressiveness in soliciting work outside' of the Union’s hiring hall, periodic unemployment fluctuations in the trade, geographic proximity to the job, etc. There was no attempt by plaintiffs to show how a person’s race correlated with these other factors to determine referral eligibility. Moreover, there was almost no evidence offered by plaintiffs to show how the referral policy impacted on blacks, other than to show that blacks were not eligible in proportionate numbers. Testimony by plain*517tiffs’ and defendants’ witnesses indicated that few journeymen relied on the referral program extensively, and the statistics offered by plaintiffs reflect the accumulated hours of many persons who obtain few of their hours through the referral policy.
Plaintiffs ask this court to infer discriminatory animus for the year 1972 from a set of statistics showing accumulated hours of ironworkers, even though these statistics do not cover the relevant time period, are affected by a number of variables, and fail to show that any black person was actually adversely affected by the referral policy. The district court’s holding that plaintiffs’ proof failed to show a prima facie violation of title VII is affirmed.12
Plaintiffs also allege that the referral policy as modified by the consent decree in 1973 violated title VII. Under the terms of the consent decree, any minority group person who registers for referral is given priority as if he or she had accumulated 6,000 hours of work experience. Since the original referral system did not violate title VII, it is difficult to see how this modification would. The district court’s holding that the referral policy after 1973 did not violate title VII is not clearly erroneous.
D. Remedy.
1. Injunctive Relief.
We affirm the district court’s enjoining the use of the high school diploma as a prerequisite for the apprentice program.
In view of our finding that the JAC selection criteria had a disproportionate impact on blacks, we direct the district court to grant permanent injunctive relief in this regard. The injunction should prohibit use of all JAC selection criteria until such time as they are proved to be job-related under the Uniform Guidelines on Employee Selection Procedures, 29 C.F.R. §§ 1607.1 to .16. Walston v. School Board of Suffolk, 566 F.2d 1201, 1204 (4th Cir. 1977); Johnson v. Goodyear Tire & Rubber Co., 491 F.2d at 1373; United States v. Georgia Power Co., 474 F.2d at 917-18. If the defendant chooses to use a ranking system as part of the selection criteria, this too must be validated under EEOC Guidelines.13
Notwithstanding that the Union’s and JAC’s compliance with the affirmative action quotas of the consent decree has led to an increase in black ironworkers, we find it necessary to enjoin the use of the JAC selection criteria until such time as they are proved to be job related. The consent decree with the Department of Justice required that 45 blacks be admitted as apprentices during the years 1974-1977. Since the defendants met this quota, the total numbers of admittees to the apprentice program for the years 1965-1978 were 438 white (87% of the total) and 68 blacks (13% of the total). When these figures are compared with the percentage of blacks in the general population of the St. Louis *518SMSA (16%) and the percentage of blacks in the general population of the State of Missouri (10%),14 it appears that the apprentice program has achieved a representative number of blacks. The improvement in the position of blacks in this case, however, is due to the JAC’s making exceptions to its usual ranking system for the years 1974-1977 in order to comply with the consent decree. In 1978, the three year quotas of the consent decree had lapsed and the defendants admitted 29 whites to the apprentice program and no blacks. In this case, reinstating old practices means that the discriminatory pattern evident for the years 1965-1973 may repeat itself for the years after 1978. The prospect of future discrimination warrants enjoining the defendants’ use of the selection criteria until such time as they are validated under the EEOC Guidelines.
An additional reason for such an injunction is that the consent decree ordered that the aptitude tests be validated under the EEOC Guidelines by submitting the tests and a content validity study to the EEOC for analysis. The tests were submitted to the EEOC but there is no evidence that a content validity study was undertaken or submitted to the EEOC. The EEOC apparently failed to object to the tests and the defendants continued to use them as part of the selection criteria. It seems that no validity study has been made of these tests, which have had a disproportionate impact on blacks. There probably will be no such validation study unless this court enjoins the use of the tests, because the consent decree has expired.15
2. Back Pay.
The Supreme Court provided in Albemarle Paper Co. v. Moody, 422 U.S. 405, 421, 95 S.Ct. 2362, 2373, 45 L.Ed.2d 280 (1975):
It follows that, given a finding of unlawful discrimination, backpay should be denied only for reasons which, if applied generally, would not frustrate the central statutory purposes of eradicating discrimination throughout the economy and making persons whole for injuries suffered through past discrimination.
This court has directed that back pay awards in title VII cases be determined consistent with the guidelines of Stewart v. General Motors Corp., 542 F.2d 445 (7th Cir. 1976), cert. denied, 433 U.S. 919, 97 S.Ct. 2995, 53 L.Ed.2d 1105 (1977); Kirby v. Colony Furniture Co., 613 F.2d 696, 706 (8th Cir. 1980); Wells v. Meyer’s Bakery, 561 F.2d 1268, 1273 (8th Cir. 1977).
In Rule III, the district court limited its award of “back pay to those individuals in the M.T.P. from 1970 to 1973 who would have, except for the lack of the high school diploma or the equivalent, been qualified for admission into J.A.C. This back pay will be equivalent to the pay of apprentices at that time for actual hours worked in those years.” 471 F.Supp. at 1343. The district court’s limitation of the class for back pay relief is inadequate for a number *519of reasons.16 First, MTP membership is irrelevant to the description of persons injured by defendants’ discrimination policies and should not limit the class for back pay relief. Victims of the defendants’ discriminatory policies did not automatically enter the MTP. Because MTP applicants had to be over 30 and JAC program applicants had to be under 30, the membership rolls of MTP for the years 1970-1973 included only a few persons who had applied to the apprentice program and were rejected because of the diploma requirement. Second, the years 1970-1973 mark the years from the start of the MTP until the consent decree, but do not encompass many of the instances of discrimination that occurred before 1970. The award grants relief only to some victims of the high school diploma requirement and does not accord any relief to those persons who were victims of the discriminatory selection criteria. Finally, the district court’s back pay order allowed no recovery by nonapplicants who could prove that they would have applied had it not been for defendants’ discriminatory policies. Cf. Teamsters, 431 U.S. at 367-68, 97 S.Ct. at 1870-1871.
In determining the appropriate back pay award, there are three issues which should be clarified. The first is whether back pay should be awarded on an individualized basis or on a classwide basis to be divided among the entire group which the plaintiffs represent. The second issue requires an estimation of the number of persons who are entitled to back pay relief and the definition of some method to identify the class members who are to receive back pay. Also, there is an issue of whether the nondiscriminatory admission policies of the defendants during the years 1974-1977 affect the back pay award.
(a) Individual or Classwide Back Pay Relief.
“Where possible, an individualized remedy should be utilized, because it will best compensate the victims of discrimination without unfairly penalizing the employer,” Stewart, 542 F.2d at 452. Teamsters, supra, explains the basic task for a district court in the back pay stage of a remedial proceeding:
The task remaining for the District Court on remand will not be a simple one. Initially, the court will have to make a substantial number of individual determinations in deciding which of the minority employees were actual victims of the company’s discriminatory practices. After the victims have been identified, the court must, as nearly as possible, ‘ “recreate the conditions and relationships that would have been had there been no” ’ unlawful discrimination. [Citation omitted] This process of recreating the past will necessarily involve a degree of approximation and imprecision * * * * [B]ecause more than one minority employee may have been denied each * * vacancy, the court will be required to balance the equities of each minority employee’s situation in allocating the limited number of vacancies that were discriminatorily refused to class members.
431 U.S. at 371-72, 97 S.Ct. at 1872-1873.
The class of potential discriminatees in this case includes persons who applied for the apprentice program during the years 1965-1974 and were rejected because they lacked a high school diploma or did not score sufficiently high on the selection criteria to be accepted. Also, persons who can prove that they would have applied for an apprentice position had it not been for the defendants’ discriminatory eligibility or se*520lection criteria are members of the class of potential diseriminatees. Teamsters, 431 U.S. at 367-68, 97 S.Ct. at 1870-1871. This class will include many of the 180 blacks who applied to be an apprentice during the years 1965-April 1974, but were not accepted. If a black applicant was rejected for a nondiscriminatory reason, that applicant would not be a member of the class of potential diseriminatees.
To determine the class of actual discriminatees requires an estimation of the number of apprentice positions that were denied black applicants by reason of the discriminatory policies. See Teamsters, 431 U.S. at 372, 97 S.Ct. at 1873; Wells, 561 F.2d at 1273 (mathematical precision should not be required). Under a nondiscriminatory selection policy, the proportion of total applicants who were black (202 of 1180; 17%) would approximate roughly the proportion of admittees who would have been black (17% of 397 total admittees = 67 = expected number of black admittees). The expected number of black admittees (67) exceeds the actual number of black admittees (22) by the difference of 45 persons. Thus, 45 persons from the class of potential discriminatees constitute the class of actual diseriminatees.
Once the size of the class of actual diseriminatees is determined, the task for the district court would be to identify which 45 persons would most likely have been selected as apprentices. The Supreme Court in Teamsters stated that once an alleged discriminatee shows that he or she applied for a position, “the burden then rests on the employer to demonstrate that the individual applicant was denied an employment opportunity for lawful reasons.”17 431 U.S. at 362, 97 S.Ct. at 1868. Given the apparent complexity and uncertainty of identifying which 45 black applicants are entitled to back pay, a classwide back pay remedy is appropriate. Stewart, 542 F.2d at 452. Guidelines for the computation of classwide back pay relief were discussed in Stewart, 542 F.2d at 452-54, and approved by this court in Kirby, 613 F.2d at 705-06, and Wells, 561 F.2d at 1274-75.
It is possible to determine with a fair degree of exactitude what the loss to the class was as. a result of the discriminatory selection process. Each year from 1965 through 1973 there were a number of apprentice vacancies that blacks were denied because of the discriminatory policies. The task for the district court on remand is to estimate for each year from 1965 through 1973 the number of apprentice vacancies that were denied blacks. For this estimation, it should be assumed that under a nondiscriminatory selection process blacks would have been admitted roughly in the samé proportion as whites. For example, if in 1969 there were ten black applicants and 40 white applicants and a total of 15 apprentices admitted, all of which were white, the district court should conclude that three blacks were denied admission by virtue of the discriminatory policies. The computations are as follows:
*521
To compute the back pay due for the three black applicants who were hypothetically discriminated against in 1969, the district court shall select three white apprentices admitted in 1969 and compute their aggregate earnings (including benefits) as an apprentice and ironworker from their date of admission in 1969 until the present. The district court shall subtract from the aggregate income of the three whites the aggregate income (including benefits and amounts earnable with reasonable diligence) of three randomly selected blacks who applied for an apprentice position in 1969 but were rejected. The difference in the respective earnings of the three white ironworkers and the three rejected black applicants shall be the total value of the back pay damages to the plaintiff class caused by the defendants’ discriminatory policies during 1969.18 This back pay sum shall be distributed pro rata among the black applicants rejected in 1969 or in a more equitable manner as determined by the district court.19
These computations should be performed for each year 1965 through 1973 as they were performed in the hypothetical. In this way, damages can be computed for the 45 blacks who were discriminatorily denied admission during the years 1965-1973, and these damages distributed among the entire class. Notice should be sent to the members of the class to afford them an opportunity to claim their damages. Although there may be no need to encourage those claimants with few interim earnings to file claims, fairness to the Union suggests that persons who had substantial interim earnings should also be brought into the remedial proceeding. The relative success of these latter persons in obtaining alternative employment suggests that some of them might *522have been the black applicants who would have been admitted as apprentices. A more accurate measure of class injury will be obtained if a large number of the rejected applicants are brought into the remedial proceeding.
(b) Effect of Changed Circumstances.
The defendants’ admission policies from 1974-1977 achieved a racial balance in the apprentice program roughly proportional to that in the general population of St. Louis and Missouri. Under the “bottom line” doctrine of Smith v. Troyan, 520 F.2d 492, 497-98 (6th Cir. 1975), cert. denied, 426 U.S. 934, 96 S.Ct. 2646, 49 L.Ed.2d 385 (1976), black applicants who were rejected for the apprentice program during the years 1974-1977 would not be entitled to back pay because the defendants’ invalidated selection criteria did not violate title VII during those years. The affirmative action program under the consent decree does not, however, affect the back pay recovery of black applicants who were denied apprentice positions for discriminatory reasons between July 2, 1965 and April 1974. The Fifth Circuit in Williams v. DeKalb County, 577 F.2d 248, rev’d on other grounds, 582 F.2d 2 (5th Cir. 1978), held: “While the existence of the affirmative action program may be considered by the district court on remand in determining whether injunctive relief is appropriate, that program does not affect the availability of back pay as a remedy.” 577 F.2d at 256. The issue in this case involves more than the mere availability of back pay relief that was at issue in Williams. Nevertheless, the defendants’ change in policy should not shorten or cap the back pay period for which relief will be granted to pre-1974 discriminatees. It is the purpose of title VII to make persons whole for injuries suffered on account of unlawful employment discrimination. Albemarle Paper Co. v. Moody, 422 U.S. at 418, 95 S.Ct. at 2372. To deny pre-1974 discriminatees back pay for the years 1974-1977 because the union subsequently admitted the claimant or some other person to the apprentice program would fail to recompense the discriminatee for his or her total injuries. To require defendants to pay back pay for 1974-1977 even though the defendant changed its policies during those years is not unfair to the defendants. The defendants have already benefited from the consent decree modifications of their selection policies because without the consent decree, the number of plaintiffs eligible for back pay would be greater.
The fact that the defendants in this case are not employers or companies but are a union local and a joint apprenticeship committee 20 does not mitigate their liability for back pay awards at this stage in the litigation. Equal Employment Opportunity Commission v. Enterprise Association of Steamfitters Local No. 638 of U.A., 542 F.2d 579, 585-86 (2d Cir. 1976), cert. denied sub nom. Rios v. Enterprise Association of Steamfitters, Local No. 638 of U.A., 430 U.S. 911, 97 S.Ct. 1186, 51 L.Ed.2d 588 (1977). See also Johnson v. Goodyear Tire & Rubber Co., 491 F.2d at 1381-82; Guerra v. Manchester Terminal Corp., 498 F.2d 641, 655-56 (5th Cir. 1974); Waters v. Wisconsin Steel Works of International Harvester Co., 502 F.2d 1309, 1321 (7th Cir. 1974), cert. denied, 425 U.S. 997, 96 S.Ct. 2214, 48 L.Ed.2d 823 (1976).
3. Attorney’s Fees.
Plaintiffs seek reversal of the district court’s finding that attorney’s fees were not warranted. Rule III, 471 F.Supp. at 1343. The prevailing party in a title VII action is entitled to an award of reasonable attorney’s fees. Civil Rights Act of 1964, § 706(k), 42 U.S.C. § 2000e-5(k); New York Gaslight Club, Inc. v. Carey, 447 U.S. 54, 62, 100 S.Ct. 2024, 2030, 64 L.Ed.2d 723 (1980); Christiansburg Garment Co. v. EEOC, 434 U.S. 412, 416-17, 98 S.Ct. 694, 697-698, 54 L.Ed.2d 648 (1978); Newman v. Piggie Park Enterprises, Inc., 390 U.S. 400, 402, 88 S.Ct. 964, 966, 19 L.Ed.2d 1263 *523(1968); Johnson v. Nordstrom-Larpenteur Agency, Inc., 623 F.2d 1279 (8th Cir. 1980); Brown v. Bathke, 588 F.2d 634, 638 (8th Cir. 1978); Donnell v. General Motors Corp., 576 F.2d 1292, 1302 (8th Cir. 1978); Boyd v. Ozark Air Lines, Inc., 568 F.2d 50, 55 (8th Cir. 1977); Allen v. Amalgamated Transit Union Local 788, 554 F.2d 876, 884 n.11 (8th Cir.), cert. denied, 434 U.S. 891, 98 S.Ct. 266, 54 L.Ed.2d 176 (1977); Firefighters Institute for Racial Equality v. City of St. Louis, 549 F.2d 506, 516 (8th Cir.), cert. denied sub nom. St. Louis v. United States, 434 U.S. 819, 98 S.Ct. 60, 54 L.Ed.2d 76 (1977); Parham v. Southwestern Bell Telephone Co., 433 F.2d 421, 430 (8th Cir. 1970); see also Mosby v. Webster College, 563 F.2d 901, 905 (8th Cir. 1977). The district court did not indicate its reasons for denying attorney’s fees. Rule III, 471 F.Supp. at 1343. Since the plaintiff prevailed in Rule III, the district court’s failure to award attorney’s fees was an abuse of discretion. This court remands this case to the district court so that attorney’s fees may be determined in accordance with the guidelines set forth by the Fifth Circuit in Johnson v. Georgia Highway Express, Inc., 488 F.2d 714, 717-19 (5th Cir. 1974); Brown v. Bathke, 588 F.2d at 637; Firefighters Institute v. City of St. Louis, 588 F.2d 235, 242-43 (8th Cir. 1978); Greminger v. Seaborne, 584 F.2d 275, 279 (8th Cir. 1978); Donnell, 576 F.2d at 1302; Di Salvo v. Chamber of Commerce, 568 F.2d 593, 599 (8th Cir. 1978); Allen v. Amalgamated Transit Union, 554 F.2d at 884; Doe v. Poelker, 515 F.2d 541, 548 (8th Cir. 1975), rev’d on other grounds, 432 U.S. 519, 97 S.C. 2391, 53 S.Ed.2d 528 (1977); see also Crain v. City of Mountain Home, Ark., 611 F.2d 726, 730 (8th Cir. 1979); Cleverly v. Western Electric Co., 594 F.2d 638, 642 (8th Cir. 1979). To ensure an adequate award, this court orders that a minimum hourly attorney’s fee of $40.00 per hour be awarded to plaintiffs for services of their attorneys in Rule I, II and III. See Crain v. City of Mountain Home, Ark., 611 F.2d at 730.
A particularly well-reasoned application of the Johnson guidelines is Cleverly v. Western Electric Co., 450 F.Supp. 507, 511-12 (W.D.Mo.1978) (Becker, Senior J.); the district court’s method was cited with approval on appeal. 594 F.2d at 642. The district court’s award should not be inconsistent with other opinions of this court. See Firefighters Institute, 549 F.2d at 516 (This court determined that an award of attorney’s fees of $3,000 was grossly inadequate); Allen v. Amalgamated Transit Union, 554 F.2d at 884 (This court stated the award of $300 for attorney’s fees was grossly inadequate); Greminger v. Seaborne, 584 F.2d 275, 279 (8th Cir. 1978) (Attorney’s fees of $1,250 in a section 1983 action was found to be grossly inadequate).
Plaintiffs also request an interim award of attorney’s fees. The leading case on interim attorney’s fees awards is James v. Stockham Valves & Fittings Co., 559 F.2d 310, 358-59 (5th Cir. 1977). In that case, the Fifth Circuit ruled that an interim award was appropriate because:
1. “of the extensive nature of the litigation in this case,” having been initiated in 1966 and tried in 1974; Id. at 358;
2. of the “key role played by ‘private Attorneys General’ in actions involving employment discrimination....” Id.;
3. the Supreme Court stressed in Albemarle the important public interest in having injunction actions brought under title VII. Id.;
. 4. of the danger that litigants will be discouraged from bringing such suits because of the risks of protracted litigation and the extended financial drain on plaintiffs and attorneys. Id.;
5. of the danger that defendants in title VII suits may be tempted to seek victory through an economic war of attrition. Id. at 359.
For these reasons, the Fifth Circuit, after having decided the liability issues in its opinion, granted an interim award of attorney’s fees. The controlling factor among those listed above is the duration of the litigation. This case has already taken many years. Rule filed his original complaint with the EEOC on June 30, 1966. Rule I, 423 F.Supp. at 375. This litigation *524was commenced on March 14, 1973. Rule II, 568 F.2d at 561. There have already been two trials and two appeals. There will have to be another remand for the remedial stages of this litigation. The Fifth Circuit in James v. Stockham Valves, supra, determined that an eleven year duration (1966-1977) warranted an interim award of attorney’s fees. This court directs the district court to make an interim award of attorney’s fees before the remedial stage of this litigation. See also Louisville Black Police Officers Organization, Inc. v. City of Louisville, 20 FEP Cases 1195, 1208 (W.D.Ky. 1979); Nicodemus v. Chrysler Corp., 445 F.Supp. 559, 560 (N.D.Ohio 1977); Johnson v. Ryder Truck Lines, Inc., 16 FEP Cases 1689, 1692 (W.D.N.C.1977); Sledge v. J. P. Stevens & Co., 18 FEP Cases 258, 259 (E.D.N.C.1976), aff’d in part, rev’d in part, 585 F.2d 625 (4th Cir. 1978), cert. denied, 440 U.S. 981, 99 S.Ct. 1789, 60 L.Ed.2d 241 (1979).
The plaintiffs also ask for attorney’s fees for this appeal. This court has allowed such fees in Crain, 611 F.2d at 730 (Attorney’s fees awarded under Civil Rights Attorney’s Fees Award Act of 1976, § 2, 42 U.S.C. § 1988); Cleverly, 594 F.2d at 642-43 (Attorney’s fees awarded under Age Discrimination in Employment Act, § 7, 29 U.S.C. § 626); Firefighters Institute, 588 F.2d at 243 (Title VII, § 706(k), 42 U.S.C. § 2000e-5(k)); Greminger v. Seaborne, 584 F.2d at 279 (Civil Rights Attorney’s Fees Award Act of 1976, § 2, 42 U.S.C. § 1988); Donnell v. General Motors Corp., 576 F.2d at 1302 (Title VII, § 706(k), 42 U.S.C. § 2000e-5(k)); Allen v. Amalgamated Transit Union, 554 F.2d at 884 (Title VII, § 706(k), 42 U.S.C. § 2000e-5(k)); Reed v. Arlington Hotel Co., 476 F.2d 721, 726 (8th Cir.), cert. denied, 414 U.S. 854, 94 S.Ct. 153, 38 L.Ed.2d 103 (1973) (Title VII, § 706(k), 42 U.S.C. § 2000e-5(k)). Counsel should be directed to file an affidavit in the district court indicating the time spent in processing the appeal of Rule III in order that an allowance of reasonable attorney’s fees can be made for the appeal. We duplicate an earlier order of this court in Cleverly v. Western Electric Co., supra, that counsel should be compensated at the rate of $50.00 per hour for partner’s time and $40.00 per hour for associate’s time on this appeal. 594 F.2d at 643.
Judgment of the district court is vacated21 and the cause remanded for entry of injunctive relief and further proceedings in accord with this opinion.22
. In 1979, Rule changed his name to Walee Abdul Hameed. For case continuity, the district court referred to him as Rule. In the original action, Rule v. International Association of Bridge, Structural and Ornamental Iron Workers, Local Union No. 396, 423 F.Supp. 373 (E.D.Mo.1976) (hereafter Rule I), the district court denied relief.
On Rule’s first appeal, this court remanded for the consideration of class claims and largely parallel individual claims under title VII of racial discrimination. See Rule v. International Association of Bridge, Structural and Ornamental Ironworkers, Local Union No. 396, 568 F.2d 558, 568 (8th Cir. 1977) (hereafter Rule II). We read Rule II as affirming Rule /’s denial of relief under 42 U.S.C. § 1981, and, consequently, these claims are not before us.
. In 1973 a consent decree was entered between the Union and the Justice Department. This decree is now expired.
. The Equal Employment Opportunity Commission filed an amicus curiae brief, urging abuse of discretion in refusal to award attorney’s fees.
. United States Bureau of the Census, Census of Population: 1970, vol. 1, Characteristics of the Population, pt. 27, Missouri, Table 148, p. 602. The statistical evidence also showed that “about 31 per cent of black males over 25 had completed four years of high school as of the 1970 census, while about 51 per cent of white males over 25 had done so.” Rule III, 471 F.Supp. at 1340.
. The district court held that the separate maintenance of the MTP and JAC programs was not discriminatory. The plaintiffs did not appeal this ruling.
. In Green v. Missouri Pacific R. R., 523 F.2d 1290, 1293-94 (8th Cir. 1975), this court identified three statistical methods of showing a disproportionate impact on minorities. It seems to be a matter of some debate whether actual applicant data (Green’s second method) or general population data (Green’s first and third methods) is the preferred statistical measure of disproportionate impact. Some cases suggest a presumption in favor of actual applicant data. See New York City Transit Auth. v. Beazer, 440 U.S. 568, 586, 99 S.Ct. 1355, 1366 n.29, 59 L.Ed.2d 587 n.29 (1979); Hester v. Southern Ry., 497 F.2d 1374, 1379 n.6 (5th Cir. 1974). See also D. Baldus & J. Cole, Statistical Proof of Discrimination 106-11 (1980); Hazelwood School Dist. v. United States, 433 U.S. 299, 308 n.13, 97 S.Ct. 2736, 2742 n.13, 53 L.Ed.2d 768 (1977). Other cases suggest that general population data can provide a basis for a showing of disproportionate impact even though the actual applicant data would indicate there was no disproportionate impact. This is particularly the case where there is some threat to the validity of the actual applicant data. See Dothard v. Rawlinson, 433 U.S. 321, 330, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977); Donnell v. General Motors Corp., 576 F.2d 1292, 1298 (8th Cir. 1978). All of these cases, nevertheless, support the proposition that a showing of disproportionate impact based on actual applicant data constitutes a prima facie violation.
. The time period of these statistics is from 1965 to April 1974. This is roughly the period of time from the effective date of title VII (July 2, 1965) until the defendants’ selection policies were changed pursuant to the consent decree between the Union and the Department of Justice. The admission policies of the defendants after April 1974-pursuant to the consent decree of November 1973 the defendants began admitting many more blacks to the apprenticeship program-are not relevant to the issue of whether defendant’s earlier policies violated title VII. Parham v. Southwestern Bell Tel. Co., 433 F.2d 421, 425 (8th Cir. 1970). “The crucial issue in a lawsuit of this kind is whether the plaintiff establishes hiring bias at the time of his rejection for employment and subsequent complaint to the EEOC, not the employment practices utilized two years later.” Id. See also Donnell, 576 F.2d at 1298 n.l 1. (“[Subsequent employment practices may bear upon the remedy, but they are not relevant to the determination of whether the employer had previously violated Title VII.”)
. If a random sample of the population were rated under the selection criteria and the criteria had no disproportionate impact on minorities, the proportions of blacks and whites that would score over 70 would be roughly equivalent. This hypothesis is called the null hypothesis. The null hypothesis creates the expectation that the same proportion of blacks and whites should score over 70 on the defendants’ selection criteria. The expected number of blacks who should have scored over 70 is the product of the number of blacks completing the application process (77) and the overall pass rate:
Overall pass rate = 595 persons scored over 70 619 ¡,ersons completed the application process
595 expected number of blacks who would 77 x = 74 = have passed if blacks passed at the 619 overall pass rate.
The observed number of black applicants who scored over 70 was 65 blacks. The difference between the expected value and observed value is 9 persons:
74 blacks would have passed if blacks passed at the overall pass rate (expected value)
-65 blacks actually passed (observed value)
9 = difference in expected value and observed value.
The Supreme Court has adopted a method for measuring the statistical significance of the difference between the expected value and observed value. See Castaneda v. Partida, 430 U.S. 482, 496-97 n.17, 97 S.Ct. 1272, 1281, 51 L.Ed.2d 498 (1977); Hazelwood School Dist. v. United States, 433 U.S. 299, 308-09 n.14, 311 n.17, 97 S.Ct. 2736, 2741-2742 n.14, 2743 n.17, 53 L.Ed.2d 768 (1977). In Rule II, this court recommended the Castaneda and Hazelwood statistical method to the district court. 568 F.2d at 567 n.12. To determine by this method whether the difference between the expected and observed values is statistically significant, divide the difference (9) by the standard deviation of the sampling distribution.
The standard deviation or standard error of a binomial distribution can be represented algebraically:
H. Klugh, Statistics: The Essentials for Research, 152 (2d ed. 1974). n = number of blacks completing the process; p = overall pass rate for all persons completing the process; g = the overall proportion of persons completing the process who scored below 70. Thus, the standard deviation of the sampling distribution is the square root of the product of the total number in the sample (n = 77) times the probability that a person would pass
(p = 595 persons scored over 70_y 619 persons completed the process
times the probability that any one person would score below 70
(g = 24 persons scored below 70 y 619 persons completed the process
*514Castaneda v. Partida, 430 U.S. at 496-97 n.17, 97 S.Ct. at 1281 n.17. The computations for the standard deviation are as follows:
To determine whether the difference between the expected and observed values is statistically significant, divide the difference between the expected and observed values (9) by the standard deviation (1.7):
expected value (74) - observed value (65) standard deviation (1.7) _ 9 1.7 -.53
The difference between the expected and observed value is 5.3 standard deviations. The Supreme Court has stated that a difference of two or three standard deviations would appear to be statistically significant. Id. Thus, the disproportionate impact of the defendant’s selection criteria is statistically significant and shows a prima facie violation of title VII.
A showing of the statistical significance of the impact of the selection criteria in this case also results from the test of the differences of independent proportions presented in Shoben, Differential Pass-Fail Rates in Employment Testing: Statistical Proof Under Title V//, 91 Harv.L.Rev. 793, 802-03 (1978).
. The calculations are as follows:
(a) Compute the overall admission rate:
375 whites were admitted + 22 blacks were admitted 595 persons were eligible for admission because they scored over 70.
The overall admission rate = 595
(b) Calculate the expected value of the number of blacks who would have been admitted to the apprentice program if blacks were admitted at the overall admission rate.
322 595 x 65 blacks who scored over 70 and were eligible for admission = 43 — expected value
(c) Subtract from the expected value (43) the observed value of the number of blacks admitted to the apprentice program (22).
43 values. - 22 = 21 = difference in expected and observed
(d) Determine the standard deviation of the sampling distribution. The standard deviation of a binomial distribution =/\/npg.
n = number of blacks eligible for admission = 65
p = overall admission rate _ 322 595
g = overall rejection rate = 198 595
(e) Divide the difference between the expected value and observed value by the standard deviation.
Difference in expected value and observed value Standard deviation g-g = 5.5 standard deviations.
. The decision not to remand this case is not inconsistent with the holding of Hazelwood, supra. In Hazelwood, the district court after a full trial, held that the government had failed to show a prima facie violation of title VII. 392 F.Supp. 1276 (E.D.Mo.1975) The Eight Circuit’s opinion discusses the evidence the defendant introduced at trial and shows that there was a full trial. 534 F.2d 805, 810, 813-14 (8th Cir. 1976) (Mr. Justice Clark) This court reversed the district court, holding that
The Government’s proof thus established a prima facie case. Hazelwood offered no evidence adequate to rebut the inference of discrimination created by the aforementioned evidence. We therefore reverse the judgment of the district court.
Id. at 813-14.
The Supreme Court vacated and remanded for a determination of whether the statistics which purported to show a prima facie violation had been gleaned from the relevant labor market. 433 U.S. at 313, 97 S.Ct. at 2744. Unlike Hazelwood, there is no issue in this case as to whether the statistics used to show a prima facie violation are appropriate. The prima facie violation in this case is shown by plaintiffs’ actual applicant data. Actual applicant data is an appropriate statistic for showing the disproportionate impact of defendants’ selection criteria. New York City Transit Auth. v. Beazer, 440 U.S. 568, 586 n.29, 99 S.Ct. 1355, 1366, n.29, 59 L.Ed.2d 587 (1979); Hazelwood School Dist., 433 U.S. at 308 n.13, 97 S.Ct. at 2742; Hester v. Southern Ry. Co., 497 F.2d 1374, 1379 n.6 (5th Cir. 1974); D. Baldus & J. Cole, Statistical Proof of Discrimination 106-11 (1980).
. See also Fisher v. Proctor & Gamble Mfg. Co., 613 F.2d 527, 542 (5th Cir. 1980) (“Since Teamsters and Evans, however, we have recognized that an otherwise bona fide seniority system ‘is not itself illegal merely because it per-. petuates the effects of pre-Act or post-Act discrimination.’ ” Quoting Pettway v. American Cast Iron Pipe Co., 576 F.2d 1157, 1189 (5th Cir. 1978)). “Instead, ‘purposeful discrimination in connection with the establishment or continuation of a seniority system is integral to a determination that the system is or is not bona fide.’ ’’ Fisher, supra, quoting James v. Stockham Valves & Fittings Co., 559 F.2d 310, 351 (5th Cir. 1977); Firefighters Inst. v. City of St. Louis, 588 F.2d 235, 242 n.11 (8th Cir. 1978).
. The district court held the plaintiffs’ evidence failed to show a discriminatory effect. 471 F.Supp. at 1342. It appears that this finding was based on the court’s application of the disproportionate impact test of Griggs. However, even if a disproportionate impact had been shown, the seniority system would not have been shown to be a prima facie violation of title VII because Teamsters immunizes seniority systems from attack under the disproportionate impact theories of Griggs. The plaintiffs’ burden in this case under Teamsters was to show facts sufficient to give rise to an inference of discriminatory intent. Where, as here, plaintiffs rely solely on statistical evidence of a disproportionate impact on blacks as the basis for inferring discriminatory intent, and offer no other circumstantial or direct evidence of defendants’ intent, the plaintiffs’ evidence must at a minimum show a disproportionate impact. And this impact alone would not be determinative of intent, except in unusual circumstances. See Village of Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U.S. 252, 265-66, 97 S.Ct. 555, 563, 564, 50 L.Ed.2d 450 (1977). If, as here, the trier of fact finds that a disproportionate impact has not been shown by the plaintiffs’ statistics, and such finding is not clearly erroneous, then plaintiffs’ statistics alone are not sufficient for inferring a discriminatory intent based on disproportionate impact.
. 29 C.F.R. §§ 1607.5(G), .3(B), .14(B)(5), .14(B)(6), .14(C)(8), and .14(C)(9). See Louisville Black Police Officers v. City of Louisville, 20 FEP Cases 1195, 1205-06 (W.D. Ky.1979).
. United States Bureau of the Census, Census of Population: 1970, vol. 1, Characteristics of the Population, pt. 27 Missouri, Table 23, p. 81, and Table 17, p. 67.
. It is true the plaintiffs lack standing to enforce the consent decree. Rule II, 568 F.2d at 565-66 n.10. Nevertheless, the consent decree between the government and the defendants does not preclude the applicants from pursuing private remedies. United States v. Trucking Employers, Inc., 561 F.2d 313, 317 (D.C.Cir. 1977); United States v. Allegheny-Ludlum Indus. Inc., 517 F.2d 826, 880 (5th Cir. 1975), cert. denied, 425 U.S. 944, 96 S.Ct. 1684, 48 L.Ed.2d 187 (1976); Williamson v. Bethlehem Steel Corp., 468 F.2d 1201, 1203 (2d Cir. 1972), cert. denied, 411 U.S. 931, 93 S.Ct. 1893, 36 L.Ed.2d 390 (1973). Cf. McClain v. Wagner Elec. Corp., 550 F.2d 1115, 1120-21 (8th Cir. 1977). The decree could not have a stare decisis effect either, since no finding of any title VII violation, the issue here, was made in the decree. See Williamson, 468 F.2d at 1204. The consent decree did not even contain a clause attempting to provide relief for individual claims by waiver or release. Cf. Doninger v. Pacific Northwest Bell, Inc., 564 F.2d 1304, 1307 (9th Cir. 1977). Of course, the survival of individual claims means the consent decree cannot moot the present action and does not bar injunctive relief.
. The district court’s back pay award appears directed at remedying the disparate wage rates between the JAC and MTP which Rule III held violated title VII. Members of the MTP during the years 1970-1973 who were victims of the disparate wage rates, however, are entitled to receive back pay regardless whether they “would have, except for the lack of a high school diploma, or the equivalent, been qualified for admission into J.A.C.” Accordingly, trainees in the MTP during the years 1970-1973 who received a lower hourly wage rate than their white counterparts in the apprentice program should receive back pay in an amount equal to the difference in the respective hourly rates of apprentices and trainees times the hours worked by trainees during those years.
. Teamsters involved an award of retroactive seniority, but there are no indications in that case that the burden to prove eligibility for back pay should be on the plaintiffs.. Thus, Teamsters, places the burden of proving which persons in the present case are not entitled to back pay on the defendants. However, this court in Donnell, 576 F.2d at 1301, a case decided after Teamsters, held that to obtain back pay relief a person who was denied an opportunity to complete a company’s apprenticeship selection criteria because he lacked a high school diploma would have to prove that “he can satisfactorily pass the further testing, screening and rating procedures established under ... [the company’s] Apprentice Plan.” Donnell is not inconsistent with Teamsters because Donnell holds that the employer may require the applicant to complete the valid, nondiscriminatory portions of a selection process in order that the employer have the opportunity to prove that an alleged discriminatee would not have been admitted. Since in the present case, the defendants have validated none of their selection criteria, these criteria cannot be used to show that a particular applicant would not have been admitted. Donnell would impose no additional requirements of proof on the present plaintiffs because there are no valid selection criteria in this case and Teamsters would shift the burden to the defendants to prove, if they could, whether particular applicants were rejected for lawful reasons.
. For guidance on the method of computing the back pay due, the district court should see Dickerson v. United States Steel Corp., 472 F.Supp. 1304, (E.D.Pa.1980). Other discussions of class back pay awards can be found in Claiborne v. Illinois Cent. R.R., 583 F.2d 143, 148-50 (7th Cir. 1978), cert. denied, 442 U.S. 934, 99 S.Ct. 2869, 61 L.Ed.2d 303 (1979); Stewart, 542 F.2d at 452-54; United States v. United States Steel Corp., 520 F.2d 1043, 1052-57 (5th Cir. 1975), cert. denied, 429 U.S. 817, 97 S.Ct. 61, 50 L.Ed.2d 77 (1976); Pettway v. American Cast Iron Pipe Co., 494 F.2d 211, 251-63 (5th Cir. 1974); Bowe v. Colgate-Palmolive Co., 489 F.2d 896, 902-04 (7th Cir. 1973). With regard to offsets, see, Bing v. Roadway Express, Inc., 485 F.2d 441, 454-55 (5th Cir. 1973) (interim earnings); Kaplan v. International Alliance of Theatrical and Stage Employees and Motion Picture Machine Operators, 525 F.2d 1354, 1362-63 (9th Cir. 1975) (amounts earnable with reasonable diligence); Hegler v. Board of Education, 447 F.2d 1078, 1081 (8th Cir. 1971) (amounts earnable with reasonable diligence under 42 U.S.C. § 1981). See also B. Schlei & P. Grossman, Employment Discrimination Law, 1227-76 (1976) and Supplement, 334-40 (1979).
. The method of distributing the back pay due the 45 “actual” discriminatees among the more than 45 claimants should not result in some persons obtaining a back pay award greater than their actual damages. Back pay is. intended to compensate for injury, not to reward plaintiffs or penalize defendants. If there are more than 45 claimants, not all claimants will receive back pay equal to the amount they would receive if they were actual discriminatees. The district court’s task on remand is to devise an equitable distribution of the amounts due. The maximum any one claimant may recover is the amount due if he were an actual discriminatee. The maximum liability of the Union is the aggregate amount of back pay that would be due 45 actual discriminatees.
. The third defendant, MTP, has not been proved to be responsible for or involved with the apprentice program’s discriminatory selection criteria.
. The district court rejected the individual claims of Walee Hameed, George Coe, and Lonnie Vanderson. Rule III, 471 F.Supp. at 1341. Hameed’s claim that he was a victim of the high school diploma requirement was rejected because the court found he was offered admission into the apprentice program and he declined. Hameed first applied to the apprentice program in 1966. Rule I, 423 F.Supp. at 375. Hameed was offered admission to the apprentice program sometime after July 1972. Id. at 376. As a rejected applicant to the apprentice program, Hameed would be entitled to share in the classwide back pay remedy, unless the Union or JAC can show that Hameed was not offered admission until 1972 because of a nondiscriminatory reason. George Coe made application to the apprentice program in March 1970, but was rejected on the basis of an insufficient composite score on the JAC selection criteria. Id. Because this court holds that the selection criteria were discriminatory in 1970, Coe is entitled to share in the classwide back pay remedy, unless the district court finds that Coe’s rejection to the apprentice program was for a nondiscriminatory reason. The burden of showing a nondiscriminatory reason for Coe’s rejection is on the defendants. Lonnie Vanderson applied for admission to the apprentice program in October 1974. Id. Because Vanderson was denied admission during a year when the selection criteria had no discriminatory impact on blacks, Vanderson is not entitled to share in the classwide back pay remedy.
. We do not invalidate the written aptitude test as suggested in the dissenting and concurring opinion. We hold simply that the district court failed to evaluate properly the overall disparate impact resulting from the use of the selection criteria, as directed in our earlier remand. 568 F.2d at 565 n.10. The written aptitude test was only one of the eight criteria, the overall impact of which were to be evaluated by the district court.