#### George A. MADDOX, William D. Abad, Eric D. Shepherd, individually and on behalf of all other persons similarly situated, Plaintiffs-Appellants, v. W. Graham CLAYTOR, Secretary of Navy, in his official capacity, his agents, employees, and successors in office, Defendant-Appellee.

No. 84-8006.

United States Court of Appeals, Eleventh Circuit.

July 12, 1985.

*1541Herbert E. Phipps, Albany, Ga., Gail J. Wright, NAACP Legal Defense Fund, New York City, for plaintiffs-appellants.

Albert L. Grieshaber, Albany, Daniel E. O’Connell, Jr., Litigation Office, Office of Gen. Counsel, Dept, of Navy, Washington, D.C., Robert L. Van Saghi, Major U.S. Marine Corps. Off. Staff Judge Advocate, Albany, Ga., John L. Lynch, Asst. U.S. Atty., Macon, Ga., for defendants-appellee.

Before RONEY and HENDERSON, Circuit Judges, and TUTTLE, Senior Circuit Judge.

ALBERT J. HENDERSON, Circuit Judge:

George Maddox and William Abad appeal individually and, along with Eric Shepherd, as class representatives from the judgment of the United States District Court for the Middle District of Georgia in favor of the Secretary of the Navy (Secretary), the ap-pellee and defendant in this Title VII action. The appellants are blacks, representing themselves1 and the class of all black civilian federal employees2 at the Marine Corps Logistics Support Base Atlantic in Albany, Georgia (the Base), who claim to have been victims of racially discriminatory promotional practices in violation of Title VII of the Civil Rights Act of 1964, as amended by the Equal Employment Opportunity Act of March 24, 1972, 42 U.S.C. § 2000e-16(b). Only the years 1977, 1978 and 1979 are at issue here.

Congress established the Base in 1952 to overhaul and repair equipment and to store military supplies. Prior to July 1,1975, the Base organization included only seven operational divisions: Comptroller, Facilities and Services, Headquarters Battalion, Material, Personnel, Plans and Systems and Repair. The Base paid its approximately 1700 civilian workers under separate federal wage scales. The Wage Grade (WG) scale, which varied in accordance with the local economy, governed over 1100 blue collar workers, while the remaining 600 or so white collar employees were under the nationally uniform General Schedule (GS) scale.

Both the GS and WG pay schedules are divided into numbered levels or grades, such as GS-5. Workers whose jobs call for different duties may nevertheless be at the same pay level. Thus, WG-5 includes not only the highest paid unskilled and semiskilled blue collar workers (food preparers, manual laborers, etc.) but also the lowest paid skilled workers (electricians, metal workers, etc.), who generally begin at that level and may progress as high as WG-16. Each pay level is subdivided into “steps,” the higher steps providing higher pay at that level. The size of this workforce remained relatively stable from 1952 to 1975. At the end of 1975, roughly 30% of the workforce was black. The 1970 Census for *1542Dougherty and Lee Counties, the Albany Standard Metropolitan Statistical Area (Albany SMS A), discloses that of 33,103 persons employed in the area, 10,069— 30.42% — were black. D.Ex. 8a, 8b.

Prior to July 1, 1975, the worldwide inventory control operations of the Marine Corps Supply Activity (MCSA) were located in Philadelphia. 821 GS and 6 WG employees staffed this Inventory Control Point (ICP).3 The overwhelming predominance of GS positions reflected the high degree of white collar skills required in obtaining, transporting and maintaining in strategic locations throughout the world a wide variety of military equipment and supplies. Of these 827 employees, about 280 — 34%— were black. R.Vol. 9 p. 50. These specialized operations used employees already trained within the Department of Defense (DOD) because the inventory personnel of even the largest private retailers lacked experience in handling such varied items in the context of worldwide, in-the-field deployment. Trial Transcript Yol. Ill, p. 55.

On July 1, 1975, ICP employees were informed, by way of a directive of the DOD, that the inventory control center would be moved in 1976 to the Base in Albany. Although the DOD strongly encouraged these employees to transfer from Philadelphia to Albany, 46% of whites and 90% of blacks declined the invitation. The transfer of ICP thus resulted in a dilution of the percentage of its black employees from 34% to 10% — 28 of the 280 transferees. Because the ICP’s responsibility for global Marine Corps inventory control continued during this period, the loss of so many of the Philadelphia workers necessarily accelerated the hiring effort for this unit.

ICP’s April, 1976 arrival in Albany also caused dramatic changes in the composition of the Base labor force. Addition of the 252 white and 28 black transferees lowered the proportion of blacks in the combined Base workforce from 30 to 26.9%. Because all or nearly all transferees were GS grade scale, dilution was much more severe with respect to the proportion of blacks in white collar jobs. Though formerly only a third of Base workers had been GS scale, now a majority of positions at the Base were white collar. Five new divisions were added to the Base’s organizational scheme: Supply Operations, Technical Operations, Procurement (Contracts), Provisioning and Logistics Systems Support.

To fill the remaining 547 white collar jobs in these five new divisions as quickly as possible, the Base first promoted WG personnel who were qualified and willing to change jobs. Unfortunately, the Base lacked the resources to train its workers for ICP positions. To overcome this impediment, the Base simultaneously embarked on a DOD-wide solicitation of applicants. Applications were also sought from colleges and other sources from which the DOD has traditionally hired these specialists. Of course, the Base continued its ordinary personnel functions with regard to all Base jobs, and area residents who qualified for federal service4 were considered for inventory command positions too.

The personnel officer’s task was complicated not only by the need to fill the positions very quickly but also by the almost kaleidoscopic array of grade levels and types of jobs. During the years 1976 through 1979, the Base workforce included 181 distinct positions which required a very broad variety of skills, education and numerous other qualifications. D.Ex. 1, 2, 4a. Even within a given type of position the duties varied considerably, depending on *1543the pay level occupied by the employee. Considering the level as well as the nature of the jobs, the Base had 581 different job categories. Further confusing the employment picture during this period are the effects of the Base’s inability to fill all the vacant ICP positions, perhaps coupled with hiring freezes, phaseouts or cutbacks. For instance, by 1979 the total workforce was only 2,225, with 528 blacks (28.7%) and 1,697 whites (76.2%).

The Base civilian employment practices are governed by the regulatory scheme contained in the *Federal Personnel Manual (FPM)*and its 26 supplements promulgated by the Office of Personnel Management (OPM). For GS positions, extensive qualification standards for each job series in the federal service are published in OPM Handbook X-118; corresponding standards for WG jobs are set out in OPM Handbook X-118C. The Secretary of the Navy added to these the “Civilian Personnel Instructions,” and the Base also issued local instructions.

Other than “career” promotions dependent solely on a worker’s seniority and satisfactory work performance at a given level,5 the Base awards promotions via a competitive process. That process is initiated by the director of the division in which a vacancy exists, who submits his description of the position for the approval of the personnel office. If the office approves the proposal, a specialist then searches the *FPM*to determine which listed position most closely corresponds to the proposed job. The *FPM*lists very specifically the basic eligibility requirements and the special skills required for every federal service position. The specialist also consults the division director, and perhaps the immediate supervisor of the vacant position, to determine whether any additional requirements are necessary. Finally, the specialist establishes a list of three to seven job related criteria (“job elements”) and devises a crediting plan under which these various special skills are assigned weighted point values. The Merit Promotion Announcement is then circulated for at least ten days and until the announced cutoff date. The announcement describes the duties and location of the position, the scope of the Base’s solicitation of applications for the vacancy (e.g., on-Base only, DOD-wide, etc.), the basic experience requirements taken from the *FPM*and the particular job elements.

Applications might be solicited from Base personnel only. More often, the Base would also consider applications from the OPM register (including all federal-qualified residents in the Albany area), from the Department of the Navy, from the entire Department of Defense, or from two or more of these groups, depending on the nature of the vacancy. For professional/technical positions, the Base recruits both on Base and throughout the DOD worldwide. For management/administrative vacancies, the Base solicits on Base, DOD-wide and throughout the federal service. Entry-level clerical workers are more often chosen from the federal registers maintained by OPM in Atlanta, and mid-level clerical positions are filled by internal promotion. The remaining GS jobs and nearly all WG occupations are filled from the Base and the OPM register. The more specialized the skills needed and the higher the grade level of the vacancy, the broader the recruitment efforts.

Applicants must complete personnel office forms detailing their work experience. Additionally, each Base worker’s annual Performance Appraisals are retrieved by the personnel office. Applicants may add any other information they choose. All this information is assembled in the applicant’s “master file.” A staffing specialist in the personnel office then reviews these files to see which applicants meet the minimum eligibility requirements dictated by the *FPM*and either X-118 (for a GS vacancy) or X-118C (for a WG position). For example, if the vacancy is for a mid-level mail and filing clerk (typing), a GS-5 posi*1544tion, the *FPM*prohibits hiring a person who lacks two years of experience, one general and one special. The X-118 sets out specific guidelines for classifying and measuring the work and school experiences that are deemed necessary to basic eligibility. Applicants without the basic qualifications are designated “unqualified.” The personnel office has no authority to deviate from the *FPM,*X-118 or X-118C.

The personnel office then requests the division director to appoint a ranking panel composed of two or usually three technical or subject matter experts familiar with the particular vacant position. The director’s appointments are subject to personnel office verification of the appointees’ ability to rank applicants for the particular job. The Base’s regulations do not require that each panel have at least one black, although on a number of occasions blacks have served as panel members. R.Ex. 43-44. The personnel office then solicits from each qualified applicant’s current supervisor (whether on or off the Base) an appraisal in accordance with the job elements set out in the Merit Promotion Announcement. These Supervisory Appraisals are added to the master files.

Under the supervision and instruction of a staffing specialist, the panel examines the master files, applies the previously developed job element crediting plan and ranks the applicants. For each job element, each panel member examines each applicant’s file for indications of past effort, training and experience, evaluating each applicant on a scale of one to four, with four denoting “outstanding” and three “satisfactory.” Then the panel members compare and discuss their ratings, reconciling their differences by consensus. Scores are sent to the personnel office, which tallies them and ranks the applicants in numerical order. Scores are kept confidential, and are known only by the ranking panel and personnel office. Those applicants who average 3.0 or higher are designated “highly qualified.” The names of the top five highly qualified applicants — or fewer if less than five are highly qualified — are placed on a certificate in alphabetical order, without disclosing the scores.

These “certified” applicants are referred to the selecting official, who is either the division director or, more often, the immediate supervisor of that particular position. The personnel office notifies the director if blacks are underrepresented at the level of the vacancy. R.Ex. 44. The selecting official must either personally interview the five employees or appoint an advisory interviewing panel to recommend one applicant. If the certificate contains only one or two names, the selecting official may send it back to the personnel office, which will add the three or four highest ranked “qualified” applicants. If the selecting official chooses to interview any of these added applicants, he must interview them all. Lee Deposition pp. 99-100.

Selection panels are usually employed when the vacancies are upper level or supervisory. The district court found that on a number of occasions blacks were panel members, and that where blacks were underrepresented at a level in which a vacancy existed, directors encouraged the selecting official and interviewing panel to select a qualified black. In some cases, qualification standards were altered in order to accommodate the selection of a black. R.Ex. 44. Finally, the selecting official decides which certified applicant gets the job. No written record is kept of the causes for the selecting panel or official’s failure to promote the other certified applicants.

The plaintiffs filed their individual and class claims on January 6, 1978. They alleged both disparate treatment of blacks and disparate impact resulting from Base promotion practices. Following extensive discovery, a four-day bench trial began on April 6, 1981. The district court heard the testimony of 44 witnesses and considered 110 depositions. The parties also admitted voluminous exhibits containing personnel data and statistical studies. A computer analyst, Martin Mador, presented statistical evidence on behalf of the plaintiffs. The defendant called two statistics experts, Drs. Charles Upton and Charles Kenny. The parties submitted proposed findings to the court in August, 1981.

*1545After extensive review, the district judge rejected these proposed findings as conclu-sory and lacking sufficient citation of support in the record and ordered the submission of revised proposed findings. The district court also granted the plaintiffs’ motion to submit the affidavit of Dr. Richard Drogin, a statistics expert who had been excluded from testifying at the trial.6 Dro-gin’s affidavit was submitted on December 14, 1982. On March 14, 1983, the defendant filed the affidavits of his experts in response to Dr. Drogin’s affidavits. The parties filed further responses through August 9, 1983. On November 4, 1983 the district court granted individual relief to Shepherd but ruled favorably to the Secretary on all other counts, finding that the defendant had successfully rebutted Abad’s prima facie showing and that the evidence did not make out prima facie cases on the remaining causes of actions.

EVIDENCE OF DISCRIMINATION

The appellants challenge the district court’s finding that the defendants countered Abad’s prima facie case and that the other plaintiffs, except for Shepherd individually, failed to carry their burdens of making out prima facie cases. The findings of fact of the district court are reversible only if they are clearly erroneous, thereby leaving the reviewing court with the definite and firm conviction that a mistake has been made. *Pullman-Standard v. Swint,*456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982); *United States v. United States Gypsum Co.,*333 U.S. 364, 68 S.Ct. 525, 92 L.Ed. 746 (1948). A unanimous Supreme Court has even more recently cautioned:

> This standard plainly does not entitle a reviewing court to reverse the finding of the trier of fact simply because it is convinced that it would have decided the case differently____ If the district court’s account of the evidence is plausible in light of the record viewed in its entirety, the court of appeals may not reverse it even though convinced that had it been sitting as the trier of fact, it would have weighed the evidence differently. Where there are two permissible views of the evidence, the factfinder’s choice between them cannot be clearly erroneous.

*Anderson v. City of Bessemer City,*— U.S. -, -, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985). Eight justices further agreed that Rule 52(a) operates not only with respect to findings based on the district judge’s credibility determinations but also to those predicated on physical or documentary evidence or inferences from other facts. *Id.*Significantly, the Court held that when an internally consistent credibility finding is challenged, the reviewing court can almost never find clear error. *Id.*at-, 105 S.Ct. at 1513.

The necessity of adhering to an appropriately deferential review here is underscored by the fact that both *Anderson*and *Pullman-Standard*concerned Title VII suits alleging racially discriminatory employment decisions.

As a class, the plaintiffs proceeded under both disparate treatment and disparate impact theories in an effort to prove that the Base made promotion decisions in a racially discriminatory manner. The evidence presented by the individual plaintiffs7 indi*1546cated they proceeded under a disparate treatment theory, and the district court analyzed their claims accordingly.

A. *Individual Claims of Discrimination*

A plaintiff asserting disparate treatment carries the ultimate burden of proving that the employment decision he challenges resulted from a racially discriminatory motive on the part of the decisionmaker. Under *McDonnell Douglas v. Green,*411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), the plaintiff must, by a preponderance of the evidence, make out a prima facie case. The model of prima facie proof suggested by the Court there requires the plaintiff to show:

> (i) that he belongs to a racial minority;

> (ii) that he applied and was qualified for a job for which the employer was seeking applicants;

> (iii) that, despite his qualification, he was rejected; and

> (iv) that, after his rejection, the position remained open and the employer continued to seek applicants from persons of complainant’s qualifications.

411 U.S. at 802, 93 S.Ct. at 1824, 36 L.Ed.2d at 677. The Court has since made clear, however, that this four-part model is not the only checklist by which to measure the plaintiff’s proof. Thus, *Furnco Construction Corp. v. Waters*cautioned: “This of course was not intended to be an inflexible rule, as the *[McDonnell Douglas*] Court went on to note that ‘the facts necessarily will vary in Title VII cases, and the specification above of the prima facie proof required from respondent is not necessarily applicable in every respect in differing factual situations.’ ” 438 U.S. 567, 575-76, 98 S.Ct. 2943, 2949, 57 L.Ed.2d 957, 966 (1978). *Accord, Texas Department of Community Affairs v. Burdine,*450 U.S. 248, 253 n. 6, 101 S.Ct. 1089, 1094 n. 6, 67 L.Ed.2d 207, 215 n. 6 (1981).

The former Fifth Circuit Court of Appeals accepted the Supreme Court’s suggestion to modify the *McDonnell Douglas*prima facie test where a wholly subjective employment system rendered the formal model an unrealistic standard. In *Crawford v. Western Electric Co., Inc.,*614 F.2d 1300, 1315 (5th Cir.1980), the panel found a prima facie case even though the black plaintiffs did not prove that they met Western’s qualifications for promotion. Noting that Western Electric used wholly subjective promotion qualification standards that were implemented and applied solely by whites, the panel “expressed a skepticism that Black persons dependent directly on decisive recommendations from Whites could expect non-discriminatory action.” *Id.*at 1316. In short, the utter subjectivity of the defendant’s qualification decisions rendered the plaintiff's burden of proving they were qualified impossible, no matter how valid their actual qualifications. Consequently, the court held that proof of the plaintiffs’ applications for promotions was, under the circumstances, proof of their qualified status for purposes of the *McDonnell Douglas*prima facie test.

Establishment of the prima facie case triggers a rebuttable presumption of discrimination. The defendant may rebut the presumption by bearing a burden of production to articulate a legitimate, nondiscriminatory reason for its decision.

With the factual questions thus framed, the plaintiff in turn has a full and fair opportunity to demonstrate by a preponderance of the evidence that the claimed reason is a mere pretext. This burden merges with the ultimate burden of persuasion, and the plaintiff must either “directly persuad[e] the court that a discriminatory reason more likely motivated the employer or indirectly [prove discrimination] by showing that the employer’s proffered explanation is unworthy of credence.” *Burdine,*450 U.S. at 256, 101 S.Ct. at 1095, 67 L.Ed.2d at 217. Under either approach, the plaintiff prevails unless the employer proves that the adverse action would have occurred even in the absence of discriminatory intent. *Mt.**1547*Healthy City School District Board of Education v. Doyle,*429 U.S. 274, 287, 97 S.Ct. 568, 576, 50 L.Ed.2d 471, 483-84 (1977); *Perryman v. Johnson Products Co.,*698 F.2d 1138, 1142 (11th Cir.1983).

1. *Maddox’s Individual Claim*

Maddox did not testify in person but at the trial submitted his pretrial deposition taken by the defendant’s counsel. The district court, assuming that the plaintiff intended to rely on this deposition, concluded Maddox had failed to make out a prima facie case. We agree.

According to his deposition, Maddox began work at the Base on August 12, 1974, as a WG-5 painter’s helper in the painting section of the repair division. Maddox Deposition p. 6. Having taken electrical courses at a local college, Maddox repeatedly asked repair shop supervisors whether there were any openings for WG-5 helpers in the auto electrical repair section, but each time he was told there were no vacancies. *Id.*pp. 4, 5, 8. Five months after he was hired, around January 1975, Maddox discovered that a white painter’s helper with only one month of Base employment had applied for an electrical repair vacancy. Maddox stated that there was no posted announcement and that he confirmed the opening by oral inquiry at the personnel office, which encouraged him to apply also. *Id.*pp. 9-11. Maddox stated that he, the white painter’s helper and perhaps others were interviewed by a panel but none were selected because someone terminated the proceedings. *Id.*p. 12. Maddox speculated that his complaints to Base officials and his union about the lack of a posted announcement may have prompted one of the officials to cancel the process. *Id.*p. 13. After January 1975, Maddox made no further applications for transfer. At some unspecified later time, but before April 1977, the Base filled two WG-5 auto electric helper positions with a white and a black from other divisions. Neither of these men had been interviewed by the original selecting panel. *Id.*pp. 9, 12. Maddox did not know anything about these men’s qualifications. *Id.*p. 25. In April 1977 he filed an EEO complaint. In July, 1977 he was made a temporary WG-5 auto electrical helper and in August the transfer became permanent. *Id.*p. 21. Maddox’s deposition also referred sketchily to other incidents, but he admitted that his sole complaint of discriminatory treatment arose from the fact that he was not transferred sooner to the auto electric section. *Id.*

Maddox’s deposition satisfies only two parts of the *McDonnell Douglas*test. Of course, he is a member of a protected group, and he applied to become a WG-5 auto electric helper. Given the district court’s finding that only highly qualified and qualified applicants were ever eligible for interviews under the Base’s promotion system, the fact that Maddox was interviewed indicates he at least met the qualification criteria. But his mere statements that the process was halted before the panel reached any decision and that after an unspecified period of time two similar positions were filled by a black and a white fall far short of proving the remaining elements — that he was rejected, and that after his rejection the position remained open, with the Base continuing to seek applicants of Maddox’s qualifications. It is hardly surprising that Maddox’s responses in a deposition taken by the opposing party fail to supply all the *McDonnell Douglas*prima facie elements. His unexplained failure to testify left his claim insufficiently defined and supported. No argument can be made here that absence of such proof should be excused under *Crawford.*The district court’s finding is not clearly erroneous.

2. *Abad’s Individual Claim*

Abad testified that he had worked in the Philadelphia ICP since 1954. In 1976, he was a GS-7 Supervisory Accounting Technician. By that time Abad had served in a supervisory capacity for seven years. R.Vol. 9, pp. 2, 10. He agreed to transfer to Albany knowing that such a supervisory position might not be available there, but that in any case he would retain his grade level and in the same field if at all possible. R.Vol. 9, pp. 13-14. Because *1548it turned out that Abad’s GS-7 position would have no supervisory duties in Albany, the Base invited him to apply for a GS-8 Supervisory Accounting Technician job in ICP that opened when the incumbent decided to remain in Philadelphia. The selecting panel, composed of one black and two whites, interviewed Abad and a longtime Base employee, Robert Slagel. The panel stated at the time that it chose Slagel because he had tenure and Abad did not. *Id.*p. 15.

Based on Abad’s testimony, the district court ruled he had proved a prima facie case but failed to rebut by a preponderance of the evidence the defendant’s articulated, legitimate reason for selecting Slagel — his tenure. This finding is not clearly erroneous. *Anderson, supra.*Like the district court, we find it unnecessary in this litigation covering the years 1977 through 1979 to consider Abad’s further complaint that his 1980 termination for unsatisfactory performance was discriminatory.

B. *Class Claims of Discrimination*

1. *Disparate Impact*

The Supreme Court has set out a three-step analysis for evaluating the evidence in disparate impact suits. *Connecticut v. Teal,*457 U.S. 440, 102 S.Ct. 2525, 73 L.Ed.2d 130 (1982); *Albemarle Paper Co. v. Moody,*422 U.S. 405, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975); *Griggs v. Duke Power Co.,*401 U.S. 424, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971). Like the *McDonnell Douglas*disparate treatment situation, this analysis does not compartmentalize the presentation of proof at the trial, but rather allows the factfinder to separate the collected evidence into its recognizable elements. Because the parties alternately bear burdens of proof by a preponderance of the evidence instead of mere burdens to produce, *Johnson v. Uncle Ben’s, Inc.,*657 F.2d 750 (5th Cir.1981), *cert. denied,*459 U.S. 967, 103 S.Ct. 293, 74 L.Ed.2d 277 (1982), the court considers all the relevant evidence from both parties to decide whether each has carried its particular burden of proof. *E.g., Equal Employment Opportunity Commission v. American National Bank,*652 F.2d 1176, 1189 (4th Cir.1981); B. Schlei and P. Grossman, *Employment Discrimination Law*1325 (2d Ed. 1983). Under *Griggs*the trial court must first determine whether the plaintiffs have proven by a preponderance of the evidence that a facially neutral employment practice of the defendant has a substantial adverse impact upon a protected group.

The thrust of the plaintiffs’ case is that the Base’s promotion system is so riddled with opportunities for decision-makers to exercise their discretion in an unguided, subjective manner that it provides a ready mechanism for whites to vent discriminatory feelings upon black applicants. In short, the facially neutral employment practice that the plaintiffs challenge as having a substantial adverse impact on blacks is the subjectivity of the promotion process. It is now settled in this circuit that the disparate impact theory may be used to attack subjective as well as objective components of an employment scheme. *Griffin v. Carlin,*755 F.2d 1516, 1522-24 (11th Cir.1985).

Except where promotions depend almost entirely on mere subjective conclusions drawn without guidance, *e.g., Rowe v. General Motors,*457 F.2d 348, 358-59 (5th Cir. 1972), it is imperative to identify the particular steps in the decisionmaking process which are susceptible to ungoverned discretion. Although the appellants insist that the Base’s entire scheme is subjective, we agree with the district court that only the selecting panel and, to a slight degree, the ranking panel procedures provide ready mechanisms for discrimination. The plaintiffs have never alleged that the eligibility and qualification standards found in the *FPM*are suspect. There was some probing by the plaintiffs into the degree of discretion exercised by personnel office staffers who draw up job descriptions and crediting plans. But the record shows that the decisions made at this stage are as circumscribed by objective criteria and division of authority as one could reasonably expect of any personnel office responsible *1549for filling 581 distinctly different types of jobs.8

The ranking panel’s application of the crediting plan to the master files could be somewhat subjective, but several safeguards operate to check the panelists’ discretion. The members proceed under the supervision of a personnel specialist who has already confirmed their qualifications to sit on the panel. They must evaluate each relevant element of each file on a mathematical scale supplied them, then resolve their differences. They must send the scores of each applicant to the personnel office. They do not play any further role in the selection process, and not even the order in which the panel ranked the applicants is known to the selecting panel. Supervisory evaluations are included in the master files, but the files also contain much information of a more concrete nature.

On the other hand, the interviewing official or panel exercises a high degree of discretion. Admittedly, objective evaluation has already taken place, and applicant interviews play a justifiably important part in the promotion process. We recognize that even under the closest supervision the reliability of interviewing by its nature depends on the interviewers’ good judgment. Moreover, the Base’s separation of the objective from the subjective inquiries of the promotion process guarantees the standardized, methodical character of the earlier stages, which are the decisive ones for all but five applicants. Inevitable and even desirable as such discretion may be, however, employers usually can implement procedures which, without reducing the panelists’ or selecting official’s authority, render that stage a much less practicable mechanism for discrimination. The requirement of a record explaining why one interviewee was selected over the other four would encourage panelists to exercise their judgment in a systematic, thoughtful way. Such a safeguard would not be unduly burdensome in view of the small number of persons involved. It might also be helpful for the personnel office to monitor thé interviewing process. These brief points do not suggest a checklist of precautions for this or any other promotion plan but simply illustrate that even subjective components of a procedure need not pose the danger of undetected discrimination.

a. *Statistical Evidence Concerning Adverse Impact*

At the trial, Martin Mador, who is a computer technician but not an expert in statistics, explained the basis for various descriptive exhibits he prepared from the litigation database.9 These exhibits provided static, “snapshot” comparisons of the positions held by black and white Base employees. For instance, Mador’s calculations indicated that during the years 1972-79, 12% to 29% of all whites occupied GS levels 11 and higher, compared with only zero to 14% of the blacks. Similarly, more than 50% of all whites in WG positions occupied level 10 or higher as opposed to less than 20% of blacks. With respect to promotions, Mador testified that the disparate proportions of whites and blacks in supervisory positions (15.9% of whites versus 5.7% of blacks) evidenced overpromotion of whites.

As the district court noted, these figures would not carry much weight even if they were based on valid assumptions. A static, descriptive summary such as this reflects little more than the racial distribution of the workforce across the various grade levels on conveniently chosen days. These calculations do not, for instance, reflect distribution during a given year, but merely at the end of each year. Nor do Mador’s exhibits shed any light on the legally relevant issue — whether subjectivity in the selection stage has an adverse impact on blacks seeking promotion. Mador’s comparative study rests on the total Base population, not on the group of applicants who *1550were interviewed,, or even on the group of applicants found qualified or the group of all applicants. The mathematical technique is not without its uses, however, and it supplies a backdrop for more sophisticated evidence. But when it is applied to summarize data so remote from the challenged stage of subjectivity, it loses much of its potential probity.

In any case, these flaws aside, the assumptions underlying Mador’s exhibits run so contrary to the realities of the Base’s employment history that the exhibits are not merely remote but misleading. Although the Base filled hundreds of vacancies by recruiting applicants who were not Base employees,10 Mador’s study assumes that all vacancies were filled by Base personnel. He also took it for granted that all workers at any particular grade, no matter what their individual jobs, possessed the qualifications and applied for all the occupations in the next higher grade. He magnified the error arising from this latter presupposition by grouping the levels of workers within each pay schedule. The resulting percentages stem from the faulty assumption that all workers at the lower levels were qualified and applied for all jobs at the higher levels. As the Court remarked in *Hazelwood:*“When special qualifications are required to fill particular jobs, comparisons to the general population (rather than to the smaller group of individuals who possess the necessary qualifications) may have little probative value.” *Hazelwood School District v. United States,*433 U.S. 299 at 308 n. 13, 97 S.Ct. at 2736, 2742 n. 13, 53 L.Ed.2d 768 at 777 n. 13 (distinguishing the low-skill job at issue in *Teamsters, supra*— driving a truck— from teaching). *Compare, e.g., Valentino v. United States Postal Service,*674 F.2d 56, 67 (D.C.Cir.1982) *with Miles v. M.N.C. Corp.,*750 F.2d 867, 872 (11th Cir.1985) (“no specific qualifications or criteria for employment”) *and with Jean v. Nelson,*711 F.2d 1455, 1496 (11th Cir.1983) (“no promulgated guidelines”). The Base has a great number of positions calling for highly specialized skills, and the Base strictly enforces the lengthy, objective eligibility requirements in the *FPM.*For these reasons, the district court did not err in giving Mador’s exhibits little weight.

We next consider the two sets of calculations submitted in the affidavit of the plaintiff’s statistics expert, Dr. Drogin. His first study compared the number of blacks promoted during various years with the number of blacks “expected to be promoted.” Examination of the affidavit, however, reveals that the quoted phrase assumes nearly as much as did Mador’s calculations. As Dr. Drogin’s affidavit explains, “[This] analysis compared the number of blacks who were promoted out of a grade during a year to the number of promotions that would be expected *if all employees in that grade at the beginning of the year had the same chance of receiving the promotion.”*R.Vol. 6 p. 1415 (emphasis added). Thus, this analysis is based on the unsupported hypothesis that all workers in a grade possessed equally the requisite eligibility and specialized qualifications for promotion to higher grades. Focusing solely on the Base workforce as the applicant pool is especially misleading here, because the Base underwent dramatic changes in its function and its personnel requirements in 1976. Pre-1976 Base employees were predominantly WG grades and most of these were relatively unskilled. No experience or training available at the Báse could equip these workers for ICP jobs. *Cf. Fisher v. Procter & Gamble Mfg. Co.,*613 F.2d 527 (5th Cir.1980). Arrival of the ICP created 547 GS vacancies, most if not all of which called for such specialized skills as to require DOD-wide recruitment. As the district judge found, “It is inappropriate to use the Base’s workforce as the sole qualified labor market where so many of the higher level positions for which plaintiffs seek promotion demand certain defined skills not possessed by base employees.” R.Ex. 49.11*E.g., Johnson v.**1551*Uncle Ben’s, Inc.,*628 F.2d 419, 425 (5th Cir.1980) (distinguishing *James v. Stockham Valves & Fittings Co.,*559 F.2d 310 (5th Cir.1977), *cert. denied,*434 U.S. 1034, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978)).

Dr. Drogin’s second analysis, however, proceeded in a much more productive direction. In that study, he used the Base’s data of the stage-by-stage results for vacancy announcements in the relevant years. His general method continued to be one of comparing the number of black promotees to the number his model assumed should have been promoted; but he made the important adjustment of correlating his assumptions respecting promotability to the Base’s objective promotion criteria. Dro-gin accomplished this correlation by limiting his attention to the actual groups of applicants for the announced positions. Hence, rather than looking to the entire Base workforce as the sole labor population, Drogin this time used much more relevant employee groups: all applicants, all who were qualified according to the *FPM,*all those highly qualified and the persons selected. Curiously, he failed to focus on the group of those certified and interviewed. Drogin compared the proportion of blacks entering each stage of the promotion process to the proportion of blacks who were in the prior stage, except for his omission of the interviewing stage. As an example, if 20% of all applicants were black, then Drogin assumed that 20% of all applicants found qualified would be black. He would then use 20% of the number of actual qualified applicants as the “expected” number of black qualified applicants. Next, he would compare the “expected” to the actual number and note the disparity.

This statistical approach is well-tailored to the plaintiffs’ claim for two reasons. First, the technique recognizes the segmented design of the Base’s promotion system. This provides the court with a study of how blacks fared at separate stages of the promotion process. In a suit attacking a promotion scheme which is subjective in some but not all stages, these stage-by-stage comparisons offer statistical pictures of proper scope. Second, by using the personnel office records for each vacancy, the plaintiffs chose the appropriate labor pools. These records include all the applicants for each position, whether they came from the outside or the Base. After all, as stated, the Base applied its promotion standards to the particular groups of applicants, not to the Base workforce as a whole. There is no allegation or evidence that the Base selected its areas of off-Base recruitment in a discriminatory fashion. Hence, the relevant pool of potential promotees is composed of all who applied in response to vacancy announcements, wherever posted.

Once he ascertained the actual and “expected” numbers of blacks and whites in each promotion stage,12 Drogin used standard deviation analysis13 to test the degree *1552to which chance could have contributed to the raw numerical differences. The Supreme Court has repeatedly recognized the strong potential of this mathematical technique for supplying an accurate statistical comparison. *E.g., Hazelwood,*433 U.S. at 311 n. 17, 97 S.Ct. at 2743 n. 17, 53 L.Ed.2d at 779 n. 17 (relying on *Castaneda v. Par-tida,*430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498, 512 n. 17 (1977)).

It is important to stress that a disparity translating into a large number of standard deviations does not automatically point to discrimination as the cause. The mathematical technique measures the probability that the calculated disparity could occur randomly — but the analysis in no way validates the calculation of the disparity itself. If the tested disparity is based on erroneous assumptions or suffers from flaws in the underlying data, then standard deviation analysis is foredoomed to yield an equally faulty result. Finally, it is important to note that no bright line of two, three or more standard deviations can be drawn to distinguish automatically between fair and discriminatory employment practices. Just as a standard deviation of two or three does not necessarily exclude legitimate causes other than chance, so a Z-value below that range does not necessarily exclude discrimination as the cause. *E.g., American National Bank,*652 F.2d at 1192. The Supreme Court has repeatedly warned, “We caution only that statistics are not irrefutable; they come in infinite variety and, like any other kind of evidence, may be rebutted. In short, their usefulness depends on all of the surrounding facts and circumstances.” *Teamsters,*431 U.S. at 340, 97 S.Ct. at 1856-57, 52 L.Ed.2d at 418.

Drogin calculated the Z-values for the disparities at each stage and grade level. In the results tabulated below, minus signs indicate underrepresentation of blacks, plus signs denote overrepresentation of blacks. Some disparities within single grades were based on such a small number of promotion decisions that no significant Z-value could be calculated for those grades individually. Affidavit of Dr. Drogin, R.Vol. 6 p. 1419. Each table is analyzed in turn.

> Table 1

> Comparison of proportion of blacks among all applicants and proportion of blacks among all qualified applicants

> Raw disparity between number of black applicants “expected” to be found qualified and number of black applicants

> Grade actually found qualified Z-Value

> GS-3 + 0.5

> GS-4 - 12.2 - 2.65

> GS-5 - 15.9 - 2.67

> GS-6 - 5.3 - 1.87

> GS-7 - 5.7 - 1.72

> GS-8 - 3.3

> GS-9 - 5.8 - 1.77

> GS-11 + 0.8 + 0.34

> GS-12 - 0.3

> GS-13 - 0.9

> GS-14 + 0.1

> All Grades - 47.96 - 4.72

This table perfectly illustrates the principle that standard deviation analysis cannot transform irrelevant data into relevant results. The Z-value of -4.72 indicates randomness is not responsible for the qualification disproportions, because such a pattern would occur by chance only seven times in a million. *Id.*But the underlying comparison is far too distant from the challenged stage of the promotion process to have substantial weight. The plaintiffs’ claim depends on their showing by a preponderance of the evidence that subjectivity, which the evidence shows to be negligible before the interviewing stage, is the *1553neutral practice having an adverse impact on blacks. “In making a prima facie case in a disparate impact suit, however, the plaintiff must not merely prove circumstances raising an inference of discriminatory impact; he must prove the discriminatory impact at issue.” *Johnson v. Uncle Ben’s, Inc.,*657 F.2d 750, 753 (5th Cir. 1981), *cert. denied,*459 U.S. 967, 103 S.Ct. 293, 74 L.Ed.2d 277 (1982). Given that the plaintiffs have not shown that the *FPM*minimum qualification standards are invalid or are applied subjectively, this table merely tends to imply that a disproportionate number of black applicants for lower level GS jobs did not possess the minimum eligibility requirements for promotion in the federal service. Furthermore, the table suggests that for the upper level positions and perhaps for the beginning level jobs blacks were disproportionately overrepresented among the group of qualified applicants.

> Table 2

> Comparison of proportion of blacks among all qualified applicants and proportion of blacks among ail highly qualified applicants

> Raw disparity between number of qualified blacks “expected” to be found highly qualified and number of qualified blacks

> Grade actually found hierhlv qualified Z-Value

> GS-3 - 3.0

> GS-4 - 2.6 - 0.76

> GS-5 - 5.0 - 1.24

> GS-6 - 5.0

> GS-7 + 2.6

> GS-8 - 0.2

> GS-9 - 1.0

> GS-11 - 2.4 - 1.01

> GS-12 - 3.0

> GS-13 + 0.7

> All Grades - 19.07 - 2.64

This table tests the possibility that chance caused the difference between the proportion of blacks among the group of all applicants who were ranked and the proportion of blacks among all those found highly qualified. Dr. Drogin arrived at a Z-Value of -2.64, indicating the pattern would occur by chance about once in a hundred times. Table 2 is somewhat more relevant than Table 1 because this table focuses on the ranking panel process, which is one step closer to the challenged interviewing stage than is the *FPM*eligibility determination. Nevertheless, in view of the general objectivity of the ranking panel process, these figures are not particularly helpful to the plaintiffs’ attack on subjectivity in the selection stage.

> Table 3

> Comparison of proportion of blacks among all qualified applicants and proportion of blacks among all promoted applicants

> Raw disparity between number of qualified blacks “expected” to be promoted and number of

> Grade qualified blacks actually promoted Z-Value

> GS-2 - 0.5

> GS-3 - 1.8

> GS-4 + 0.3 + 0.12

> GS-5 - 5.2 - 2.11

> GS-6 - 1.8

> GS-7 - 0.1

> GS-8 - 0.9

> GS-9 - 1.4

> GS-10 + u

> GS-11 - 1.9

> GS-12 - 1.5

> GS-13 - 0.7

> All Grades - 14.43 - 2.69

The Z-Value of -2.69 indicates the pattern of Table 3 would occur by chance approximately one in one hundred times, but the usefulness of this table is undercut by its failure to adhere to the established facts about the Base’s selection system. Because the interviewees in nearly all cases were drawn solely from those ranked highly qualified, inclusion here of those who were merely qualified distorts the comparison. Only in the relatively few instances when there were fewer than five highly qualified applicants and the selecting panel requested additional names would any qualified persons be certified. The truly relevant comparison would have been that between certified applicants and selected applicants.

> *1554Table *i*

> Comparison of proportion of blacks among all highly qualified

> applicants and proportion of blacks among

> all promoted applicants

> Raw disparity between number of highly qualified

> blacks “expected" to be promoted and

> number of hierhlv aualified blacks

> Grades actually promoted Z-Value

> GS-3 + 0.2

> GS-4 + 0.4

> GS-5 _ 4.2

> GS-6 *—*1.2

> GS-7 *—*1.1

> GS-8 *—*1.3

> GS-9 *—*0.7

> GS-10 + 1.1

> GS-ll _ 1.6

> GS-12 _ 0.6

> GS-13 - 0.5

> All Grades - 9.96 - 2.47

Comparing all the i tables, it is readily apparent that the last is closer than the rest to focusing on the issue raised by the plaintiffs. To the extent, however, that not more than five of each group of highly qualified applicants were interviewed, the lumping together of all highly qualified persons introduces a substantial inaccuracy. We are left to wonder why Dr. Drogin did not include in his affidavit a comparison of certified interviewees and those selected. This stage in the promotion competition is the very one involving the subjectivity that plaintiffs challenge. Even the raw disparities would have provided some information. The omission is particularly worrisome because in each successive table Dr. Drogin’s comparisons generally show less and less disparity, in terms of standard deviations, as they move toward the subjective selection stage.

Finally, Dr. Drogin supplied a fifth table comparing the proportion of blacks who applied to blacks who were ultimately promoted. This summary table offers no information not contained in Tables 1 through 4, and its aggregation of the various segments of the promotion process makes it less useful.

After considering all of Dr. Drogin’s calculations, the district court concluded that the only “somewhat meaningful comparisons” were those made in Tables 3 and 4. R.Ex. 47. As we have noted above, in finding these more helpful the district court proceeded correctly. The trial court then considered the responses of the defendant’s experts, who submitted affidavits in opposition to that of Dr. Drogin. In particular, Dr. Upton charged that Dr. Dro-gin had not analyzed each promotion competition separately. Upton concluded from reviewing Drogin’s affidavit that Drogin had lumped together the data for all announcements within each grade level, then performed his statistical analysis for each level to determine whether a disproportionate ratio of whites had been successful in the various stages. By indiscriminately aggregating all promotions at a given grade, Upton pointed out, Drogin had included the promotions without any black applicants. Including such racially noncompetitive promotions would increase the overall number of whites selected. After all, if no blacks applied for a position, then selection of a white was inevitable and could not possibly have resulted from discrimination. In his reply affidavit, Dr. Drogin responded to this criticism, “Upton is completely wrong here. I did do the competitive promotion analysis on an announcement by announcement basis.” R.Vol. 6 p. 1461.

The district court found as a fact that Drogin had aggregated data as described by Upton. Rejecting Tables 3 and 4 for various reasons, the district court added, “For example, Dr. Drogin’s calculations are not made on a promotion by promotion basis. Promotions where no blacks applied are thrown in with promotions where blacks did apply____ Defendant’s experts’ other criticism of the weaknesses in Dr. Drogin’s analysis is valid.” R.Ex. 47.

The appellants do not dispute the impropriety of such aggregation. Instead, they challenge the district court’s finding as clearly erroneous. The appellants argue that Upton’s criticism was irrelevant and, as such, did not create a credibility issue to be resolved by the trial court, but rather left uncontradicted Drogin’s affidavit. They rely on a prefatory statement: “Before discussing [Drogin’s] results, it should be noted that ... I have not attempted to verify either Drogin’s data or calculations *1555and cannot vouch for their accuracy. Nonetheless, I use these numbers for what they are worth.” R.Vol. 6 p. 1384. The thrust of the plaintiffs’ attack is that Upton’s charge of aggregation was by his own admission groundless and hence irrelevant. The district court did not understand the quoted statement to have this meaning, and we agree. Upton did not condemn his own analysis, but merely observed that he was assuming — for purposes of criticizing Drogin’s statistical theories — that the data used by Drogin was accurate, and that Drogin had performed the necessary multiplication, subtraction, etc., correctly. Upton was simply evaluating Drogin’s mathematical technique, and taking it for granted that the arithmetic and underlying facts were correct. Consequently, Upton’s criticism is directed squarely to Drogin’s description of his own methods.

Essentially, then, the plaintiffs ask us to hold as a matter of law that a statistician’s criticism of another’s analytical techniques is *per se*irrelevant unless he has reviewed the other’s actual worksheets and database. This we decline to do. The weight of all the relevant evidence is for the district judge in the first instance. In preferring Upton’s criticism over Drogin’s reply, the district judge made a credibility finding that is not reversible under *Anderson.*In any case, the district court also rejected the tables for several additional reasons, and the appellants have not shown this finding to be unsupported by the evidence.

In support of their statements that Ma-dor’s studies and Drogin’s first analysis misleadingly failed to account for the relevant labor pools, qualifications and other key variables, the defendant’s experts submitted more sophisticated statistical models of their own. Dr. Kenny performed a “job opportunity analysis” which reflected the fact that the Base recruited widely and frequently filled vacancies by hiring outsiders. Dr. Kenny grouped base jobs into 9 categories and compared the proportion of blacks filling vacancies, whether by internal promotion or by accession, with the proportion of blacks in “the relevant labor market” for each job category. Dr. Kenny created his hypothetical “relevant labor market” by first determining for each category how many vacancies were filled by people from the Base and how many by those from the outside. He then averaged the percentages of blacks in the Base workforce and the various outside labor markets. For example, if one third of the vacancies in a category were filled by promotions, the weight of one third would be given to the proportion of blacks on the Base, and the weight of two thirds to the proportion of blacks in whichever outside labor market was solicited (the OPM list, the Navy, the DOD, etc.). In the table below, positive disparities indicate favorable overselection of blacks, while negative numbers indicate underselection.

> Job Census Category

> Disparity (in standard deviations)

> (1976) (1977) (1978)

> Professional/Technical + 3.53 + 4.70 + 5.56

> Managerial/Administrative + 0.87 + 0.02 - 1.69

> Sales Worker - 0.46 - 0.74 0.00

> Clerical Worker - 1.28 - 1.09 + 0.26

> Craft Worker - 0.60 - 1.76 — 0.41

> Operative - 0.12 - 1.65 - 2.85

> Transport Worker - 0.45 + 0.77 _ 1.17

> Laborer + 0.14 - 2.12 + 0.70

> Service Worker - 1.39 - 2.04 _ 1.03

D.Ex. 24. Comparison of this study with those of Mador and Drogin’s first analysis vividly reveals the size of the error introduced when the plaintiffs’ experts assumed that the Base workforce was the sole labor market for filling the vacancies. Although Dr. Kenny’s model fails to distinguish among the qualifications of applicants, the evidence shows that Dr. Kenny’s failure in this regard produced figures less favorable to the defendant. See Table 1, *supra.*

Dr. Upton submitted two even more complex studies of promotions during the years 1977 through 1979. In his first, he used multiple linear regressions to analyze promotion decisions relative to a set of independent variables which he assumed were accurate predictors of individual success in the promotion process. Among these variables were age, educational level, length of time on the job and time since last promotion. Dr. Upton’s second study, a logit analysis, also employed these independent variables. The district judge admitted Dr. Upton’s analyses but directed that they be repeated and broken down according to the *1556Base divisions and staff offices in which the vacancies originated. The table below summarizes Dr. Upton’s recalculation of his prior studies. As before, negative numbers are unfavorable to blacks, positives indicative preferential treatment of blacks.

> Division or Disparity (in standard deviations)

> Staff Office WG GS

> Central Design/Program Activity 0.00 -t- 0.42

> Comptroller 0.00 - 1.17

> Contracts 0.00 + 0.14

> Dep. Chief of Staff 0.00 - 0.26

> Facilities & Services — 0.47 - 1.11

> Headquarters 0.49 0.00

> Logistics 0.00 + 0.81

> Material + 0.08 - 0.02

> Supply Systems 0.00 0.00

> Personnel 0.67 + 1.45

> Provisioning 0.00 + 0.26

> Repair - 0.51 + 0.91

> Supply Operations - 0.36 - 0.78

> Technical Operations 0.00 + 0.65

> Total _ 0.52 - 0.29

Nearly all these calculated disparities are small, and the largest of them, + 1.45 for Personnel, gives the advantage to blacks. Ten disparities reflect favorably to blacks, ten favor whites and in ten cases there is no disparity at all. As with all statistics, it remains to determine whether the basis for these calculations was valid.

The district court properly looked to the relevancy tests for regression analyses enunciated in *Eastland v. Tennessee Valley Authority,*704 F.2d 613, *mod.,*714 F.2d 1066 (11th Cir.1983), *cert. denied sub nom. James v. Tennessee Valley Authority,*— U.S. -, 104 S.Ct. 1415, 79 L.Ed.2d 741 (1984). The district court concluded that Dr. Upton had chosen relevant, reasonable variables that were likely to have a large influence on promotion decisions. The appellants now attack this finding largely on the ground that educational level is not as important as the area of education. The evidence indicates that both factors might be important, depending on the type of job and grade level. Such a record does not reveal the district judge’s finding to be clearly erroneous. In any case, the appellants exaggerate the district court’s degree of reliance on Dr. Upton’s studies. R.Ex. 59.

b. *Anecdotal Evidence of Adverse Impact*

During the years in issue, the Base continuously employed over 500 blacks. At the trial, only a dozen employees testified to events probative of discrimination.14 The district court noted that these witnesses had indeed been denied promotion but that blacks were repeatedly involved in these particular decisions, whether as interviewing panelists, staffing specialists, supervisors or as a division director. In many of the instances described, another black was chosen for the job. R.Ex. 53-54. The only named plaintiff who prevailed individually was Eric Shepherd. Without belaboring the details of his claim, we note simply that Shepherd complained of being ranked merely qualified and consequently not interviewed for a position. He testified that his supervisor wanted another applicant, who was white, to get the job. The other applicant was selected. Such evidence established Shepherd’s prima facie case for his individual case but offers little proof of discrimination for class purposes.

Having reviewed the statistical and anecdotal evidence, we cannot say that the district court was clearly erroneous in finding that the plaintiffs failed to prove by a preponderance of the evidence that subjectivity in the promotion process had an adverse impact on blacks. The statistics presented by the plaintiffs either rested on unrealistic assumptions or, when the assumptions were reasonably accurate, strayed from the issue. The very sparse individual testimony, although indicative of one instance of discriminatory ranking, did little to bring “the cold numbers convincingly to life.” *Teamsters,*431 U.S. at 339, 97 S.Ct. at 1856, 52 L.Ed.2d at 417. The district court correctly concluded that the plaintiffs did not make out a prima facie case of disparate impact.

2. *Evidence of Disparate Treatment*

In an action alleging class-wide disparate treatment, the plaintiffs must prove *1557by a preponderance of the evidence that racial discrimination was the employer’s “standard operating procedure — the regular rather than the unusual practice.” *Teamsters,*431 U.S. at 336, 97 S.Ct. at 1855, 52 L.Ed.2d at 416 (footnote omitted). Evidence of mere isolated or “accidental” or sporadic discriminatory acts will not suffice to show a pattern or practice of discrimination. *Id.*Such a broad and complex inquiry cannot be easily conducted within the bounds of the *McDonnell-Douglas*three-part framework, which is better suited to the smaller area of individual claims. *Perryman v. Johnson Products Co., Inc.,*698 F.2d 1138, 1143 (11th Cir. 1983) .

We agree with the district court’s finding that the evidence above did not prove that the Base made it a regular practice to discriminate against blacks. Without restating our analysis of the flawed statistical evidence, we observe simply that it generally reveals that objective promotion criteria not attacked by the plaintiffs caused the disproportionate promotion of whites. The anecdotal evidence was sparse, considering the size of the plaintiff class, and much of that was unpersuasive and conclu-sory. *E.g., Metrocare v. Washington Metropolitan Area Transit Authority,*679 F.2d 922, 929-30 (D.C.Cir.1982) (six instances among class of 400 insufficient to show pattern or practice); *Ste. Marie v. Eastern Railroad Association,*650 F.2d 395, 405-07 (2d Cir.1981) (two instances). Additionally, the district court found that on numerous occasions the Base had accorded black applicants preferential treatment. We have no difficulty in agreeing with the trial court’s conclusion that the plaintiffs failed to prove the Base regularly practiced discrimination in its promotion decisions.

*Affirmative Action Plans*

The appellants also seek relief based on the defendant’s failure to implement an affirmative action plan in accordance with Rule 717(b) of Title VII. Precedent of this circuit is directly contrary to their position. In *Ferguson v. Veterans Administration,*723 F.2d 871 (11th Cir. 1984) , this court held that the hospital’s failure to install such a plan did not give rise to Title VII claim. In so holding, the panel said, “Without repeating here the analysis there made, we simply adopt as the law of this Circuit the reasoning and conclusion of the Fourth Circuit in *Page v.*Bolger----” 723 F.2d at 872 (citing *Page v. Bolger,*645 F.2d 227 (4th Cir.) (en banc), *cert. denied,*454 U.S. 892, 102 S.Ct. 388, 70 L.Ed.2d 206 (1981)). *Page*held that a post office’s failure to implement an affirmative action scheme did not give a Title VII right of action to a black alleging denial of a promotion. The plaintiff instead must carry the burden of showing a case of discriminatory impact or treatment. The appellants failed in this respect. Furthermore, as pointed out earlier, there is evidence that the Base repeatedly afforded blacks preferential treatment in the promotion process.

*Validation Studies*

The appellants finally assert that the Base failed to comply with governing federal employment regulations, and that this noncompliance entitles them to relief. This argument is refuted by the plain language of the cited regulations, 29 C.F.R. § 1607*et seq.*29 C.F.R. § 1607.1B provides, “These guidelines do not require a user to conduct validity studies of selection procedures where no adverse impact results.” Consequently, even if plaintiffs could, as a matter of law, state a claim based on these regulations — a question we do not decide— it would not affect the outcome of this case in view of their failure to prove adverse impact.

The judgment of the district court is AFFIRMED.

1

. Shepherd prevailed in the district court on his claim for individual relief and appeals only as a class representative. The Secretary does not appeal from the judgment in favor of Shepherd individually.

2

. The class excluded employees of “tenant activities” operating on the base.

3

. Prior to July 1, 1975, the ICP staff had been reduced from over 1000 positions to the 827 which existed at the time of the transfer to Albany.

4

. The Base personnel officer testified that federal law precluded hiring directly from the non-federal workforce, except under the Veterans’ Readjustment Act. Consequently, individuals who were not already federal employees had to be listed on registers kept by the Office of Personnel Management in Atlanta before they were eligible to apply for Base jobs. Thus, no separate list contained only applicants from the Albany Standard Metropolitan Statistical Area. These applicants were included, if qualified for federal service, on the Atlanta OPM list.

5

. The district court found that most promotions were made through the competitive process, which is the focus of this lawsuit.

6

. One year before trial the defendant served interrogatories requesting the names of plaintiffs’ experts. The plaintiffs did not notify the Secretary that Dr. Drogin and Dr. James Outtz would testify until ten days before trial. The court therefore excluded their testimony pursuant to Rule 26(e), Fed.R.Civ.P.R. Vol. 4, p. 816.

7

. Counsel for the appellants now claims that the testimony of Shepherd and Abad and the deposition of Maddox were offered only to prove the class claims, and that these plaintiffs did not have the opportunity to litigate their individual claims. This argument is frivolous and contradicts^ another assertion made by the appellants. In support of their allegation that twelve employees besides Shepherd were entitled to individual relief, counsel for the appellants states, "In its opinion, the lower court identified twelve class members whom it concluded ‘were persuasive on the issue of discrimination in the promotion process.’ ’’ Brief of Appellants p. 55. In quoting a fragment of this one sentence from the district court’s opinion, counsel omits the footnote that follows: "This is not to say that each of those individuals could make out an *1546individual case of discrimination but merely that the court finds merit in their testimony in determining the class question of discrimination.” R.Ex. 53, n. 11.

8

. The fact that the personnel office was staffed predominantly by whites during the time frame of this litigation is not relevant to a determination of the degree of subjectivity built into personnel office functions, although it may be significant to other questions.

9

The parties stipulated to the accuracy of the litigation database.

10

. The arrival of ICP in 1976 so changed the Base's workforce needs that even as late as the year 1980, when approximately 700 internal promotions were made, the Base also filled 280 jobs via accessions through OPM, Navy-wide and DOD-wide recruitment.

11

. One of the defendant’s experts, Dr. Kenny, prefaced his analysis with a study very similar *1551to Mador’s. Dr. Kenny’s purpose was simply to supply the court with a "naive" exhibit, so that his additional, much more sophisticated statistics could be compared side by side. Dr. Kenny’s preliminary study carries no more weight than Mador’s, as Dr. Kenny himself testified.

12

. “Most all announcements in the raw data are for promotions in GS grades, with relatively few in WG and other pay plans.” Affidavit of Dr. Drogin, R. Vol. 6 p. 1419. Therefore, Dr. Dro-gin’s second study evaluates only GS grade vacancies. The high proportion of GS promotions reflects the great number of upper level GS vacancies occasioned by ICP’s transfer. Noncompetitive employment standards, such as the Veterans Readjustment Act requirement that the Base seek qualified veterans before posting vacancy announcements, applied more often to WG than GS jobs. The non-competitive processes are not an issue in this case.

13

. The "standard deviation” is the square root of the product of the total number in a sample (e.g., the total number of applicants) times the probability of a black’s being found qualified (the ratio of blacks in the group of all applicants) times the probability of a white’s being found qualified (the ratio of whites in the group of all applicants). Accordingly, if for a given promotion there were 50 black applicants and 50 white applicants, the statistician would assume the probability of finding a black qualified to be 0.5, and the probability of finding a white qualified to be 0.5. Using 100 as the total number in the sample, the standard deviation would be 5.0. This number is a yardstick permitting the statistician to calculate the likelihood that a given disparity occurred solely as a result of chance. The disparity is measured by comparing the number of blacks actually found qualified to the number of blacks "expected” to be found qualified. Thus, if thirty total applicants are found qualified, the statistician assumes that *1552fifteen should be black, based on the fact that blacks comprised half of all applicants.

If twenty-five whites but only five blacks were found qualified, then the difference between the expected and actual number of qualified blacks would be -10. The negative sign indicates un-derrepresentation of blacks. This raw disparity is divided by the calculated standard deviation to arrive at a figure of -2.0. This final figure is known as the "Z-value” for the raw disparity. This Z-value is an index of random probability. Consequently, from a Z-value of -1.96, it would be concluded that there was a one-in-twenty chance that the raw disparity resulted solely through random distribution. The same probability would apply if blacks had been overrepresented by twenty-five to five, but the Z-value would be positive instead of negative.

14

. The district court rejected as conclusory and unpersuasive the testimony of another dozen Base employees. R. Ex. 53. There is no in-depth attack on this finding, which is not clearly erroneous.