
996 F.Supp. 1156 (1998)
Johnny REYNOLDS, et al., Plaintiffs,
v.
ALABAMA DEPARTMENT OF TRANSPORTATION, et al., Defendants.
Civil Action No. 85-T-665-N.
United States District Court, M.D. Alabama, Northern Division.
March 18, 1998.
*1157 *1158 Robert L. Wiggins, Jr., Ann K. Wiggins, Russell W. Adams, Abigail P. Van Alstyne, Kimberly C. Page, Scott Gilliland, and Kell A. Simon, Gordon, Silberman, Wiggins & Childs, Birmingham, AL, for Johnny Reynolds, Cecil Parker, Frank Reed, Ouida Maxwell, Martha Ann Boleware, Florence Belser, Peggy Vonsherie Allen, Jeffrey W. Brown.
Claudia H. Pearson, Nakamura & Quinn, Birmingham, AL, for Robert Johnson.
*1159 Raymond P. Fitzpatrick, Jr., R. Scott Clark, J. Michael Cooper, Fitzpatrick, Cooper & Clark, Birmingham, AL, for William Adams, Cheryl Caine, Tim Colquitt, William Flowers, Wilson Folmar, George Kyser, Becky Pollard, Ronnie Pouncey, Terry Robinson, Tim Williams, Michael Grant, John D'Arville, Andrew McCullough.
Thomas R. Elliott, Jr., Allen R. Trippeer, Jr., Lisa W. Borden, C. Dennis Hughes, London & Yancey, Birmingham, AL, William H. Pryor, Jr., Atty Gen. for the State of Alabama, Montgomery, AL, for Alabama Dept. of Transp., Alabama State Personnel Dept., Jimmy Butts, Halycon Vance Ballard, Fob James.
William P. Gray, Jr., Gray & Jauregui, Montgomery, AL, for Fob James.
Elaine R. Jones, Norman J. Chachkin, NAACP Legal Defense Fund, New York City, for NAACP Legal Defense and Educational Fund, Inc., amicus.
Barbara R. Arnwine, Thomas J. Henderson, Richard T. Seymour, Teresa A. Ferrante, Lawyers' Committee for Civil Rights Under Law, Washington, DC, for The Lawyers' Committee for Civil Rights under Law, amicus.

MEMORANDUM OPINION
MYRON H. THOMPSON, Chief Judge.
In this 13-year-old class-action lawsuit, the plaintiffs charged the defendants with employment discrimination based on race in the Alabama Department of Transportation. The plaintiffs are African-Americans, and they represent a class of African-American merit and non-merit system employees and unsuccessful applicants. The defendants include the Alabama Department of Transportation, the Alabama State Personnel Department, and several state officials.
On April 16, 1997, the court entered an order requiring that the defendants pay the plaintiff class the sum of $34,732,487.00 in backpay pursuant to two mathematical formulas that the parties adopted for determining whether plaintiff class members are eligible for backpay, and for calculating the amount of backpay, if any, each class member is entitled to receive.[1] The award resolves the backpay claims of approximately 2,400 plaintiff class members, and actually provides backpay to 2,137 class members for the discrimination they faced in the time period from 1979 to 1997.[2] The April 16 order was based on a number of summary findings in earlier orders. This memorandum opinion expands on these findings and explains in more detail the basis for the April 16 order.

I. BACKGROUND
A general and chronological overview is necessary for proper discussion of the issues before the court.

May 21, 1985
The nine plaintiffs in this lawsuit are Johnny Reynolds, Ouida Maxwell, Martha Ann Boleware, Florence Belser, Peggy Vonsherie Allen, Jeffrey Brown, Robert Johnson, Cecil Parker, and Frank Reed. Reynolds filed this lawsuit on May 21, 1985, and the other plaintiffs were allowed to intervene over the next seven years. They charged the defendants with widespread and long-lasting race discrimination, and advanced claims based on theories of "disparate treatment" and "disparate impact." The plaintiffs based this lawsuit on the following: Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C.A. §§ 1981a, 2000e through 2000e-17; the fourteenth amendment to the United States Constitution, as enforced by 42 U.S.C.A. § 1983; and 42 U.S.C.A. § 1981. The jurisdiction of the court has been invoked pursuant to 28 *1160 U.S.C.A. § 1343 and 42 U.S.C.A. § 2000e-5(f)(3).

October 8, 1986
The court entered an order certifying a plaintiff class as follows: (1) all black merit system employees employed by the Transportation Department at any time since May 21, 1979; (2) all black non-merit system employees of the department who have unsuccessfully sought employment as merit system employees with the department at any time since May 21, 1979; and (3) all black non-employees who have unsuccessfully sought employment as merit system employees with the department at any time since May 21, 1979.[3] Subclasses (1) and (2) therefore consisted of "employees" of the department, and subclass (3) consisted of "non-employees."

1988
The parties reached a full settlement of this case, but the court refused to approve the proposed consent decree in the face of numerous objections from the members of the plaintiff class.[4] The court explained that "there are five critical factors which together conclusively counsel against" the settlement.[5] "First, the record developed by the parties is insufficient to support the difference in treatment between the six named plaintiffs and all the other class members. Second, the record is insufficient to justify a result which would in effect deny to hundreds of class members, whether they like it or not, an opportunity to have ever had their claims heard in a court of law. Third, there is nothing in the record upon which the court could base its affirmative approval of the EIT requirement. Fourth, the court cannot turn a blind eye to the fact that from the present record it appears that, of those class members who appear to have any interest in this litigation, the overwhelming majority strongly oppose it. And fifth and finally, the record is insufficient as to several issues regarding the legality of the proposed consent decree."[6]

1991
In January 1991, following shortly after the court's rejection of the first proposed settlement, the parties submitted a second proposed consent decree. The court provisionally approved the consent decree and set in motion the processes for notice to the plaintiff class members of the proposed settlement and their opportunity to opt-out of the settlement and file any objections they may have.[7] Over the following two months, a number of class members opted-out, and there were two additional attempts to intervene in this litigation. In light of these events, and the defendants' position that the events made it impossible to settle fully the on-going litigation, the defendants exercised their option to withdraw from the second proposed consent decree.[8] The court then entered an order that the proposed consent decree was not approved.[9]

1992
The trial began and extended, with some breaks, over several months, from June 15, 1992, to November 25, 1992. The plaintiffs first reintroduced findings and orders from an earlier case, United States v. Frazer, civil action no. 2709-N (M.D.Ala.),[10] which was consolidated with this case,[11] and then proceeded to introduce new evidence from the time period following Frazer.
*1161 United States v. Frazer: For the first three-quarters of this century, the State of Alabama and its agencies excluded African-Americans, because of their race, from employment other than in low and menial positions, and throughout the last quarter of this century, despite outstanding court orders, the Transportation Department manipulated, or even circumvented, State personnel procedures to avoid hiring and promotion of African-Americans into responsible and non-menial jobs.
In the late 1960s, the United States brought an action against the Alabama State Personnel Department challenging personnel practices which it contended intentionally discriminated against African-American applicants and employees. In 1970, in United States v. Frazer, 317 F.Supp. 1079 (M.D.Ala.), the court agreed with the United States, and found that agencies of the State of Alabama had engaged in a State-sanctioned policy of manipulating and circumventing the State's personnel procedures to avoid the hiring and promotion of African-Americans. Id. at 1084-87. The court found intentional, pervasive, systematic exclusion and avoidance of black employees and applicants throughout numerous State departments.
The evidence demonstrated that racial discrimination was accomplished in several ways, many of which involved manipulations of personnel practices and procedures to exclude eligible and qualified black employees from competing for jobs. The evidence overwhelmingly showed refusals to hire, or even to interview, African-Americans who had qualified and appeared on the certificates of eligibles, despite an urgent and constant need to fill positions. Id. at 1087. It also showed that agencies maintained racially segregated facilities in their buildings. Id. Indeed, John S. Frazer, director of the Personnel Department, testified to his belief that the race of applicants was a legitimate factor for consideration in selecting employees. Id. at 1085.
The Frazer court found that "defendants' systematic refusal to appoint Negro applicants and their preference for lower-ranking white applicants constitute unlawful race discrimination[,] ... a clear violation of the equal protection clause of the Fourteenth Amendment." Id. at 1089-90. The court entered similar findings on the defendants' recruitment and advertising practices.
The Frazer court entered an order broadly prohibiting State officials from "engaging in any employment practices, including recruitment, examination, appointment, training, promotion, retention, or any other personnel action, for the purpose or with the effect of discriminating against any employee, or actual or potential applicant for employment, on the ground of race or color." Id. at 1090. The court further imposed what has come to be known as the "no-bypass rule," which provides that State officials "shall not appoint or offer a position to a lower-ranking white applicant on a certificate in preference to a higher-ranking available Negro applicant, unless the defendants have first contacted and interviewed the higher-ranking Negro applicant and have determined that the Negro applicant cannot perform the functions of the position, is otherwise unfit for it, or is unavailable." Id. at 1091.
Six years later, in the same litigation, similar allegations were again before the court. The United States charged that State personnel practices were systematically and deliberately manipulated to prevent blacks from competing with white applicants for jobs and promotions. In an order entered in August 1976, the court found a pattern and practice of racial discrimination in employment in the Transportation Department (then known as the Highway Department). See United States v. Frazer, civil action no. 2709-N, 1976 WL 729 (M.D.Ala. Aug.20, 1976).
Specifically, the Frazer court found that the new defendants, including the Transportation Department, "avoided compliance with the decrees in this case by examining job registers maintained by the Personnel Department of the State of Alabama and by requesting certificates of eligibles only at times when no blacks were available for certification." Id. at *4. The court also pointed out other evidence of discriminatory practices, including maintaining registers on a non-continuous basis (establishing a register *1162 and not adding any persons until that register is exhausted and another exam is administered), or "closing" a register for as long as two years. In this way, all-white registers were maintained. Id. at *5-*6. The court observed, "Progress toward erasing the effects of prior exclusionary practices upon the basis of race has been minimal and in many instances non-existent." Id. at *6.
The Frazer court also recounted the story of one black applicant's attempts to obtain a position with the State, and the elaborate lengths to which the Personnel Department went to avoid him. This occurred despite the fact that he was first on the register for the position, and that the Alabama Development Office Assistant Director found him "extremely well qualified." Id. at *4-*5.
The Frazer court entered a more detailed order requiring, among other things, that defendants validate all written tests. It also ordered that State officials "shall insure that blacks who are appointed to ... job classifications common to several agencies shall be appointed to all agencies in which such vacancies occur. No defendant shall attempt to avoid this provision by deferring requests for certification until blacks are unavailable." Id. at *7. One of the injunction's specific provisions required that the defendants "engage in intensive recruitment for black applicants for ... Graduate Civil Engineer." Id.
New Evidence: The evidence presented reflected that, during the years following the court's 1976 findings in Frazer, defendants continued to engage in the same pattern and practice of racial discrimination. By use of these practices, the evidence reflected, the defendants could preclude black applicants from applying for the historically white job classifications for prolonged periods, extending such exclusion into the late 1980s for some larger and more important job classifications. The most obvious of these practices, condemned and enjoined in 1976, was the refusal to permit applications for years at a time while the existing register used to fill vacancies was either all-white or predominantly white. In the 1980s, when African-Americans began to apply for positions where registers had been exhausted, applicants were suddenly subjected to a battery of new screening criteria and examinations. No evidence established that these criteria were job-related, nor validated as required by the Frazer injunction.
For example, the first qualification imposed on applicants for the Graduate Civil Engineer positions, an entry level job, was that they graduate from an "accredited" program, which eliminated graduates from most predominantly black schools. In mid-1979, however, a graduate of Southern University's accredited Civil Engineering program learned of a Graduate Civil Engineer job at the Transportation Department and attempted to apply for it. Josh Chapple testified at trial, and the Department's internal documents corroborated his testimony, that, instead of processing Chapple's application in the normal fashion according to the established criteria and procedures, both the Transportation Department and the Personnel Department subjected him to a series of delays and special requirements. Among them were: (1) a requirement that he pass the "engineer-in-training," also known as the "EIT," examination, though the defendants did not require that of white applicants; (2) a requirement that he take additional college course work in geology and transportation science before they would accept his application, though they did not post such course work on the job announcement or require it of white applicants; and (3) various other roadblocks catalogued on a daily basis in a Transportation Department internal memorandum dated November 3, 1978.[12] In another, later in-house memorandum, dated March 16, 1984, the Transportation Department's minority recruiter wrote: "[A] door to potential black [Graduate Civil Engineer]'s from predominantly black Southern University was slammed when, on November, 1978, the qualifications which had been sufficient for many years for white [Graduate Civil Engineer]'s were found to be unsatisfactory" *1163 for the first black applicants who satisfied them.[13]
Finally, when two African-American applicants on the register were to be hired because of the no-bypass rule of Frazer, and ten more African-American graduates appeared on the Graduate Civil Engineer employment register, the defendants suddenly abolished the register. The new job announcement included the EIT test as a posted requirement. The defendants, in an unabashed echo of their earlier racially discriminatory treatment of Chapple, declared the ten African-American applicants ineligible to reapply, despite their having successfully competed and ranking high enough on the register to be selected and despite the affirmative duty placed on the defendants by the Frazer injunction to "engage in intensive recruitment for black applicants for ... Graduate Civil Engineer."[14]Frazer, 1976 WL 729, at *7.
Chapple's story is one of the most compelling. But there was testimony from other witnesses of numerous other instances of racially discriminatory employment practice  far too many instances to recount here. One example, however, was plaintiff class member Ganiu Alabi.[15] Alabi testified that in spite of his qualifications, which included college degrees in petroleum and civil engineering, passing the EIT exam, and teaching labs for college engineering courses, his applications with the Transportation Department for civil engineering jobs were repeatedly denied. Instead, he was hired as an Engineering Assistant I, a position which requires only a high school diploma, in a geographic area more than 150 miles from his home. Neither his supervisor, his supervisor's supervisor, nor his supervisor's supervisor's supervisor had a college degree in engineering. In addition, Alabi rode in a Transportation Department truck from Fort Deposit, Alabama, to his work site with his supervisor throughout the year of his employment. His supervisor refused to permit him to ride in the cab of the truck, though it was not occupied. From the driver's seat, the supervisor would spit tobacco juice out the window, striking Alabi in the face. Alabi described the insulting incident as follows:
"[MR. ALABI]: ... [The supervisor] chews tobacco and makes sure to spit it out while the truck was in motion. I ended up with most of the juice in my face.
"[PLAINTIFFS' COUNSEL]: Did you complain about that?
"MR. ALABI: Yes, I did.
"[PLAINTIFFS' COUNSEL]: Yes, you did?
"MR. ALABI: He told me, `tough shit, it was a privilege to ride in the truck, not a right.'"[16]
In addition to these insulting behaviors, Alabi's supervisor also expressed his opinions that blacks with engineering degrees were inferior to whites with similar qualifications, and that blacks were lazy and sat around watching television and collecting welfare. Finally, despite Alabi's continuing attempts to be considered for engineering jobs better suited to his qualifications, and despite a transfer to another area, he had not, at the time of the 1992 trial, been considered for an entry level engineering job. He was not even promoted to an Engineering Assistant-II. He left the Transportation Department for a engineering job with the Alabama Department of Natural Resources.
Other evidence established that the Transportation Department had posted no job announcements, nor received applications in certain job categories, for as long as seven years, far longer than the two years that the court condemned as discriminatory in Frazer. For example, the defendants refused to receive applications for Civil Engineer-I and -II positions from 1974 to 1987, except *1164 for one three-week period in 1979 and a second three-week period in 1984. The defendants still did not take Civil Engineer-II applications up to the entry of consent decree I  opening that classification for only nine weeks in 20 years. Similar statistics were presented for many other job classifications. Evidence also showed maintenance of multiple registers, which supervisors could preview before determining from which to fill a job and which they could then use to manipulate the selection process so as assure the selection of persons whom the supervisors wanted, despite the relative qualifications of those under consideration and despite any roadblock the no-bypass rule might have place in the selection process.[17] The 1976 Frazer injunction specifically condemned previewing registers. Frazer, 1976 WL 729, at *4.
Just before completion of the plaintiffs' case, the parties announced that they might be able to settle the litigation again.

1993
The parties reached a third, albeit only partial, settlement, subsequently embodied in three consent decrees. In the wake of this new settlement, the court allowed a group of non-class members  consisting mostly of white employees of the Department of Transportation, and now commonly referred to as the "Adams intervenors"  to intervene and challenge any race-conscious provisions in the settlement.[18]

March 16, 1994
The court approved one of the consent decrees, now known as "consent decree I."[19] The court reaffirmed the certification of a plaintiff class, with subclasses, as set forth in the order of October 8, 1986. The other two proposed consent decrees are currently under the court's consideration.
Consent decree I was a comprehensive document addressing the classwide issues raised in this litigation. It completely revamped and updated the personnel policies and practices at the Transportation Department in an attempt to undo the extensive history of racial discrimination that had infected the process for many decades.
Starting from the ground up, the consent decree abolished all the existing registers at the Transportation Department (article IV), and directed the creation of new job validations (article II), new exams (article III), and the resulting new registers. Article VI specifically identified the form the new registers could take and set forth the policies the department would use in working with and maintaining the registers. Article VII set forth the policies for working with certificates of eligibles drawn from the registers. Finally, article VIII set forth policies for conducting interviews of applicants. In the period leading to the foregoing being fully operational, the consent decree provided for provisional appointments to any open positions (article IV).
To augment the new hiring procedures and to ensure that the existing Transportation Department employees who had been the victims of the discrimination were able to compete fully for positions, the consent decree required that they receive information about the job opportunities available to them within the department (article X), participate in a rotation of duties and assignments to give them experience in various jobs (article XIV), and receive training that they had been denied over the years (article XVI). The consent decree also required that the *1165 Transportation Department engage in aggressive recruitment to encourage potential black applicants to apply for jobs at the department, particularly engineering jobs (article I).
The Transportation Department's engineering jobs were particularly profoundly effected by discrimination, and article XIII directed that the department take a number of actions to rid these jobs of discrimination and ensure the appointment of black engineers. Finally, the consent decree contained a number of other provisions governing the Transportation Department's policy against racial harassment (article XVII), the appointment of relatives (article XVIII), general provisions relating to the consent decree (article XIX), further proceedings regarding class members' individual claims (article XX), and attorneys' fees (article XXI).

July 5, 1995
On July 5, 1995, the court entered an order dividing the plaintiff class into three groups: (1) the named plaintiffs; (2) all witnesses who testified at the 1992 trial; and (3) the remainder of the plaintiff class.[20] This division was part of the court's larger plan for proceeding with resolution of the class members' individual claims pursuant to article XX of consent decree I, which provides, in part, as follows:
"Further negotiations and proceedings are required to resolve the claims for monetary and non-monetary remedies for individual members of the class (including the named plaintiffs and intervenors), provided however, that this Decree does not in and of itself entitled any such class member to such remedies. Such claims shall be resolved first by settlement negotiations and then, to the extent not resolved by settlement negotiations, by the Court."[21]
In its July 5 order, the court indicated that members of groups one and two would have the opportunity to have their claims heard individually, and set forth procedures to begin this process. The court also indicated that it was considering methods, including the use of a formula, for resolving the claims of members of group three.

August 28, 1995
After the approval of the consent decree I, the parties attempted to settle some of the remaining issues in this lawsuit, including how to calculate eligibility for and the amount of backpay for class members. These negotiations took place pursuant to article XX of consent decree I. As part of their effort to agree on formulas for calculating backpay, the attorneys and experts for the plaintiffs and the Department of Transportation submitted on August 28, 1995, what is now called the "August 28 report."[22] For purposes of discussion of the issue now before the court, the report contains essentially two formulas, one to calculate "eligibility" for backpay (the eligibility formula) and another to calculate the "amount" of backpay (the amount formula) for class members. The eligibility formula is, in part, as follows:
"Pursuant to prior Orders of the Court, the parties have met and discussed the points of agreement and disagreement between them on the formula for resolving further remedies under Article Twenty of Consent Decree I. The parties agree to the following:
1. Backpay for class members who have been employed by the Alabama Department of Transportation (formerly the Alabama Highway Department)1 will be determined by a multiple regression formula constructed as follows:
a. Class members will be categorized into cohort groups within line of progression or job families in which they worked or applied. For example, the Civil Engineer line of progression or job families is the one that begins with Engineering Assistant I and proceeds through Civil Engineering VII. The Highway Maintenance Technician line of progression or job family is the one that begins with Highway *1166 Maintenance Technician I or Laborer and proceeds through Highway Maintenance Superintendent and/or other supervision of HMT's or Laborers.
b. The statistical method of `ordinary least squares' will be used to determine the weight each regression factor played in determining salary. For each cohort group, a multiple regression equation will be determined using non-racial job-related factors actually used by the State Personnel Department plus race as an additional independent variable (coded as `black equals one,' and `white equals zero'). For those cohort groups for which the coefficient of the race variable is statistically significant from zero (defined as at least a number of standard deviations of ____ or other threshold standard),2 the formula will then be used to compute expected earnings of each class member in the same way as the following example.
n. 1. The parties have not yet agreed as to whether other remedial issues can be resolved through the agreed-upon formula, but are continuing to discuss this issue.
n. 2. The parties are in disagreement as to the handling of the effects of pre-1979 disparities at this point. The Department of Transportation proposes that the claimants be divided and examined in two categories of employees (i) the earnings of all employees hired after the effective date (January 1979), and (ii) the increments in earnings after January 1979 of those who are hired before January 1979. Then regression analysis can be utilized to measure in a similar fashion the impact of race on earnings. Again, if the race coefficient is found to be statistically significant, then claimants will be all those whose actual earnings are below their level based on the estimated formula. The parties also are continuing to discuss the appropriate number of standard deviations or other threshold standard for determining which cohort groups have sufficient racial disparities in salary to be subject to the formula set forth above."[23]
The report then concluded with an acknowledgment of full "agreement" to the formula conditioned upon "non-acceptance" within a set time period by either party.
The amount formula is as follows:
"Assume that years of service (`S'), years of education (`E') and race (`R') resulted in the following equation where race is a significant factor:
Expected salary = $9000 + 200 × S + 300 × E - 1000 × R
This indicates a base salary of $9,000 with an additional $200 for each year of service and $300 for each year of college education as determined by multiple regression of such factors and that African-Americans with comparable service and education earn $1,000 less than their white counterparts. With these assumptions, the formula set forth above would compute expected earnings for a class member having 2 years of service (`S') and 4 years of education (`E') as follows:
Expected Salary = $9000 + 200 × 2 + 300 × 4 + 1000 (for a total of $11,600 in expected earnings if there had been no racial discrimination)
This analysis will be performed for each year of the liability period. Backpay for this class member would be the foregoing Expected Salary of $11,600 minus his actual pay salary for the same time period with interest for the difference computed at NLRB-IRS interest rates compounded quarterly.
c. The parties agree that any regression factor must satisfy the following conditions in order to be used in the equations and calculations: (1) it was actually utilized by the State Personnel Department in determining qualifications of competing candidates for the job classifications in question throughout the period of liability (1979-1995); (2) it does not have disparate impact on the plaintiff class or otherwise perpetuate the effects of past discrimination by the defendants against such class or if it does, it is valid, job related, and consistent with business necessity; and (3) it was not the subject of any remedial provision of the Consent Decree in this action. The foregoing standards will apply to all regression factors, including those listed in ¶ 1 of the Expert Report of Dr. Ephraim Asher dated August 10, 1995, namely: race, seniority, years of experience (where applicable), years of education (where applicable), educational degrees *1167 and certifications (where applicable). The parties have not agreed that these factors satisfy the foregoing standards for inclusion in the agreed upon formula or calculations."[24]
The August 28 report's conclusion provided:
"2. Counsels' tentative agreement in this regard is subject to each party's acceptance of these terms, and other resolution of outstanding issues with respect to the issues in footnotes 1 and 2 hereinabove. Written notice of non-acceptance must be filed with the Court and served by the close of business on Friday, September 1, 1995. Discussion of issues not resolved herein may continue to be discussed after that date."[25]
Neither side rejected the formula within the time allowed, and the formula thus became a binding agreement.

September 11, 1995
The plaintiffs and the Transportation Department submitted another joint report, signed by counsel for both sides, and now called the "September 11 report," stating that, "Pursuant to the instructions of the Court, the parties have determined the issues related to implementation of Article Twenty that they have resolved by agreement and those that must be resolved by the Court at the hearing scheduled for September 14, 1995."[26] The parties therefore made clear two separate points of agreement in the September 11 report: first, that "they have determined the issues related to implementation of Article Twenty that they have resolved by agreement"; and, second, that they "have determined ... those that must be resolved by the Court."[27]
In accordance with the first agreement in the September 11 report, the parties stated that, first, "The multiple regression formula agreed upon by the parties is set forth in the Report of Points of Agreement and Disagreement Regarding Formula for Determination under Article Twenty of Consent Decree I."[28] The parties then listed six items for "resolution" by the court as part of their second agreement. They stated in the September 11 report that,
"The parties have agreed that the Court must determine the following issues that have not yet been agreed upon:
1. Should the remedial formula that the parties agreed upon in the Joint Report of August 28, 1995, be restricted to the job families that satisfy a test of statistical significance, or should some other threshold standard be adopted? If a strict test of statistical significance is to be adopted, what probability level should be adopted and should it be determined by a one tailed or two-tailed test?
2. May class members dissatisfied with the results of the formula opt-out for an individualized trial and, if so, under what conditions?
3. Should the Court adopt the adjustment proposed by the [Alabama Department of Transportation] for the effects of pre-1979 disparities in footnote 2 of the Joint Report of August 28, 1992?
4. Should the multiple regression formula be extended to the non-employee class members and, if so, what modifications may be necessary to do so? If not, what method of determining remedies should be adopted under Article Twenty of Consent Decree for non-employee class members?
5. Should constructive employment service histories and expected current job classifications be determined by reference to the job classification in the applicable job family that corresponds to the salary level in the salary range established by the State Personnel Department? If not, what method of determining job awards and constructive service histories should be adopted?

*1168 6. Should the back-pay awarded to each class member be adjusted upward to compensate for increased tax-rates or tax obligations from receiving such pay in a lump sum in 1995 rather than in bi-weekly installments during the period from 1979 through 1994?"[29]

September 14, 1995
A hearing was held on the issues identified in the September 11 report for "resolution" by the court. At the hearing, the court stated that it had never been confronted with an agreement where it was essentially suppose to fill in the blanks in the agreement. The court asked the parties to reaffirm the court's understanding that the parties wanted it to, in fact, "resolve" the parts left open in the formulas in the August 28 report. In other words, this was not a mediation hearing, but a resolution hearing. The parties reaffirmed this understanding of the August 28 report and the September 11 report.[30]
Indeed, the only issue of dispute with regard to the court's role was whether the court's resolution of the blank or ambiguous parts of the August 28 report would be subject to appellate review. The Transportation Department argued that there should be appellate review, and the plaintiffs argued that consent decree I and the August 28 report did not allow for such. The court noted that the issue of appellate review need not be resolved at that time, but emphasized that the import of the dispute was that the parties agreed that filling in the blanks in the formulas was for the court and that the court's actions, subject only to arguable appellate review, were binding.[31]

November 30, 1995
The court entered an order, pursuant to Rule 706(a) of the Federal Rules of Evidence, appointing Mr. Ben Fine, an attorney and professor of mathematics, to serve as an expert witness as to mathematical and statistical issues.[32]

January 22, 1996
The court, at the request of the defendants, and over the strong objection of the plaintiffs, entered an order modifying the formula for calculating the amount of back-pay contained in the August 28 report.[33] The August 28 report referred to two formulas, as follows:
"Expected salary = $9000 + 200 × S + 300 × E - 1000 × R
. . . . .
"Expected Salary = $9000 + 200 × 2 + 300 × 4 + 1000 (for a total of $11,600 in expected earnings if there had been no racial discrimination)"[34]
The court rejected the defendants' argument that "the addition of the race coefficient in the second equation [was] a mistake."[35] The court explained that, "First, it is unlikely that the department believed when it signed the August 28 report that the second equation contained a minus sign because the equation in which the alleged mistake exists is solved and the addition is complete and correct. If the result of the equation had been given as $9,600, rather than $11,600, it would be plausible that the department thought that the sign before the $1000 term was a minus. Not only does the sign appear as a plus, the result of the equation, which is given twice, reflects that the $1000 term was added to the rest of the equation. Further, the parties discussed this very equation throughout their negotiations on August 28, 1995. According to the plaintiffs, when the department's expert proposed a formula that included race as a factor, and included blacks and whites in the database, but also added the race factor twice, they agreed to it because it would result in higher awards for class members. *1169 Also, the department's attorney and expert both signed the report. Thus, at the end of the August 28 negotiations, the department was fully aware of the contents of the report."[36]
The court further explained that "the August 28 report contained a provision which gave the parties from Monday, August 28, through Friday, September 1, to review the report and back out of it if they wished. The department did not indicate in any way during this time that it had any reservations about the report. Indeed, on Friday, September 1, 1995, in a teleconference with counsel for the plaintiffs and the department, the court told the parties that it was confused by the fact that the first equation subtracted the race coefficient while the second equation added the race coefficient, and asked counsel for the department directly if the second equation was correct. The department's counsel assured the court that both equations were correct and noted particularly that the parties intended for the sign to switch from a minus in the first equation to a plus in the second equation. Thus, not only did the August 28 report provide the parties with time to review the report on their own before being bound, but the court itself directed the department's attention to the very equation now at issue and asked it whether it intended for the equation to read as it did. Of course the fact that the parties had the opportunity to review the report does not establish that the report is free from mistakes. However, the fact that counsel for the department told the court directly that the equation at issue said what the department wanted it to say indicates that the equation was not a mistake."[37]
The court nevertheless relieved the defendants of compliance with the second equation as written and modified the August 28 report. The court wrote that, "it appears that the two equations at issue cannot logically be reconciled. As explained above, the two equations purport to calculate the same thing, but they use different methods and produce different results. Because the August 28 report does not explain how the various equations are to be used together, the report is susceptible to at least two different facial interpretations: that the parties intended that each class member receive $1,000 more than similarly situated whites, or that they intended that each class member receive $1,000 less than similarly situated whites. The result of the contradiction between the two equations is that the August 28 report is ambiguous."[38] The court explained that the following new equation, fashioned by the court, "will best accomplish the parties' intentions and resolve the ambiguity in the August 28 report would be one that combines both the first and second equations, with the result that the race coefficient is canceled out or eliminated":[39]
"Expected salary = B + 200 × years of service + 300 × years of education."[40]
The court further wrote: "In this equation, B is equal to the base salary calculated using only whites in the database. The analysis determined that each year of service contributed $200 to the final salary and each year of education contributed $300. Again, these values were calculated using only whites in the database. The `years of service' and `years of education' terms are used as examples of the kinds of factors that might eventually go into the equation. The court should not be understood to have decided the actual components of the equation; it has not. Rather, the court is demonstrating the construction of the equation. Because the race coefficient is already contained in B, it is neither added nor subtracted. The equation constructed by the court accomplishes the goals of the parties because it will calculate what a class member would have earned in the absence of discrimination. Because the department did not discriminate against white employees, only the salaries of whites will be used to calculate the base salary and the values of each term of the equation."[41]


*1170 May 13, 14, and 15, 1996

The court held a hearing on a number of issues regarding the backpay formulas for eligibility and amount.

May 16, 1996
After the May 13-15 hearing, the court entered a summary order of its general findings and conclusions for determining eligibility for and the amount of backpay for all class members.[42] After noting that, under the August 28 report, "class members will be divided into cohort groups, and backpay will be calculated using the backpay equation for those class members who are in eligible cohorts,"[43] the court found as follows:
"(1) Class-wide liability. The court finds that the entry of consent decree I, entered on March 16, 1994, 1994 WL 899259, operated as a finding of class-wide liability.
"(2) Determining eligibility. Eligibility for application of the backpay equation will be determined at the cohort level. The structure of the eligibility formula will be as follows:
(a) The court presumes that a cohort will include all the job categories within a line of progression, and will encompass the entire department. To overcome this presumption, the department must demonstrate convincingly that a line of progression should be subdivided into more than one cohort, by division or otherwise.
(b) The burden is on the department to show convincingly that a cohort should be excluded. The plaintiffs and the department may submit any evidence they desire to show how the burden of showing `convincingly' translates into a statistical test.
(c) All individuals within an otherwise eligible cohort shall be eligible for backpay, to be determined in the manner described below, without having to pass any additional statistical test. In other words, there will be no `accounting of error around the fitted line' using a prediction interval, confidence interval, or any other method.
"(3) Backpay equation. The backpay equation will be structured as defined in the January 22 order. The components of the regression analysis will be determined as follows:
(a) The parties shall determine a set of job-related factors upon which to regress. The goal is to select the set of factors that best models pay, according to good statistical practice. At this stage, the parties shall ignore the possibility that some factors are race-tainted, and the focus should be purely statistical and econometric.
(b) The parties shall negotiate to determine which, if any, of these explanatory variables should be excluded because it fails any of the following tests described in the August 28 joint report: (1) the factor was actually used by the State Personnel Department in determining whether to promote or hire; (2) the factor does not have a disparate impact on the class, that is, the factor itself is not significantly correlated with race, except that a factor may be used if it is valid, job-related, and consistent with business necessity; and (3) the factor was not the subject of any remedial provision of consent decree I.
(c) If the parties are unable to agree on the factors to include in the regression analysis, the court will resolve the dispute. The court's focus will be on whether the disputed factor fails any of the tests described above."[44]
On that same day, the court issued another order setting a hearing for May 21, 1996, as to, first, "whether the use of appraisal scores in the multiple regression analysis violates any of the three requirements for a valid regression factor listed in ¶ 1(c) of the August 28 report," and, second, "any other factor which any party contends should be included in the multiple regression analysis."[45]*1171 The court added that, "Any party seeking to include any factor other than education, years of seniority, and appraisal scores in the multiple regression analysis must submit its briefs and evidentiary materials regarding such factor(s) pursuant to the schedule outlined in the May 15 order."[46]
In that same order, based on the findings and conclusions in the general order, the court held that, at the May 21 hearing it would also make specific determinations regarding the non-licensed engineer line of progression. The court stated that it would "determine whether the non-licensed engineer line of progression is eligible for backpay, and if so, by what formula backpay will be calculated. In other words, the court will make the following determinations for this line of progression: (a) whether the entire line of progression should constitute a cohort or whether it should be subdivided in some manner into smaller cohorts; (b) whether the cohort (or cohorts) within the line of progression suffered discrimination as a cohort, in other words, whether the cohort (or cohorts) is eligible for the backpay equation; and (c) what factors should be included in the multiple regression analysis."[47] The court concluded that "It is the intent of the court that any concern regarding the non-licensed engineer line of progression be raised at the May 21 hearing so that the eligibility and backpay formulas can be applied to this line forthwith. In other words, as to non-licensed engineers, speak now or forever hold your peace."[48]

May 21 and 22, 1996
The court held a hearing regarding the issues listed in its May 16 orders.

May 28, 1996
The court entered an order, based on the evidence presented at the May 21-22 hearing, summarizing its findings as to the non-licensed engineer line of progression.[49] After noting again that it was seeking to determine "the final eligibility and backpay formula for the non-licensed engineer line of progression,"[50] the court found as follows with regard to the non-licensed engineer line of progression:
"(1) Eligibility formula.

(a) The entire non-licensed engineer line of progression shall constitute a cohort group. It shall not be subdivided into smaller cohort groups, and all white employees in the line of progression will be included in the cohort group.
(b) This cohort group shall be eligible for the backpay equation if the race coefficient is less than or equal to zero. In other words, if the race coefficient is greater than zero, the cohort group shall be excluded from the backpay equation. See United States v. United States Steel Corp., 520 F.2d 1043, 1054 (5th Cir.1975), (to exclude subclass, defendant must `show convincingly ... that a given group of discriminates outearned, or at least earned as much as,' similarly situated non-class employees), cert. denied, 429 U.S. 817, 97 S.Ct. 61, 50 L.Ed.2d 77 (1976).
The purpose of the eligibility formula is to determine whether the pay experience of black employees in a cohort group, as compared with that of white employees in the same cohort group, meets a statistical test. The statistic the court will use to compare black and white pay experiences will be the coefficient of race in a multiple regression equation, where the logarithm of pay is the dependent variable and years of service, the logarithm of education, and race are the independent variables. Race will be used as an indicator variable, taking the value of one equals black and zero equals white. Thus, a negative race coefficient indicates that the average salary of black employees is less than the average salary of white employees when adjusted for years of service and education. The court will set some number of standard deviations at or above zero as the statistical threshold. If the race coefficient exceeds that threshold, the defendants will be *1172 deemed to have rebutted the presumption of discrimination flowing from the finding of class-wide discrimination, and the members of that cohort group shall be ineligible for the backpay equation. The court rejects the defendants' suggestion that the threshold should be minus 1.645 standard deviations for two reasons. First, the court is convinced that the proper threshold is at least zero, and more probably a positive number. Second, to impose a threshold at the level suggested by the defendants would render meaningless the presumption that, because of the finding of class-wide discrimination, class members are entitled to backpay. However, because the plaintiffs are willing to accept, as to this cohort group only, a threshold of zero, the court need not determine at this time whether it would be appropriate to impose a higher threshold test of eligibility than zero. For example, under such a test, the threshold might be plus 1.645 standard deviations.*
n. * At the May 21-22 hearing, the department objected to this statistical test for eligibility. It urged the court to adopt a test of minus 1.645 standard deviations to determine eligibility for the backpay equation. The court overruled this objection because it believes that the proper threshold is at least zero, and more probably a positive number. In any event, the court believes that the non-licensed engineer line of progression would pass even under the department's test, which would make the objection moot. In order to determine whether the objection actually is moot, the department shall show whether the cohort group would have been eligible for the backpay equation even if the court had adopted the department's test of minus 1.645 standard deviations.
"(2) Backpay equation.

(a) The only variables to be included in the regression analysis are years of education and years of service.
(b) No adjustment shall be made for the possibility that the years of service factor might have a disparate impact on the plaintiff class."[51]
The court concluded that "the parties shall jointly file by 3:00 p.m. on Friday, May 31, 1996, the results of the eligibility formula and backpay equation for the non-licensed engineer line of progression."[52]

May 31, 1996
The parties filed a joint report under seal of the results of the application of the eligibility and backpay formulas to the non-licensed engineer line of progression. For the first time, however, the defendants raised the contention in court that "no employee class member should receive back-pay for any period during which the employee had less than one year of service."[53] This was the first that the court had heard that the defendants contended that class members with less than one year of service should be excluded from a cohort.

June 11, 1996
The court entered an order setting the following issues for submission on July 5, 1996: "(1) whether there are class members missing from the database; (2) whether the database contains incomplete or inaccurate information regarding years of service and years of education for some class members; (3) whether backpay should be calculated for the period since December 31, 1995; (4) whether the Graduate Civil Engineer and other non-licensed engineer lines of progression should be included in another cohort group; (5) whether class members who `worked or applied' in the non-licensed engineer line of progression, but were never classified within that line of progression, should be included in the non-licensed engineers cohort group for the purposes of the backpay and eligibility formulas; and (6) whether backpay should be calculated for class members *1173 who have less than one year of service."[54]

October 16, 1996
The court entered an order holding that backpay for the non-licensed engineer line of progression should not exclude calculations for plaintiff class members who have less than one year of service.[55]

October 23, 1996
The court entered an order holding that, under the August 28 report, the backpay for the non-licensed engineer line of progression should extend beyond December 31, 1995, through 28 days before the date of distribution of backpay and need not be repeated.[56]
With regard to whether backpay should extend beyond December 31, 1995, the court explained: "Nothing in the August 28 report suggests that backpay should be terminated on December 31, 1995. Under the report, the backpay determination is based on whatever relevant information is available at the time the determination is made. The only prospective temporal limitation on the backpay determination is, therefore, the amount of backpay information available at the time the determination is made, and thus when the determination is made."[57] The court further stated: "This understanding not only follows from the August 28 report, it serves a very important interest in this litigation. The court has repeatedly instructed that it is time to put the August 28 report into effect. This understanding of the backpay determination furthers this instruction in two ways. First and obviously, the plaintiff class is interested in having the backpay determination and distribution done as soon as possible, so that class members can receive their money. Second, the Department of Transportation should be interested in the same because its liability for backpay will not cease to grow until there has been a determination and distribution of backpay."[58]
With regard to next issue, the court rejected the plaintiffs' contention that the backpay formula would be reapplied indefinitely until plaintiff class members were placed in appropriate positions. The court explained: "First, the formula is a product of negotiations between the parties pursuant to ¶ 2 article XX of consent decree I. The formula is contained in the August 28 joint report and is very detailed. The formula contains no language suggesting that it is to be applied more than once or repeatedly. Second, the attorneys for all of the parties have, throughout the history of litigation, never suggested that the formula would be applied more than once. See order of October 16, 1996 (`The court agrees with the plaintiffs that the defendants' one-year-of-service objection, not raised until May 31, comes too late.')."[59] The court further stated that, third and finally, "Plaintiffs' counsel ... envisioned a one-time determination of backpay followed immediately by a determination of the appropriate salary level and job classification."[60]
The court added that, "Admittedly, with the current pace of the litigation, the salary-level and job-classification determinations may not follow with the immediacy plaintiffs' counsel expected."[61] The court nevertheless observed that "this disappointment does not detract from the fact that counsel for the parties envisioned that the backpay determination would be a one-time event under the August 28 report."[62]
The court also recognized that the plaintiffs had correctly noted that "trial courts have not only the power but the duty to provide relief that will so far as is reasonably possible eliminate the discriminatory effects of past discrimination, and that this relief typically includes backpay until the date of instatement or reinstatement. See, e.g., Albemarle *1174 Paper Co. v. Moody, 422 U.S. 405, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975); Nord v. U.S. Steel Corp., 758 F.2d 1462 (11th Cir. 1985); Pettway v. American Cast Iron Pipe Co., 576 F.2d 1157 (5th Cir.1978), cert. denied, 439 U.S. 1115, 99 S.Ct. 1020, 59 L.Ed.2d 74 (1979)."[63] The court nevertheless concluded that "The plaintiffs overlook ... that the backpay formula is a product of a settlement. `A settlement is in large measure a reasoned choice of a certainty over a gamble, the certainty being the settlement and the gamble being the risk that comes with going to trial.' Paradise v. Wells, 686 F.Supp. 1442, 1446 (M.D.Ala.1988). The plaintiffs here took the certainty, which may be much less than what would have been obtained at trial. However, it could also be much more."[64]

November 7, 1996
The court entered an order holding that, under the August 28 report, class members who "worked or applied" in the non-licensed engineer line of progression, but were never classified in that line of progression, should not be included in the non-licensed engineers' cohort group for purposes of the eligibility formula.[65]

November 22, 1996
The court entered an order holding that, under the August 28 report, backpay for the non-licensed engineer line of progression should not include an accounting for possible increased tax consequences to members of the plaintiff class.[66]

November 25, 1996
The court entered an order requiring that the Department of Transportation submit to the court, by December 31, 1996, a final report for backpay for the non-licensed engineer line of progression.[67]

December 5, 1996
The court entered an order modifying its October 23 order to read that, under the August 28 report, the backpay for the non-licensed engineer line of progression should extend through 60 days before the date of distribution of backpay and need not be repeated.[68]
The court also entered an order requiring the Department of Transportation to submit to the court, by December 31, 1996, a final report for backpay for the following lines of progression: Highway Maintenance Technician/Laborer, Clerical, Accounting, Audit, Data, Electronic, Equipment, HMT-Specialty, Licensed Engineers, Right of Way, and Trades.[69] The report was to reflect backpay as of December 6, 1996.

December 31, 1996
The Transportation Department filed a final report for backpay for the following lines of progression: Non-licensed Engineer, Highway Maintenance Technician/Laborer, Clerical, Accounting, Audit, Data, Electronic, Equipment, HMT-Specialty, Licensed Engineers, Right of Way, and Trades.[70]

January 3, 1997
The court entered an order granting, without explanation, plaintiffs' motion in limine for a finding of class-wide liability in their favor.[71] The motion was filed in anticipation of the resumption of the 1992 trial.
The court also entered an order stating that "the class-wide formulas contained in the August 28, 1995 report ... apply, in the language of the report, to plaintiff `class members who have been employed by the Alabama Department of Transportation' and *1175 does not allow for opt-out by those class members."[72]
The court also entered an order adopting the following recommendation of Court-Appointed Expert Ben Fine: "that the use of a multiple regression equation to calculate backpay is appropriate where the cohort numbers at least 8," and that "[f]or smaller cohorts, ... data from different years [should be combined] within a line of progression until the pool contains at least 12 data points."[73]
The court entered another order adopting the recommendation of Court-Appointed Expert Fine for the redistribution of backpay among class members.[74] The court explained that "Mr. Fine proposes the use of a redistribution formula which he postulates captures as well as possible the nature and extent of the losses suffered by individual class members, and which has no inherent statistical biases toward any segment of the class. Moreover, the formula represents a true compromise between the positions advanced by the parties."[75]

January 21, 1997
The court entered a memorandum opinion in support of its order entered on November 7, 1996, holding that, under the August 28 report, class members who "worked or applied" in the non-licensed engineer line of progression, but were never classified in that line of progression, should not be included in the non-licensed engineers' cohort group for purposes of the eligibility formula.[76]
The court also entered an order setting up further procedures for the determination of backpay for the members of the plaintiff class excluded from that cohort by its November 7 order, but who still might be entitled to backpay as members of the cohort.[77]

March 27, 1997
The court entered an order requiring that the Transportation Department submit a final report for backpay for all lines of progression, as of February 14, 1997.[78] The court stated that the final report should be structured such that some unresolved backpay issues may each be resolved later and separately, and that, with the report, the court will immediately enter an order for final payment to those lines of progression, for payment to the plaintiff class within 60 days of February 14, 1997. The court reaffirmed that the Transportation Department's report and the court's final payment order are subject to the condition set out in earlier orders that, if an anticipated determination or distribution of backpay is delayed by some legal action  such as a motion for reconsideration or correction or an appeal  the backpay would then extend through the resolution of that legal action, until 60 days before the actual distribution of backpay to the plaintiff class. Therefore, for example, if there is an appeal and if the appellate court should determine that plaintiffs are entitled to backpay (either as determined by this court or with modifications), backpay would include the time of the appeal and the time on remand, until 60 days before there is actual distribution of backpay to the plaintiff class.

April 16, 1997
The court entered an order requiring that the defendants pay the plaintiff class the sum of $34,732,487.00 in backpay, pursuant to the two mathematical formulas contained in the August 28 report.[79] The order was as follows:
"Pursuant to the order entered March 27, 1997 (Doc. no. 1710), and article XX of consent decree I, 1994 WL 899259 (March *1176 16, 1994), it is the ORDER, JUDGMENT, and DECREE of the court that:
(1) Judgment is entered in favor of the plaintiff class, Johnny Reynolds, et al., and against defendants Alabama Department of Transportation, State Personnel Department, et al., for claims of racial discrimination in employment.
(2) The plaintiff class of employees and former employees employed as regular full-time employees shall have and recover from defendants Alabama Department of Transportation and State Personnel Department, et al., the sum of $34,732,487,1 consisting of $17,450,077 in backpay and $17,282,410 in interest, for periods of time through February 14, 1997, during which they were employed as regular full-time employees in lines of progression to which they were formally assigned.
(3) The foregoing recovery includes only those claims and employees determined by the court to be within the joint report of the parties filed August 28, 1995 (Doc. no. 727) and not expressly or otherwise reserved by the court for separate consideration.
(4) The court retains jurisdiction of this action for all purposes.
(5) The foregoing backpay and interest recoverable shall be paid by the defendants within 60 days of February 14, 1997 pursuant to the conditions set out in the court's order of March 27, 1997 (Doc. no. 1710).
(6) Payment of the sum set forth herein shall be made to the attorney for the plaintiff class, Robert L. Wiggins, Jr. of the law firm Gordon, Silberman, Wiggins and Childs, P.C., who shall promptly place the sums in an escrow account paying reasonable interest until such further orders of the court regarding distribution of such recovery to the individual members of the class eligible to participate in such distribution.
(7) Nothing in this judgment shall be construed to address any right to appeal.
(8) Pursuant to Federal Rule of Civil Procedure 54(b), the court `direct[s] the entry of a final judgment as to one or more but fewer than all of the claims ... upon [the] express determination that there is no just reason for delay.'
(9) The court reserves the right to, and will later enter, memorandum opinions on matters related to this judgment as indicated in its orders of May 16, 1996 (Doc. no. 1023), May 28, 1996 (Doc. no. 1042), January 3, 1997 (Doc. no. 1467), and other orders and matters, including issues discussed during the two telephone conference calls held today.2
n. 1 The amount of judgment varies from the defendants' final backpay report, filed April 4, 1997 (Doc. no. 1745), by $6,818. By representation of the parties in a conference call today, this additional amount was the result of agreement by the experts on an adjustment to the method of calculating amounts for the small group cohorts. The parties agree upon the total listed above.
2 The parties have submitted proposed orders and objections to those orders. The failure of the court to include language of the proposed orders should not be taken as an indication that the court has reached any issues raised by the proposed language, or otherwise resolved any substantive issues not hereto reached by the court, or reached and addressed the merits of any of the objections filed by the parties."

April 22 and 25, 1997
On April 22, 1997, the defendants appealed from the court's April 16 order,[80] and on April 25, 1997, the Adams intervenors filed a notice of appeal from the same order.[81] These appeals are still pending.

September 15, 1997, to the Present
On September 15, 1997, the trial of this case resumed, and has continued, with periodic recesses, through the date of entry of this memorandum opinion. The purpose of this portion of the trial is to address the individual claims for injunctive relief of the members of plaintiff groups one and two, as identified in the court's order entered July 5, 1995. These proceedings, like the negotiations concerning backpay, are being conducted pursuant to article XX of consent decree I.


*1177 II. DISCUSSION
In its order entered April 16, 1997, the court stated that it "reserves the right to, and will later enter, memorandum opinions on matters related to this judgment."[82] In this memorandum opinion the court now supplements the following earlier findings: (1) consent decree I amounted to a finding of class-wide discrimination; (2) eligibility for the backpay equation will be determined at the cohort group level; (3) each line of progression will constitute a cohort group unless the defendants show convincingly that the line of progression should be subdivided; (4) each cohort group shall be eligible for the backpay equation unless the defendants show convincingly that the cohort group should be excluded; (5) all individuals within an otherwise eligible cohort group are eligible for the backpay equation; and (6) the regression analysis for the backpay equation shall consist of years of education and years of service. These findings are related in that they all depend, to a greater or lesser degree, upon the precise legal posture of this case. Therefore, the court will first explain the legal posture of the case, and then explain the findings and burdens described above, which flow from the court's determination of the legal posture.
Title VII prohibits two types of discrimination: "disparate treatment" and "disparate impact." With the former, a plaintiff must prove intentional discrimination. Texas Dep't of Community Affairs v. Burdine, 450 U.S. 248, 253, 101 S.Ct. 1089, 1093, 67 L.Ed.2d 207 (1981). With the latter, however, the plaintiff challenges "practices that are fair in form, but discriminatory in operation," Griggs v. Duke Power Co., 401 U.S. 424, 431, 91 S.Ct. 849, 853, 28 L.Ed.2d 158 (1971); the plaintiff need not prove intentional discrimination. Id. at 430, 91 S.Ct. at 853.
To prevail on a class-wide (as opposed to solely an individual) disparate-treatment claim, a plaintiff must show, first, class-wide liability, and, second, if class-wide liability is established, that he or she is a covered a person entitled to relief based on the class-wide liability finding.[83] More specifically, at stage one, "it is incumbent on the class to establish that an employer's [illegal] employment practices have resulted in cognizable deprivations to it as a class," Baxter v. Savannah Sugar Refining Corp., 495 F.2d 437, 443 (5th Cir.1974),[84] that is, establish "that racial discrimination was the company's standard operating procedure," International Bhd. Of Teamsters v. United States, 431 U.S. 324, 337, 97 S.Ct. 1843, 1855, 52 L.Ed.2d 396 (1977). "At that juncture of the litigation, it is unnecessarily complicating and cumbersome to compel any particular discriminate to prove class coverage by showing personal monetary loss. What is necessary to establish liability is evidence that the class of black employees has suffered from the policies and practices of the particular employer." Baxter, 495 F.2d at 443-44. If the class can do this, the case proceeds to stage two, where "the burden shifts to the employer to prove that the plaintiff was not, in fact, the victim of discrimination." Cox v. American Cast Iron Pipe Co., 784 F.2d 1546. 1559 (11th Cir.1986). "In other words, once a pattern and practice of discrimination is established, a rebuttable presumption that plaintiff was discriminated against because of [plaintiff's race] and is entitled to recovery obtains. The employer may overcome this presumption only with clear and convincing evidence that job decisions made when the discriminatory policy was in force were not made in pursuit of that policy." Id. This stage two presumption is, however, "tempered by an initial burden on the individual employee to bring himself within the class and to describe the harmful effect of the discrimination on his individual employment position." Pettway v. American Cast Iron Pipe Co., 494 F.2d 211, 259 (5th Cir.1974). This initial burden is only a light burden, *1178 with the "maximum burden that could be placed on the individual claimant [being] to require a statement of his current position and pay rate, the jobs he was denied because of discrimination and their pay rates, a record of his employment history with the company and other evidence that qualified or would have qualified him for the denied positions, and an estimation of the amount of requested back pay. The employer's records, as well as the employer's aid, would be made available to the plaintiffs for this purpose. The burden then shifts to the company to challenge particular class members' entitlement to back pay." Id. at 259-60.
This simple two-stage process, however, while appropriate in most cases, is not workable in cases in which it is difficult to determine whether a particular subgroup of employees falls within the "covered class." In such a case, an additional step is necessary. The initial step (proof of illegal policies and practices, for which the plaintiff class has the burden of proof) and the final step (determination of individual loss, for which the defendants bear the burden of disproving, upon an initial showing by the class member of possible harmful effect) remain the same. Between them is an important intermediate step designed to determine whether particular subgroups of the larger class should be excluded. In such cases, before all the members of the plaintiff class are entitled to present their individual claims for relief, the court must identify "the groups of employees within the larger class who are entitled to proceed to Stage II and the presentation of individual back pay claims." United States v. United States Steel Corp., 520 F.2d 1043, 1051 (5th Cir.1975). In United States Steel, the district court had certified an extremely large and diverse plaintiff class, made up of employees from "different plants, departments, job classifications, and earned seniority levels," id., and these various groups of employees were affected differently by the employer's discriminatory practices. The district court denied backpay to the entire plaintiff class because it could not determine how the various discriminatory practices had affected employees from different plants and departments. Id. Because the employer used specific, and different, discriminatory practices at its different plants and facilities, all the employees at one facility were affected similarly. In reversing the denial of backpay, the former Fifth Circuit Court of Appeals held that the district court should have divided the class into subgroups, and determined whether each subgroup had been affected by discrimination. This was appropriate because the court could, from the evidence presented, determine the "effects [of discrimination] as to given groups of employees." Id.
This intermediate step, however, is appropriate only "rarely" and "if the defendant's evidence has drawn into substantial question the group's entitlement to move into Stage II." Id. at 1054 (emphasis in original). The defendant must "show convincingly" that the subgroup is not entitled to backpay. Id. Thus, the defendant has the initial and substantial burden in this intermediate step to draw into substantial question the subgroup's entitlement to move into stage two. Only "if" the defendant has met this burden need the plaintiff subgroup respond, and, in contrast to the defendant's difficult burden, the plaintiff subgroup need only make a "reasonable argument" that the defendant's statistical evidence is distorted or that, even though there is no statistically significant difference between the pay of the plaintiff subgroup and their white comparators, the members of the subgroup have still been victims of discrimination. For example, the defendant's showing can be defeated "if the class representative can make a reasonable argument ... that a significant number of members might have earned even more than their white contemporaries but for the continued effects of discrimination. Positive proof by each member of the group is not necessary at that point. The representative need only raise on behalf of the class a reasonable inference of `cognizable (economic) deprivations to it as a class.'" Id. at 1054-55 (quoting Baxter, 495 F.2d at 443). Thus, this additional step will be appropriate only rarely, and when it is, the subgroup's burden is a very light one. The presumption is that recovery is "nearly certain." Id. at 1055.
To prevail on a disparate-impact claim, a court must similarly initially determine classwide *1179 liability, followed by a further determination, if class-wide liability is established, of whether a particular person is entitled to relief under the class-wide umbrella. The first stage of class-wide liability has three subparts. First, the plaintiff must identify the specific employment practice challenged, and, further, must show that the challenged practice falls significantly more harshly on one group than another  that is, that the practice under attack has created "adverse impact." Wards Cove Packing Co., Inc. v. Atonio, 490 U.S. 642, 656, 109 S.Ct. 2115, 2124, 104 L.Ed.2d 733 (1989).[85] If this showing is made, the burden then shifts to the defendant to produce evidence of job relatedness for the employment practice. The defendant's burden is one of production not persuasion, for the burden of persuasion always remains with the plaintiff. Finally, if the defendant satisfies its burden, the plaintiff may prevail only if he or she shows that the defendant's justification for the practice has no basis in fact or that another practice, without a similarly undesirable adverse effect, would also serve the employer's legitimate employment interests. Id. at 660, 109 S.Ct. at 2126. "Of course, any alternative practices which [a plaintiff may] offer up in this respect must be equally effective as [the defendant's] chosen ... procedures in achieving [the defendant's] legitimate employment goals." Id. at 661, 109 S.Ct. at 2127. Furthermore, because "Courts are generally less competent than employers to restructure business practices," id. (quoting Furnco Constr. Corp. v. Waters, 438 U.S. 567, 578, 98 S.Ct. 2943, 2950, 57 L.Ed.2d 957 (1978)), "the judiciary should proceed with care before mandating that an employer must adopt a plaintiff's alternative selection ... practice in response to a Title VII suit." Id.
Finally, it is most important to keep in mind that the issue before the court is backpay. Binding circuit law is clear that, because backpay determinations must be based on a "quagmire of hypothetical judgments," Pettway, 494 F.2d at 260  that is, the court must engage in a "what-if" determination of myriad possible events, including what jobs the class members would have applied for and have obtained, what announcement and posting system would have been in place, what training would have been afforded, what vacancies would have been available, and how long these vacancies would have been open, all in the absence of discrimination  the calculation of "the precise amount of backpay" is simply an "impossibility." Id. "Therefore, in computing a back pay award two principles are lucid: (1) unrealistic exactitude is not required, (2) uncertainties in determining what an employee would have earned but for the discrimination, should be resolved against the discriminating employer." Id.

A. Class-wide Discrimination
In its order entered May 16, 1996, the court held that the plaintiffs were entitled to a finding of class-wide liability.[86] Because neither consent decree I, nor the August 28 report, expressly indicated whether class-wide discrimination has been established, this holding arguably appears at first blush to be implausible. Indeed, it would arguably appear that, with this omission, the court would be compelled to conclude that the issue had been left open, with the plaintiffs and the defendants simply to litigate the issue upon resumption of the trial pursuant to ¶ 2 of article XX of consent decree I. In other words, the court would, after hearing the remainder of the evidence, decide whether the plaintiffs had met their initial burdens of establishing class-wide liability under their theories of disparate treatment and disparate impact.
However, and most significantly, both the plaintiffs and the defendants agree that the decree should not be read as silent on the liability issue.[87] Instead, the plaintiffs maintain *1180 that, with the decree, class-wide disparate-treatment and class-wide disparate-impact liability was established and thus that this case is at either a remedial intermediate stage or stage two. And the defendants maintain that, under the decree, not only has class-wide liability not been established in the plaintiffs' favor but the plaintiffs are even precluded from establishing such; indeed, implicit in the defendants' argument is the contention that class-wide liability has been found in their favor. The defendants argue that the plaintiffs must be required to try each class member's case individually under the McDonnell Douglas approach and are not allowed to "connect[] themselves to some class-wide discrimination."[88]
Therefore, the parties agree that the court is not confronted with a circumstance where the issue of class-wide liability is left open, to be litigated later.[89] And both the plaintiffs *1181 and the defendants point to the following language in the decree to support their common position that the issue of class-wide liability has been resolved: "The following terms and provisions of this Consent Decree are accordingly agreed to in final and complete resolution of all class issues which have been asserted in the case, subject to the provisions of this Decree providing for further proceedings, including but not limited to Articles 20 and 21."[90] What the plaintiffs and the defendants disagree about, however, is what additional inference to draw from this provision  that is, whether, under the decree, class-wide liability has been resolved in favor of the plaintiffs, or whether class-wide liability has been resolved in favor of the defendants.
A consent decree or judgment has the attributes of a contract and thus, as with a contract, its meaning "must be discerned within its four corners." United States v. Armour & Co., 402 U.S. 673, 682, 91 S.Ct. 1752, 1757, 29 L.Ed.2d 256 (1971). In some cases, however, this cannot be done because a term is ambiguous. "A contract term is ambiguous if [it is] `reasonably susceptible to more than one interpretation. ...'" Orkin Exterminating Co., Inc. v. F.T.C., 849 F.2d 1354, 1360 (11th Cir.1988) (quoting Fabrica Italiana Lavorazione Materie Organiche, S.A.S. v. Kaiser Aluminum & Chemical Corp., 684 F.2d 776, 780 (11th Cir.1982)). To determine whether a writing is ambiguous, the court must first assess the plain meaning of the language of the writing and determine whether there are two possible reasonable interpretations. Dahl-Eimers v. Mutual of Omaha Life Ins. Co., 986 F.2d 1379, 1382 (11th Cir.1993). If the court determines that the contract is ambiguous, it must then engage in what is essentially a fact-finding mission and "endeavor to ascertain the true intent of the parties[,] ... and then, so far as it is possible so to do consistently with legal principles, give effect to that intention." Pickren v. United States, 378 F.2d 595, 599 (5th Cir.1967). When faced with an ambiguous term and the task of determining the intention of the parties, the court may rely "upon certain aids to construction.... Such aids include the circumstances surrounding the formation of the consent order, any technical meaning words used may have had to the parties, and any other documents expressly incorporated in the decree." United States v. ITT Continental Baking Co., 420 U.S. 223, 238, 95 S.Ct. 926, 935, 43 L.Ed.2d 148 (1975). In other words, "Assuming that a consent decree is to be interpreted as a contract, it would seem to follow that evidence of events surrounding its negotiation and tending to explain ambiguous terms would be admissible in evidence." Id. at 238 n. 11, 95 S.Ct. at 935 n. 11 (quoting Twenty-fourth Annual Antitrust Review, 72 Col. L.Rev. 1, 23 n. 148 (1972)). Here, for purposes of resolution of the individual claims, the phrase at issue is definitely ambiguous as to whether class-wide liability has been found in favor of the plaintiffs or the defendants, for the phrase only states that there has been "final and complete resolution of all class issues"; the phrase does not indicate in whose favor resolution has been found.
Having embraced this fact-finding mission, this court concludes, based on several factors, that the phrase means resolution of class-wide liability in favor of plaintiffs. The first piece of evidence is mountainous: it is the consent decree itself. Arguably, because defendants often acquiesce to relief without admitting liability, the defendants could maintain that the consent decree itself should not be taken as evidence, one way or the other, on the issue of liability. But here, the defendants make no such argument, and, instead, argue that the consent decree is evidence on the issue, albeit evidence, they say, in their favor. With this evidentiary concession, however, the court must conclude that the consent decree points overwhelming in one direction: that of liability in favor of *1182 plaintiffs. Consent decree I provides for detailed and reticulated class-wide relief in favor of plaintiffs. For example, the decree requires recruitment (article I), provisional appointments (article IV), proportional assignments (article XI), rotation of job duties (article XIV), reclassification (article XV), and training (article XVI). The premise of this extensive relief can only be a finding of class-wide liability. Indeed, the consent decree cannot be logically interpreted as anything other than as an extensive effort to redress existing class-wide discrimination.
In addition, the structure of consent decree I reinforces this conclusion. As explained earlier, to prevail on either a disparate-treatment or disparate-impact class-wide claim, a court must initially determine class-wide liability, followed by a further determination, if class-wide liability is established, of whether a particular person is entitled to relief under the class-wide umbrella. This two-stage approach is mirrored in consent decree I. The preamble to consent decree I provides, as stated, that "The following terms and provisions of this Consent Decree are accordingly agreed to in final and complete resolution of all class issues which have been asserted in the case, subject to the provisions of this Decree providing for further proceedings, including but not limited to Articles 20 and 21."[91] Article XX of the decree then calls for "[f]urther negotiations and proceedings ... to resolve the claims for monetary and non-monetary remedies for individual members of the class ..., provided, however, that this Decree does not in and of itself entitle[ ] any such class member to such remedies."[92] And more specifically, the phrase "this Decree does not in and of itself entitle[ ] any such class member to such remedies" closely parallels the language used in Pettway v. American Cast Iron Pipe Co., 494 F.2d 211 (5th Cir.1974), to describe a case in stage two of a Title VII class action: "the presumption in favor of a member of a class discriminated against does not per se entitle an employee to back pay without some individual clarification." Id. at 259. See also United States Steel, 520 F.2d at 1053 (quoting this language at the beginning of its discussion of how to proceed "once the class representative has made out a prima facie case of systemic discrimination").
The settlement notice sent to plaintiff class members further mirrors this two-stage structure.[93] Paragraph 4 of the notice provides as follows: "The purpose of the settlement is to put into effect a set of procedures and goals which will resolve the class issues in this case at the earliest possible time so that the remedies in that phase of the case can become effective without having to await resolution of the second phase of the case involving claims of entitlement of particular class members to monetary and other individual forms of relief."[94] Paragraph five of the notice further provides in part as follows: "The proposed Consent Decree, by itself, does not guarantee that any particular member of the class will be entitled to back pay or front pay, but it also does not limit the amount of such relief to which any class member may be entitled in the future proceedings to be held on that phase of the case."[95] Read together, these paragraphs indicate that the parties envisioned the case as having two separate phases, one to determine whether class-wide discrimination had occurred, and a second to determine individual entitlement.
Moreover, the defendants' reading of consent decree I would be in direct contravention of the notice sent to plaintiff class members. As stated, defendants contend that, under the consent decree, the plaintiffs are foreclosed from attempting to link individual class-members' claims with any class-wide finding, and, as a result, must try each class member's case as if it were an individual claim. The defendants further posit that the logical extension of their argument is that *1183 the court cannot consider disparate-impact claims at all (individual or class-wide) because disparate-impact proof is by nature class-wide.[96] With this understanding, plaintiff class members who have individual claims based in whole or in part on a disparate-impact theory  and the plaintiffs and the defendants agree that there are class members with such claims  are now foreclosed from pursuing those claims.[97] The notice sent to plaintiff class members, however, said just the contrary: that the consent decree "does not limit the amount of ... relief to which any class member may be entitled in the future proceedings to be held on that phase of the case."[98] Similarly, although the plaintiffs could still pursue individual disparate-treatment claims if the court were to accept the defendants' reading of the consent decree, the plaintiffs could not pursue such claims to the extent they were based in whole or in part on class-wide discrimination; in other words, some disparate-treatment claims would be foreclosed in whole or in part. Again, the notice to the plaintiff class said the contrary.
But more importantly, the defendants must surely have realized that a restriction on the right of plaintiff class members to pursue all disparate-impact claims and on the right of plaintiff class members to pursue some disparate-treatment claims in whole and in part is much too important not to have been mentioned in the settlement notice sent to the plaintiff class. Such failure, if true, could arguably be viewed as gross deceit. The court instead concludes that there simply was no such restriction.[99]
Furthermore, the foreclosure of all disparate-impact claims and some disparate-treatment claim in whole or in part would have been a serious factor  and, indeed, more than likely a derailing one  in the court's consideration of whether to approve the settlement. The effect of the settlement would have been to sacrifice class members with class claims for the benefit of class members with individual claims neither based on nor linked to any class-wide discrimination. Such discriminatory treatment, without any logical basis, between members of the plaintiff class is very suspect, if not impermissible. See Holmes v. Continental Can Co., 706 F.2d 1144, 1151-61 (11th Cir.1983) (court must look with suspicion and reluctance on relief given at the expense of the rights of absent members of classes; and class counsel could not cut off claims the individual claims of class members without their permission); Reynolds v. King, 790 F.Supp. 1101 (M.D.Ala.1990) (same).
In addition, the court is convinced by other evidence presented by the parties that they deliberately chose to use this language in consent decree I  "final and complete resolution of all class issues"  in order to make it clear that stage one of the case had ended and that the case was going to move to stage two or, at least, to an intermediate stage. First of all, at the fairness hearing held on January 19, 1994, in a prelude to the court's approval of consent decree I, counsel for the plaintiffs stated that Wayne Leonard, a plaintiff class member who was specifically named and provided injunctive relief under *1184 article XIII of the decree,[100] could also seek backpay in "stage 2," which he described as the phase of the case in which an individual plaintiff "will be given the opportunity to show that he's been an individual victim."[101] The Transportation Department's attorney objected, but his objection was limited to whether Leonard, because he was specifically named and awarded relief in the proposed decree, would be entitled to any further relief at all, and in particular "in Phase 2 of this case."[102] In other words, the issue was "additional relief"; defendants' counsel was taking issue with a class member who has been given specific relief under the decree receiving any addition relief. Defendants' counsel did not take issue with plaintiffs' counsel overall characterization that, after entry of the consent decree, the case would be in "stage two." Second, at a hearing held on September 14, 1995, on the backpay formula, counsel for the State Personnel Department echoed this interpretation in part. Said counsel agreed that the case was no longer at the point at which "the Plaintiffs have to establish class-wide discrimination," but rather were "somewhat in the middle."[103] He could not define for the court exactly where this `middle' ground lay, but the import of his testimony to the court was that the case was no longer in a posture where the plaintiffs were encumbered to establish class-wide liability.[104] And his later comments reinforced this understanding. He stated that the goal of both the consent decree and the backpay formula was to set up a procedure to determine first whether "a plaintiff was in categories A through 5,"[105] meaning, for example, a person "who was an engineering assistant two and got shut out of taking the E A 3 exam."[106] If the person fits into such a category, according to defendants' counsel, "he or she then gets to be a presumed victim and gets to go forward."[107] (Emphasis added.) This "presumption" is consistent with the understanding that there has already been a finding of class-wide liability at stage one.
Although a court should be reluctant to draw from a defendant's silence in a consent decree or settlement a finding of liability  because, as stated, defendants often enter *1185 into settlements for relief without an admission of guilt  the silence presented here comes with baggage that cannot be overlooked. Twice this court rejected settlements presented by the parties, once in 1988 and again in 1991. In each of these instances, the proposed consent decrees contained disclaimers of liability.[108] While the court is reluctant in general to rely on silence alone, the circumstances of the silence in consent decree I reinforce the conclusion that the parties intended a finding of class-wide liability in favor of plaintiffs.[109]
It is also noteworthy that the formula contained in the August 28 report addresses the issue of liability from a class-wide perspective. The first step of the agreed-upon framework for determining who is eligible for backpay is to organize class members "into cohort groups within [the] line of progression ... in which they worked or applied." Then, using a multiple regression equation with job-related factors and race as the variables, the formula will determine whether the "coefficient of the race variable is statistically significant from zero." This class-wide approach  which is based on "cohorts," "groups," and "lines of progression"  completely and unequivocally refutes the defendants' contentions that plaintiff class member claims must be considered individually under the McDonnell Douglas approach and that plaintiffs cannot "connect themselves to some class-wide discrimination."[110] Moreover, the formula is described throughout the August 28 report as "remedial" and there is no reference to the need for any liability determination, thereby indicating that the parties viewed the liability phase of the litigation as completed.[111]
It is also not without import that the document now before the court is the August 28 report, which contains the backpay formula. The court's role with regard to that report, and hence to the formula, is quite different from its role with regard to consent decree I. The formula represents the parties' agreement on several important principles. First, they have agreed to use a mathematical formula to make the complex and individualized determination of whether class members should receive backpay. Thus, the parties agreed to trade a small degree of impression for the efficiency of determining a backpay award without dozens of individual trials.[112] Second, the formula, as described below, recognizes that pay disparities can result from many factors, including chance. To account for this, the parties have agreed that class *1186 members will be entitled to backpay only if the disparity in pay is sufficiently large to allow the court to conclude that the disparity is the result of racial discrimination, rather than chance. Although the formula is based on an agreement between the parties, there are also substantial points of disagreement. Therefore, the parties have further agreed that the court should fill in the various aspects of the formula and resolve the disagreements. In essence, the parties have agreed upon a framework, and agreed that the court should fill in the details.[113] Thus, it could be argued that the court's gap-filling role under the formula is more extensive than its interpretive role under consent decree I, and that, even in the absence of a finding of class-wide liability under the consent decree, the court could still find such as part of its role in filling in the gaps in the formula. So as to make the record complete, the court holds, for the reasons already given, that even in the absence of a class-wide liability finding under the consent decree, the court would still find class-wide liability under the formula.[114]
Finally, to further emphasize how severely the defendants' argument presses credibility, the current posture of the case must be considered, taking particular note of the court's order, entered July 5, 1995.[115] In that order, which followed after the entry of consent decree I, the court broke the plaintiff class into three groups: (1) the named plaintiffs; (2) all witnesses who testified at the 1992 trial; and (3) the remainder of the plaintiff class. Moreover, article XX of consent decree I provides for subsequent proceedings on the "claims for monetary and non-monetary remedies for individual members of the class," without exclusion of any class member. This division in the July 5 order was therefore made in aid of the future process of resolving the individual claims of the plaintiff class members. If it is true that a finding in favor of the defendants on class-wide liability was part of consent decree I, it would have been nonsensical for the court to divide the class this way for further proceedings. The benefit that normally accrues to the individual plaintiffs in a class action would have been lost, and there would have been no tie to bind them.
In General Tel. Co. of the Southwest v. Falcon, 457 U.S. 147, 102 S.Ct. 2364, 72 *1187 L.Ed.2d 740 (1982), the Supreme Court explained that "The class-action device was designed as `an exception to the usual rule that litigation is conducted by and on behalf of the individual named parties only.' Class relief is `peculiarly appropriate' when the `issues involved are common to the class as a whole' and when they `turn on questions of law applicable in the same manner to each member of the class.' For in such cases, `the class-action device saves the resources of both the courts and the parties by permitting an issue potentially affecting every [class member] to be litigated in an economical fashion under Rule 23.'" 457 U.S. at 155, 102 S.Ct. at 2369 (quoting Califano v. Yamasaki, 442 U.S. 682, 700-701, 99 S.Ct. 2545, 2557-2558, 61 L.Ed.2d 176 (1979)). Admittedly, it could be argued that, after consent decree I, the court should proceed to hear claims of the nine named plaintiffs, and perhaps the claims of the other 70 or so class members whose claims were the subject of the 1992 trial. But absent an overarching finding in favor of the plaintiff class as a whole, there really is no logical or practical basis for the court to hear the claims of the thousands of other class members, including, those class members covered by the August 28 report. And, similarly, absent such a finding, there is really no logical or practical basis for the group approach that consent decree I and the August 28 report take for future resolution of class members claims. Instead, the court should have simply de-certified the class and allowed the thousands of plaintiff class members to file individual lawsuits to pursue their claims. Without the common feature of a finding of liability in their favor, there is no basis for the court's current plans to try the claims of all the plaintiff class members' claims as consent decree I and the July 5 order provide.

B. Determining Who Is Eligible for Backpay
As stated in the August 28 report, the first step of the agreed-upon framework for determining who is eligible for backpay is to organize class members "into cohort groups within [the] line of progression ... in which they worked or applied." Then, using a multiple regression equation with job-related factors and race as the variables, the formula will determine whether the "coefficient of the race variable is statistically significant from zero."[116] If so, "the formula will then be used to compute expected earnings of each class member" within the cohort group.[117] Race will be used as an indicator variable, taking the value of one equals black and zero equals white. Thus, a negative race coefficient indicates that the average salary of black employees is less than the average salary of white employees when adjusted for the agreed-upon job-related factors. Beyond this general agreement, the parties disagree about the following issues: (1) whether a cohort group should include all employees from an entire line of progression or whether lines of progression should be subdivided in some way; (2) the factors to be included in the multiple regression analysis; (3) who has the burden of establishing whether a cohort group should be included in or excluded from the backpay equation; and (4) the appropriate statistical test for determining whether a cohort group should be included in or excluded from the backpay equation.
In resolving these disputes, the court must, of course, keep in mind that, because backpay determinations must be based on a "quagmire of hypothetical judgments," Pettway, 494 F.2d at 260, the calculation of "the precise amount of backpay" is simply an "impossibility." Id. "Therefore, in computing a back pay award two principles are lucid: (1) unrealistic exactitude is not required, (2) uncertainties in determining what an employee would have earned but for the discrimination, should be resolved against the discriminating employer." Id.

1. The Composition of a Cohort Group
The plaintiffs argue that each line of progression should constitute one cohort group, and that employees from the entire Transportation Department, regardless of division or years of service, should be included in the cohort group. The defendants argue that a cohort group should include the employees of only one or two divisions, rather than the *1188 entire Transportation Department, and that the cohort group should not include those white employees who have worked longer than the black employee with the longest tenure in a given cohort group. The August 28 report does not give a detailed definition of "cohort group." It states that a cohort group is a group of employees who worked or applied for jobs within the same line of progression. "For example, the Civil Engineer line of progression or job families is the one that begins with Engineering Assistant I and proceeds through Civil Engineering VII."[118] Further, "[c]lassifications within a line of progression will not be separated for analysis."[119] There is no further description of cohort group in the August 28 report.
The Alabama Department of Transportation is divided into nine geographical divisions and one central office.[120] The nine geographical divisions are as follows: division one, Guntersville; division two, Tuscumbia; division three, Birmingham; division four, Alexander City; division five, Tuscaloosa; division six, Montgomery; division seven, Troy; division eight, Grove Hill; and division nine, Mobile. There is also a central office, located in Montgomery.[121] When people apply for jobs at the Transportation Department, they can designate the division or divisions in which they would like to be assigned.[122] There is a common pay scale for all divisions; employees with the same job classification earn the same salary in Guntersville as they do in Mobile.[123]
Jobs at the Transportation Department are divided into groups called lines of progression. The first job in the line of progression is the entry-level job, with the other jobs within the line purportedly carrying a higher degree of responsibility or requiring more skill and experience. Most employees move upward within a single line of progression; however, some employees move from one line of progression to another.[124] The same lines of progression are used in all divisions.

a.
The defendants first argue that cohort groups should include employees from only one or two divisions, rather than employees from the entire Transportation Department. They contend that grouping all employees from across the state into one cohort group increases the risk of finding discrimination where none exists, and vice-versa. For example, if employees from one or two divisions were the victims of discrimination, but employees from the other divisions were not, a state-wide analysis might reveal no discrimination. On the other hand, a state-wide analysis might indicate that there was discrimination against all black employees across the state when in reality there was particularly extreme discrimination against employees in only one or two divisions. The defendants claim that each division has a distinct culture that would affect pay and promotions.[125] According to the defendants, such a culture could be the result of "different employees [and] different supervisors,"[126] and the fact that, although the department has the same "standards of operation" across the state, "those standards are interpreted ... and ... applied" differently *1189 from location to location.[127] Thus, one division may have a discriminatory culture, and another may have an equal-opportunity culture. Dividing cohort groups by division would be a way to ensure that only those class members who were the victims of discrimination received backpay.
The plaintiffs lodged several objections to the defendants' argument that cohort groups should be restricted to employees from one or two divisions. First, they claim that subdividing cohort groups by division is contrary to the parties' August 28 report. Second, they argue that class members lost employment opportunities because they were denied the opportunity to transfer from one division to another as often as white employees were allowed. According to the plaintiffs, including employees from all divisions in the same cohort group is a way to account for these lost opportunities. Third, they contend that subdividing cohort groups by division, resulting in smaller cohort groups, will cause the statistical tests to be performed on the cohort groups to be less accurate. Finally, they argue that separating employees into subgroups by division is illogical because pay decisions are made at the department level, not at the division level.
Once again, the court turns to United States Steel for guidance. As stated, in that case, the district court denied backpay to most of the plaintiff class because the class was so large and diverse that the court could not determine which of the employer's discriminatory practices had affected which employees. The former Fifth Circuit reversed and remanded for the district court to divide the plaintiff class into subclasses. The discriminatory practices had affected different subgroups within the larger class in different ways. Because there had been a "large variety of employment practices [which had] coalesced to greater and lesser degrees to affect groups of black employees" in different ways, not all black employees should be in the same subclass. 520 F.2d at 1051. The court of appeals wrote that the district court should draw "subclass lines on the basis of the objective commonality of particular [discriminatory] effects as to given groups of employees." Id. The principal goal was to determine whether there were relatively homogenous subgroups within the larger class in which the black employees had been treated similarly by the employer. The district court was to consider the "contexts and effects of the unlawful practices" in determining how to divide up the class. Id. Thus, the district court was to divide the class into subgroups based upon some unifying thread that linked all the employees in a particular subgroup to each other.
In this case, the court is convinced that cohort groups that include employees from within one line of progression, drawn from the entire department, will best fulfill the principles outlined in United States Steel. As stated, the court must identify relatively homogenous subgroups within the larger class in which the black employees were treated similarly by the Transportation Department. The evidence in this case reflects that the defendants' discrimination was statewide and not specific to one or two divisions, and that pay and promotional decisions were made by the same criteria throughout the state. The evidence also reflects that different discriminatory practices were used in different lines of progression, and that different pay and promotional criteria were used for different lines of progression. Therefore, the court is convinced that lines of progression which include employees from across the state are internally cohesive but different from one another.
Evidence from the 1992 trial supports the inference that the defendants' pay and promotional criteria and their discriminatory practices were focused state-wide and were not focused division by division. First, the pay ranges for jobs are set for the entire state. The different geographical divisions do not have different salary ranges.[128] Second, two of the defendants' main discriminatory practices were used state-wide, and were not confined to one or two divisions. One of the ways in which the defendants discriminated against black employees and *1190 applicants was to maintain several registers for one job. Such registers place employees or applicants in rank order according to certain criteria, and the defendants made promotions based upon a candidate's rank on a register. Because the different registers relied upon different criteria, they resulted in different rankings. The evidence at trial suggested that the defendants maintained several registers so they could avoid promoting or hiring black persons. If a black employee had the highest ranking on a given promotional register, the defendants would turn to another register, on which a white employee would typically be ranked higher, and select the employee from that register, thus avoiding the high-ranking black employee. These registers were maintained at the department level. There were not separate registers for the different divisions at the department. Another of the defendants' discriminatory practices was to subject potential promotees to the EIT examination, a requirement that had been adopted, according to preliminary evidence, to avoid the hiring of African-American applicants who had become eligible for appointment based on the non-EIT criteria used for the appointment of whites in the previous decades when African-Americans were barred from even being considered appointment. This examination was administered to employees seeking jobs and promotions throughout the state; it was used in all divisions. Taken together, this evidence strongly supports the inference that the defendants' pay decisions and their discriminatory practices were consistent state-wide, and that class members were treated similarly in all divisions.
The parties have agreed that cohort groups should include employees from only one line of progression, and the court is convinced that the line of progression is a grouping that is consistent with the principles of United States Steel. First, because employees at the Transportation Department typically move sequentially through the jobs in a line of progression, keeping black employees out of entry-level jobs effectively shut them out of upper-level jobs. Second, the defendants used different discriminatory practices in the different lines of progression, so that all class members seeking employment in a particular line of progression were subjected to roughly the same treatment. Taken together, this evidence demonstrates that the defendants' discriminatory practices fell somewhat similarly on all class members across the state. However, the evidence also shows that different discriminatory practices were used in the different lines of progression. Therefore, black employees from across the state, but within a single line of progression, were subjected to roughly similar discriminatory treatment. There is no evidence to support subdividing cohort groups by division.
Several additional factors support the court's conclusion that each cohort group should include all employees from across the state from one line of progression. First, in the August 28 report, the parties agreed that the employees in a cohort group would come from the same line of progression. The report states that "[c]lass members will be categorized into cohort groups within line of progression or job families in which they worked or applied."[129] Thus, the plain language of the August 28 report provides some support for the inference that the parties intended that cohort groups would include employees from the entire Transportation Department. The testimony of the defendants' expert witness at the September 14, 1995, hearing on the eligibility formula and backpay equation provides further support for this inference. At that hearing, the defendants' expert testified that the statistical analysis to determine eligibility for backpay would be performed "on the job category,"[130] thus equating an undivided job category with a cohort group. He further testified that "you regress the earnings in this job category of every person in that job category."[131] Finally, he stated that the relevant cohort "group" would be from "a particular job title," and that "[i]n that job title ... you *1191 combine the earnings of everybody" when performing the regression analysis.[132] These statements support the inference that, when the parties entered into the August 28 report, they did not contemplate subdividing cohort groups by division.
Second, although the defendants have suggested that different divisions perform different tasks and work different hours, and that employee experience and education and supervisor training and attitudes vary from division to division,[133] there is simply no evidence that this is true. For example, there is no evidence that non-licensed engineers from the Mobile division perform tasks different from those performed by similar employees from the Birmingham division, or that supervisors in the Montgomery division have attitudes different from those possessed by supervisors in the Tuscumbia division. Indeed, the defendants' expert witness acknowledged as much when he admitted that his assertion that there were "cultural" differences between divisions came from his experience at other companies, and not from "any empirical study as to how the Department of Transportation works."[134] Finally and most importantly, there is no evidence to suggest that, if "cultural" differences do exist within the Transportation Department, the culturally distinct groups within the department are divisions as opposed to lines of progression or some other grouping of employees.
Finally, in addition to considering the principles announced in United States Steel, the court must consider another factor. Because the parties have agreed to use a statistical test to determine eligibility for backpay and calculate the amount of backpay, the court must take also take into account good statistical practice in deciding the composition of cohort groups. The parties agree that, in general, statistical tests are more accurate when performed on large samples.[135] In other words, a larger number of people in the sample pool will result in "greater statistical power,"[136] which means that it is more likely that the result of any statistical analysis done on the sample pool is accurate. In this case, "power would be the probability of finding discrimination when it exists."[137] Therefore, although, for reasons that follow, this factor should not be controlling, good statistical practice supports the court's decision to include employees from across the state in the same cohort group.

b.
The defendants next argue that cohort groups should exclude those white employees who have more years of service than the longest-serving black employee in the cohort group. According to the defendants, including only same-seniority white employees, rather than all white employees, improves the ability of the regression analysis to predict pay.[138] They argue that, because long-serving whites have relatively high salaries due to their many years of service, including them in the cohort group will exaggerate the backpay due to class members who have worked a much shorter time. Although the defendants admit that "[l]ogically ... there is no reason" not to include long-serving white employees in the cohort group if class members competed with those white employees for promotions,[139] they maintain that "[s]tatistically ... there is a good reason to limit [the cohort group] to [employees having] the same seniority."[140] The defendants contend, and the plaintiffs admit, that the "R-squared value" is higher when the cohort group is restricted to same-seniority white employees rather than all white employees. *1192 The R-squared value represents the extent to which the regression factors explain the variation in salary;[141] however, and of equal importance, the R-squared value does not measure the validity of the assumptions underlying the regression factors. The R-squared value can be expressed in percentage terms; for example, an R-squared value of 50% means that the regression factors explain 50% of the variation in salary. According to the defendants, the regression factors explain approximately 89% of the variation in pay when only same-seniority whites are included. On the other hand, when all white employees are included, the regression factors explain approximately 70% of the variation in pay.[142] From this, the defendants urge the court to conclude that including only same-seniority whites in the cohort group produces a more accurate result because the R-squared value is higher.
The plaintiffs argue that excluding longserving whites from the cohort group is contrary to the August 28 report and that it does not accurately reflect the way the defendants make promotional decisions. They claim that class members often compete for promotions with white employees who have far more years of service than the longestserving black employee. Thus, class members have lost promotional opportunities to white employees who, if the court adopts the defendants' suggestion, would be excluded from the cohort group. Further, they argue that the court should not determine the composition of the cohort group solely by the R-squared value. Although they admit that the R-squared value is higher when only same-seniority white employees are included in the cohort group, they maintain that a higher R-squared value does not necessarily mean that the formula fits the data better. They argue that it is possible to have a high R-squared value and a relatively poor fit.[143] However, they argue that the R-squared value will go up simply by reducing the number of people in the cohort group.[144] In other words, because there is "more data" in the cohort group which includes all white employees, there will necessarily be "more variability" in that data, which will lower the R-squared value.[145]
The court need not determine whether a higher R-squared value necessarily means that the result is more accurate to conclude that, on the facts of the this case, the defendants' argument is without merit. Particularly compelling is the defendants' admission that including all white employees in the cohort group is "logically" sound given the way the defendants actually determine who receives promotions. Thus, logic works against the defendants' proposal. Further, because the defendants admit that it is possible that simply reducing the number of people in the cohort group could increase the R-squared value,[146] good statistical practice does not necessarily support their position. The purpose of the formula is to determine what class members would have earned in the absence of discrimination; the goal is not to construct a statistical test that ignores the realities of the defendants' decision-making process. If the only goal were to increase the ability of the formula to explain the variation in salaries, the court could restrict the sample size in any number of ways. However, as stated, the court's definition of the cohort group must guided by departmental practice. Because class members competed for promotions against white employees with all levels of seniority, there is no reason to restrict the cohort group to same-seniority white employees.

2. Factors to Be Included in the Multiple Regression Analysis
After class members have been divided into cohort groups, the next step in the proposed eligibility formula is to determine the *1193 factors to be included in the multiple regression equation. Multiple regression analysis is a way to determine the contribution of various factors to the employee's salary. The analysis includes a dependent variable  actual pay  and factors which help explain the level of pay. The analysis also includes a race coefficient, which measures the amount of pay that is left unexplained by the agreed-upon job-related factors. The equation must include only those factors which actually influence pay. Under the August 28 report, before a regression factor can be included in the multiple regression analysis, it must satisfy three conditions. First, it must have been "actually utilized by the State Personnel Department in determining qualifications of competing candidates."[147] Second, it must not have a "disparate impact on the plaintiff class or otherwise perpetuate the effects of past discrimination ... or if it does, it is valid, job related, and consistent with business necessity."[148] Finally, it must not have been "the subject of any remedial provision of" consent decree I.[149]

a.
The parties have agreed that years of education and years of service will be included in the regression equation,[150] and the plaintiffs argue that these are the only two factors which should be included in the regression analysis. The Transportation Department contends that appraisal scores should be included as a third factor. The plaintiffs claim that the use of appraisal scores would violate the August 28 report because the appraisal scores have not been used by the State Personnel Department in the manner required by the August 28 report. All employees of the Transportation Department receive evaluations every year. Each employee receives an appraisal score of between 0 and 100. Employees receiving scores between 71 and 100 are considered to "exceed standards," and they receive a 5% raise. Those who receive scores between 51 and 70 are considered to "meet standards," and they receive a 2½% raise. Employees who score below 51 receive no raise.[151]
The defendants argue that appraisal scores are used in two ways. First, appraisal scores are used to determine whether an employee receives a raise. The plaintiffs respond that this use of appraisal scores is irrelevant to the issues the formula addresses because almost every employee receives a full 5% raise. They claim that, although appraisal scores are related to pay, they do not explain why there is a difference between the salaries of black and white employees because, as stated, employees almost always receive 5% raises. Indeed, of the 16,740 appraisals scores received by employees, 16,641 were between 71 and 100.[152] In other words, 99 .4% of employees  both black and white  received a full 5% raise.
Appraisal scores were also used to help determine who received a promotion. Employees are selected for promotion from one of two lists: the open-competitive register or the promotional register. Appraisal scores were not used at all with the open-competitive registers. It appears that, of the promotions received by class members between 1983 and 1995, approximately 64% of the promotions were from the open-competitive register.[153] Thus, appraisal scores played no role at all in the majority of promotions received by class members. As to the promotional registers, appraisal scores played only an indirect role in awarding promotions. The defendants averaged the employee's three most recent appraisal scores, and this average accounted for 10% of the employee's numerical score on the promotional register. The plaintiffs contend that, because appraisal scores played a small role in promotional *1194 decisions for class members, appraisal scores should not be included as a regression factor. The defendants admit that appraisal scores make up only 10% of an employee's score on the promotional register.[154] However, they argue that, because promotions are often decided by one or two points, anything that contributes to an employee's score is important.
As stated, for a factor to be included in the regression equation, it must have been actually used by the State Personnel Department in making promotional decisions; in other words, the analysis must include only those factors actually used to set employees' salaries. Because almost every appraisal lead to a full 5% raise, it appears that appraisals had no meaningful role in determining who received a raise; raises were virtually automatic. Further, as to promotions, appraisal scores were used for only a fraction of the class, and when they were used, they were used in an indirect way. Therefore, the court concludes that appraisal scores did not play a meaningful role in determining promotions.[155] Accordingly, appraisal scores shall not be included as a factor in the regression analysis.

b.
Although the plaintiffs agree that years of service should be included as a regression factor, they argue that there should be some adjustment to remove racial taint. The defendants respond that such an adjustment was foreclosed by the parties' agreement to use years of service. During the hearing on backpay issues, the court asked counsel for the plaintiffs whether years of service should be "validated," in other words, adjusted in some way for racial taint.[156] Counsel for the plaintiffs responded that whether a factor was racially tainted, and therefore prohibited by the August 28 report, was a relevant question only when the parties were in dispute as to whether a factor should be included in the regression equation.[157] Because the parties had agreed that years of service would be included, it was not subject to the provisions of the August 28 report.[158] In other words, by agreeing that years of service would be a regression factor, the parties had agreed that it would not be adjusted for racial taint. Moreover, the parties' agreements regarding the proposed backpay and eligibility formulas left many issues unresolved, and whether to adjust years of service for racial taint was simply not one of the unresolved issues. Because the parties agreed that it would be included, and agreed that it would not be adjusted for the possibility of racial taint, the court rejects the plaintiffs' argument that years of service should be some adjusted for racial taint.
Finally, the parties have agreed that logarithm adjustments on pay data shall be used at the eligibility level; unadjusted actual salaries shall be used in backpay calculations for eligible individuals; and logarithm adjustments shall be used for education data at both the eligibility level and the backpay *1195 equation level.[159] In other words, the eligibility formula will include the logarithm of pay, the logarithm of years of education, and the actual years of service.

3. Whether a Cohort Group Should Be Included in or Excluded from the Backpay Equation
The next issue the court must address is how to determine whether a cohort group is eligible for the backpay equation. The purpose of the eligibility formula is to determine whether the pay experience of black employees in a cohort group, as compared with that of white employees in the same cohort group, meets a statistical test. As stated, the statistic the court will use to compare black and white pay experiences will be the coefficient of race in the multiple regression equation, where the logarithm of pay is the dependent variable and years of service, the logarithm of education, and race are the independent variables. Race will be used as an indicator variable, taking the value of one equals black and zero equals white. Thus, a negative race coefficient indicates that the average salary of black employees is less than the average salary of white employees when adjusted for years of service and education. The size of the race coefficient determines whether the members of a cohort group are eligible for the backpay equation. The parties have agreed that only those cohort groups for which the coefficient of race is "statistically significant from zero" will be eligible for the backpay equation.[160]
The parties disagree about how big the race coefficient must be to be considered "statistically significant from zero." They agree, however, that this determination depends in part on whether the plaintiffs or the defendants have the burden of proving that a cohort group should be included or excluded.[161] In other words, if the plaintiffs must prove that a cohort group should be included in the backpay equation, then the statistical test would resolve doubts in favor of the defendants. On the other hand, if the burden is on the defendants to exclude a cohort, then the statistical test would resolve doubts in favor of the plaintiffs. Thus, the court first determines who bears the burden of proof and how great that burden is before choosing a statistical test that accomplishes this.

a.
As stated, the plaintiffs must first prove there was class-wide discrimination, and, if successful, the defendants then bear the burden (tempered by a light initial burden on the plaintiff class member to describe a harmful effect of the discrimination) of showing by clear and convincing evidence that the job decision at issue was not made pursuant to their discriminatory policy. In this case, the way that the parties can fulfill these burdens has been modified by agreement of the parties. First, as discussed more fully above, whether there was class-wide discrimination was resolved by the entry of consent decree I. The burden was properly on the plaintiffs at stage one, and they fulfilled that burden upon the entry of consent decree I, which amounted to a finding of class-wide discrimination. As to stage two  the determination of individual loss  the parties have agreed to use a mathematical backpay formula to determine how much each eligible class member will receive in backpay. The court will address the content and operation of the backpay formula separately. What is important here is that the parties have adopted the well-established Title VII allocation of burdens of proof, albeit with some agreed-upon limitations on the evidence that the parties can use to meet their burdens at each stage, and an agreement regarding what the parties will have to show to satisfy their burdens. For example, in a typical stage two proceeding, a class member can rely on anecdotal evidence of his or her treatment by the defendant to satisfy his or her burden or to respond to evidence presented by the defendant in an effort to satisfy its burden. However, in this case, the parties have agreed that individual class members may not use this often-powerful *1196 evidence; class members are limited to statistical evidence. Nevertheless, that the parties have agreed to limit the type of evidence the plaintiffs may use does not mean that the parties have been relieved of their respective Title VII burdens.
But importantly here, there is an intermediate step, between stage one and stage two, at which the defendants can avoid liability as to a whole cohort group. This is the step that is referred to as the eligibility formula. The parties disagree about who should bear the burden of proof at this step. The defendants contend that the burden should be on the plaintiffs. They first argue that, because the trial of this case was not finished,[162] stage one has not been completed. Therefore, the eligibility formula must determine class-wide liability. They also contend that requiring them to show that a cohort group should be excluded from the backpay equation would violate the August 28 report, which, they argue, requires the plaintiffs prove that a cohort group should be included in the backpay equation.
The plaintiffs respond that, because class-wide discrimination has been established, the burden should be on the defendants to show that a given cohort group is not eligible for the backpay equation. They argue that, under longstanding Eleventh Circuit law, after stage one has been concluded in the plaintiffs' favor, the entire plaintiff class is presumptively entitled to move to stage two, where the defendant, subject to an initial burden on a class member of showing economic injury, bears the heavy burden of showing that the class member is not entitled to backpay. The plaintiffs, however, do not claim that each member of the class is entitled to backpay. Rather, they claim that every cohort group is presumptively entitled to move to stage two, subject only to the defendants' intermediate-step right to show that a particular cohort group was either not discriminated against or that a particular cohort group suffered no economic harm from the discrimination. Thus, under the plaintiffs' argument, the plaintiffs have the burden of proof at stage one to show that there was class-wide discrimination, and the defendant has the burden at stage two to show that a class member is not entitled to backpay. However, they claim that, in the intermediate step in which the defendants are given the opportunity to avoid liability as to an entire cohort group, the burden of proof should be on the defendants to show that a plaintiff subgroup, or cohort, is not entitled to move to stage two.

b.
The defendants' argument that the eligibility formula must place the burden of proof on the plaintiffs reflects a misunderstanding of the posture of this case. As stated, the entry of consent decree I amounted to a finding of class-wide discrimination, thereby concluding stage one. Because there is a large and diverse plaintiff class, the court has concluded, and the parties agree, that there should be an intermediate step before the case is fully in stage two. It is this intermediate step, with its burden of proof that the parties incorporated into the eligibility formula of the August 28 report. The structure of the eligibility formula supports this conclusion. Stated generally, and as explained previously, Title VII requires the court to sharpen its focus as the case progresses: first, at stage one, it is concerned with large-scale, class-wide practices; then, if an intermediate step is warranted, it considers practices affecting particular subgroups within the affected class; and finally, at stage two, it looks at the affects of these practices on individual members of the plaintiff class. The eligibility formula is not concerned with class-wide issues, nor is it concerned with individual issues. Instead, its focus is on cohorts, or subgroups, within the plaintiff class. It is therefore apparent that the eligibility formula, with its focus on subgroups, is comparable to the intermediate step under Title VII.
With this conclusion, the court must further conclude that the defendants bear the burden of proof under the eligibility formula. As stated, an intermediate step is appropriate only "if the defendant's evidence has drawn into substantial question the group's entitlement to move into Stage II," id. (emphasis *1197 in original), and thus the defendant bears the burden of proof at this step. Because the eligibility formula and the intermediate step are comparable, the defendants here similarly bear the burden of proof under the eligibility formula.[163]
The court must now determine how to translate this burden into a statistical test.

4. The Statistical Threshold Test
The court has concluded that the plaintiffs have carried their stage one burden of establishing class-wide discrimination, but that the plaintiffs are not yet entitled to move fully into stage two, or the backpay equation. This case is now at an intermediate step, with the burden on the defendants to show that a cohort group should be excluded from the backpay equation. The parties have agreed that they will use a statistical test to do this. Under the August 28 report, only those cohort groups for whom the race coefficient is "statistically significant from zero (defined as at least a number of standard deviations of ____ or other threshold standard)" will be included in the backpay equation. Another way to state this requirement, and the way the parties discussed it during the May 1996 hearing, is to compare the average salary of black employees with that of white employees in the same cohort group. The averages are plotted as straight lines on a graph, and the distance between the lines represents the difference between the average salaries. The distance between the two lines can be expressed as a number of standard deviations. If the difference between the average salaries is statistically significant for a cohort group, then the black employees in the cohort group would be eligible for the backpay equation.[164] Statistical significance can be expressed in at least two ways, each of which is a different side of the same coin. The first way involves measuring the difference as a number of standard deviations. The second way involves determining to a specified degree of certainty whether the difference is due to chance. If this specified degree of certainty is reached, then the court would infer that the difference was due to discrimination. For example, the court could decide that if, based upon the statistical evidence, it was 90% certain that the difference between black and white salaries was not due to chance, then it would infer that the difference was due to racial discrimination. That the court would infer racial discrimination, and not some other explanation, is based upon the evidence already presented, the agreements of the parties, and the presumptions that flow from these agreements.
The defendants argue that, to include a cohort group, the average salary for black employees in a cohort group must be less than the average salary for white employees by more than 1.65 standard deviations using a one-tailed test.[165] Put another way, unless the court can determine first that the average black salary was less than the average white salary, and then conclude with approximately 95% certainty that this difference was not due to chance, the cohort group should be excluded from the backpay equation.[166] The defendants further argue that a cohort group should be excluded from the backpay equation if the black average salary is equal *1198 to or greater than the white average salary.[167]
The plaintiffs argue that, to exclude a cohort group, the court must find that the average salary of the black employees in a cohort group is greater than the white average by more than 1.65 standard deviations. In other words, if the court found that the black average was higher than the white average for a cohort group, and it could conclude with 95% certainty that the difference was not due to chance, then the cohort group would be excluded from the backpay equation. According to the plaintiffs, if the average black salary is more than the average white salary, but less than 1.65 standard deviations more, the court cannot exclude chance as the reason for the difference. And, because the burden is on the defendants to exclude a cohort group, the court must resolve doubts in favor of the plaintiffs. In other words, if the black average is equal to the white average, or greater than the white average by less than 1.65 standard deviations, the defendants have not overcome the presumption that there was discrimination.
As part of its determination of the appropriate statistical threshold, the court must consider what the "null hypothesis" is in this case. A null hypothesis represents what the observer predicts or expects to find from the data. It is analogous to a presumption; the court assumes it to be true, but will, upon the proper showing, reject it and conclude that it is false. The statistical threshold tests described above are ways to compare the null hypothesis to the observed data; if the difference between the null hypothesis and the observed data is sufficiently large, then the court will reject the null hypothesis in favor of an "alternative hypothesis." The plaintiffs contend that the null hypothesis at this stage should be that there was racial discrimination. This means that the court should presume that the black average salary is less than the average white salary and that it should disturb the presumption that the white average salary is higher only if the statistical evidence showed clearly that the black average was greater than the white average. The defendants have not stated what the null hypothesis should be. However, the threshold standard they advocate suggests that they believe that the null hypothesis should be that there was not discrimination, because their proposed statistical test resolves doubts in their favor.
The court is convinced that, in this case, its consideration of the appropriate null hypothesis is guided by several legal considerations. First, because the plaintiffs have shown at stage one that there was class-wide discrimination, the court expects that the average salary of black members of the cohort group will be less than the average white salary. See Cox, 784 F.2d at 1559 ("once a pattern and practice of discrimination is established, a rebuttable presumption that plaintiff was discriminated against because of [plaintiff's race] and is entitled to recovery obtains"). Furthermore, at the intermediate step, a subgroup may be subjected to exclusion from this presumption only "if the defendant's evidence has drawn into substantial question the group's entitlement to move into Stage II." United States Steel, 520 F.2d at 1054 (emphasis in original). Thus, the defendants bear the burden of proof at this step as well. Therefore, based upon the presumption arising from the plaintiffs' success at stage one and based on the substantial burden the defendants bear at the intermediate step, the court expects that the line representing the average black salary will be below the line representing the average white salary. To reject this hypothesis  to decide that there has been no discrimination  the line representing the average black salary must be above the line representing the average white salary by a significant margin. To do *1199 otherwise  to exclude a cohort group even if the line representing the average black salary is below the line representing the average white salary  would be to make the presumption of discrimination and the intermediate-step burden of proof borne by the defendants meaningless.
The court has concluded that, to exclude a cohort group, the average black salary must be greater than the average white salary. Now the court must determine how much greater the black average must be to exclude the cohort group. This determination depends upon how confident the court is that the null hypothesis  that there was discrimination  is true. If the court is firmly convinced that the null hypothesis is true, it would take a strong showing to convince the court otherwise. On the other hand, if the court has some doubts about whether the null hypothesis is true, then a much weaker showing will be enough to convince the court to reject the null hypothesis. In this case, the parties have agreed that the difference between the average black salary and the average white salary must be statistically significant. Further, they agree that a difference of 1.645 standard deviations, which can be expressed as a "confidence level" of 95%, is statistically significant.[168] At this level, the court can be convinced to a 95% degree of certainty that the average black salary is actually higher than the average white salary, and that this difference is not due to chance. At this degree of confidence, the court can be certain that, despite the defendants' class-wide discrimination, the members of that particular cohort group did not suffer economic harm because of the discrimination.[169]

C. The Backpay Equation
Under the approach outlined in the August 28 report, after class members are organized into cohort groups and the regression analysis is performed to determine whether the members of each cohort are eligible to present individual backpay claims, an agreed-upon formula "will then be used to compute expected earnings of each class member."[170] This step is referred to as the backpay formula. In an order entered on January 22, 1996,[171] the court outlined the structure of the backpay formula as follows:
"Expected salary = B + 200 × years of service + 300 × years of education"
In this equation, B is equal to the base salary calculated using only whites in the database. The hypothetical analysis determined that each year of service contributed $200 to the final salary and each year of education contributed $300. These values will be calculated using only whites in the database.
After the January 22 order, there are two remaining issues: whether all individuals within an otherwise eligible cohort group would be eligible for the backpay equation and what factors would be included in the regression analysis. In the summary order entered on May 16, 1996, the court concluded that all individuals within an eligible cohort group would be eligible for the backpay equation, and that the regression analysis for *1200 the backpay equation would consist of years of education and years of service. The court will now provide the reasons for these conclusions.

1. Whether All Class Members Within an Eligible Cohort Group Are Eligible for Backpay
As stated, the eligibility formula affords the defendants an opportunity to exclude the members of a cohort group from the backpay equation if they can show that the cohort group has not suffered discrimination. For those cohort groups which are found to be eligible for the backpay equation, the defendants seek to require that the individual class members in that cohort make an additional statistical showing of discrimination before they are entitled to backpay as computed by the backpay formula. They refer to this additional step as "accounting for error around the fitted line." The "fitted line" is a line representing what a white employee with a specified combination of years of experience and years of education would expect to earn. The defendants maintain that this line, like all statistical estimates, will contain some error. In addition, they argue that a class member may have earned less than the estimated salary simply by chance. To account for the risk that the estimated salary is in error, and the possibility that a class member's low salary is due to chance, the defendants seek to place a "prediction interval" around the line representing expected pay. This interval would include the range into which 95% of white employees with given years of experience and education would be expected to fall. Only those black employees whose pay fell below the interval would receive backpay. Put another way, only those black employees whose pay put them into the bottom 5% of whites would receive backpay. This requirement would amount to a second eligibility test. First, each cohort group is required to pass a statistical test before the members of the cohort group are eligible to have their backpay calculated. The defendants' proposal would then impose a second statistical test on the members of all eligible cohort groups, requiring each class member to show that her salary was less than the salaries of 95% of the whites in her cohort group. If it was, then she would be eligible for backpay, which would be the amount that her salary fell below the expected white salary.
The defendants admit that this additional statistical hurdle is not mentioned in either the August 28 report[172] or the January 22 order.[173] However, they claim that the additional step is "implied in the" January 22 order,[174] and is necessary in good statistical practice. They argue that a cohort group might pass the statistical test at the cohort level  the eligibility formula  and be considered eligible for backpay if a few class members had extremely low pay, even though most class members earned as much as their white counterparts.
According to the plaintiffs, when the parties entered into the August 28 report, they recognized that there might be some error around the fitted line. However, they maintain that when the parties agreed that all class members in an eligible cohort group would be eligible for backpay  implicitly rejecting the sort of second threshold test the defendants now seek  they did so as part of a compromise. The plaintiffs agreed that they would not seek backpay for class members who earned more than the average white salary in exchange for the defendants' agreement not to seek a second eligibility test.[175] This concession was significant, since all members of an eligible cohort are presumed to have suffered discrimination following the finding of class-wide liability. Indeed, credible evidence strongly suggests that higher-earning black employees may well have suffered greater losses from discrimination than lower earning black employees.[176] However, as part of the process of *1201 resolving this case, the plaintiffs agreed not to seek backpay for such class members as long as all class members would be eligible for backpay without having to pass a second statistical test.
Based upon the August 28 report, the September 11 report, and the January 22 order, the court agrees with the plaintiffs. Although the defendants maintain that both the August 28 report and the January 22 order imply that there will be a statistical threshold test at the individual level, there is no such test described in either document. Indeed, not only does the August 28 report not mention the possibility that members of eligible cohort groups will have to pass a second eligibility test, the report states that the backpay "formula will ... be used to compute the expected earnings of each class member" in an eligible cohort group.[177] Further, the fact that the August 28 report describes the statistical test to be applied at the cohort group level suggests that if the parties intended that there would be a second such test, it would be mentioned. Similarly, although the September 11 report purports to list the issues to be determined by the court on the backpay and eligibility issues, it does not mention the possibility that members of eligible cohort groups will have to pass what amounts to a second eligibility test. Finally, there is no mention of such a test in the January 22 order. Although the form of the group eligibility test and the expected salary formula have been modified by the court's January 22 and May 16 orders, no individual eligibility test was ever inserted between the group eligibility test and the backpay calculation.
The court has concluded that imposing a second eligibility test is inconsistent with the parties' various agreements. In addition to this reason, there is another, equally valid, reason to reject the defendants' suggestion that there be a second statistical threshold test. As stated, the finding of class-wide discrimination means that a member of the plaintiff class is presumed to have been the victim of discrimination. The defendants have the opportunity to rebut this presumption if they can show convincingly that there was no discrimination in a particular cohort group. If they fail to make this showing, then, under the August 28 report, the individuals within the cohort group are eligible for the backpay equation. To deny backpay to each member of an eligible cohort group unless he or she can show that his or her salary is less than the salaries of 95% of comparable whites is precisely to shift the burden back to the individual, rendering nugatory the finding of class-wide discrimination. Because imposing a second statistical threshold test would, in practice, substantially eviscerate the finding of class-wide liability, the court rejects any individual statistical showing of discrimination.

2. Factors to Be Included in The Multiple Regression Analysis
The final step in the backpay equation is to determine the factors to be included in the multiple regression analysis. Earlier, the court discussed the factors to be included in the multiple regression analysis in the eligibility formula. The parties have advanced the same arguments as to the factors to be included in the backpay equation as they made regarding the factors to be included in the eligibility formula. The court reaches the same conclusion as to this equation as it did as to the eligibility formula. The only factors will be years of service and years of education. Logarithm adjustments shall be used for education data; unadjusted actual salaries shall be used in backpay calculations for eligible individuals.[178] In other words, the backpay formula will include unadjusted actual salary, the logarithm of years of education, and the actual years of service.[179]


*1202 CONCLUSION
The backpay awarded on April 16, 1997, was based on the findings reached in orders and memorandum opinions before that date as well as on the additional findings reached in this memorandum opinion. It is important to remember that these findings were informed by three important circumstances. First, the backpay award was based on a negotiated document  the August 28 report. Because the underlying document was a product of negotiation, there were no supporting findings of fact and conclusions of law to guide the court in its effort. Therefore, in resolving the matters left open by the September 11 report and in resolving other disputed matters that arose in interpreting the August 28 report, the court has had the very difficult task of uncovering, if not divining, the intent of the parties and the spirit of their negotiations.
Second, because the April 16 backpay award was a product of negotiations, it reflects not what each party may actually be entitled to, but rather tradeoffs for both sides. In particular and most dramatically, for example, each plaintiff class member is to receive only a one-time payment of backpay, rather than, as he or she might be entitled, both backpay and frontpay, the latter being for the time period until his or her entitlement to injunctive relief is resolved and, if warranted, he or she is placed in an appropriate position. To be sure, therefore, the defendants, with just a one-time payment of backpay, will be discharged of both their backpay and frontpay obligations for the alleged wrongs at issue. However, the plaintiff class stands to gain as well. They will not only have the certainty of some payment for their alleged loss, they will not have to wait until the issue of injunctive relief is resolved, a matter which will probably be much more complicated and which will probably take much more time to be completed.
Finally, the backpay award was the product of an evolutionary process. With the above concerns in mind, the court began with what was an appropriate but still extraordinary measure: the modification of the August 28 report at the request of the defendants. The court, with these same concerns, then proceeded to make findings regarding, among other things, class-wide liability, the structure of the eligibility formula, the structure of the backpay formula, the tax consequences of the backpay formula, the right of class members to opt-out, and whether the backpay award should be a one-time event or should be repeated until appropriate injunctive *1203 relief  including the placement of some class members in their appropriate positions  is completed. The court reached its findings seriatim. Each finding was, at least, in part based on earlier ones and with a view toward the whole picture. Many of the findings are therefore in some measure, either implicitly or explicitly, interrelated and interdependent. The elimination of, or change in, one finding would warrant revisiting, and could warrant revising, other findings.
NOTES
[1]  See order, entered April 16, 1997 (Doc. no. 1785).
[2]  For the group of class members actually receiving backpay, the average amount of backpay per person is approximately $16,250. Taking into account the entire group of class members whose claims were resolved by this award, which includes 260 class members who were determined to be ineligible for backpay, the average amount of backpay per person is approximately $14,450. Of course, because the class members have been employed by the Transportation Department at various times for various periods, and because the pay rates differ for the many different jobs at issue, the range of backpay for the plaintiff cases is broad.
[3]  See order, entered October 8, 1986 (Doc. no. 82).
[4]  See Reynolds v. King, 790 F.Supp. 1101 (M.D.Ala.1990).
[5]  Id. at 1114
[6]  Id.
[7]  See order, entered January 29, 1991 (Doc. no. 244).
[8]  See notice of withdrawal or cancellation, filed March 19, 1991 (Doc. no. 259), and letter, filed March 19, 1991 (Doc. no. 260).
[9]  See order, entered March 22, 1991 (Doc. no. 265).
[10]  When originally filed, this case was styled United States v. Frazer, civil action no. 2709-N (M.D.Ala.). It is currently styled United States v. Ballard, civil action no. 2709-N (M.D.Ala.), because, after December 4, 1981, Halycon Vance Ballard replaced John S. Frazer as the named defendant in the case.
[11]  See order, entered July 31, 1992 (Doc. no. 434).
[12]  Plaintiffs' supplemental memorandum in support of the goals of proposed consent decree, filed March 7, 1994 (Doc. no. 538), appendix A.
[13]  Id.
[14]  This event was described in the March 16, 1984, memorandum as follows: "Perhaps the most undigestible example of practices which negatively affect minority employment is the one in which the [Graduate Civil Engineer] register which included ten minorities was abolished on March 30, 1983 by the apparently arbitrary inclusion of the requirement that the EIT examination be passed." Id.
[15]  See transcript of third day of trial, held June 17, 1992, at 3-56.
[16]  Id. at 20-21.
[17]  Multiple registers were formed simultaneously for certain job classifications with applicants being eligible for each register on the basis of different entrance requirements. The types of registers formed simultaneously for a single job classification included: (a) open-competitive registers; (b) promotional registers; and (c) reemployment registers. Applicants are determined to be eligible for each of these types of registers on the basis of different criteria. Applicants eligible for both an open-competitive and a promotional register would be ranked on both, but their scores and ranks on each register could, and often would, be different because the scoring procedures differ from one register type to another and the number and identity of persons on each type register are different. An applicant who is ineligible for one type of register could be eligible for the other type.
[18]  See Reynolds v. Roberts, 846 F.Supp. 948 (M.D.Ala.1994).
[19]  See Reynolds v. Alabama Dep't of Transp., 1994 WL 899259 (M.D.Ala. Mar.16, 1994) (Doc. no. 553).
[20]  See order, entered July 8, 1995 (Doc. no. 665).
[21]  Reynolds, 1994 WL 899259, at *27.
[22]  See report of points of agreement and disagreement regarding formula for determination of remedies under article twenty of consent decree I, filed August 28, 1995 (Doc. no. 727) (hereinafter cited as "August 28 report").
[23]  August 28 report, at 1-2.
[24]  Id. at 3-4.
[25]  Id. at 4.
[26]  Joint report regarding issues to be determined by the court on back-pay formula, filed September 11, 1995 (Doc. no. 740), at 1.
[27]  Id.
[28]  Id.
[29]  Id. at 1-2.
[30]  See transcript of first day of hearing on statistical formula utilization, individual claims, and attorneys' fees, held September 14, 1995 (hereinafter cited as "transcript of September 14, 1995, hearing"), at 157-60.
[31]  Id.
[32]  See order, entered November 30, 1995 (Doc. no. 845).
[33]  See Reynolds v. Alabama Dep't of Transp., 926 F.Supp. 1077 (M.D.Ala.1996).
[34]  Id. at 1080 (quoting August 28 report, at 3).
[35]  Id. at 1081.
[36]  Id. (footnote omitted).
[37]  Id.
[38]  Id. at 1082.
[39]  Id. at 1083-84.
[40]  Id.
[41]  Id. (footnotes omitted).
[42]  See order, entered May 16, 1996 (Doc. no 1023).
[43]  Id. at 1.
[44]  Id. at 2-3. The court further noted that "whether the eligibility formula or backpay equation will use transformed data is not reached at this time, pending the parties' negotiations on this issue. The parties shall jointly file a report by no later than 4:00 p.m. on Friday, May 17, 1996, informing the court of the result of their negotiation."
[45]  Order, entered May 16, 1996 (Doc. No. 1024).
[46]  Id.
[47]  Id.
[48]  Id. (emphasis added).
[49]  See order, entered May 28, 1996 (Doc. no. 1042).
[50]  Id. at 2 (emphasis added).
[51]  Id. at 2-4. The court then ordered "that logarithm adjustments shall be performed on pay data at the eligibility level; unadjusted actual salaries shall be used for the calculation of the backpay equation; and logarithm adjustments shall be used for education data in both the eligibility formula and the backpay equation." Id. at 4. See order, entered May 20, 1996 (Doc. no. 1030).
[52]  Order, entered May 28, 1996 (Doc. no. 1042) at 4-5.
[53]  Joint submission under seal of results of eligibility formula and back-pay equation with respect to the non-licensed engineer line of progression, filed May 31, 1996 (Doc. no. 1048), at 5.
[54]  Order, entered June 11, 1996 (Doc. no. 1072).
[55]  See order, entered October 16, 1996 (Doc. no. 1296).
[56]  See order, entered October 23, 1996 (Doc. no. 1307).
[57]  Id. at 8.
[58]  Id. at 9.
[59]  Id. at 4.
[60]  Id. at 7.
[61]  Id.
[62]  Id.
[63]  Id.
[64]  Id. at 7-8.
[65]  See order, entered November 7, 1996 (Doc. no. 1319).
[66]  See order, entered November 22, 1996 (Doc. no. 1338).
[67]  See order, entered November 25, 1996 (Doc. no. 1347).
[68]  See order, entered December 5, 1996 (Doc. no. 1404).
[69]  See order, entered December 5, 1996 (Doc. no. 1403).
[70]  See defendants' report on final backpay formula calculations, filed December 31, 1996 (Doc. no. 1453).
[71]  See order, entered January 3, 1997 (Doc. no. 1461).
[72]  Order, entered January 3, 1997 (Doc. no. 1467).
[73]  Order, entered January 3, 1997 (Doc. no. 1465).
[74]  See order, entered January 3, 1997 (Doc. no. 1464).
[75]  Id.
[76]  See Reynolds v. Alabama Dep't of Transp., 955 F.Supp. 1428 (M.D.Ala. 1997).
[77]  Id.
[78]  See order, entered March 27, 1997 (Doc. no. 1710).
[79]  See order, entered April 16, 1997 (Doc. no. 1785).
[80]  See notice of appeal, filed April 22, 1997 (Doc. no. 1804).
[81]  See notice of appeal, filed April 25, 1997 (Doc. no. 1815).
[82]  Order, entered April 16, 1997 (Doc. no. 1785).
[83]  It is important to emphasize that the court is addressing the establishment of a class-wide liability claim, not a claim based solely on individual liability.
[84]  In Bonner v. Prichard, 661 F.2d 1206, 1209 (11th Cir.1981) (en banc), the Eleventh Circuit Court of Appeals adopted as binding precedent all of the decisions of the former Fifth Circuit handed down prior to the close of business on September 30, 1981.
[85]  For a discussion of the various methods of establishing significant disparate impact, see Richardson v. Lamar County Bd. of Educ., 729 F.Supp. 806, 816 (M.D.Ala.1989) (Thompson, J.), aff'd, 935 F.2d 1240 (11th Cir.1991).
[86]  See order, entered May 16, 1996 (Doc. no. 1023).
[87]  See transcript of telephone conference, held September 3, 1997, at 8; transcript of telephone conference, held September 9, 1997, at 6-7; transcript of first day of non-jury trial, held September 15, 1997, at 32; see also defendants' motion for clarification of burden of proof, or, in the alternative, to continue trial, filed on May 19, 1997 (Doc. no. 1874).

The Adams intervenors take issue with both the plaintiffs' and the defendants' positions, and argue that the consent decree is silent on the issue. Their counsel stated:
"And I think that the plaintiffs are arguing that there is an admission. And I think the defendants are that's foreclosed, and it can't be reopened. We're saying that the Consent Decree doesn't say what it doesn't say."
Transcript of first day of non-jury trial, held September 15, 1997, at 30.
However, although they did not sign the August 28 report, and do not consent to the use of a formula, the Adams intervenors do not oppose the use of a mathematical formula to settle backpay claims for "individually identified victims of the defendants' past discrimination." Adams intervenors' opposition to plaintiffs' proposal to use a formula to award relief under Article XX of consent decree I, filed January 9, 1996 (Doc. no. 885), at 1. However, they object to the use of a formula for any other relief, such as instatement or promotions. Id.; Adams intervenors' statement of position concerning backpay formula issues, filed May 6, 1996 (Doc. no. 1005).
[88]  Transcript of telephone conference, held September 9, 1997, at 7.

In McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), the Supreme Court established an allocation of the burden of production and an order for the presentation of proof in Title VII non-class-wide, individual discrimination cases. St. Mary's Honor Ctr. v. Hicks, 509 U.S. 502, 506, 113 S.Ct. 2742, 2746, 125 L.Ed.2d 407 (1993). Under the McDonnell Douglas approach, an employee has the initial burden of establishing a prima-facie case of unlawful race discrimination by a preponderance of evidence. 411 U.S. at 802, 93 S.Ct. at 1824. A prima facie case requires "evidence adequate to create an inference that an employment decision was based on a[n] [illegal] discriminatory criterion." Teamsters v. United States, 431 U.S. 324, 358, 97 S.Ct. 1843, 1866, 52 L.Ed.2d 396 (1977). An employee may establish a prima facie case of discrimination by showing: (1) he belongs to a protected class; (2) he was subjected to an adverse job action, such as a discharge or a failure to promote; (3) his employer treated similarly situated employees outside his classification more favorably; and (4) he was qualified to do the job. McDonnell Douglas, 411 U.S. at 802, 93 S.Ct. at 1824.
If the employee establishes a prima-facie case, the burden then shifts to the employer to rebut the presumption by producing sufficient evidence to raise a genuine issue of fact as to whether the employer discriminated against the employee. This may be done by the employer articulating a legitimate, non-discriminatory reason for the employment decision, which is clear, reasonably specific and worthy of credence. The employer has a burden of production, not of persuasion, and thus does not have to persuade a court that it was actually motivated by the reason advanced. McDonnell Douglas, 411 U.S. at 802, 93 S.Ct. at 1824; Texas Dept. of Community Affairs v. Burdine, 450 U.S. 248, 253-55, 258, 101 S.Ct. 1089, 1093-94, 1096, 67 L.Ed.2d 207 (1981). "If the trier of fact finds that the elements of the prima facie case are supported by a preponderance of the evidence and the employer remains silent, the court must enter judgment for the plaintiff." O'Connor v. Consolidated Coin Caterers Corp., 517 U.S. 308, 116 S.Ct. 1307, 1309, 134 L.Ed.2d 433 (1996).
Once the employer satisfies this burden of production, the employee then has the burden of persuading the court that the proffered reason for the employment decision is a pretext for discrimination. The employee may satisfy this burden either directly by persuading the court that a discriminatory reason more than likely motivated the employer or indirectly by persuading the court that the proffered reason for the employment decision is not worthy of belief. By so persuading the court, the employee satisfies his ultimate burden of demonstrating by a preponderance of the evidence that he has been the victim of unlawful discrimination. Burdine, 450 U.S. at 256, 101 S.Ct. at 1095.
[89]  Based the evidence presented, the court credits the representations of plaintiffs' and defendants' counsel, who were signatories (either personally or through prior counsel) to the consent decree and the August 28 report, that the consent decree should not be read as silent on the issue of class-wide liability. Although the Adams intervenors, who were not signatories to the decree or the report, lack standing to challenge the award of backpay to the plaintiff class and thus have no basis to challenge this reading of the consent decree and the report for backpay purposes, the court will still note that it rejects their reading of the consent decree as being silent on the issue of class-wide liability.
[90]  Reynolds, 1994 WL 899259, at *2.
[91]  Reynolds, 1994 WL 899259, at *2 (emphasis added).
[92]  Id. at *27 (emphasis added).
[93]  See order, entered December 10, 1993 (Doc. no. 499), exhibit A.
[94]  Id. (emphasis added).
[95]  Id.
[96]  During the first day of the resumption of trial in this lawsuit, the exchange between the court and defendants' counsel was as follows:

"THE COURT: And it's defendants' position that all class-wide issues are resolved, that the Court did not address it again, the disparate impact on a class-wide basis, all I can do is consider these claims on a Burdine approach, and that's it. Am I correctly summarizing that?
"[DEFENDANTS' COUNSEL]: Yes.
"THE COURT: And also because disparate impact is by nature class-wide, I can't consider disparate impact claims at all.
"[DEFENDANTS' COUNSEL]: Yes."
Transcript of first day of non-jury trial, held September 15, 1997, at 32.
[97]  Indeed, the defendants have amended their defenses in this litigation to assert that the plaintiffs' disparate-impact claims are barred by the eleventh amendment to the United States Constitution. See Reynolds v. Alabama Dept. of Transp., 976 F.Supp. 1431 (M.D.Ala.1997); see also defendants' motion to dismiss disparate impact claims, filed August 27, 1997 (Doc. no.2063).
[98]  Order, entered December 10, 1993 (Doc. no. 499), exhibit A.
[99]  In addition, the court finds it incredible that the defendants would not have mentioned such a restriction to the court, if such existed.
[100]  Paragraph 5(a) of Article XIII provides:

"The following persons (if they have Civil Engineering or Civil Engineering Technology degrees) will be offered employment in the [Graduate Civil Engineer] job or in the job they would now hold with the Highway Department in the absence of the EIT and associated requirements (including the recency of degree requirement), whichever is higher, with the following credited service dates:


                                  CREDITED SERVICE DATE
     Alfedo Acoff                     March 30, 1983
     Peggy Vonsherrie Allen           March 30, 1983
     Christopher Zaubuike             March 30, 1983
     Jeffery W. Brown                 March 30, 1983
     Willie F. Franklin               March 30, 1983
     Macon Hinton                     March 30, 1983
     Wayne M. Leonard                 March 30, 1983
     Ronald D. Newsome                March 30, 1983
     Adenrele Odutola                 March 30, 1983
     Rickey Richardson                March 30, 1983"
(emphasis added).                           Transcript of September 14, 1995, hearing, at 38.

[101]  Transcript of fairness hearing, held January 19, 1994, at 46.
[102]  Id. at 47.
[103]  The exchange was as follows:

"THE COURT: Let me say, what you're telling me is we're not clearly at a point where there has been no finding or that the Plaintiffs have to establish class-wide discrimination, but at the same time we don't have all what you call the `baggage' from all the other cases. It seems like we're somewhat in the middle.
"[DEFENDANTS' COUNSEL]: I think that's where we are, frankly.
[104]  The court cannot overlook that it noted its dissatisfaction with the posture of the case as posited by defendants' counsel. The court stated that "If we're in the middle, which is a horrible place to be  because nobody knows where we are, that could be anywhere between here and Jupiter...." Id.
[105]  Id. at 44.
[106]  Id.
[107]  Id. at 45 (emphasis added).
[108]  See proposed consent decree, filed July 19, 1988 (Doc. no. 183), article XIII, at 42; proposed consent decree, filed March 22, 1991 (Doc. no. 266), article XIV, at 38-39.
[109]  The court has also reviewed the representations of the attorneys who were involved in the drafting of consent decree I and the August 28 report, and the court specifically credits the representations of plaintiffs' counsel as to what the parties intended with regard class-wide liability in consent decree I and in the August 28 report. See, e.g., transcript of September 14, 1995, hearing, at 34-35.
[110]  Transcript of telephone conference, held September 9, 1997, at 6.
[111]  At times, defendants' counsel has suggested that the dispute over class-wide liability may be more one of "linguistics" rather than substance. See e.g., transcript of September 14, 1995, hearing, at 29. The court does not quite understand what defendants' counsel meant by this comment.

The court does, however, agree that consent decree I and the August 28 report could be understood to mean that the parties intended that the case proceed `as if' there had been a finding of class-wide liability in favor of plaintiffs without the defendants actually having to admit it. In other words, the parties agreed to the `procedural posture' that the plaintiffs would enjoy the benefit of a finding of class-wide liability without the defendants having admitted such. Indeed, the court adopts this approach as an alternative resolution of the class-wide liability issue.
[112]  For example, in their memorandum concerning remaining formula issues, filed on July 5, 1996 (Doc. no. 1112), at 3, the defendants stated that the formula represents a "settlement" of backpay issues, and it "does not result in a realistic calculation of how much backpay should be awarded, or to whom." See also Pettway, 494 F.2d at 260 ("The method of calculating a class-wide back pay award must not be rigid. This results from the impossibility of calculating the precise amount of back pay.... Therefore, in computing a back pay award two principles are lucid: (1) unrealistic exactitude is not required, (2) uncertainties in determining what an employee would have earned but for the discrimination, should be resolved against the discriminating employer.").
[113]  Counsel for the plaintiffs and defendants agreed that, although the parties had agreed to use a formula, they expected the court to work out many of the details. See transcript of second day of hearing on statistical utilization, individual claims, and attorneys' fees, held September 15, 1995 (hereinafter cited as "transcript of September 15, 1995, hearing"), at 426-433.
[114]  In an order entered on January 22, 1996, at the request of the Transportation Department, and over a strong objection from the plaintiffs, the court modified the August 28 report so as to relieve the department from compliance with it as written. See Reynolds v. Alabama Dep't of Transp., 926 F.Supp. 1077 (M.D.Ala.1996). It important to note that, if it should be determined on appeal that the court erred in its finding of class-wide liability, the court believes, for the reasons that follow, that this January 22 order should be set aside, and a holding entered in favor of the plaintiffs.

As explained earlier in this memorandum opinion, the court agreed to the Transportation Department's request despite the following: (1) the defendants were fully aware at the time the August 28 report was filed that the second equation in the report indicated that the race coefficient was to be added  that is, they did not make a mistake in drafting the equation; and (2) after specific questioning by the court as to whether the parties intended for the sign to switch from a subtraction sign in the first equation to an addition sign in the second equation, defendants' counsel responded that they did, and that both equations were correct. Id. at 1081-82. The court's decision to modify the report was strongly informed by the belief that, in calculating "what a class member would have earned in the absence of discrimination," id. at 1084, the parties would follow the traditional class-action approach for determining backpay, with the plaintiffs having the benefit of a class-wide determination of liability in their favor. In other words, the plaintiffs would not have sacrificed anything under the formula that they would have enjoyed had they been successful in a full trial. Absent this premise, the plaintiffs' argument  that it was the specific intent of the parties that the race factor be added twice because, simply put, it would result in higher awards for the class members  takes on a different meaning in retrospect. The parties would then have agreed that the Transportation Department would pay more in return for the plaintiffs' having given up their opportunity to establish class-wide liability at trial and in return for class-wide liability not being assumed under the formula.
[115]  See order, entered July 5, 1995 (Doc. no. 665).
[116]  August 28 report.
[117]  Id.
[118]  August 28 report, at 1-2.
[119]  Supplemental joint report on points of agreement regarding proposed formula for article twenty backpay remedies, filed May 3, 1996 (Doc. no. 1007), at 9.
[120]  Defendant's report concerning organization of department and distribution of classifications, filed July 5, 1996 (Doc. no. 1111).
[121]  Id.
[122]  See transcript of fifth day of hearing on back pay, individual claims, etc., held May 22, 1996 (hereinafter cited as "transcript of May 22, 1996, hearing"), at 729-730.
[123]  See transcript of telephone conference, held July 10, 1996, at 13.
[124]  Defendant's report concerning organization of department and distribution of classifications, filed July 5, 1996 (Doc. no. 1111), at 4.
[125]  See transcript of first day of hearing on back pay, individual claims, etc., held May 13, 1996 (hereinafter cited as "transcript of May 13, 1996, hearing"), at 89.
[126]  Transcript of fourth day of hearing on back pay, individual claims, etc., held May 21, 1996 (hereinafter cited as "transcript of May 21, 1996, hearing"), at 507.
[127]  Transcript of May 21, 1996, hearing, at 508.
[128]  See transcript of telephone conference, held July 10, 1996, at 13.
[129]  August 28 report, at 1-2.
[130]  Transcript of September 14, 1995, hearing, at 240.
[131]  Id. at 233.
[132]  Id. at 116.
[133]  See transcript of May 21, 1996, hearing at 512-514.
[134]  Id. at 520.
[135]  See Id. at 520.
[136]  Transcript of May 13, 1996, hearing, at 108.
[137]  Transcript of third day of hearing on back pay, individual claims, etc., held May 15, 1996 (hereinafter cited as "transcript of May 15, 1996, hearing"), at 394.
[138]  See transcript of May 22, 1996, hearing, at 678.
[139]  Id. at 699.
[140]  Id. at 699-700.
[141]  See transcript of May 13, 1996, hearing, at 59.
[142]  See special supplemental report of David Lasater, filed May 16, 1996 (Doc. no. 1025), exhibits 7 and 8.
[143]  See transcript of May 22, 1996, hearing, at 744.
[144]  See id. at 745.
[145]  See id.
[146]  See id. at 714.
[147]  August 28 report, at 3.
[148]  Id. at 3-4.
[149]  Id. at 4.
[150]  See supplemental joint report on points of agreement regarding proposed formula of article twenty backpay remedies, filed May 3, 1996 (Doc. no. 1007), at 8.
[151]  See plaintiffs' memorandum on back-pay formula for hearing on May 21, 1996, filed May 20, 1996 (Doc. no. 1029).
[152]  See expert report of May 20, 1996 of Dr. Edwin L. Bradley and Dr. Dennis D. Wallace, filed May 20, 1996 (Doc. no. 1027), at 3.
[153]  Id.
[154]  Defendants' pre-trial memorandum concerning formula issues, filed May 9, 1996 (Doc. no. 1014), at 11; see also deposition of Tommy Flowers, taken December 18, 1991, filed with the court, at 211 (although appraisal scores are of some very limited utility, they "should not be overly relied upon").
[155]  In addition to arguing that appraisal scores are not used by the defendants in a meaningful way, the plaintiffs claim that appraisal scores are race-tainted. That is, they claim that, on average, black employees received lower appraisal scores than white employees. The defendants respond with two arguments. First, they maintain that most appraisal scores are not racetainted. Second, they claim that, for those few divisions in which appraisal scores are racetainted, they can remove the taint by raising the average appraisal score for black employees to the same level as that of white employees but preserving the ranking of black employees relative to one another. Because the court has concluded that appraisal scores were not used in a meaningful way, it does not reach this issue. However, the court notes that credible evidence reflects that the defendants' proposed method of removing the racial taint was ineffective, and that the defendants' method of detecting taint was extremely weak.
[156]  See transcript of May 15, 1996, hearing, at 237.
[157]  See id.
[158]  Id.
[159]  See order, entered May 20, 1996 (Doc. no. 1030) letter, filed May 20, 1996 (Doc. no. 1028).
[160]  August 28 report, at 2.
[161]  See transcript of May 13, 1996, hearing, at 21-22, 23.
[162]  The resumption of this trial has been ongoing since September 15, 1997.
[163]  With the above descriptions and conclusions regarding the August 28 report, one could reasonably conclude that the report reflects a carefully crafted bargain. The plaintiffs gave up the right to present non-statistical evidence at stage two and agreed to allow the defendants to attempt to exclude a cohort group even though the defendants had not drawn into question the right of the subgroup to move to stage two. In return, the defendants agreed that statistical proof would be sufficient to prove economic harm, thereby entitling a class member to backpay.
[164]  See transcript of May 22, 1996, hearing, at 644, 648-649.
[165]  See defendants' pre-trial memorandum concerning formula issues, filed May 9, 1996 (Doc. no. 1014), at 5.

Using a one-tailed test, 1.65 standard deviations equates to approximately 95% confidence. In other words, if two figures differ by 1.65 standard deviations, and they are based upon a normal distribution, the court can be approximately 95% certain that the difference is not due to chance or random distribution. The parties have agreed that a one-tailed test is the appropriate test. Id. at 4.
[166]  Because 95% certainty corresponds to approximately 1.65 standard deviations, applying either test will yield the same result.
[167]  In addition, the defendants make an argument that there is a "band of error" around the line depicting the average white salary, and that the black average must be below the white average by at least the amount of this band of error for the difference to be considered statistically significant. The defendants maintain that if the black average salary is within the band of error, but below the white average salary, the difference between the two averages could be due to chance. See transcript of May 22, 1996, hearing, at 647-48. Because, as explained later, the court rejects the defendants' position altogether, there is no need to address the band-of-error argument.
[168]  See defendants' memorandum concerning case law on "convincing" statistical level of significance, filed June 7, 1996, at 3 (Doc. no. 1068) (1.645 standard deviations is statistically significant); plaintiffs' memorandum on when to reject the "null hypothesis," filed June 7, 1996, at 7 (Doc. no. 1067) (.05 confidence level appropriate to reject the null hypothesis). To be sure, the defendants argue that the court should exclude a cohort group if the line representing the average black salary is 1.645 standard deviations below the line representing the average white salary. As stated, the court has concluded that the line representing the average black salary must be above the line representing the average white salary. What is important here is the defendants' position that a difference in average salary of 1.645 standard deviations is statistically significant.
[169]  Because the parties have agreed that the difference must be statistically significant, and because they also agree that a difference of 1.65 standard deviations is sufficiently statistically significant, the court need not decide whether either the burden of proof placed on the defendants at the intermediate step, or the burden of proof placed on them at stage two to defeat a class member's claims, is comparable to a difference of 1.65 standard deviations. What the court can say, however, is that, in statistical terms, the confidence level would have to be very high in both instances.
[170]  August 28 report, at 2.
[171]  Order, entered January 22, 1996 (Doc. no. 896).
[172]  See transcript of May 14, 1996, hearing, at 272.
[173]  See id. at 274.
[174]  Id. at 275, 278-279.
[175]  See transcript of May 15, 1996, hearing, at 381.
[176]  See expert report of May 8, 1996 of Dr. Edwin L. Bradley and Dr. Dennis D. Wallace, filed May 8, 1996 (Doc. no. 1012), appendix A. The plaintiffs' experts compared black and white employees in the same percentile of earnings within their respective racial groups. This comparison indicates that higher-earning black employees may well have suffered greater losses from discrimination than lower-earning black employees.
[177]  August 28 report, at 2 (emphasis added).
[178]  See order, entered May 20, 1996 (Doc. no. 1030); letter, filed May 20, 1996 (Doc. no. 1028).
[179]  The parties agree that the amount formula does not provide for backpay to the plaintiff class members whose salaries exceeded the average salaries of their white counterparts, although these class members may very well have still been victims of race discrimination. However, as circuit law has made clear, the calculation of "the precise amount of backpay" is an "impossibility." Pettway, 494 F.2d at 260. The amount formula, therefore, simply makes a generalized estimate of what the class, as a whole, is entitled to receive in backpay. As a means of attempting to provide each class member with an amount of backpay that matches the amount of discrimination he has faced, the court adopted the "redistribution" formula of Court-Appointed Expert Fine. See order, entered January 3, 1997 (Doc. no. 1464). This formula uses the differences between a class member's actual pay and the average salaries of black comparators and white comparators to compute a class member's share of the total backpay award, taking into account that only a portion of the individual variation in class members' salaries is attributable to racial discrimination. See report of expert witness Benjamin L. Fine on small cohort and redistribution issues, entered December 18, 1996 (Doc. no. 1443), at 6-9.

The redistribution formula adopted by the court is as follows:
                     A                BP - AP
                    ---               -------
"Backpay award =     B  (WP - BP)  +     2       , where
WP = the pay that a typical white employee with the same years of service and years of education as a given class-member would have earned, as determined by plugging those years into the backpay equation;
BP = the pay that a typical black employee with the same years of service and years of education as a given class-member would have earned, as determined by plugging those years into a multiple regression equation of the same form as the backpay equation, but derived from the black cohort members;
AP = the class-member's actual pay for the year or years in question;
A = the total backpay awarded to the cohort using the backpay equation; and
B = the total backpay awarded to the cohort as determined by the assigning to each class-member an amount of backpay equal to
                     (BP - AP)
                     ---------
     (WP - BP)   +       2     ."
Id. at 2.

