#### Jewel C. RICH, Lawrence C. Collier, John F. Craig, Tommy Franklin, John Langley, Jose M. Tafoya, and Bobby G. Chappel, Plaintiffs, v. MARTIN MARIETTA CORP., Defendant.

Civ. A. No. C-3109.

United States District Court, D. Colorado.

Feb. 26, 1979.

*589Lawrence A. Wright, Jr., Wright & Francis, Kiowa, Colo., Gary L. Palumbo, Sheldon, Bayer, McLean & Glasman, P. C., Denver, Colo., for plaintiffs.

Richard L. Schrepferman, Brent V. Manning, Holme, Roberts & Owen, Denver, Colo., for defendant.

MEMORANDUM OPINION AND ORDER

SHERMAN G. FINESILVER, District Judge.

Plaintiffs and the class they represent allege that defendant Martin Marietta *590Corp. discriminated' against them because of their race, sex, color, or national origin thereby denying them equal employment opportunities in violation of federal law. The claims relate to defendant’s promotional policies. There are also allegations by two of the named plaintiffs (Ms. Rich and Mr. Tafoya) that defendant has retaliated against them for their having filed charges with the Equal Employment Opportunity Commission. The claims, and this court’s jurisdiction, arise under Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C. §§ 2000e through 2000e-17 (1976) as well as under 42 U.S.C. § 1981 and 28 U.S.C. § 1343(4) (1976).

The seven named plaintiffs are black female (Ms. Rich),* black male (Mssrs. Franklin, Langley, Collier, Craig, and Chappel), and Hispano-American male (Mr. Tafoya) citizens of the United States, all of whom reside in the district of Colorado. The class they represent includes all female, black, and Hispano-American employees of Martin Marietta’s Waterton (Colorado) facility as of May 11, 1971.

By stipulation of the parties, the trial was bifurcated. The instant trial was had on the issue of liability alone and was further limited to the issue of liability solely as to the seven named plaintiffs. Broad based discovery has, nonetheless, gone forward and plaintiffs presented plant-wide statistical evidence in support of their individual claims.

We have carefully considered all the evidence adduced at both trials (the matter has been before the court previously) and have reviewed the exhibits and all other matters of record. With the exception of plaintiffs Rich and Chappel, none of the plaintiffs has met their initial burden of establishing a prima facie case of employment discrimination under Title VII. Defendant has rebutted Ms. Rich’s prima facie case but has not rebutted Mr. Chappel’s. We conclude, therefore, that there is Title VII liability towards Mr. Chappel alone of all the named plaintiffs. None of the plaintiffs has succeeded in establishing a case of employment discrimination under 42 U.S.C. § 1981.

We thus find in defendant’s favor as to six of the plaintiffs, find liability against defendant as to one of the plaintiffs, and will determine Mr. Chappel’s remedy in subsequent proceedings.

Our findings and conclusions follow:

I

This lawsuit had previously been before the court in a trial which resulted in a judgment for defendant on all counts. That judgment in the earlier trial was reversed and the cause remanded to this court, with instructions, for further proceedings. *Rich v. Martin Marietta Corp.,*522 F.2d 333 (10th Cir. 1975). The Circuit Court reversed and remanded for reconsideration of plaintiffs’ request for additional discovery, for reconsideration of the question of class certification, and for reevaluation of plaintiffs’ claims.

All of plaintiffs’ discovery requests have now been granted. Defendant has spent a large amount of time and money developing and collecting statistical information for plaintiffs. All statistics have been adjusted so as to exclude American Indians and Oriental males. *See, Rich, supra,*522 F.2d at 337, 343, 346, and 346 n.12.

The class has been certified according to plaintiffs’ request. Having already conducted full discovery, the parties have agreed to holding separate trials on the individual and class claims. Trial on the issue of liability as to the class will, accordingly, be set in due course.

The court has reevaluated the plaintiffs’ claims. In so doing, we have relied upon the evidence which was presented at the first trial and that which has now been adduced at the second trial. *See, Rich, supra,*522 F.2d at 347, 349. We have considered the claims anew and have made findings and conclusions in light of the comments and guidance contained in the Tenth Circuit’s opinion.

*591Before weighing the supplemental evidence adduced at the second trial, it would be well briefly to review the state of the evidence as it stood at the end of the first trial.

This is a promotions case. At issue are various of defendant’s promotional policies. Defendant has more than one promotion policy because it has more than one class of employee. Defendant, an aerospace manufacturer employing upwards of 5,000 persons at its Waterton plant,1 groups its employees into three relevant classes. Those categories are “salaried,” “hourly-out-of-unit,” and “hourly-in-unit.”

The salaried employees are professionals, mostly engineers, together with officials or managers. This group accounts for roughly half of defendant’s labor force. The salary grades are designated numerically from 40 to 50. The lowest salary grade is 40, the highest is 50. These employees are promoted from one grade to another strictly on the basis of merit as determined by a “totem pole” evaluation system. Under this system, salaried employees are competitively rated and are ranked, in order of their performance, relative to one another. A salaried employee’s position on the totem pole is highly determinative of the employee’s likelihood of promotion.

The hourly out-of-unit employees include technicians, office and clerical workers, craft (skilled) and operative (unskilled) workers. The hourly out-of-unit grades are designated numerically from 12 to 1, and alphabetically, A and B.2 The lowest hourly out-of-unit grade is 12, the highest is A, with the normal progression being through the numerical grades to the letter grades. Promotions of these hourly technicians through their own ranks is based upon a combination of qualifications and seniority. A promotion in this category is first offered to the most senior qualified employee in the job family group. A second sort of promotion, a promotion out of the hourly ranks and into the professional category (that is, from “hourly to salary”) is also a possibility. Hourly to salary promotions are made strictly on the basis of merit.

Hourly in-unit employees constitute the third category. These employees are represented by a collective bargaining unit. Promotions in this category are awarded solely on the basis of seniority.

The seven plaintiffs are all long term employees of defendant corporation. As noted, they are black female (Ms. Rich), black male (Mssrs. Franklin, Langley, Collier, Craig, and Chappel), and HispanoAmericans (Mr. Tafoya). They represent varied job progression ladders and careers. Ms. Rich is an engineer, Mr. Franklin an accountant, Mr. Langley a developer, Mr. Collier a millwright, Mr. Craig a millwright, Mr. Chappel an electrician, and Mr. Tafoya an electronic developer. Over the broad period of time involved here, their specific job titles varied as their responsibilities rose or fell as a consequence of promotions, demotions, or reclassifications.

As a group, and during most of the relevant time period, the seven plaintiffs were generally either salaried or hourly out-of-unit employees. Those who were professionals (salaried) claim that they were not promoted as rapidly as other, white male, salaried co-workers. Those who were technicians (hourly out-of-unit) contend that they were neither promoted within the technician ranks as rapidly as other, white male, hourly co-workers nor offered the desirable promotions into the professional ranks (hourly to salary promotions) as were the other workers. All allege that this asserted difference in treatment is the result of defendant’s use of the impermissible factors, race, sex, color, or national origin. They allege that the evaluation systems used by defendant to determine promotions were impermissibly subjective and that such subjectivity tainted the ratings.

*592Each plaintiff filed a charge with the Equal Employment Opportunity Commission in the latter part of 1969.3 The instant lawsuit, initially filed on May 11, 1971, resulted.

In our earlier, unpublished ruling we made extensive findings of fact of which the foregoing recitation is but a part. We will not retravel ground already covered. The Tenth Circuit, in an appendix to its opinion, summarized our findings as to each of the individual plaintiffs. For the present purposes, we too shall use the Tenth Circuit’s summary as our own. We incorporate it as Appendix I to this opinion.

We earlier held, for reasons noted, that the evidence, as it then stood, was insufficient to make out a prima facie case. We were not convinced, on the record then before us, that plaintiffs’ statistical evidence showed any discrimination in promotions nor were we convinced that the plaintiffs had shown themselves to be qualified for promotions to available positions. Plaintiffs were, however, afforded an overly limited range of discovery in the first trial. Such limitations tended to frustrate the plaintiffs’ efforts at the earlier trial.

The instant, second trial has proceeded after wide ranging discovery. Both sides have introduced supplemental evidence. Some of this new evidence relates directly to the non-statistieal side of the lawsuit and so directly compliments the evidence of the first trial. Most, indeed the great majority, of the new evidence is statistical, however, and (because of the greater scope of discovery) stands wholly independently of the statistical evidence adduced at the first trial. Because of the defects of the statistics of the first trial, and because of the complete and sophisticated statistical presentation made at the second trial, we disregard entirely all earlier statistics.

With this basic outline of events as background, we now proceed to analyze plaintiffs’ various allegations in some detail, weighing the crucial evidence on each issue. We include in our analysis appropriate evidence from each of the two trials.

II

Plaintiffs allege that defendant denied them promotions, impermissibly discriminating on the basis of race, sex, color, or national origin in violation of Title VII and of 42 U.S.C. § 1981.

Plaintiffs’ general theory of the case is that they each were qualified for promotion, that there were available positions into which they could have been promoted, and that there is evidence of discrimination in defendant’s promotion policies from which it can be inferred that these qualified plaintiffs were denied available promotions because of their sex, race, national origin, or color. The massive volume of evidence may be logically clustered into three general groups, paralleling plaintiffs’ claims, as follows: (a) evidence of qualifications for promotion, (b) evidence of available positions, and (c) evidence (statistical and otherwise) tending to show the presence or absence of an inference that defendant’s promotional policies had a discriminatory intent or impact.

We treat separately each area and, in turn, summarize the more important evidence.4 Where conflict exists, we note our findings of fact on such issues.

*593A

Plaintiffs allege that they were qualified for promotion. Defendant disputes this allegation. Much, indeed most, of the first trial consisted of testimony pertaining to the individual qualifications and work experience of the several plaintiffs. The Tenth Circuit’s summary of our earlier findings is attached hereto as Appendix I. In brief, it may be said that plaintiffs have each made a showing of lengthy tenure and of certain levels of experience.

Plaintiffs have offered no supplemental evidence concerning qualifications, resting instead on the record developed at the first trial. Defendant, for its part, has offered supplemental evidence, both general and specific, which expands upon its assertion that these plaintiffs were simply not qualified to receive promotions sooner than they, in fact, received them.

Generally, defendant offered additional evidence to show that seniority was not a particularly relevant factor in awarding promotions such as these plaintiffs sought. As salaried and hourly out-of-unit employees, these plaintiffs were in line for promotions of three kinds: salaried, hourly out-of-unit, and hourly to salary. The evidence remains undisputed that salaried and hourly to salary promotions are determined solely on the basis of merit. While seniority does play a part in determining hourly out-of-unit promotions, performance plays at least as great a part.

Specifically, defendant’s supplemental evidence further explained the hourly out-of-unit structure (including definition of the A and B grade levels), the hourly to salary promotion trends (including an analysis of labor pools), and, finally, offered some further explanation as to two of the plaintiffs (Ms. Rich and Mr. Collier).

With respect to the hourly out-of-unit structure, defendant’s supplemental evidence expanded upon evidence already in the record. As noted, the grades ascend from 12 to 1 and then from B to A. Hourly out-of-unit employees include technicians as well as office and clerical, skilled, and unskilled workers. The technicians are, predominantly, in the higher grades. The highest grades are, of course, the A and B levels.

There was testimony as to the distinction between A and B level technician job tasks. Mr. Charles A. Hall (a supervisor in the engineering propulsion laboratory) stated that engineering technician A’s were qualified to supervise other technicians, to do engineering work such as fluid flow or instrument calibration, or to do planning. An A technician was expected to be able to set up, run, and command a test in a safe manner. Mr. Thomas Johancen (a supervisor and a Millwright A) testified that the A millwright was qualified to overhaul pumps, compressors, cranes, boilers, and exhaust systems. Mr. Johancen further testified that the A electrician was qualified to work with wiring schematics, conduits, and electrical codes in the installation of compressors, pumps, and new machines, and in repair of electric motors. In all cases, the B level technician generally assisted the A level or performed work calling for less initiative, skill, and experience.

With respect to the hourly to salary promotion trends, defendant’s supplemental evidence tended to show that the higher hourly out-of-unit grades were both more qualified for, and more likely to get such promotions. Defendant’s exhibit BBBB notes that, using data as of December 31, 1967 as an example, most (that is, 95%) of the A and B level workers were performing jobs with high technical requirements. By comparison, only 12% of the employees in hourly labor grades 1-6 and only 3% of the employees in grades 7-12 were in technical jobs. As previously noted, the salaried positions were professionals, for the most part engineers doing work of a technical nature.

*594Dr. Roy Yamahiro (a manager responsible for performance evaluations) testified that, for an A or B level technician, promotion from hourly to salary was a normal movement upward. This promotion would represent a continuation and advancement of their already developed skills and progressively increasing initiative and responsibility. Dr. Yamahiro noted that, for the next several grades of hourly workers (grades 1-6), promotion from hourly to salary was not a normal movement upward. Those in this group who were promoted to salary generally advance as a supervisor or as an official or manager. Dr. Yamahiro’s testimony was based upon a personal review of every single hourly to salary promotion, by name and date, from 1965 through 1971.

Defendant characterized such unrefuted supplemental evidence on this score as establishing relevant “labor pools” with respect to hourly to salary promotions. Defendant referred to the A and B grades as the high pool, grades 1-6 as the medium pool, and grades 7-12 as the low pool.5

Finally, with respect to two of the plaintiffs, defendant introduced supplemental evidence to explain and clarify matters brought up at the first trial.

Mr. Robert Anschicks (a supervisor for whom Ms. Rich had worked) further explained why, in his opinion, the plaintiff Ms. Rich was not qualified for promotion from salary grade 43 to salary grade 45. He noted that, though she had some ten years’ experience, it was not progressive and that she had poor knowledge of load paths. He concluded that she was not technically qualified for promotion and did not have the proper work habits. On recross examination, Mr. Anschicks explained that he had recommended Ms. Rich for advancement in 1968 in the hope that more challenging work might somehow increase her interest and improve her poor attendance record. This last matter is referred to in *Rich, supra,*522 F.2d at 349-50 (Appendix A).

Mr. Johancen testified that the plaintiff Mr. Collier was not offered a promotion from hourly grade B to A in 1969. Referring to Defendant’s Exhibit U from the first trial, the witness described that January 24, 1969 document as a reclassification review. Mr. Collier, through his response on that form, had stated that he was not then interested in going to Millwright A. The reclassification review form was not an offer of promotion but was, apparently, a form used, generally, to ascertain employee preferences. Defendant did not thereby necessarily indicate that it deemed Mr. Collier to be qualified for promotion at any time prior to June of 1972 (when he was, in fact, promoted). This testimony relates to matters alluded to in *Rich, supra,*522 F.2d at 353 n.2 (Appendix A).

Based upon the evidence of the first trial and the supplemental evidence adduced at the second trial, we make the following findings of fact with respect to qualifications: Length of experience was not a major factor in the relevant promotional policies of defendant. Although plaintiffs were, in no case, the most qualified persons for promotion, they did show generally that they had had lengthy tenure and had gained certain experience working for the defendant company.6 We find that there is a significant difference in qualifications between A and B level technicians. We fur*595ther find that there are relevant labor pools for hourly to salary promotions. The high pool includes hourly out-of-unit grades A and B, the medium pool includes grades 1-6, and the low pool includes grades 7-12. Finally, we find that defendant did not consider Ms. Rich to be technically qualified for promotion in 1968 and that defendant did not consider Mr. Collier to be qualified for promotion in 1969.

B

Plaintiffs allege that there were available positions into which they could have been promoted. Defendant vigorously contests this allegation.

Plaintiffs’ theory of the case is that the asserted violations are _ continuing violations, not requiring any showing of specific promotions within 90 or 210 days of plaintiffs’ having filed charges with the EEOC. Defendant argues that plaintiffs must point to specific promotion openings within 210 days preceding the filing of charges with the EEOC.7

Plaintiffs have offered no supplemental evidence concerning the availability of positions into which they could have been promoted. They rest upon the record of the first trial. Defendant, on the other hand, did introduce supplemental evidence.

Mr. Leland Gillespie (a manager in compensation, wage, and salary) testified to the absence of relevant hourly out-of-unit promotions within the 210 days prior to Mssrs. Tafoya, Langley, Craig, and Collier’s having filed charges with the EEOC.8 Mr. Anschicks testified that there were no relevant salaried promotions during the 210 days before Ms. Rich filed charges with the EEOC. None of this testimony was countered by plaintiffs nor was it seriously undermined on cross-examination.

We find that defendant’s testimony on this score was reasonable, credible, and worthy of belief. We, accordingly, find that there were no relevant, promotions during the 210 days before the dates on which Ms. Rich, Mr. Tafoya, Mr. Langley, Mr. Craig, and Mr. Collier filed charges with the EEOC,

C

Plaintiffs allege that defendant’s promotional policies have had a discriminatory intent or impact. Defendant denies that this is the case. The evidence on this score is both statistical and non-statistical. Because of the importance of the statistical evidence in this law suit, we shall discuss it separately from the non-statistical evidence.

*Non-Statistical Evidence*

Both plaintiffs and defendant have supplemented the circumstantial, non-statistical evidence of the first trial. Plaintiffs’ supplemental evidence relates to the company’s evaluation system (which they contend to be impermissibly subjective), to events surrounding a certain public demonstration, and to various tabulations of minority positions at the defendant company. Defendant has responded. In addition, defendant has adduced supplemental evidence with respect to its affirmative action plan.

As to the evaluation system, plaintiffs’ witness, Mr. John Smith (an acting section chief in the library) testified that, though he personally gave fair ratings, he thought that he could have been unfair if he had wanted to be. The. witness stated that, though he had complied with certain of defendant’s written directions for preparation of evaluations, he did not have formal instructions on how to fill out the forms. Mr. Smith testified that he was cognizant of the fact that Martin Marietta had an *596affirmative action plan during the period 1969-70 (the witness thought that this was the period during which he had acted as a supervisor in the library). He described the plan as a “numbers game” which was being pushed by upper management to increase the numbers of minority employees.

Defendant’s witness, Dr. Yamahiro, qualified as an expert in the field of employee performance appraisals, stated that the evaluation forms used by defendant were, in his opinion, more objective than the forms used internally by the Equal Employment Opportunity Commission or by the Department of Justice. He noted that the reason defendant’s forms might have some element of subjectivity involved is due to the nature of Martin Marietta’s business. Where jobs are not easily definable and where job tasks are not repetitive or redundant, it becomes harder to be wholly objective. Dr. Yamahiro testified that defendant had sought to increase objectivity in its ratings by designing the forms so that a rating official was required, first, to describe the actual job assignment of the employee being rated and, then, to measure the employee’s performance against his particular job tasks. The witness stated that defendant had also sought to increase objectivity by ensuring that a second official review the evaluations prepared by the initial rating official. Based upon his review of defendant’s written evaluation policy, the witness concluded that the evaluations were objective.

As to the public demonstration, Mr. Tommy Franklin (one of the plaintiffs) testified that he had asked for a vacation day in order to participate in a civil rights demonstration against Martin Marietta which was scheduled to take place during his working hours. Mr. Franklin did not get a vacation day, took the day off anyhow, and received a written reprimand as a result. Mr. John Smith testified that he knew of the planned demonstration in advance and that he had been told to make sure that all of his employees reported for work on the day in question. He stated that, following the demonstration, the defendant company investigated to determine whether employees who had called in sick had, instead, participated in the demonstration.

Defendant’s witness, Mr. Bobby Frank Leonard (a manager in employee relations) testified that reprimands had issued to white and black employees alike who, without prior authorization, had not reported to their regularly scheduled work shift because of the demonstration.

As to minority positions in the company, plaintiffs offered several tabulations. Exhibits 107 and 109 are the more significant of the exhibits in this category. Exhibit 107 demonstrates the average time spent in grade as an Electrician B prior to promotion to Electrician A. While HispanoAmericans averaged 18 months and whites averaged 24.3 months in grade, the exhibit reflected that blacks averaged 52.6 months in grade. As previously noted, *see*Appendix I, infra, plaintiff Chappel was an Electrician B for the entire relevant period 1965 through 1971. Exhibit 109 demonstrates the average time spent in grade as a Millwright B prior to promotion to Millwright A. Whites averaged 14.3 months, HispanoAmericans 16.3 months, yet blacks averaged 68.3 months in grade. As previously noted, plaintiffs Craig and Collier were both Millwright B’s at various times between 1969 and 1971.

Defendant has tendered modified exhibits corresponding to plaintiffs’ exhibits 107 and 109. The modified exhibits are adjusted so as to exclude post-1971 data.9 Modified 107 shows average time in grade for Electrician *597B as 24.3, 12, and 37.3 months for white, Hispano-American, and black employees, respectively. Modified 109 shows average time in grade for Millwright B as 14.2, 17.5, and “_” months for white, Hispano-American, and black workers, respectively (there were no black Millwright B’s who were promoted to A during 1966-69).

Plaintiffs’ other tabulations included exhibits showing accounting department employees with college degrees such as plaintiff Franklin had, as well as other exhibits which showed salary levels, workforce composition, and other background data on defendant company.

Defendant likewise introduced several tabulations. The more significant of these were defendant’s series FFFF1 to 7 and GGGG1 to 14. Series FFFF compared each individual plaintiff’s promotion history during the relevant period 1966-69 against the promotion history of white males who had been initially hired during or in close proximity to the starting dates of the plaintiffs and into the same or similar initial job position and labor grade. Series GGGG compared the individual plaintiffs against white males who happened to be in comparable situations as were plaintiffs at each relevant promotion point. These exhibits sought to match the plaintiffs with white males who had the same degree of lengthy tenure and experience as did the plaintiffs. Defendant’s witness, Dr. Gollob, testified that these exhibits showed the individual plaintiffs to be generally in the mid range, receiving neither more nor less promotions than the majority of comparable white males. He concluded that these exhibits did not support any claim of discriminatory promotions.

Defendant’s other tabulations included exhibits showing workforce composition, salary levels, and other background information on defendant company. The court excluded certain of those exhibits as being irrelevant. Plaintiffs repeatedly represented, and the record is absolutely clear, that this is a promotions case. It is not a hiring case nor is it a disparate pay case.

Finally, in the category of non-statistical circumstantial evidence, defendant introduced supplemental evidence concerning its affirmative action plan.

Mr. Leonard testified that the defendant company had, in late 1967 or early 1968, determined to do something about the fact that it had no black Millwright A’s. The company tried, without success, to recruit black Millwright A’s in 1968. The company sought to promote its black Millwright B’s and established a special training program in 1968 in order to qualify black Millwrights for promotion.

Mr. Leonard testified to defendant’s affirmative action plan in general, noting that his office had reviewed every promotion during the period commencing in 1966 and had checked, in each instance, to see whether there were any qualified minorities who could fill the job. The witness stated, further, that defendant company had never had a policy of segregating its job classifications. By way of explanation, the witness noted that prior to 1965 janitors had been locked in place by provisions of a union contract but that the contract had been revised in 1965, correcting that situation.

The supplemental evidence adduced at the second trial complements the basic facts we found to have been established at the first trial. Upon weighing the supplemental evidence, we find as follows: The supplemental evidence regarding evaluations adds little to the record as it stood at the conclusion of the first trial. Defendant did reprimand its employees who walked off the job to attend a demonstration, but did so across the board, treating white and minority employees the same. Black Electrician B’s spent more time in grade than white Electrician B’s and there were no black Millwright B’s promoted to A before 1969. The individual plaintiffs generally fared no worse in promotions than did white males of comparable tenure and experience. Defendant instituted an affirmative action plan, with particular attention to the Millwright grades, as early as 1968.

*598These findings are consistent with those we made at the earlier trial and directly complement our earlier findings. With respect to the non-statistical circumstantial evidence, we adhere to the basic factual determinations we made at the first trial except to the extent they may be expressly modified by our findings made above on the basis of supplemental evidence.

*Statistical Evidence*

By far the greater part of the evidence at this second trial was statistical. Including each of defendant’s sub-exhibits, there were well over one hundred separate statistical exhibits admitted into evidence. Each side presented an expert witness who testified as to the meaning and weight which should be afforded the various statistics.

As a preliminary overview, we note that the statistical evidence was aimed at showing promotion trends (and the significance of such trends) in each of the promotion categories,10 for each of the sex and ethnic groups to which the plaintiffs belonged,11 and for each of the relevant years.12 The statistics were variously derived from two slightly different data bases13 and were analyzed by the respective experts in accordance with three different methodologies.14

We first summarize the statistics developed under each of the three methodologies. We then make direct comparisons of the various figures, grouping the figures by promotion category.

*(1) Plaintiffs’ 4Á’s Rule*

Plaintiffs’ Exhibit 131 both defined and explained the working of the Vs’s rule. According to the rule, as defined by plaintiffs, if the affected class’ representation in a job group is less than Vs’s of the majority representation, then adverse impact is said to exist.

Plaintiffs’ Exhibits 124, 125, 126, and 133 apply the Vs’s rule to defendant’s promotion decisions. In each case for which he did calculations, plaintiffs’ expert, Dr. Pearson, first determined a promotion rate for white males and promotion rates for blacks, Hispano-Americans, and females. He then compared the rates and, wherever the promotion rate of the affected group was less than Vs’s that of white males, he concluded that there was an adverse impact for that group.

*599Plaintiffs’ expert performed calculations separately for salaried, hourly-out-of-unit, hourly-in-unit, and hourly to salary promotions. In addition, there was a separate calculation for hourly to salary (officials and managers). In all instances but one (hourly to salary, officials and managers, 1966), he used tape data. He did these calculations for the years 1966-69.

The result was a showing of some adverse impact (as defined by plaintiffs’ expert) in some 32 specific instances. It was the expert’s conclusion that this showing established an overall adverse impact.

We summarize plaintiffs’ evidence below. For ease of analysis, we have used a tabular form broad enough to encompass like summaries of the exhibits which are to follow. We have replaced the numerical values with three symbols: a indicates a promotion rate for the group which is less than Vs’s the rate for white males, a “ + ” indicates a promotion rate higher than the rate for white males, and “0” indicates a null value (that is, a rate which is less than that of white males but greater than 4/s’s of that rate). Blanks merely indicate the absence of any calculation for a particular field.

[See following illustration.]

*600Table (1): Plaintiffs' 4/5's Rule This table is derived from plaintiffs' Exhibits 124, 125, 126, and 133.

Table (1) reflects Mr. Pearson’s showing of adverse impact in 32 instances. The table also shows 18 instances where the affected group had higher promotion rates than did white males and 6 instances of null values.

*601There has been no serious challenge to the raw data upon which plaintiffs’ calculations are based, nor has there been any challenge to the arithmetical correctness of the calculations. We find the exhibits in question to be reasonable, credible, and worthy of belief. We, accordingly, find that, in 32 cases out of the 56 cases examined under this method, there is a showing of adverse impact as defined by the *%’s*rule.15

*(2) Plaintiffs’ Calculations of Statistical Significance*

Plaintiffs’ Exhibit 132 explains the concepts behind one probability test for determining statistical significance of observed disparities. Plaintiffs’ expert, Dr. Pearson, describes his statistical model as one which measures the “significance of difference between two proportions.”

The model begins with the assumption that there is no expected difference in the anticipated performance among the population groups. The hypothesis is then tested by calculating the standard error and the Z statistic. A conclusion about the initial hypothesis may be drawn from the Z statistic. A Z statistic of less than 1.96 (roughly two standard deviations) is within the normal distribution and tends to confirm the initial hypothesis. In the instant context, such a value would indicate that the affected group is receiving an expected promotion rate. A Z statistic equal to or greater than 1.96 occurs less than 5% of the time in a normal distribution and means that the initial hypothesis may be rejected. In the instant context, such a value would indicate that the proportions do not come from the same distribution. Such a statistically significant difference between the groups would be evidence of. ad verse impact.

' Plaintiffs’ Exhibits 127, 128,129, 130, and 134 apply the “statistical significance” test described above to defendant’s promotion decisions. Plaintiffs’ expert performed selected calculations separately for certain salaried, hourly-out-of-unit, hourly-in-unit, and hourly to salary promotions. There was a separate calculation for certain hourly to salary (officials and managers) promotions. Plaintiffs’ expert did calculations based upon selected manual and tape data for certain years between 1966 and 1969. Only statistically significant adverse differences in proportions (Z scores equal to or greater than 1.96) were presented.

The result of the calculations for statistical significance was a showing of adverse impact in 14 specific instances. It was the expert’s conclusion that this showing enhanced the demonstration of impact under the 4/6’s rule and that it tended to confirm the existence of an overall adverse impact.

We summarize plaintiffs’ evidence below. • For ease of analysis, we have used a tabular form identical to that used previously in table (1). We have again replaced the numerical values with symbols. As the exhibits in question presented only adverse impacts, the only symbol which appears is a ” for each such instance. Blanks merely indicate the absence of any calculation for a particular field.

*602Table (2): Plaintiffs' Test for Statistical Significance*

Table (2) reflects Dr. Pearson’s showing of adverse impact, as defined by his probability test, in 14 specific instances.

There has been no serious challenge to the raw data upon which plaintiffs’ calculations are based, nor has there been any *603challenge to the arithmetical correctness of the calculations. We find the exhibits in question to be reasonable, credible, and worthy of belief. We, accordingly, find that, in the 14 cases examined under this method, there is a showing of adverse impact as defined by this test.16

*(3) Defendant’s Calculations of Statistical Significance*

Defendant’s expert witness, Dr. Gollob, explained his methodology at some length, both in oral testimony and through exhibits. His two written reports, Exhibits EEE and BBBB, well explain the concept behind his probability test. He characterized his model as a “lottery system.” The statistical methods employed to establish inferences based upon that model were described as a “normal approximation to the binomial” and as a “hypergeometric distribution.”

In brief, the lottery assumed, in the case of salaried, hourly-out-of-unit, and hourly-in-unit promotions, that the individual employees should have an equal likelihood of being promoted and that any employee might receive more than one promotion in each year. Relevant probabilities were calculated by the binomial and are summarized in Exhibit EEE and Exhibits S-l to S-5 which are attached to Exhibit EEE. The lottery assumed, in the case of hourly to salary promotions, that individual employees in the same labor pools should have an equal likelihood of being promoted and that there was a negligible chance that any one employee might receive more than one hourly to salary promotion in a single year. Relevant probabilities for hourly to salary promotions were calculated by the hyper-geometric and are summarized in Exhibit BBBB and Exhibits BBBB-1 to BBBB-9 which are attached to Exhibit BBBB.

Under both variants of the lottery system, a factor equivalent to a Z score was derived. In Dr. Gollob’s terminology, the 5% rule of thumb was used to isolate occurrences which are outside a normal distribution. In this context, such values indicate a statistically significant difference between the two groups.17 Defendant described those cases where the Z score equivalent was less than 1.96 as being inside the bounds of chance and described values of 1.96 or higher as being outside chance.

In addition to the summary defense exhibits already noted, Defendant’s Exhibits EEE-1B to TTT-3 present 108 separate applications of the “statistical significance” test described above. In applying the lottery test to defendant’s promotion decisions, defendant’s expert performed separate calculations for all salaried, hourly-out-of-unit, hourly-in-unit, and hourly to salary promotions. Dr. Gollob used all the manual data and all the tape data available for every year from 1966 to 1971. He performed several separate calculations for hourly to salary promotions, one ignoring the relevant labor pools, others taking the labor pools into account, and additional ones which focused on hourly to salary (officials and managers) by labor pool. He presented his results in every case, showing not only instances of statistically significant adverse promotion rates, but also showing instances where there were null values (within chance) and positive values (statistically significantly higher promotions for the minority groups than for white males).

The result of these calculations for statistical significance was a showing of adverse impact in 20 specific instances. The calculations also show 23 instances where the minority groups received a statistically significantly greater promotion rate than did white males and 197 instances of null values (variations of promotion rates within chance). Defendant’s expert concluded that this showing strongly supports the belief that neither blacks nor Hispano-Americans were adversely affected by Martin *604Marietta’s promotion policies. Dr. Gollob concluded that the overall pattern of results also supports the belief that females were not adversely affected.

We summarize defendant’s evidence below. For ease of analysis, we have used a tabular form identical to that used previously in tables (1) and (2). We have replaced numerical values with symbols: a ” indicates a promotion rate for the group significantly lower than the rate for white males, a “ + ” indicates a promotion rate significantly higher than the rate for white males, and a “0” indicates a null value, that is, a rate which lies within the bounds of chance. Blanks merely indicate the absence of any calculation for a particular field.

Table (3) reflects Dr. Gollob’s showing of adverse impact, as defined by his probability test, in 20 specific instances. The table also shows 23 instances where the affected group had significantly higher promotion rates than did white males and 197 instances of null values.

Table (3): Defendant's Test for Statistical Significance This table is derived from defendant's Exhibits S-l, S-5, BBBB-1, BBBB-8, and BBBB-9

*605

There has been no serious challenge to the raw data upon which defendant’s calculations are based, nor has there been any challenge to the arithmetical correctness of the calculations. We find the exhibits in question to be reasonable, credible, and worthy of belief. We, accordingly, find that, in 20 cases out of 240 cases examined under this method, there is a showing of adverse impact as defined by this probability test. We also find that, in the great majority of instances, there is no adverse impact.

*(4) Direct Comparisons of Plaintiffs’ and Defendant’s Figures*

Having summarized the mass of statistical data in a standardized tabular form, it becomes a simple matter to make direct comparisons among the several exhibits. Appendix II, attached to this opinion, is a set of four charts which make those corn*606parisons for salaried, hourly-out-of-unit, hourly-in-unit, and hourly to salary promotions respectively. We shall refer to those Appendix II charts in more particularity later on in the course of this opinion.18

For now we simply note that there are certain differences in results depending upon whether tape or manual data were used and whether (for hourly to salary promotions) labor pools were taken into account or not. In addition to those differences, which turn upon which raw data were selected, there are further differences which result from the use of one or another of the three methodologies chosen. Surprisingly, the major dichotomy is *not*between the plaintiffs’ two methodologies on the one hand and the defendant’s methodology on the other. Rather, the chief distinction is between results obtained by plaintiffs’ 4/5’s Rule and those results obtained by either of the tests for statistical significance (plaintiffs’ or defendant’s).19

We have already made certain observations concerning the data bases (see note 13, *supra)*and labor pools (see pages 593-594, 595). We have likewise noted the salient features of each of the three methodologies used by the expert witnesses (see note 14, supra; pages 598-606) and made the factual finding that the various calculations under each method are internally sound. The determination as to which of the data bases, labor pools, or statistical methodologies are the more probative is a legal conclusion which we shall address presently.20

Ill

The well known case, *McDonnell Douglas Corp. v. Green,*411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), supplies an example of the kind of showing a plaintiff must make to establish a prima facie case. 411 U.S. at 802, 93 S.Ct. 1817. The importance of *McDonnell Douglas*lies not in its specification of certain discrete elements of proof “but in its recognition of the general principle that any Title VII plaintiff must carry the initial burden of offering evidence adequate to create an inference that an employment decision was based on a discriminatory criterion illegal under the Act.” *Int’l Brotherhood of Teamsters v. United States,*431 U.S. 324, 358, 97 S.Ct. 1843, 1866, 52 L.Ed.2d. 396 (1977). That is to say that the plaintiff must show the occurrence of actions “from which one can infer, if such actions remain unexplained, that it is more likely than not that such actions were ‘based on a discriminatory criterion illegal under the Act.’ ” *Furnco Const. Corp. v. Waters,*438 U.S. 567, 576, 98 S.Ct. 2943, 2949, 57 L.Ed.2d 957 (1978) *(quoting*from *Teamsters,*supra).

There is a wide range of evidence which, in differing factual situations, might serve to satisfy that burden and establish a *607prima facie case. *See, McDonnell Douglas,*supra, 411 U.S. at 802 n.13, 93 S.Ct. 1817. The particular method suggested in *McDonnell Douglas*was never intended to be regarded as rigid or ritualistic. The central focus of the inquiry is always whether the employer is treating some people less favorably than others because of their race, color, religion, sex, or national origin. *Furnco, supra,*438 U.S. at 576, 98 S.Ct. at 2949.

The mandate of the Tenth Circuit contains additional guidance for further proceedings in the instant case which we are, of course, bound to follow.21 After noting that the elements of a prima facie case are flexible and varied, the appellate court did give an intimation of at least one set of elements which would serve to make out a prima facie case in the instant context. Where a plaintiff has shown “[1] that he is qualified, he need only show [2] a discriminatory impact, and [3] that he was among the class of employees who could have been considered for promotion.” *Rich, supra,*522 F.2d at 348 (numerals added).

IV

We conclude that five of the seven pláintiffs have failed to establish a prima facie case of employment discrimination under Title VII. Of the seven plaintiffs, only Ms. Rich and Mr. Chappel have met their initial burden of proof.

Plaintiffs have patterned their case in the fashion suggested by the Tenth Circuit. They have urged that they each were qualified for promotion, that there were available positions into which they could have been promoted, and that these qualified plaintiffs were denied available promotions because of the discriminatory intent or impact of defendant’s promotional policies. We make our conclusions of law on these three elements of plaintiffs’ claims, in turn, and in the same order in which we have made our findings of fact.

A

Lengthy tenure together with knowledge and experience, in the context of this case, will establish qualifications. *Rich, supra,*522 F.2d at 348. In this second trial, the parties have argued whether the appellate court went on to hold that each of these plaintiffs was, in fact, qualified for promotion or whether it left the factual question open. We conclude that the court did, in practical effect, so hold. Once qualification is understood primarily in terms of longevity, it must follow, on the facts of this case, that these plaintiffs are qualified for promotion.

B

It would appear at least as firmly established that these plaintiffs were among the class of employees who could have been considered for promotions. The Tenth Circuit has held that there is no necessity to point to any specific opening within 90 (or 210) days prior to plaintiffs’ having filed charges with the EEOC. Plaintiffs have alleged a continuing violation, hence the timing is inconsequential. *Rich, supra,*522 F.2d at 347, 348.

It is apparent then that two of the three elements necessary to at least one relevant form of prima facie case are present here.22*608The only item left for plaintiffs to show is “discriminatory impact.” Given the presence of the other two elements, if the plaintiffs, or any of them, can show a “discriminatory impact,” then a prima facie case will have been established. We now turn to this crucial element.

C

In the instant case, “discriminatory impact” could be established by a showing of discriminatory intent or by a showing of significantly discriminatory results of facially neutral practices. It may fairly be said that plaintiffs here have sought to show both and have thus attempted to make out a case both under the theory of disparate treatment and the theory of disparate impact.23

It is not entirely clear that the Tenth Circuit, in 1972, used the word “impact” in the specialized sense it has subsequently gained. Defendant goes so far as to urge that the court of appeals has since questioned its own holding in *Rich*for that reason, *citing, Olson v. Philco-Ford,*531 F.2d 474, 478 (10th Cir. 1976) for that proposition.

We conclude that defendant misconstrues *Rich.*When the Tenth Circuit used the term “impact,” it is now clear that it must have meant that it was incumbent upon plaintiffs in *Rich*to show such an impact either by showing motive (to establish disparate treatment) or by showing significantly adverse results of neutral practices (to establish disparate impact). We conclude that such an understanding of “impact” is certainly consistent with the mandate in this case and is sufficient to dispel any asserted conflict with subsequent cases. Indeed, such an understanding would seem the only logical choice. It explains not only the comments in *Olson, supra,*but also the directions in *Rich*itself that, on remand, this court reconsider the evidence and *“determine whether the plaintiffs have proven a prima facie case.” Rich, supra,*522 F.2d at 347 (emphasis added). It is quite clear that the court of appeals never intended a prima facie case to be established whenever a plaintiff merely shows that he or she was qualified for a promotion that was, in fact, given to a qualified member of another sex or ethnic group. Defendant’s concerns on this score are, thus, unfounded.

As noted, we earlier (in the first trial) found the circumstantial evidence on this key element of “discriminatory impact” to be unconvincing. Though the court of appeals has directed this court to reconsider this evidence, there is no hint that it determined any of our underlying findings of fact to have been clearly erroneous. Building upon the factual findings made at the first trial, we shall reevaluate the circumstantial evidence as to each plaintiff.

We likewise earlier found the statistical evidence on this crucial element of impact to be unpersuasive. There was er*609ror here, arising from the fatally narrow scope of discovery which, in turn, caused the statistics offered at the first trial to be unsatisfactory. This error frustrated the search for truth and left doubts as to the merits of plaintiffs’ claims. *Rich, supra,*522 F.2d at 343. The Tenth Circuit has directed this court to consider additional statistical evidence and then determine anew whether plaintiffs have established a prima facie case.24 Indeed, it is apparent that the statistical evidence is of utmost importance in this case and that

> [particularly in light of the contention of the defendant and the findings of the [trial] court that the circumstantial evidence was ambiguous, it became the more necessary for plant-wide statistics and facts to be obtained and presented, *for they very likely would prove crucial to the establishing or failure to establish a prima facie case.*

*Rich, supra,*522 F.2d at 344 (footnote omitted) (emphasis added). Disregarding the defective statistics of the first trial entirely, we shall consider the relevant additional statistical evidence as it relates to each plaintiff.

It is necessary, however, preliminary to considering the statistics, to determine which of the data bases, labor pools, or statistical methodologies are the more probative.

There was some difference in results depending upon whether manual or tape data were selected. Both sets of data were supplied by defendant. Defendant concedes that the tape data does not include information on certain employees who had worked at Martin Marietta during the relevant period (1965-71) but who may have left the company before it changed over to computer record keeping (circa 1971 — 72). Defendant explained its reasons for so having set up its tape data in the ordinary course of its business. Defendant also explained the difficulties which stood in the way of reconstructing the tape data specially for this lawsuit. Plaintiffs do not challenge defendant’s good faith on this score, nor do we. Indeed, the variance in results produced by choice of data base is not predictable nor is it one-sided. Sometimes the manual data will show an instance of adverse impact where tape data shows none, sometimes it is the tape data which shows an instance of adverse impact while the manual does not.

Despite its justifiable explanation for the variance in data bases, we nonetheless conclude that defendant must be bound by the data it produced and that defendant must bear the risk of uncertainty created by its different data bases.25 We will resolve any possible doubts in plaintiffs’ favor. We have considered any data source, manual or tape, that reflects adverse impact, even though the other data source might not show a corresponding instance of adverse impact.

There was a rather substantial difference in results depending upon whether (for hourly to salary promotions) relevant labor pools were used. Statistics, such as those produced by both parties at the first trial and by plaintiffs at the second trial, which ignore the labor pools present an entirely different picture than do the statistics which take the labor pools into account.

We have found, as a factual matter, that labor pools do exist at Martin Marietta. The evidence on this score is *610abundantly clear, overwhelming, and uncontradicted. It must follow, both legally and logically, that the proper comparisons must be between the racial, sex, and ethnic composition of results under defendant’s promotional policies and the racial, sex, and ethnic composition of its qualified employee population in the relevant labor pools. *See, Hazelwood School District v. United States,*433 U.S. 299, 308, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977). Where, as here, the salaried workers are, for the most part, professionals performing technical jobs; where, as here, the hourly workers include a predominance of office and clerical, skilled and unskilled workers in the lower grades and a predominance of technical workers in the higher grades; and where, as here, it is clearly proven that the higher grade technicians are the more likely to be promoted from hourly to salary, it cannot realistically be maintained that the qualified employee pool for these promotions consists of the undifferentiated mass of hourly employees.

On the clearly established facts of this case, it simply cannot seriously be argued, for example, that a janitor at Martin Marietta and a Millwright A (though both hourly workers) have equivalent qualifications for promotion from the hourly ranks to the professional positions held by defendant’s salaried employees. We conclude that the more probative statistics are those which take labor pools into account and we are compelled to reject those statistics which ignore the labor pools.26

Finally, there were differences in results depending upon which of the three methodologies was used to define an instance of adverse impact.

In this general regard, it has been noted that the crux of the current method of proof in discrimination cases is the presentation of percentage differences sufficiently substantial to suggest bias. Note, *Beyond the Prima Facie Case in Employment Discrimination Law: Statistical Proof and Rebuttal,*89 Harv.L.Rev. 387, 393 (1975). The problem comes in deciding, given an observed difference in percentages, just what degree of disparity constitutes a significant or substantial disparity. This is a question which has not clearly been resolved. *Id.*at 393 n.26; *see also,*Note, *Employment Discrimination: Statistics and Preferences Under Title VII,*59 Va.L.Rev. 463, 477-80 (1973).27 Indeed, it can be one of the more *611perplexing questions in a case such as this, tending to leave the parties as well as the court in the unsatisfactory position where unguided intuition has, seemingly, been the touchstone.

Recent cases have taken the lead in using statistical techniques of one sort or another and, in so doing, have provided sorely needed clarification in how to approach and resolve this problem. *See, Hazelwood School District v. United States,*433 U.S. 299, 308-09 n.14, 311 n.17, 97 S.Ct. 2736 (1977) (using the binomial distribution in a Title VII case); *Castaneda v. Partida,*430 U.S. 482, 496-97 n.17, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977) (using the binomial distribution in a jury selection case); *Otero v. Mesa County Valley School District,*568 F.2d 1312, and footnote at 1316 (10th Cir. 1977) (recommending consideration of the binomial methodology of the *Hazelwood*case in an analogous situation).28

In the presentation of evidence in the instant case, both parties have anticipated these recent trends in the direction of somewhat more sophisticated statistical techniques. *See, e. g.,*the authorities collected, *supra; see also,*Shoben, *Differential Pass-Fail Rates in Employment Testing: Statistical Proof Under Title VII,*91 Harv.L.Rev. 793 (1978). Both plaintiffs and defendant have presented the court with calculations performed under one or more methodologies tailored to providing a principled basis for interpreting the significance of an observed difference in raw percentages. Defendant relied squarely upon the more important of the recent cases, using a hyper-geometric distribution and also the binomial distribution which has been expressly approved in the *Hazelwood, supra, Castaneda, supra,*and *Otero, supra,*eases. We shall compare each of plaintiffs’ two methodologies to the method selected by defendant.

Plaintiff relied, first, upon the %’s Rule. It should be noted at the outset that this rule is not, strictly speaking, a “statistical” method at all. It is no more or less than a straightforward comparison of raw percentages, with a mechanical rule of thumb then applied in a regular manner so as to substitute uniformity for the “flexibility” *(see,*note 27, *supra)*which has characterized other such ball park comparisons. It has the virtue of simplicity and, as it has been uniformly adopted by four federal agencies,29 it has the companion virtue of providing the potential for predictability of results in discrimination cases. The rule should not, however, be given deference beyond its due. Its narrow primary use is clearly set forth in the explanatory information which emphasizes that the rule does “not address the underlying question of law. [It] discussfes] only the exercise of prosecutorial discretion by the Government agencies themselves.” 43 Fed.Reg. at 38291. (1978) (footnote omitted). Again, it is noted that “rule of thumb” is *“not a legal definition of discrimination,*rather it is a practical device to keep the attention of enforcement agencies on serious discrepancies. . . .” *Id.*(emphasis added).

It is apparent that, while by no means conclusive, the 4/s’s Rule might well produce some evidence of discrimination. In determining how much weight to give such evidence, we are guided, in part, by the observation that “statistics are not irrefutable; they come in infinite variety and, like any other kind of evidence, they may be rebutted. In short, their usefulness depends on *612all of the surrounding facts and circumstances.” *Teamsters, supra,*431 U.S. at 340, 97 S.Ct. at 1856, 1857 (citation omitted). In the context of the case at hand, we could well say that, if the Vs’s Rule calculations were all the evidence we had before us, we might well find them to be highly persuasive and we might seriously consider using the benchmarks developed by the government agencies to help interpret the figures. But, while it may supply an inference of discrimination, the inference of the Vs’s Rule (resting, as it does, upon untested intuition) is not a strong one. And, while the Vs’s Rule may produce some evidence of discrimination, we are confident that the binomial distribution (approved by the Supreme Court, and the Tenth Circuit, and used by defendant) produces much better evidence.

On the particular facts and circumstances of this case (not the least of which was the ability of defendant’s expert witness to educate the court in his discipline), we reject the calculations based upon plaintiffs’ Vs’s Rule in favor of those calculations based upon defendant’s test for statistical significance. In so holding, we do not mean to be understood as ruling either that a plaintiff must always produce precise calculations of statistical significance in employing statistical proof,30 or that the Vs’s Rule can never be relied upon by a plaintiff. What we hold is merely that, in this case, the reliability of plaintiffs’ evidence has been effectively disparaged and its probative value reduced to negligible proportions by defendant’s evidence. On the facts of this case, we resolve the question in defendant’s favor.

Plaintiffs relied, secondly, upon their own test for statistical significance. On cross examination, plaintiffs’ expert witness testified to the effect that his method was the same as that approved by the Supreme Court in *Hazelwood, supra,*and *Castaneda, supra.*That is to say, plaintiffs must have used the binomial distribution, as did defendant. Indeed, defendant’s expert witness agreed that the results obtained in those instances where both he and plaintiffs’ expert performed corresponding calculations for statistical significance were consistent.31 The only major difference that defendant’s expert could see was a matter of approach rather than method. That is, while plaintiffs’ expert only carried through those calculations which yield an instance of adverse impact (14 cases in all), defendant’s expert did calculations in all cases, turning up not only instances of adverse impact (20 cases) but also cases where minorities received the expected range in promotions and cases where minorities were promoted at significantly higher rates than were white males (197 and 23 cases, respectively).

Based upon the testimony and exhibits of the trial, we are prepared to accept the two tests for statistical significance as having equivalent evidentiary weight. While we recognize that the results obtained under the tests were not identical, we conclude that they are consistent with one another. We will consider both plaintiffs' and defendant’s tests for statistical significance. Resolving any possible doubts in plaintiffs’ favor, we will hold defendant to whichever test for statistical significance (plaintiffs’ or defendant’s) shows an instance of adverse impact, even though the other test might not show a corresponding instance of adverse impact.

We now summarize our conclusions concerning the statistics. We accept both the manual and tape data bases, holding defendant accountable for whichever shows instances of adverse impact. We reject plaintiffs’ calculations under the Vs’s Rule in favor of calculations based upon the tests for statistical significance. Finally, we accept both plaintiffs’ and defendant’s tests *613for statistical significance, holding defendant accountable for whichever shows instances of adverse impact. Having, thus, resolved the salient issues with respect .to the statistical evidence,32 we are prepared to analyze it (together with the circumstantial evidence) with respect to each plaintiff.

Our conclusions of law follow: (In the interest of brevity, we shall not repeat, in each instance, the observations that (a) our earlier findings of fact with respect to the circumstantial evidence remain essentially undisturbed and are summarized in Appendix I, *infra,*and (b) in each case, when we 'discuss the effect of the statistics, we will disregard the calculations based upon the Ve’s Rule, disregard calculations which do not take labor pools into account, and will combine the two data bases and the two tests for statistical significance as outlined above).

*Ms. Rich:*

In 1965, she was an associate engineer. In 1966, she was promoted to full engineer. The relevant years for her Title VII claims are 1965-69 (see note 12, *supra).*She is a black, female, salaried employee. She was eligible for promotions within the salaried ranks.

We have already found that Ms. Rich was qualified and that there were available promotions. We now evaluate the evidence to determine whether the third factor, “impact,” is present.

No new circumstantial evidence has been introduced on Ms. Rich’s behalf. The relevant statistics are displayed in Chart A, Appendix II. For black, salaried employees there are no instances of adverse impact.33 For female, salaried employees there are two instances of adverse impact (in 1967 and in 1969).34

We conclude that Ms. Rich has shown an “impact.” Through statistics, she has demonstrated that she was in a group (female, salaried employees) which suffered a significantly adverse impact as a result of facially neutral promotion policies. She has, thus, established a prima facie case of employment discrimination under Title VII.

*Mr. Chappel:*

In 1965, he was an Electrician B. He remained an Electrician B throughout the period 1965-69. He is a black, male, hourly out-of-unit (high labor pool) employee. He was eligible to be promoted within the hourly ranks and for hourly to salary promotion throughout the relevant period.

We have already found that Mr. Chappel was qualified and that there were available promotions. We now evaluate the evidence to determine whether the third factor, “im- “ pact,” is present.

Significant additional circumstantial evidence has been introduced on Mr. Chappel’s behalf. We refer to plaintiff’s exhibit 107 which shows that black Electrician B’s averaged 52.6 months in grade to 24.3 months averaged for whites. Defendant’s modified exhibit 107 still shows that blacks spent a longer average time in grade (37.3 months in grade) than did white males.

The relevant statistics are displayed in two charts. Chart B, Appendix II, is relevant to show black, hourly out-of-unit pro*614motions. There is no instance of adverse impact.35 Chart D, Appendix II, is relevant to show black, hourly to salary promotions. There is no instance of adverse impact.36

While the statistics here do not establish an “impact,” we, nonetheless, find the circumstantial evidence to be convincing. Evaluating the circumstantial evidence anew and in light of the comments contained in the Tenth Circuit’s opinion, we are compelled to conclude that the circumstantial evidence establishes an “impact.” We conclude that Mr. Chappel was in a group (black, male Electrician B’s eligible for promotion to Electrician A) which suffered a significantly adverse impact from defendant’s facially neutral promotion policies. He has, thus, established a prima facie case of employment discrimination under Title VII.

*Mssrs. Franklin, Langley, Collier, Craig, and Tafoya:*

Mr. Franklin was a senior accountant in 1965 and was promoted to associate analyst in 1967. He is a black, male employee who, during the period 1965-69, was an hourly out-of-unit (prior to 1967) or a salaried (after 1967) employee. He was, thus, at various relevant times, eligible for promotions within the hourly ranks, promotions from hourly to salary, and promotions within the salaried ranks.

Mr. Langley was a developer in 1965. He was demoted for a brief time in 1966. He is a black, male employee. Throughout the period 1965-69, he was an hourly out-of-unit employee and, thus, eligible for promotions within the hourly ranks and from hourly to salary.

Mr. Collier was a janitor in 1965. He was transferred in 1967 to a helper position and promoted in 1969 to Millwright B. He is a black, male employee. During the period 1965-69, he was eligible for promotions within the hourly ranks and from hourly to salary.

Mr. Craig was a janitor in 1965. He was transferred in 1967 to a laborer position and promoted in 1968 to helper. He was promoted to Millwright B in 1969. He is a black, male, hourly employee eligible for two types of promotion (within the hourly ranks and from hourly to salary) during the relevant period.

Mr. Tafoya was an electronic developer in 1965. He remained in this hourly out-of-unit position throughout the period 1965-69. He is an hispano male.

We have already found that each of these five employees was qualified and that there were available promotions. We now evaluate the evidence to determine whether the third factor, “impact,” is present.

Some new circumstantial evidence was introduced on behalf of certain of these plaintiffs. We refer to the evidence relating to promotional histories of accountants with degrees and that relating to the aftermath of the demonstration (both offered on behalf of Mr. Franklin). We also refer to plaintiffs’ exhibit 109 which shows the average time in grade for Millwright B’s prior to promotion to Millwright A (offered on behalf of plaintiffs Craig and Collier).

The statistics relevant to these five plaintiffs are displayed in three charts. Chart A, Appendix II, is relevant to show black, salaried promotions and relates to Mr. Franklin. There is no instance of adverse impact.37 Chart B, Appendix II, is relevant to show black (relating to Mssrs. Franklin, Langley, Craig, and Collier) and hispano (relating to Mr. Tafoya) hourly out-of-unit promotions. There is no instance of adverse impact.38 Chart D is relevant to show black and hispano hourly to salary promotion and relates to all five of these plain*615tiffs. There is no instance of adverse impact.39

The statistics here do not establish an “impact.” Neither does the circumstantial evidence. We have reevaluated our findings of fact based upon the circumstantial evidence of the first trial and again conclude that they do not establish an “impact.” We have carefully considered the new circumstantial evidence and reach the same conclusion.

In this regard, we have given particular consideration to plaintiffs’ exhibit 109 which shows that black Millwright B’s spent an average of 68.3 months in grade while whites spent 14.3 months. Defendant’s modified exhibit 109 only shows that no blacks at all were promoted from Millwright B to A before 1969.

We are persuaded, however, that neither Collier nor Craig has shown that he, personally, suffered from defendant’s promotional policies here. Neither became a Millwright until 1969. As of the time they filed charges later that same year, they had not only not personally spent 68 months in grade, but had not even spent close to 14 months (the average for white males). We also note that it was in 1968 that defendant implemented an affirmative action plan. That plan, implemented before either of these plaintiffs became a Millwright, and which they both took advantage of, does much to dispel the inferences which exhibit 109 might raise about the situation of black Millwrights generally. We conclude that the circumstantial evidence of exhibit 109 does not establish an “impact” for either Mr. Craig or Mr. Collier.

We conclude that all of these five plaintiffs have failed to show one element essential to their prima facie case. They have thus not met their initial burden and have not established a prima facie case of employment discrimination under Title VII.

*Retaliation Claims:*

Both Ms. Rich and Mr. Tafoya claim that defendant retaliated against them for their having filed charges with the EEOC. There has been no new evidence on this score. We have reevaluated our earlier findings and we conclude that there is no showing that either of these plaintiffs suffered retaliation.

SUMMARY:

We have now granted all of plaintiffs’ discovery requests. We have certified the class. We have reevaluated the plaintiffs’ claims. In so doing, we have relied upon evidence which was presented at the first trial and that which has now been adduced at the second trial. We have considered the claims anew and have made our findings and conclusions in light of the comments and guidance contained in the Tenth Circuit’s opinion.

We have considered plaintiffs’ theory of the case and, for the most part, have accepted it.40 We have analyzed the three *616elements (qualifications, availability of positions, and impact) which plaintiffs advanced. Though all of the plaintiffs succeeded in establishing the first two elements, only Ms. Rich and Mr. Chappel were able to show the crucial, third element.

This is, at its heart, a statistical case. As the Tenth Circuit noted, the statistics to be adduced at the second trial “very likely would prove crucial to the establishing or failure to establish a prima facie case.” *Rich, supra,*522 F.2d at 344 (footnote omitted). That observation has proven to be true. We heard the testimony of the two opposing experts (and might note, in passing, that we found the testimony of Dr. Gollob, defendant’s expert, to be much the more satisfying) and we have studied all of the statistical exhibits. Other than in Ms. Rich’s case, the statistics failed to support plaintiffs’ position. We have made lengthy findings as to the plethora of statistics admitted into evidence. By so doing, we have endeavored to develop as complete a record as possible in order better to facilitate possible appellate review and in the hope of minimizing the expense and delay, should further proceedings materialize.

We note, finally, that over the course of two trials, we have had the opportunity to observe the demeanor and to hear the testimony of the individual plaintiffs, their supervisors, and others. We are fully satisfied that there simply has been no purposeful discrimination in promotional policies at Martin Marietta. We are likewise satisfied that the evaluation systems were not, in fact, used to cloak any policy of discrimination. Such showing of “impact” as has been made in this case is based upon significantly adverse results of policies that were neutral on their face.

V

As Ms. Rich and Mr. Chappel both met their initial burden of showing a prima facie case, the burden has now shifted to defendant as to them. Because we had concluded at the first trial that none of the plaintiffs had established a prima facie case, we had no occasion earlier to dwell upon what sort of showing defendant here need make to rebut the prima facie case.

The Court has repeatedly held that, in order to dispel the adverse inference from a prima facie case, the employer need only “articulate some legitimate, nondiscriminatory reason for the employee’s rejection.” *Keene State College v. Sweeney,*-U.S.-, 99 S.Ct. 295, 58 L.Ed.2d 216 (1978); *Furnco Const. Co.*v. *Waters,*438 U.S. 567, 578, 98 S.Ct. 2943, 2950, 57 L.Ed.2d 957 (1978); *McDonnell Douglas Corp. v. Green,*411 U.S. 792, 802, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). *See also, Diggs v. Western Electric Co.,*587 F.2d 1070, 1073 (10th Cir. 1978).

The employer “need not prove that he has pursued the course which would both enable him to achieve his own business goal *and*allow him to consider the *most*employment applications.” *Furnco, supra,*438 U.S. at 577, 98 S.Ct. at 2950. Nor does Title VII impose a duty to adopt employment decisions that maximize the advancement of minority employees, at least until a violation has been shown. *Id.*A prima facie showing is not the equivalent of a factual finding of discrimination and the employer, in rebutting, must be allowed some latitude to introduce evidence which bears on his motive. *Id.*at 580, 98 S.Ct. at 2951.

As to Ms. Rich, the defendant has not only “articulated” such a legitimate business justification, but has also “proven” it by a clear preponderance of the evidence. Defendant has proven that Ms. Rich’s rating was the lowest in her department, section, and salary grade of 43. Defendant’s witnesses were unanimous in agreeing that Ms. Rich’s low rating was well deserved. *See,*appendix I, *infra.*In these specifics we have found no reason to doubt defendant’s witnesses and we have made the factual finding that Ms. Rich was rated at the bottom, and properly so.41

*617We construe *Washington v. Davis,*426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597

Even though she possessed the minimal qualifications for promotion and even though she was a member of a group which experienced an adverse impact, it is clear that defendant has articulated and proven that there was a legitimate, nondiscriminatory reason for not promoting this *particular*individual. It is not simply that she is not the “most qualified.” It is not just that she has not shown why she was “not certified as being at the top of the list.”42 The problem is that she was, plainly speaking, the very lowest rated of defendant’s employees and the very last who should ever expect to be promoted. We do not engage in any theoretical application of principles of business management or of industrial relations, but based upon common sense it must be clear that there is a legitimate business justification, if not in promoting the most qualified, at least in refraining from promoting the worst performers and thereby rewarding employees inversely on the basis of merit.

We conclude that defendant has clearly rebutted Ms. Rich’s prima facie case. As there has been no convincing evidence that defendant’s business justification is pretextual, we conclude that Ms. Rich has not prevailed on her Title VII claim.

As to Mr. Chappel, defendant has not articulated a nondiscriminatory reason for having failed to promote him. We conclude, therefore, that Mr. Chappel has prevailed on his Title VII claim and that defendant is liable to Mr. Chappel.

VI

All plaintiffs have also alleged a civil rights claim under 42 U.S.C. § 1981.

(1976) as authority for the proposition that a plaintiff under the civil rights statutes must show a discriminatory intent in order to recover. *See also, Stover v. Chicano Police Officer’s Ass’n,*426 U.S. 944, 96 S.Ct. 3161, 49 L.Ed.2d 1181 (1976), *vacating mem., Chicano Police Officer’s Ass’n v. Stover,*526 F.2d 431 (10th Cir. 1975).43

Extending the relevant period through 1971 (see note 12, supra) and searching the record, it is clear that none of the plaintiffs have shown such intent on the part of Martin Marietta. The two plaintiffs who have made a prima facie Title VII case did so by showing that facially neutral policies of the defendant have had a disparate impact upon groups to which they belong. Neither they nor any of the other plaintiffs have established the presence of discriminatory intent.44

We conclude that each of the claims based upon the civil rights statute has failed. None of the plaintiffs has prevailed on the § 1981 claims.

VII

Accordingly, and for the reasons stated above, we find and conclude that Mr. Chappel has prevailed against defendant on his Title VII claim. With respect to all other claims and all other named plaintiffs, the defendant Martin Marietta Corp. has prevailed.

The remedy to which Mr. Chappel is entitled will be determined in future proceed*618ings, the course of which will be set by separate order of the court.

ORDER

We find the issues joined as follows:

Mr. Chappel has prevailed against the defendant on his Title VII claim. His remedy will be determined at a later date.

Defendant Martin Marietta has prevailed against Ms. Rich, Mr. Franklin, Mr. Langley, Mr. Collier, Mr. Craig, and Mr. Tafoya on their Title VII claims.

Defendant Martin Marietta has prevailed against all plaintiffs on their claims under the Civil Rights Act, 42 U.S.C. § 1981.

This order contains and shall constitute the Findings of Fact and Conclusions of Law required by Rule 52 of the Federal Rules of Civil Procedure. Judgment shall not enter on this order at this time. Further proceedings, consistent with this order shall be set by separate order of the court.

APPENDIX I *

SUMMARY OF THE TRIAL COURT’S FINDINGS AND CONCLUSIONS FROM THE FIRST TRIAL

A. Jewel Rich

First hired August 6,1957 as an associate engineer, Mrs. Rich was promoted on January 10,1966 to full Engineer. She received merit increases approximately once a year, but did not receive another promotion during the remaining time that she worked for the company. She had a Bachelor’s Degree in Fine Arts and had had several years’ experience in engineering design prior to starting work for the Martin Company. Her rating was the lowest in her department, section and salary grade of 43. On the totem pole she was shown to have more experience than all except two of the 21 employees of her grade. She had more seniority and more formal education than about half. However, neither education, seniority nor experience were the criteria which were considered for promotion in and of themselves.

Her performance was not evaluated highly by her supervisors, all of whom were white and male. At the same time, she was shown to have performed her work on time and free from substantial error; she had creative ability and found some of her- tasks boring; her evaluation rating showed that she needed technical improvement. Notwithstanding this, she was recommended in October 1963 for promotion and again in August 1965, but it was not until January 1966 that the promotion came about. Her supervisor did recommend in May 1968 that she be given more responsibility once an opening occurred. At trial, two of her former supervisors said that she was deficient in her knowledge of “load paths” or structural design capability. Mr. Coan testified that the quality of her work was good and that her accuracy was sufficient, but that she just wasn’t good enough for any grade better than that which she occupied, which was 43. He stated that although she did not suffer in comparison with other employees in areas such as accuracy, prompt performance and fidelity to design criteria, it was in subjective areas such as attitude, initiative and dependability that she suffered.

The workings of the totem pole were described by Mr. Coan: He, as unit chief or head, would meet with the group engineers to discuss and rate their subordinates. Output, dependability and reliability were the criteria. Mr. Anschicks, assistant to the section chief, added that employees were rated in the order of their value to the company. The unit head after meeting with the group engineers would then meet with the section chief to go over the ratings, but the section chief in essence ratified the ratings of the unit heads and group engineers. They all agreed that Mrs. Rich’s low rating was proper.

In March 1970, several people in Mrs. Rich’s department were laid off. As a re-*619suit of her low rating on the totem pole, she was one of them. When she protested her section chief, Mr. Pratt, told her that the alternative would be for her to take a job in the publications department as a creative illustrator. Although the salary and rating were the same, she considered this a downgrade, so she met with Vice-President Purdy, and she felt that he indicated another job would be found. He testified, however, that there was a misunderstanding; that he had only urged her to take the illustrator job. She refused this and was laid off. After that, the number of people working on her project, “Skylab” was doubled.

Mr. Anschicks testified that there were no promotions in Mrs. Rich’s department during 1969, and that there were only two in 1968. However, the totem pole revealed that four people were hired in a grade above hers between September 3 and October 6, 1969.

The trial court found (as to Rich):

There were no openings for promotions in 1969, notwithstanding that the totem pole revealed that four persons were hired in the grade above hers (between September 3 and October 6, 1969). The court further found that the company did not discriminate against Mrs. Rich at any time prior to her filing the charge and that she was promoted in accordance with her abilities and qualifications. She was at the bottom of the totem pole and the decision to lay her off was reviewed at several levels. The creative illustrator job was the only one available for her at the time. She chose to reject that. The company did not discriminate against Mrs. Rich in discharging her.

B. Tommy Franklin

Hired August 18, 1959 as an Accountant B, Franklin had then completed a two year course in accounting at the Barnes school and had taken correspondence courses in accounting. He had also enrolled in Regis College in 1957 and was attending Regis part-time at the time that he was hired. He obtained his degree from Regis in 1963. He was promoted to Accountant A on July 3,1961, to Senior Accountant on September 30, 1963, and to Associate Analyst, his first salaried position, on August 7, 1967, and then to Specialist Finance on February 1, 1971.

Franklin’s performance evaluations were average to good. In July 1968, his evaluation as Associate Analyst showed that he had made great improvements both in quantity and quality of work. His supervisor in 1966-67 had stated that he should learn to use control techniques and should learn all facets of the billing operation. His supervisor, Mr. Wasserstein, testified that he did not feel confident in Franklin’s work; that Mr. Franklin was good at his job, cost billing, but was not very good at logic or catching errors. His next supervisor, Mr. Critchfield, said that he was better at repetitive jobs than the new tasks. There were no promotions over Franklin during 1969. However, two employees were promoted to his same grade. In March 1969, Critchfield was promoted from grade 43 to 45, but no one was promoted to fill that opening.

Wasserstein’s testimony was that he made out employee performance evaluations based on his impression as to how the work was being done. There were no written guidelines for a determination of promotability. It was apparently unnecessary for an opening to exist in order for an employee to be promoted. According to Wasserstein, when Franklin was promoted to a salaried position in 1967, the position he occupied did not change. The section chief determined who got raises and promotions. One of Franklin’s contentions was that he was prevented from getting cross-training in other areas of the department, whereas white employees received this. This fact prevented him from getting a promotion. However, the supervisors testified that there was no regular program of cross-training. This was done when there was time, but there was not often time. At the same time, they testified that Franklin had the same opportunities as everybody else.

The trial court found:

*620Franklin was promoted according to his ability, job knowledge, experience and future advancement potential. Franklin was given the same opportunity as his co-workers for cross-training. Defendant did not discriminate against Franklin on the basis of race either in promotion or opportunities for training.

C. Jose Tafoya

Hired as an electrical mechanic on June 28, 1957, he was in November of that year either reclassified or promoted to Analytic Associate. The evidence is unclear as to whether this was a reclassification or promotion.

On March 16, 1961, he was promoted to Engineer E & E (grade 41), a salaried position.

April 6, 1964, he was demoted in the course of a reduction in force to Electronic Developer. November 23,1970, he was promoted to Analytic Associate (grade 41).

In March 1973, he was demoted in lieu of layoff to Developer.

He was considered for promotion to Assistant Foreman in March 1969, but an employee who supposedly had more experience was chosen ahead of him. He had previous supervisory experience, although he had not been formally given a foreman’s position.

In March and April 1969, several employees were promoted to salaried positions from Tafoya’s department. Mr. Seal testified that two of these were asked for by name by the department to which they were promoted. Of the four named by Tafoya as being promoted over him, two were structural mechanics, according to Mr. Seal, with different skills.

Tafoya was shown to have been a good worker and had received good evaluations consistently. They said, however, that in 1969 Tafoya’s attitude deteriorated and he did not stick to his job. However, in June 1969 he is shown to have received an excellent rating with respect to his attitude both toward fellow employees and toward supervisors. Job experience, attitude and previous performance were described as the criteria applicable to promotions.

Tafoya maintained that he was harassed and intimidated following the filing of charges with the EEOC. The day following the service of charges, which date was January 8,1970, Tafoya and his supervisor, Mr. Fischer, got into an argument and the supervisor accused Tafoya of not being on the job on time and not working hard enough. The project that he was working on had to satisfy a deadline. He was transferred to another job, and Mr. Baylis, the manager of the Industrial Relations Department, called a meeting. Tafoya, Fischer, the Director of Employee Relations, and some other people were present. According to Baylis this meeting was called merely to determine what happened. Tafoya believed that the meeting was meant to intimidate him and, according to him, he was not allowed to tell his side.

The trial court found:

Tafoya had named several employees who were promoted over him. These promotions took place more than 90 days prior to his filing charges with the EEOC. According to the court, he failed to meet the criteria of *McDonnell-Douglas v. Green,*411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973).1

The court further found that the defendant made promotions based on a bona fide promotion system and that there was no reason to believe that Tafoya’s not being promoted was due to national origin. The court also found that the holding of the meeting was not for the purpose of unlawful harassment or retaliation for Tafoya’s having filed a charge with the EEOC.

D. John Langley

First hired June 6, 1958 as an E & E Fabricator, in 1959 he was promoted to *621Developer E & E. During two brief periods in 1964 and 1966, he was demoted as a result of a reduction in force. Otherwise, he remained a Developer until April 24, 1972, when he was promoted to a salaried position, Manufacturing Engineer. In 1973, he was laid off instead of taking a demotion to Developer. The termination was not in issue.

Langley’s evaluations were consistently good. They contain statements that he was a good employee, dependable, who did an outstanding job. Mr. Seal, the general foreman, testified that Langley was a very good employee, but that he did not think that he would make a good supervisor because he was too quiet. Seal also said that he did not believe that Langley could direct people. Mr. Bookhamer, also a supervisor, said that Langley was promoted in 1972 because he had received on the job training as a planning engineer. This is offered as an explanation for his having remained in the position of Developer for 12 years.

The trial court found:

That Langley failed to establish that the company promoted others into jobs for which he was qualified. The court found that he was promoted in 1972 because by then he had attained the requisite qualifications. The court went on to say generally that the company policy for promoting employees from hourly jobs to salaried positions was non-discriminatory; that it was based on ability, experience, job performance and the availability of a job.

E. Lawrence Collier and John Craig

These two men were first hired in 1961 as janitors. However, Collier left about a month later for the Army, and was rehired as a janitor in August 1963. Collier was transferred August 14, 1967 to Helper in the Maintenance Department. On January 6, 1969, he was promoted to Millwright B, but was demoted to Helper on March 9, 1970. He was promoted again to Millwright B on February 8, 1971 and to Millwright A June 19, 1972. Craig was transferred to Laborer October 23,1967. He was promoted to Helper March 18, 1968, and to Millwright B February 3, 1969. He was demoted to Helper March 9, 1970, promoted to Millwright B May 18,1970, and promoted to Millwright A May 17, 1971.

Both of these men were high school graduates, and Craig had taken college courses while working at Martin. The position of janitor was conceded to be a blind alley. In order for an employee to be promoted he had to be transferred to laborer or helper so that he could progress in the trade classifications, such as Millwright, Carpenter, etc. Collier requested such a lateral transfer August 21, 1963, soon after he was rehired by the company. He asked for another transfer in December 1966 as did Craig, but neither received a transfer until the latter half of 1967, at which time they were finally offered Millwright B jobs. At the end of December 1968, they accepted, though Collier had signed a preference form indicating that his first choice was Carpenter B. At the end of January 1969, Collier was offered and refused promotion to Millwright A.2,*

In 1969, the company established a training program for millwrights.** Both Collier and Craig enrolled, but dropped out for a couple of months and were reinstated and finished the course. It included eight weeks of remedial reading and arithmetic, general skill related courses, a term of specific skills courses and on the job training. Collier and Craig said they dropped out because the training was not helpful and the company was hiring white Millwright A people from outside. Prior to their being offered Millwright A positions, Collier and Craig were offered jobs as stockkeeper and *622vehicle operator. This was in line, according to Mr. Ferguson, Manager of Plant Services, with the company policy of offering all helpers a stockkeeper job when it became available whether or not there had been a request by the employee. In May 1970, after having been demoted to Helper, Collier was again offered a Millwright B position, but he turned this down because he had been unofficially offered a carpenter job. Later he accepted the Millwright B job.

Collier testified that the company’s policy at the time he was hired was to employ blacks and older white men as janitors, whereas young white men were initially hired as helpers and laborers. It was the position of the company, as expressed by Mr. Ferguson, that Collier and Craig were not qualified for promotions to Millwright A until they were actually promoted, but the record shows that no blacks held the Millwright A position until sometime in 1971. However, by 1972 all of the black Millwirght B’s had been promoted to A’s. There were 35 Millwright A’s between January 1966 and January 1973. Twenty-eight were white. Of these 28 white Millwright A’s, 11 were hired with no previous experience as B’s. All seven of the black Millwright A’s were promoted from the B rank. For the whites who were promoted from Millwright B, 15 months was the average time spent in B, whereas the black Millwrights who were promoted had to spend 68 months of service on the average as Millwright B’s.

The trial court found:

That Collier and Craig failed to prove that they were qualified for the Millwright A position before they were promoted. Meanwhile, they were trained on the job. The fact that there were no black Millwright A’s before 1971 was due to the fact that there were no black persons who were qualified but there was no discrimination against Collier and Craig on account of race.

F. Bobby Chappell

Hired May 15, 1957 as a janitor, he was transferred to Helper November 17, 1958 and promoted to Electrician B on February 15, 1960. There is one brief demotion to Helper in 1965. Otherwise, he remained as an Electrician B until May 17, 1971, when he was promoted to Electrician A.

The performance evaluations were fairly good. He was said to be cooperative. He had been given two trial periods as an A Electrician before he was promoted. On each occasion he was told he was not qualified. The testimony of Mr. Ferguson was that he was unable to hook up properly or to work very fast. Mr. Ferguson testified that all B Electricians seeking promotions went through the trial period.

Between January 1966 and January 1973, there were 44 A Electricians. Five of these were black and four were Spanish-American. No black or Spanish-American Electrician A’s were hired without previous experience as an Electrician B, but of the 35 white Electrician A’s, 15 were hired without previous B experience. The average number of months spent as a B Electrician for the remaining 20 whites was 24 months. The average months spent in the B classification for the black and Spanish-American A electricians was 47 months. Five of the nine blacks and Spanish-Americans were not promoted until 1971 or after. Since 1970, the number of B Electricians has decreased, whereas the number of A Electricians has increased.

The trial court found:

That Chappell was not qualified as an Electrician A at the time he filed charges with EEOC. He failed to show that white employees were promoted to that position at any time during which he was qualified. There was no discrimination against Chappell on the basis of race.

*623APPENDIX II

DIRECT COMPARISONS OF PLAINTIFFS’ AMD DEFENDANT'S FIGURES */

Chart A: Salaried Promotions

*624

Chart C: Hourly In-Unit Promotions

*625Chart D: Hourly to Salary Promotions

*626

*

 Mrs. Rich passed away prior to the second trial, we nevertheless consider her claims.

1

. Total employment during the years 1966 to 1971 ranged from 5,300 to 7,300.

2

. There are, as well, as insignificant number of miscellaneous and ungraded hourly positions. Those miscellaneous grades have minimal relevance to the general promotional patterns and grade structures.

3

. Plaintiff Rich filed with the EEOC on October 31, 1969, Franklin on August 27, 1969, Langley on October 27, 1969, Collier on August 23, 1969, Craig on August 23, 1969, Chappel on November 4, 1969, and Tafoya on December 3, 1969.

4

. In the course of our opinion, we shall refer to various of the testifying witnesses of the second trial. For convenience, we list all of the witnesses here.

Plaintiffs called three witnesses:

> Dr. David Pearson (qualified as an expert in statistical analysis),

> Mr. John W. Smith, III (an acting section chief), and Mr. Tommy Franklin (one of the plaintiffs).

> Defendant called seven witnesses:

> Mr. Robert Anschicks (a supervisor),

> Mr. Thomas Johancen (a supervisor),

> Mr. Charles A. Hall (a supervisor),

> Dr. Harry Gollob (qualified as an expert in statistical analysis),

> Dr. Roy Yamahiro (a manager responsible for performance evaluations),

> *593Mr. Bobby Frank Leonard (a manager in employee relations),

> and Mr. Leland Gillespie (a manager in compensation, wage, and salary).

> With the exception of the expert witnesses, Mr. Pearson and Dr. Gollob, all of the witnesses are employees or former employees of defendant Martin Marietta.

5

. These labor pools are further supported by defendant’s exhibit BBBB which summarizes the promotion trends. Over the years 1966-71, promotions of A and B level employees from hourly to salary ranged between 11.2% to 16.1%. During the same time frame, promotions of employees in labor grades 1-6 from hourly to salary ranged between 3.5% and 5.5% while promotions of grades 7-12 from hourly to salary ranged from 0.0% to 1.2%.

6

. This finding is based upon the record of the first trial. It should be noted, however, that plaintiffs have not all shown a particularly lengthy tenure in the specific jobs they held (as opposed to length of service in the company) during the relevant period. Mr. Craig, for example was a janitor in 1965. He was promoted to Laborer in 1967, to Helper in 1968, to Millwright B in 1969, and (after a brief, two-month demotion in 1970) promoted to Millwright A in 1971. For the promotion history of the other plaintiffs, see *generally,*the summary of our earlier findings which is attached as Appendix I. The relevant time period is noted at footnote 12 *infra.*

7

. *See,*42 U.S.C. § 2000e-5(e). The statute, as in effect at the time the instant charges were filed, provided for a time limitation of 90 days. The statute further provided for a longer, 210 day period where (as here) recourse was initially sought from a state or local agency. In the first trial, there was much focus on the 90 day period. In the instant trial, defendant has directed its proof to the 210 day period. *See, Rich, supra,*522 F.2d at 348 n.14.

8

. We admitted this evidence, over plaintiffs’ objection, for such weight as it might have. See, however, note 21, infra.

9

. Plaintiffs’ Exhibits 107 and 109 were admitted over defendant’s objection. Defendant pointed out that both exhibits were based on data for the time frame 1966-73 and that, as the data extended beyond 1971, the exhibits were defective for the same reason that certain of defendant’s exhibits (offered at the first trial) were. *See, Rich, supra,522*F.2d at 346. Because plaintiffs had derived the exhibits in question from information provided by defendant in response to interrogatories 83 and 84 propounded prior to the first trial, we admitted the exhibits but granted defendant leave to file adjusted exhibits. Defendant filed its modified Exhibits 107 and 109 on October 30, 1978.

10

. The categories are salaried, hourly-out-of-unit, hourly-in-unit, and hourly to salary. The hourly to salary category was further subdivided into' other classifications (including labor pools).

11

. Those groups are black, Hispano-American, and female. There were also analyses done on the combined groups.

12

. For the Title VII counts, the relevant years are 1965 (the year in which the Act took effect) through 1969 (the year in which the EEOC charges were filed). See, *Rich, supra,*522 F.2d at 339 n.2, 346. For the § 1981 counts, the relevant years are 1965 through 1971 (the complaint was filed in 1971, there is a six year statute of limitations). See, *Zuniga v. AMFAC Foods, Inc.,*580 F.2d 380, 386-87 (10th Cir. 1978).

The first full, relevant year for which statistics were available is 1966. The statistics in evidence are for various of the years 1966-71.

13

. We refer to the data bases as “manual” and “tape.” The manual data derives from Martin Marietta’s manual system of maintaining personnel data. In mid to late 1972, Martin Marietta converted to a computerized system. The basic data for the computerized system is kept on a computer tape and the tape data derives from that source.

Manual data on promotions are available for the years 1966-69, tape data for the years 1966-71. The most significant difference between the two data bases is that the tape data does not include information on employees who had worked at the Waterton plant during the relevant years but who were no longer working there as of May 11, 1971.

14

. Plaintiffs analyzed the data in two ways: by the “Vs’s Rule” and by the “significance of difference between two proportions” test. Defendant analyzed the data utilizing a “lottery” model employing a binomial distribution in certain instances and a hypergeometric distribution in other cases. Both plaintiffs’ significance of the difference test and defendant’s lottery model are probability tests. They both make use of the 5% upper and lower bound, or the two standard deviation level, in determining statistical significance.

15

. It is significant to note, however, that lines 4 and 5 of table (1) which reflect hourly to salary promotions are based upon calculations that do not take the relevant labor pools into account.

*

 This table is derived from plaintiffs’ Exhibits 127, 128, 129, 130, and 134.

16

. It is significant to note, however, that lines 4 and 5 of table (2) which reflect hourly to salary promotions are based upon calculations that do not take the relevant labor pools into account.

17

. Dr. Gollob testified, without contradiction, to the effect that the “Z score,” the “two standard deviation,” and the “5% rule of thumb” are synonymous or equivalent terms. We, thus, use those expressions interchangeably.

18

. Two observations are worthy of note at this point.

> The first is the obvious one, which might tend to become obscured by the very volume of statistical evidence, that we are not engaged in an hypothetical exercise in the academic discipline of statistics. We have summarized the statistical evidence at some length in the preceding tables and have further displayed that evidence in the four charts which are attached as Appendix II in order to make explicit the basis for our findings of fact. The statistics, of course, are relevant only insofar as they “comport to the specific issues presented.” *Rich, supra,*522 F.2d at 346. In the further course of this opinion, we shall draw upon the voluminous data to present, much more narrowly, those particular sets of statistics which are of relevance to the specific claims of the seven plaintiffs.

> The second observation is equally obvious. It should go without saying that the tables and charts we are using are but convenient means of referring to the original exhibits. We have examined each of the some one hundred exhibits and, while we are fully satisfied that our tables and charts are accurate representations, we base our findings squarely on the underlying exhibits. We use the tables and charts only as an aid in presenting our findings.

19

. Dr. Gollob testified to the effect that the overall pictures presented by plaintiffs’ and defendant’s tests for statistical significance were consistent. Indeed, defendant’s test shows more instances of adverse impact (20 instances) than does plaintiffs’ test (14 instances).

Those results under the tests for statistical significance may be contrasted with the results obtained by the Vs’s Rule (some 32 instances of adverse impact).

20

. See pages 609-613, *infra.*

21

. There has been rapid development in Title VII jurisprudence since the time the mandate issued. Defendant contends that we are not bound to follow the mandate insofar as it may have been contradicted by subsequent cases. Defendant cites several such apparently conflicting intervening cases.

No purpose would be served by exhaustively analyzing such cases. In the first place, we conclude that there are no truly irreconcilable conflicts. In the second place, even were we to have found inconsistencies, it is not for us to reconcile possible conflicts between panels of the 1 Oth Circuit or between that circuit and the Supreme Court. The mandate herein is the law of the case and our duty is to follow it as best we can.

22

. We have considered, and we reject, defendant’s argument that such findings of fact as we have made concerning qualifications and availability of positions (see pages 594-595, 595; see *generally*Appendix I) ought to lead to a contrary result. The Tenth Circuit had such facts as these before it when it rendered its opinion in this matter. As there was no hint that the court of appeals determined any of the *608facts to be clearly erroneous, we can only conclude that these facts are irrelevant.

We have, nonetheless, weighed the evidence and made detailed findings of fact in order to develop as complete a record as possible. We endeavor, by so doing, to minimize the likelihood of further costly and time consuming proceedings in this matter.

23

. Disparate treatment is the “most easily understood type of discrimination.” *Teamsters,*supra,431 U.S. at 335-36 n.15, 97 S.Ct. at 1854. It occurs where the employer simply treats some people less favorably than others because of their race, color, religion, sex, or national origin. In such a case, proof of discriminatory motive is critical, though motive may sometimes be inferred. *Id.*

Disparate impact is not so obvious an evil. It involves employment practices which are neutral on their face but which result in a comparatively harsh impact on one group, not justified by business necessity. In such a case, proof of discriminatory motive is not required. *Id.*What a plaintiff must show is that the facially neutral standards in question select applicants in a significantly discriminatory pattern. *Dothard v. Rawlinson,*433 U.S. 321, 329, 97 S.Ct. 2720, 53 L.Ed.2d 786 (1977).

As either of the two theories may be applied to the same set of facts, *Teamsters, supra,*431 U.S. at 336 n.15, 97 S.Ct. 1843, it follows that plaintiff in a job discrimination case need not always prove that the employer had a specific intent to discriminate. *E. g., Muller v. United States Steel Corp., 509*F.2d 923, 927 (10th Cir.), *cert. denied,*423 U.S. 825, 96 S.Ct. 39, 46 L.Ed.2d 41 (1975).

24

. Statistics might have some probative value in determining whether given actions are discriminatorily motivated. *Furnco, supra,*438 U.S. at 580, 98 S.Ct. at 2951. They are, thus, a factor which may be considered in a disparate treatment case.

Statistics are even more clearly relevant in a disparate impact case. Absent explanation, it is ordinarily to be expected that nondiscriminatory practices will in time result in a workforce more or less representative of the racial and ethnic population in the community from which employees are hired. *Teamsters, supra,*431 U.S. at 339-40 n.20, 97 S.Ct. 1843.

25

. On the current state of the record, we can find no basis in fact for rejecting one data source completely in favor of the other. Both sources are relatively reliable, both provide relevant information, and, though they overlap to some extent, there are cases where one of the data sources provides pertinent information not available in the other.

26

. This is no academic point. The differences are significant. We might note that, though the primary focus of this case, as defined by the plaintiffs, is on defendant’s promotional policies and not upon its initial hiring or initial classification practices, there are strong intimations that many minorities are concentrated among the lower hourly grade positions. They are, thus, concentrated, for whatever reason, in hourly positions where promotion to salary is unlikely.

We have considered, and reject, plaintiffs’ argument that a definition of labor pools assumes the result that defendant would have us reach (that is, absence of discrimination). Defendant, for its part, has supported its theory of labor pools with hard evidence. Plaintiffs have offered no evidence at all to support its suggest tion that minorities were initially *hired*into lower hourly grades in a discriminatory fashion and that more minorities *should have been*placed in the higher hourly grades initially. In addition to being unsupported by any evidence, such suggestions would appear both outside the scope of this lawsuit and unconvincing on the question whether, vel non, labor pools exist.

We likewise reject plaintiffs’ argument that use of labor pools, as it reduces the aggregate size of the populations involved, leads to too small a sample to be statistically meaningful. Though the point is strongly argued, there is no evidence to support it. We find the testimony of defendant’s expert, Dr. Gollob, to be persuasive on this point. We also note that plaintiffs’ argument does not directly challenge defendant’s proposition that labor pools exist.

27

. The Virginia Law Review article observes that

> [a]s yet the courts have not identified the point at which the impact . . . becomes substantial enough to shift the burden of persuasion to the defendant. Apparently the courts purposely attempt to remain flexible in order to accommodate distinctive features in each setting. As one court has put it, “[t]he question of what is a ‘small’ membership in relation to black workers in a demographic area is a question of degree.”

> At present the courts of appeals characterize substantiality as a factual issue, refusing to reverse a district court unless its finding is ‘clearly erroneous.’

59 Va.L.Rev., *supra,*at 477-78 (footnotes omitted).

28

. *See also,*Holley and Feild, *Using Statistics in Employment Discrimination Cases,*4 Employee Relations L.J. 43 (Summer 1978) and cases collected, *Id.*at 52-53 (cases using phi correlation coefficients); at 53 (cases using chi-square and phi correlation); at 53 (cases using t-tests); *Id.*at 54-55 (cases using regression analysis and considering the use of analysis of variance, ANOVA). *And see, United States v. Virginia,*454 F.Supp. 1077 (E.D.Va.1978) (using the binomial).

29

. The Rule has been adopted by the EEOC, the Civil Service Commission, the Department of Labor, and the Department of Justice. 43 Fed. Reg. 38290 (August 25, 1978) (to be codified in 29 C.F.R. § 1607 [EEOC]; 5 C.F.R. § 300.103(c) [Civil Service]; 41 C.F.R. § 60-3 [Labor]; 28 C.F.R. § 50.14 [Justice]).

Citations hereinafter will be to the Federal Register. On cross examination, plaintiffs’ expert accepted this version of the 4/s’s Rule as an accurate statement of the rule.

30

. See, *Hazelwood, supra,*433 U.S. at 311 n.17, 97 S.Ct. 2736.

31

. While plaintiffs’ expert stoutly maintained that there was a difference in method, we find the testimony of Dr. Gollob, defendant’s expert, to be the more reasonable and credible. Dr. Gollob explained the assumptions upon which he based his lottery model and those assumptions appear soundly based.. We find Dr. Pearson’s dispute with Dr. Gollob’s method to be inconsequential.

32

. We briefly note, and reject, plaintiffs’ argument that *only its*statistical evidence may be considered in determining whether a prima facie case has been established. We do not construe the mandate in this case as so directing and, in the absence of such direction, plaintiffs’ position is simply untenable. *Cf., Hazelwood, supra,*433 U.S. at 310-12, 97 S.Ct. 2736 (by implication). *Accord, James v. Newspaper Agency Corp.,*591 F.2d 579, 583 (10th Cir. 1979).

33

. Chart A, line (1). We disregard the values from Table 1 because they are based on the Vs’s Rule. Table 2 is blank. Table 3 consists entirely of null values.

34

. Chart A, line (3). We disregard Table 1. Reading across, Table 2 shows an impact, using manual data, in 1969 and, using tape data, in 1967. Reading across, Table 3 shows an impact in 1969 (manual) and in 1970 (tape). Combining the data bases and the two tests for statistical significance, the result is a showing of adverse impact in the years 1967 and 1969. We disregard the year 1970 because it is outside the relevant Title VII time frame (see note 12, *infra).*

35

. Chart B, line (1).

36

. Chart D, line (1). We disregard the values of Table 1 because they are based upon the 4/5’s Rule. Table 2 is blank. There are null values in every instance in Table 3.

37

. Chart A, line (I).

38

. Chart B, lines (1) and (2).

39

. Chart D, lines (1) and (2). Note that the values for Hispano employees, which have as their source Table 3, line (4), should be disregarded. Those values do not take labor pools into account.

40

. We do reject, however, plaintiffs’ theory that subjectivity *alone*can serve to establish an impact.

Though it might foster conditions in which discrimination can be practiced, *see, Muller v. United States Steel Corp.,*509 F.2d 923, 928 (10th Cir.), *cert. denied,*423 U.S. 825, 96 S.Ct. 39, 46 L.Ed.2d 41 (1975), subjectivity gains its operative significance where it is accompanied by *other*factors which strongly indicate the presence of discrimination. *Cf., Muller, supra,*and cases collected, *id.*at 928 (noting that where the *"results*give a strong indication that discrimination is being practiced, the cases condemn subjective standards . . . .”) (emphasis added).

While perhaps suspect, subjective standards do not, of themselves, create a prima facie case. This is the more so upon the uncontradicted showing here that the aerospace industry does not allow for strictly objective, quantitive evaluations. Indeed, we would be hard pressed to fashion a method which would wo,rk satisfactorily and also be appreciably less subjective than the practices here challenged.

We are not unmindful that courts are “generally less competent than employers to restruc- . ture business practices, and unless mandated to do so by Congress they should not attempt it." *Furnco, supra,*438 U.S. at 578, 98 S.Ct. at 2950. *Cf., Olson, supra,*531 F.2d at 478 (referring to Pandora’s box).

41

. The Tenth Circuit has summarized our factual findings of the first trial. Among our findings summarized therein are these: “Her rating was the lowest in her department, section and *617salary grade of 43,” Appendix I, *infra*at p. 618, and “They [the section chief, unit head, and group engineers] all agreed that Mrs. Rich’s low rating was proper.” *Id.*at p. 618.

42

. Plaintiff Rich’s failure to show those factors has not prevented this court from finding that she was qualified for promotion. *See,*note 22, *supra; Rich, supra,*522 F.2d at 347.

We are, however, not concerned with qualifications at this point. We are now considering these factors as evidence which bears upon defendant’s motive in light of the fact that the prima facie case only permits an inference of discriminatory animus *in the absence of explanation. See, Furnco, supra,*438 U.S. at 579, 98 S.Ct. at 2951.

43

. *And see, Chicano Police Officer’s Ass’n v. Stover,*552 F.2d 918, 920-21 (10th Cir. 1977) (on remand).

44

. Because we resolve the § 1981 claims on this ground, we have no occasion to consider whether all of the plaintiffs have presented claims cognizable under this statute.

*

This summary is reprinted, verbatim, from the Tenth Circuit’s opinion. *Rich, supra,*522 F.2d at 349-54. Numbered footnotes herein are by the Tenth Circuit and are numbered as in the original. Asterisked footnotes are those which have been added by this court.

1

. Presumably, the trial court was referring to the requirement spoken of in the case that a plaintiff show a position was available. The trial court presumes that since no one else was promoted within 90 days, no position was available, and therefore no discriminatory act took place within 90 days before the charge was filed.

2

. Collier does not explain why he refused this promotion. Defendant does not explain why Collier was considered qualified for Millwright A in January 1969, but not qualified before his promotion in June 1972.

*

The evidence at the second trial has clarified the situation described in note 2. See, page 4594, *supra.*

**

The evidence at the second trial has clarified this point as well. See, pages 597, 598, *supra.*

*

 These charts are drawn from the tables described at pages 598-606, *supra.*

Table 1 reflects plaintiffs’ Vs’s Rule. Table 2 reflects plaintiffs’ test for statistical significance. Table 3 reflects defendant’s test for statistical significance.

Tables 1 and 2 (reflecting plaintiffs’ 4/ü’s Rule and plaintiffs’ test for statistical significance, *624respectively) were subdivided. In each case, line 4 represented hourly to salary promotions generally while line 5 represented hourly to salary — officials and managers. Neither took labor pools into account.

Table 3 (reflecting defendant’s test for statistical significance) was also subdivided. Line 4 ignored the relevant labor pools. Lines 5, 6, and 7 took the labor pools into account and show the high, medium, and low labor pools, respectively. Line 8 reflects hourly to salary— officials and managers, taking labor pools into account.

*

 Line 8 of table (3) which reflects hourly to salary (officials and managers) is based upon calculations which took relevant labor pools into account. Since there were no statistically significant differences in any category, we have compressed the data on line 8 rather than present it in expanded form as per lines 5, 6, and 7.