Pegues v. Mississippi State Employment Service

POLITZ, Circuit Judge: Rosie Lee Pegues, Rebecca Gillespie, Mary Boyd and Robert Williams, residents of Bolivar County, Mississippi, brought suit against the Mississippi State Employment Service (MSES), John E. Aldridge, Ernest C. Lindsey, the United States Secretary of — 762 — Labor, the United States Department of Labor and its division, the United States Employment Service (USES), contending that the defendants engaged in individual and classwide discrimination in violation of Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e, et seq., 42 U.S.C. §§ 1981 and 1983 and the thirteenth and fourteenth amendments to the Constitution.1 The named plaintiffs represent a class of black and female applicants who have sought or who may hereafter seek job referrals from MSES’s Bolivar County office located in Cleveland, Mississippi. After an extended bench trial, the court entered judgments dismissing both the individual and class action Title VII claims. Pegues v. Mississippi State Employment Serv., 488 F.Supp. 239 (N.D.Miss.1980). Plaintiffs raise a plethora of issues on appeal, assigning errors of fact and law to the final judgment and two intermediate rulings. We affirm in part, reverse in part, render and remand for the fashioning of an appropriate remedy. Procedural History Following receipt of the requisite right-to-sue letters from the Equal Employment Opportunity Commission in January 1972, plaintiffs filed suit against the state defendants charging the MSES Cleveland office with discrimination in the classification, referral, and testing of black and female applicants for employment referral within the Bolivar County labor market. Plaintiffs charged racial and sexual discrimination in: (1) the assignment of occupational classifications to blacks and females; (2) the acceptance and servicing of certain employer job orders; (3) the administration of employment tests to blacks; (4) the failure to refer blacks and females to available jobs; and (5) the referral of blacks and females to lower paying and less desirable jobs. The federal defendants were joined as indispensable parties under Fed.R.Civ.P. 19(a). 57 F.R.D. 102 (N.D.Miss.1972). An amended complaint filed thereafter alleged a statewide class, and attacked regulations and guidelines promulgated by the Secretary of Labor which purportedly allowed MSES to discriminatorily classify and refer applicants, and allegedly required MSES to use employment tests developed by USES which disproportionately impacted against blacks.2 The state defendants cross-claimed, seeking indemnity from the federal defendants for any adverse money judgment based on their compliance with federally-mandated policies and procedures.3 A motion by plaintiffs requesting certification of a statewide class of blacks and females seeking referral from all state MSES offices, filed in 1974, was finally heard in February 1978. The court certified a class confined to persons seeking job — 763 — referrals from the Bolivar County MSES branch. In March 1978, the district court granted the federal defendants’ motion for summary judgment,4 ruling, inter alia, that the 1972 amendments to Title VII barred imposition of liability upon USES in the event classification, referral or testing functions performed by MSES under federal supervision were adjudged illegal. Because of the dual possibility that plenary injunctive relief could not be secured from the state defendants in the Secretary’s absence, and the state might be entitled to indemnity should back-pay or attorneys’ fees be assessed against it, the court declined to dismiss the state’s cross-claim. On appeal, plaintiffs challenge the district court’s conclusion that referral of job applicants by the MSES office was free of race and gender discrimination. They further argue that the court erred in finding that employment tests administered by the Cleveland office were job-validated and did not impact adversely on black applicants. Plaintiffs challenge the court’s admission of expert testimony on test validation, grant of summary judgment in favor of the federal defendants on the basis of the 1972 amendments to section 701(e), 42 U.S.C. § 2000e(c), and refusal to certify a statewide class. Limitation of the Class Plaintiffs sought certification of a statewide class and the intervention of persons complaining of practices in MSES offices throughout the state. Finding the request untimely and concluding that a statewide class was unwieldy and unnecessary, the district court limited-the class to Bolivar County and denied intervention. Appellate review of this ruling is governed by an abuse of discretion standard. Payne v. Travenol Laboratories, Inc., 673 F.2d 798 (5th Cir.), reh'g denied, 683 F.2d 417 (5th Cir.), cert. denied, -U.S.-, 103 S.Ct. 452, 74 L.Ed.2d 605 (1982). Implicit in this deferential standard of review is the recognition of the essential factual nature of the certification inquiry and the district court’s inherent power to manage and control pending litigation. When measured against this standard, we are not prepared to say that the district court’s effort to efficiently manage this complex litigation constituted an abuse of discretion. See McGowan v. Faulkner Concrete Pipe Co., 659 F.2d 554 (5th Cir.1981). I. CLASS CLAIMS A Title VII class action may be brought under two theories: disparate treatment or disparate impact. Either theory may prove applicable to the same set of facts. Wheeler v. City of Columbus, Miss., 686 F.2d 1144 (5th Cir.1982). In a disparate treatment case the plaintiff class must prove the existence of a pattern and practice of race or gender-based discrimination. See International Brotherhood of Teamsters v. United States, 431 U.S. 324, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977). Discriminatory intent must be established, by either direct or circumstantial evidence. Wheeler v. City of Columbus, Miss. Facially neutral practices which impact more severely on one group than another are subject to attack under the disparate impact theory. Dothard v. Rawlinson, 433 U.S. 321, 97 S.Ct. 2720, 53 L.Ed.2d 786 (1977); International Brotherhood of Teamsters v. United States. Proof of discriminatory purpose is not required in a disparate impact case. — 764 — Plaintiffs charge the MSES Cleveland office with racial and sexual discrimination in three practices: assignment of occupational codes, referrals, and testing.5 All three practices allegedly impacted in a significantly adverse manner upon black and female applicants. Plaintiffs cast their evidence as to each practice in the disparate impact model. However, we conclude that only the testing issue fits within this evidentiary framework. A brief description of the operation of the Cleveland office during the relevant period will assist in focusing the plaintiffs’ class claims. This office, like all other MSES branch offices in Mississippi, functioned as a labor exchange, matching qualified applicants with available jobs. Employers made known openings by placing “job orders.” Applicants made known their availability by requesting job referrals. The Cleveland office accounted for approximately 25% of all new hires in the Bolivar County labor market. On the initial visit, each applicant was given an application form, questioned as to job preferences and directed to the interviewer who handled job codes corresponding to the preferences expressed. Until 1978, job codes were six-digit numbers representing a specific family of jobs in the federal Dictionary of Occupational Titles (DOT), a Department of Labor publication.6 Once routed to the appropriate interviewer, the applicant was assisted in completing the application form, and questioned about education, vocational training, work experience, skills, work preferences, and personal interests and characteristics. Based on this information, the interviewer selected and inscribed the appropriate DOT code on the application. Work experience was a primary consideration in the coding process, although other factors were weighed, in765 eluding the types of employment available in the area. The code issued an applicant who was not fully qualified, lacked the requisite experience, or needed further training, included an “x.” The interviewer’s duties included the processing of employer job orders. A typical order contained information from the employer concerning the job, the number of vacancies, the desired number of referrals per vacancy, and the education and experience thresholds required. Interviewers had authority to determine whether any educational or experiential criterion was sufficiently job-related, and if not, whether further investigation was necessary before the job order was processed. Interviewers were encouraged to dissuade employers from imposing arbitrary hiring requirements, and job orders discriminating on the basis of sex or race were not to be serviced by MSES personnel. After obtaining the necessary information, the interviewer coded each job vacancy listed in the job order. The matching and referral decision was facilitated by tests designed to ascertain job capabilities. In the absence of a sufficient number of applicants with a code identical to a job order, applicants with codes within the occupational family were referred. The discretion of the interviewer was unavoidably involved in this process. Plaintiffs introduced extensive documentary and testimonial evidence designed to show that the state defendants discriminated in the classification and referral of blacks and women, contrary to federally prescribed policies. Implicit in this claim is the contention that the interviewers abused their discretion in coding and referring. Plaintiffs also endeavored to prove that the battery of tests, albeit uniformly administered without regard to race, operated disproportionately to exclude blacks. Because the classification and referral practices complained of effectively turn on discretionary decisions, they do not fall within the category of facially neutral procedures to which the disparate impact model is traditionally applied. Pouncy v. Prudential Ins. Co. of America, 668 F.2d 795 (5th Cir.1982); C. Sullivan, M. Zimmer and R. Richards, Federal Statutory Law of Employment Discrimination, § 1.5(c) (1980). Selection processes which rely on subjective judgments, despite the corralling by objective standards, provide the opportunity for the intentional discrimination cognizable in a disparate treatment action. See Payne v. Travenol Laboratories, Inc. We must therefore analyze plaintiffs’ challenge to the classification and referral systems under the disparate treatment modality. Their challenge to the aptitude tests, generally regarded as neutral selection mechanisms, will be evaluated under the aegis of the disparate impact theory. A. Classification and Referral As noted, we evaluate the classification and referral claims under the disparate treatment theory, which requires proof of discriminatory animus. To prevail, plaintiffs must demonstrate more than “the mere occurrence of isolated or ‘accidental’ or sporadic discriminatory acts. [Rather they must show] by a preponderance of the evidence that discrimination was the [defendants’] standard operating procedure— the regular rather than the unusual practice.” International Brotherhood of Teamsters v. United States, 431 U.S. at 336, 97 S. Ct. at 1854. A prima facie case may be established by the use of statistics if a sufficiently substantial, or “gross,” disparity in the treatment of the favored and disfavored groups can be shown. Hazelwood School District v. United States, 433 U.S. 299, 97 S.Ct. 2736, 53. L.Ed.2d 768 (1977). In such cases statistical disparities, standing alone, may justify an inference of discriminatory motive. International Brotherhood of Teamsters v. United States; Payne v. Travenol Laboratories, Inc. Moreover, as we stated in Payne: The statistical showing of disparate result may also be buttressed with evidence of a history of discrimination practiced by the employer, individual instances of discrimination, and opportunities to discriminate that exist in the employer’s decision-making processes. If the statistical disparity — 766 — is insufficient alone to establish a prima facie case, the plaintiff may get over his or her initial hurdle by combining statistics with historical, individual, or circumstantial evidence. (Citations omitted.) 673 F.2d at 817. Should the plaintiff succeed in establishing a prima facie case, the defendant may overcome the presumption of discrimination thus raised by discrediting the plaintiff’s statistical evidence or by advancing a nondiscriminatory rationale for what appeared to be discriminatory conduct. Wheeler v. City of Columbus, Miss.; Williams v. New Orleans Steamship Ass’n, 673 F.2d 742 (5th Cir.), reh’g denied, 688 F.2d 412 (5th Cir. 1982). Affirmations of good faith selection of the most qualified applicant will not satisfy this burden. Failure by defendants to rebut a prima facie case warrants the conclusion that Title VII has been violated. Statistical evidence must be regarded with a substantial degree of caution. See New York Transit Auth. v. Beazer, 440 U.S. 568, 99 S.Ct. 1355, 59 L.Ed.2d 587 (1979); Pouncy v. Prudential Ins. Co. of America. Although competent to prove employment discrimination, “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 all the surrounding facts and circumstances.” International Brotherhood of Teamsters v. United States, 431 U.S. at 340, 97 S.Ct. at 1856. We have repeatedly warned of the need for considered and refined statistical analysis in the context of Title VII class actions. Pouncy v. Prudential Ins. Co. of America; Rivera v. City of Wichita Falls; Wilkins v. University of Houston, 654 F.2d 388 (5th Cir.1981), vacated and remanded, -U.S.-, 103 S.Ct. 34, 74 L.Ed.2d 47 (1982), aff’d on remand, 695 F.2d 134 (5th Cir.1983). Discrimination in Classification Plaintiffs presented quantitative evidence of the disproportionate classification of blacks and women in stereotypic, less remunerative occupations during selected years between 1970 and 1976. No testimony, lay or expert, was offered to explain the significance of this data, nor was an appropriate test of statistical significance applied. Evidence of individual instances of discriminatory treatment of blacks and women during the classification process, and of the state defendants’ noncompliance with federal directives, was also introduced. Without indicating whether such evidence, in the aggregate, sufficed to make out a prima facie case of discrimination, the district court concluded that plaintiffs had failed to sustain their ultimate burden of proof under an impact theory.7 Several charts were offered to show a disproportionate classification of blacks in codes for less desirable service occupations, and of women in lower paying jobs. These exhibits reflect imbalances, but do not show that race or sex, rather than work preferences, experience, education, and the state — 767 — of the job market caused the imbalances. As thus presented, these figures are of little probative value. D. Baldus & J. Cole, Statistical Proof of Discrimination, § 1.22[23] (1980). At first glance, two related series of exhibits focusing on race in the classification of persons of equivalent education appear illuminating. Upon closer examination, the probative value dims. In the first series, one exhibit reflected that in 1970, 90 black women and one white woman, all with at least eight years of education, were coded for domestic labor. Other exhibits portrayed a continuation of this trend, to a lesser degree, in 1972, 1974 and 1976. Work preferences were identified for 1970 only; of the 44 coded as maids that year, 28 opted for non-domestic work. There was no analysis of this data and no quantification of the white women in the pool who received more desirable codes. The records do not show job preferences for 1972, 1974 and 1976, an omission which detracts from the weight of the figures and militates against any meaningful comparison of the races. The second series of exhibits, organized according to educational levels, contrast black and white classifications for the year 1974. One exhibit reveals that 265 black women with an elementary school education, constituting % of the females in this category who applied in 1974, were coded for service occupations, while only 16,,white women were similarly coded. Twelve black and 9 white women in this cross-section of 1974 applicants were assigned the clerical and sales code characteristically dominated by whites; 2 black and 0 white women were assigned codes within the professional, managerial and technical category. Past experience, work preference, and the availability of alternate jobs at the time of interviewing, information which is contained in the record, were not compiled or considered by the plaintiffs. Nor were the figures subjected to statistical analysis. The same comparative analysis was employed with respect to the classification, in 1974, of black and white men with no more than a seventh grade education. Again, such critical variables as experience, work preference and jobs available at the time each applicant was interviewed were not incorporated in the data, nor was statistical methodology utilized to discount the possibility that apparent racial discrepancies were not due to random selection. Substantial disparities in the assignment of service or farmwork codes to black and white men with an education at or above the eighth grade level were also shown pursuant to this analysis. Occupational preferences and job availability were again omitted. Work histories, although measured by the data, were widely divergent. No statistical test of significance was used to evaluate these disparities. In the final series of exhibits, raw data in the form of seven charts, each of which lists the name, education, work preference and experience of applicants of a specific race/sex group, together with the codes assigned in the years 1970 and 1974, were offered. Plaintiffs produced no evidence which explained or collated this data for purposes of comparison between favored and disfavored groups. The particular variant or variants to be compared among such groups was not disclosed. Scrutinizing these charts for differences in the classification of similarly qualified blacks and whites, or males and females, within a certain code, discloses that there is no indication of the size of the total applicant pool and the proportion thereof of each group. None of the recognized tests of statistical significance was performed in an attempt to demonstrate the unlikelihood that differential coding could be ascribed to chance rather than race or gender. Reasoned assessment of disparities in classification of blacks and females evinced in these exhibits thus cannot be made. While precise calculations of statistical significance are not essential to statistical proof, Hazelwood School District v. United States, no valid conclusions regarding the relationship of observed selection patterns to the defendants’ behavior can be drawn absent some minimal framework for analy — 768 — sis. Plaintiffs bear this burden. See Rivera v. City of Wichita Falls; Vuyanich v. Republic Nat’l Bank of Dallas, 505 F.Supp. 224, 234 (N.D.Tex.1980); A. Smith and T. Abram, Quantitative Analysis and Proof of Employment Discrimination, 1981 U.Ill.L. Rev. 33. Mindful though we are that simple comparisons of percentages are acceptable where a strong inference of discrimination has previously been raised, Rivera v. City of Wichita Falls, such is not the case here. No pattern or practice of discriminatory treatment is otherwise established by a combination of plaintiffs’ anecdotal and statistical evidence. It is not for the court, trial or appellate, to search the voluminous record for data omitted from plaintiffs’ comparative analyses, compensate for the failure to filter out the combined effects of factors unrelated to race or sex, choose the appropriate statistical methodology, and insert therein select parts of the array of figures presented. See Miller v. Weber, 577 F.2d 75 (8th Cir.1978). See generally Wilkins v. University of Houston.8 Discrimination in Referral To establish a prima facie case of discrimination against class members in referrals, plaintiffs offered statistics, bolstered by historical, anecdotal and circumstantial evidence, to demonstrate that defendants disproportionately excluded qualified black and female applicants from employment opportunities. This comparative evidence was based on the assumption that all persons with the same job code were similarly qualified for a particular occupation. Plaintiffs first took aim at defendants’ alleged practice of servicing discriminatory sexual preferences of employers. They offered evidence of a pattern of sexually segregated referrals to a major local employer, Travenol Laboratories, during the period December 1969-May 1970. Women were referred exclusively to lower paid assembler jobs, and men to better paid material handler jobs, in statistically significant numbers.9 Both were entry-level positions, demanding no special skills or training. — 769 — These statistical disparities gain added dimension when examined in the context of evidence that the Cleveland office accepted job orders in which the employer’s gender preference was expressed. Also relevant in this regard are two admonitions issued by the Department of Labor in June 1968 and May 1969, ordering the Cleveland branch to cease the servicing of discriminatory employer sex preferences, and to investigate the validity of such preferences and record the results. The office did not investigate the suspect job orders processed after receipt of the Department of Labor’s admonitions. Plaintiffs also challenged defendants’ systematic referral of applicants to positions other than those for which they were classified. In 1970, of the 68 persons referred out-of-code to the more attractive clerical and sales occupations, 58 were white. Eight of these individuals were overqualified according to their assigned code and may therefore be eliminated. In contrast, only 10 black persons were similarly referred, three overqualified. Conversely, of the 68 applicants referred out-of-code to less desirable service employment, 24 were white, three overqualified, and 34 black. These categories are further divided to show that 20 of the 21 white women referred to service jobs were matched with employers seeking waitresses, while 26 of the 34 black women receiving service referrals were accorded opportunities for stereotypical domestic or cook positions. Cognizant of the lessened probative value of statistical evidence where the sample size is small, due to the incremental increase in the possibility of sampling error, we must nonetheless guard against an overly facile rejection of discrimination claims. Two conflicting interests must be weighed: the danger of prejudice to the defendant posed by drawing inferences of discrimination from evidence consisting of a handful of selection decisions, and the unfairness to the Title VII claimant of imposing unattainable standards for proof of discriminatory intent. EEOC v. American Nat’l Bank, 652 F.2d 1176 (4th Cir.1981), reh’g denied, 680 F.2d 965 (4th Cir.), cert. denied, - U.S. -, 103 S.Ct. 235, 74 L.Ed.2d 186 (1982). Given our conclusion that a discriminatory pattern of sexually disparate referrals for a portion of 1970 has been demonstrated, we are satisfied that the evidence bearing on out-of-code referrals may properly serve to strengthen the prima facie case of discriminatory treatment.10 Plaintiffs next assail the state defendants’ selection of applicants for referral on the basis of unvalidated educational and experiential requirements. As to the educational requirements, plaintiffs rely upon charts detailing what plaintiffs deem to be unreasonable minimum education requirements of certain employers for various job vacancies in 1970 and 1976, together with census data revealing lower levels of education among blacks and women in Mississippi. The lay witness who compiled these charts acknowledged employing her subjective judgment with respect to the reasonableness of a given educational requirement. A similar study on the experience requirements was likewise based on this witness subjective determination of reasonableness. These rudimentary analyses did not purport to gauge the impact, in numerical terms, upon black and female applicants in Bolivar County by comparison with the appropriate — 770 — cross-section of the relevant labor market. Absent proof of disparate impact, no invidious discrimination can be shown under the disparate treatment theory. Pouncy v. Prudential Ins. Co. of America; Rivera v. City of Wichita Falls. Pointing to evidence that a disproportionately smaller percentage of black men and women was referred to available positions in 1970 than their concentration in various referral pools (all applicants with a code corresponding to that of the job to which referrals were made) would justify, plaintiffs employed the standard deviation test approved in Castaneda v. Partida to show that the difference between actual and expected numbers of blacks referred was statistically significant. After painstaking study of the record, we conclude that the underlying data used to evaluate racial disparities in referrals of black men and women to clerical and sales occupations are so seriously flawed as to negate plaintiffs’ suggestions of statistical significance. The computational errors which undermine the value of calculations pertaining to the clerical and sales occupational codes are not extant in the other eight codes. However, the calculations as to these eight are not persuasive; they all fail to incorporate the primary factor influencing referral— experience. There is no basis in the record for discounting the obvious significance of this factor. Absent due consideration of the experiential component of the referral decision, plaintiffs’ standard deviation analyses furnish insufficient support for the proposition that defendants’ referral decisions were tainted by racial bias. Statistical evidence drawing comparisons between mean hourly rates of pay per referral, and encompassing referrals to occupations in all nine DOT code families from 1974 through 1978, was presented to demonstrate that average wages for black and female referrals were exceeded, in statistically significant proportions, by average wages for white and male referrals. Based on this data, plaintiffs’ expert, Dr. Charles Mann, testified that application of a “two-tailed” test of significance, designed to determine whether differences in the mean hourly wages of black, white and female referrals were statistically significant for the years 1974-1978, produced, positive results. Dr. Mann’s computations would appear to support an inference that the probability that protected group members were referred, on the average, to less remunerative employment because of chance alone was extremely small. Albeit impressive, Dr. Mann’s computations do not take into account the relative qualifications of persons referred during the relevant period. The referral pools upon which his analyses rest were not arranged so as to eliminate those who were denied referral to better paying positions because of the lack of necessary ability or skills. Pouncy v. Prudential Ins. Co. of America; Rivera v. City of Wichita Falls. Dr. Mann’s model is grounded on the unfounded assumption that all persons were qualified for referral to higher paid jobs. A more meaningful analysis would have compared minority and nonminority mean salaries for referrals falling within a single code family. This approach would have disclosed whether black and female applicants possessing education, experience and skills equivalent to those of their white and male co-applicants, were referred in disproportionate numbers to lower paying occupations. Because the raw data are deficient for failing to recognize that “a number of factors operate simultaneously to influence the amount of salary” associated with a particular referral, Wilkins v. University of Houston, 654 F.2d at 402, the findings of statistically significant disparities derived therefrom will not permit an inference of discrimination.11 — 771 — Plaintiffs contend that statistically significant discrepancies in the frequency of referrals for whites and blacks during the years 1974 through 1978 have been established. These data tell us nothing of the relative qualifications of blacks and whites in the available applicant pools, or of the requirements imposed by the employers to whom referrals were made. Factors other than race may explain the variations in referral rates observed. To conclude otherwise would necessitate an impermissible degree of speculation. There remains for consideration plaintiffs’ claim that discrimination pervaded defendants’ job development process, which entailed MSES solicitation of employer job orders on behalf of specific applicants for whom the office had no suitable openings. Job development could be undertaken for persons who either possessed unusual skills or training or who were difficult to place due to the paucity of jobs they could perform. A chart excerpting selected portions of defendants’ evidence shows that on various dates during July 1974 through August 1978, the local office’s self appraisals indicated that the percentage of black placements linked to job development was lower than the percentage of black applicants. Plaintiffs’ failure to narrow the applicant pool to those presumptively eligible for participation in the job development process, as above defined, prevents the comparison of the number of blacks qualified for job development to the number receiving this service. We are not unmindful that defendants’ reliance on the subjective judgment of their interviewers in arriving at a decision on specific job development casts doubt on the legitimacy of the process, Payne v. Travenol Laboratories, Inc., but are not persuaded that this element of subjectivity overcomes the fundamental defect in plaintiffs’ figures. Standing alone, therefore, these statistics have insufficient probative value. Defendants’ Rebuttal Much of the state defendants’ statistical evidence, introduced through their expert, Dr. Linda Malone, was devoted to rebutting Dr. Mann’s calculations of statistical evidence. Her analyses related to applicant rates of referral and mean salaries for the years 1974 through 1978, and did not address plaintiffs’ prima facie proof of discrimination in servicing of employer sex preferences between November 1969 and mid-1970, and out-of-code referrals in 1970. Given our rejection of Dr. Mann’s statistical presentation and the restricted scope of defendants’ rebuttal statistics, we need not review the probative value of Dr. Malone’s studies. This leads to our determination whether defendants’ remaining evidence, primarily qualitative in nature, adequately counters plaintiffs’ prima facie showing. First, as to evidence of sex-segregated referrals to Travenol, defendants contend that they subsequently terminated this practice. Second, defendants claim that five of the 36 employer gender preferences serviced by the Cleveland office were patently reasonable. Notwithstanding these assertions, the record contains no explanation for the different treatment accorded females and thus does not shield the defendants from the consequences of their discriminatory practice. Finally, defendants maintain that their conduct cannot be scrutinized in a vacuum, insisting that overwhelming evidence of their good faith efforts to assist black and female applicants within the confines of a depressed labor market mitigates against a finding of discrimination. Any ostensible discrepancies in the referral rates of members of the protected classes must, in their view, be attributed to the essentially rural character of the area and the severe educational and experiential deficiencies characteristic of Bolivar County’s predominantly black population. — 772 — We have no doubt that the poor socio-economic conditions endemic to Bolivar County, fostered in part by the displacement of black agricultural workers following the mechanization of farm labor in the 1960s, predetermined work patterns in the area. MSES’s Cleveland office endeavored to cope with the resultant influx of uneducated and unskilled persons seeking employment by instituting comprehensive job training programs and, in the words of the district court, by doing “what they could by way of classification and referral to try to help the applicants obtain whatever suitable work might be available, without regard to ... race or sex.” 488 F.Supp. at 245. It is likewise important to note that disparities in referrals of whites and blacks have been steadily narrowing over the years. Payne v. Travenol Laboratories, Inc. Guided by Teamsters, however, we are not persuaded that such affirmations of good faith, coupled with evidence of improvement in referrals of black applicants, overcome plaintiffs’ prima facie proof of sex and race-based discrimination during 1969-70. Accordingly, plaintiffs are entitled to judgment on their claim of class wide sex discrimination during the limited period for which a pattern of disparate treatment was established. This cause shall be remanded for the fashioning of an appropriate remedy for the infractions occurring during the relevant 1969-70 period. B. Discrimination in Testing All MSES offices utilized certain vocational aptitude tests, developed and supplied to them by the Department of Labor through the USES. Three forms of test batteries are challenged: S-28 Table-worker, S-270 and S-270R Licensed Practical Nurse, and S-282 and S-282R Nurse Aide. Each of these batteries, termed a Specific Aptitude Test Battery (SATB), is comprised of two or more aptitudes measured by the General Aptitude Test Battery (GATB). Binding prescriptions for state agency use of the tests have been promulgated by the Department of Labor, and are set forth in Part II of the Employment Security Manual, Sections 9000-9999. Since 1947, the Department of Labor has distributed differing versions of the SATB and GATB tests to the state employment services. Throughout the ensuing years USES has been engaged in research aimed at validating these tests for minorities. After the Supreme Court’s decision in Griggs v. Duke Power Co., 401 U.S. 424, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971), USES undertook a comprehensive revalidation program. An interim policy was instituted in the fall of 1972 to monitor state testing, pending completion of the revalidation program. This policy mandated the referral of minority group applicants in “not less than the same ratio as the minority group represented in the applicant flow in the local office area, provided there is a sufficient number of applicants who are otherwise qualified, consistent with Federal law.” MSES administration of S-28 was governed by the interim policy until January 1973;12 the LPN and Nurse Aide tests were thus regulated until the revalidation process was completed in the mid-1970s. Title VII permits the administration of “any professionally developed ability test” on the condition that such test is not utilized to discriminate against persons protected by the Civil Rights Act of 1964. 42 U.S.C. § 2000e-2(h). Dothard v. Rawlinson, 433 U.S. 321, 97 S.Ct. 2720, 53 L.Ed.2d 786 (1977); Albermarle Paper Co. v. Moody, 422 U.S. 405, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975). This selection technique must be evaluated pursuant to the disparate impact model. A plaintiff may establish a prima facie violation by demonstrating that a facially neutral examination exerts “a significantly discriminatory impact.” Connecticut v. Teal, - U.S. -, 102 S.Ct. 2525, 2531, 73 L.Ed.2d 130 (1982). — 773 — If such an impact is demonstrated, whether by statistics or other evidence, the defendant is called upon to show that the examination is job-related, or bears “ ‘a manifest relationship to the employment in question.’” Id. (quoting from Griggs v. Duke Power Co., 401 U.S. at 432, 91 S.Ct. at 854). The proponent of the test must establish its job performance validity.. Ensley Branch of the N.A.A.C.P. v. Seibels, 616 F.2d 812 (5th Cir.1980), cert. denied, 449 U.S. 1061, 101 S.Ct. 783, 784, 66 L.Ed.2d 603 (1981); Scott v. City of Anniston, Alabama, 597 F.2d 897 (5th Cir.1979), cert. denied, 446 U.S. 917, 100 S.Ct. 1850, 64 L.Ed.2d 271 (1980). If the defendant offers persuasive evidence, the plaintiff may still prevail by proving that the use of the test was merely pretextual, Connecticut v. Teal, or that less discriminatory alternatives existed. Albemarle Paper Co. v. Moody. To prove their claim that the Tableworker, Nurse Aide and LPN tests excluded disproportionate numbers of blacks from referral, plaintiffs introduced statistical evidence comparing failure rates of white and black applicants. The district court determined that plaintiffs’ proof did not establish a prima facie case of disparate impact, due principally to their mischaracterization of certain scores. 488 F.Supp. at 253. Looking first to the possible impact of the S-28 examination, the pertinent data reflect that in 1971,13 whites and 32 blacks scored “below norm.” However, no perceptible barriers to referral existed for recipients of scores in the higher “below norm” range. We thus lack a reliable statistical base from which to assess the significance of the observed disparity. See Connecticut v. Teal; Albemarle Paper Co. v. Moody. A different approach was adopted by plaintiffs in an attempt to convince the district court that blacks were test-selected for referral to nurse’s aide training at a county hospital in disproportionately fewer numbers than other applicants. From 1971 through 1976, 180 blacks (11.3%) and 278 persons of other racial or ethnic backgrounds, primarily white (49.3%), all of whom were classified under the nurse aide code, were referred to the hospital’s training program. Application of the standard deviation formula to these figures by plaintiffs’ expert, Dr. James Outzz, confirmed that the racial difference was statistically significant. It is well settled that a plaintiff need not establish the adverse impact of an aptitude test solely on the basis of comparative pass/fail rates of blacks and whites, but may proffer statistical proof of differences in the proportions of blacks and whites gaining entry to the desired employment opportunity. Hameed v. International Ass’n of Bridge, Structural and Ornamental Iron Workers, Local Union No. 396, 637 F.2d 506 (8th Cir.1980); James v. Stockham Valves and Fittings Co., 559 F.2d 310 (5th Cir.1977); Watkins v. Scott Paper Co., 530 F.2d 1159 (5th Cir.), cert. denied, 429 U.S. 861, 97 S.Ct. 163, 50 L.Ed.2d 139 (1976). Notwithstanding this rubric, the referral component of the applicant pool must be tied to test selection, the variable to be measured, before referral rates may be used as indicia of failure. As the district court aptly observed, Dr. Outzz had no knowledge of who among those referred had taken the nurse aide test. Because the SATBs were developed to facilitate referral of inexperienced, untrained and entry level workers to skilled positions, they were not administered to experienced applicants who had manifested some proficiency in the occupation examined.13 Information identifying members of the applicant pool tested, their scores, and their subsequent referral or nonreferral was available to plaintiffs, but was not collated. In light of this critical omission, we decline to infer from the opaque figures presented that all applicants referred to — 774 — nurse’s aide training were first required to take the S-282. A survey of S-270R scores of applicants assigned the licensed practical nurse code in the years 1970, 1972, 1974 and 1976, shows that of the 66 persons completing the S-270R battery, 13 of 29 blacks and 0 of 37 whites received a failing score. Test performances of 2 black and 2 white applicants are omitted. One black woman, tested by another agency, was referred to the county hospital for training. Plaintiffs describe the sample of applicants tested at one point as composed of 75 persons; at another point they refer to 62 persons. Since the outlines of the relevant sample are imprecise, the majority and minority concentrations cannot be ascertained as a prelude to application of probability theory. Addition of the four persons for whom no data are available further distorts the figures. Where the sample size is small, a few test scores may significantly skew the overall disparity, thus reducing the reliability of any inference which might be drawn from minority “fail” rates. While the small size of the sample does not necessarily justify repudiation of plaintiffs’ empirical analysis, we perceive none of the evidentiary signals of discrimination typically relied upon to bolster such analyses. S. Booth and J. McKay, Legal Constraints on Testing and Evolving Trends in The Law, 29 Emory L.J. 121, 157 (1980); see, e.g., James v. Stockham Valves and Fittings Co. Compare Rivera v. City of Wichita Falls (14 of 35 Mexican-Americans who applied in 4-year period failed employment test, statistically significant showings of adverse impact alone deemed sufficient to make out prima facie case); Wilkins v. University of Houston (issue of applicability of statistical methodology to small number of positions, 14, not resolved inasmuch as diverse and specialized credentials required). Regardless of whether the injection of the element of uncertainty attributable to the size of the minority sample alone warrants rejection of plaintiffs’ data, we are compelled to the view that this factor, in conjunction with the other problems above noted, precludes a reasoned evaluation of these data. We therefore perceive no prima facie case of disparate impact resulting from the administration of the S-270R test. When viewed in the aggregate, the statistical evidence supports the district court’s finding that the tests under consideration were not discriminatory in their impact upon black applicants. Absent proof that an employment test exerts a substantially disproportionate racial impact, no inquiry may be undertaken into its job relatedness, or validity. See Albemarle Paper Co. v. Moody; Rivera v. City of Wichita Falls; Moore v. Southwestern Bell Tel. Co., 593 F.2d 607 (5th Cir.1979).14 II. INDIVIDUAL CLAIMS The four named plaintiffs, all of whom are black, appeal the district court’s determination that they had not been discriminated against by the state defendants. In order to establish a prima facie case of disparate treatment, each plaintiff must prove: (1) membership in a protected group; (2) application and coding for an occupation for which the Cleveland office was making referrals; (3) failure to secure a referral; and (4) later referral of a nonmember of the protected group. See Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981); McDonnell-Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). Upon the plaintiff’s — 775 — establishment of a prima facie case, the defendants are called upon to dispel the presumption of discriminatory treatment thus created by articulating a legitimate, nondiscriminatory reason for the particular plaintiff’s treatment. If the defendants come forward with such proof, the plaintiff, who at all times retains the burden of persuasion, may demonstrate that the justification proffered by defendants was a mere pretext designed to conceal discrimination. This goal may be achieved either by proving that a discriminatory reason more likely motivated the defendants’ action, or by discrediting the defendants’ articulated explanation. Texas Department of Community Affairs v. Burdine. Applying the McDonnell-Douglas test, as modified, to the district court’s findings of fact, 488 F.Supp. at 241—242, we conclude that three of the named plaintiffs, Pegues, Williams and Boyd, failed to adduce prima facie proof of intentional discrimination.15 Although we attach no significance to the inability of plaintiffs to cite the referral of any similarly or less qualified male and/or white to positions to which they believe they should have been referred, they were obligated, at a minimum, to introduce evidence attesting to the availability of a position for which they were coded but were not referred. See Harrell v. Northern Elec. Co., 672 F.2d 444 (5th Cir.), modified on reh’g, 679 F.2d 31 (5th Cir.), cert. denied, - U.S. -, 103 S.Ct. 449, 74 L.Ed.2d 603 (1982). We discern no such evidence in the record. As to Rebecca Gillespie, however, we find that a prima facie case has been demonstrated. Gillespie was a black female with an eighth grade education and experience as a waitress, maid and factory worker. She first applied to the Cleveland office in 1968, and expressed a desire for anything but domestic labor, including in particular a job at Travenol Laboratories. Notwithstanding her background and stated preference, she was coded for service work. Upon earning a 10th grade GED certificate in July 1971, and being aware of Travenol’s educational criterion, she advised the Cleveland office of her achievement and repeated her request for a factory referral. Her coding was not re-evaluated in light of this pertinent change in circumstances. Defendant Lindsey testified that the office was still engaged in referring applicants to Travenol at the time of Gillespie’s July 1971 visit. Although not formally rejected, Gillespie was passed over in favor of other, similarly qualified applicants, some of whom were white. By way of rebuttal, defendants elicited testimony from Gillespie as to her five full-term pregnancies between 1970 and 1975, and various benefits in the form of training and referral that defendants had conferred upon her between 1968 and 1970. The record reflects that at this time Travenol relied exclusively upon MSES referrals to fill vacant factory positions. Therefore, Gillespie could not have secured a position without assistance from the Cleveland office. Given her factory experience and enhanced education, we do not believe the reasons articulated constitute a legitimate rationale for defendants’ failure to reconsider her service classification and provide an opportunity for employment at Travenol. She is entitled to relief. III. CONCLUSION We conclude that plaintiffs succeeded in establishing a pattern and practice of race and sex-based disparate treatment during 1969 and 1970. We further conclude that Rebecca Gillespie has sufficiently proven her individual claim of discrimination. We render judgment accordingly, thus modifying the decision of the district court which, in all other respects, is affirmed. We remand for entry of a decree on liability in accordance herewith, and for further pro — 776 — ceedings as may be deemed necessary for the fashioning of an appropriate remedy. AFFIRMED in part, REVERSED in part, and REMANDED. Footnotes [1] Claims for alternative remedies for employment discrimination under 42 U.S.C. §§ 1981, 1983, and the constitutional amendments will be considered only if violations can be established on grounds different from those asserted under Title VII. Plaintiffs cite no such distinctions. We thus address only the Title VII claims. See Rivera v. City of Wichita Falls, 665 F.2d 531 (5th Cir.1982). [2] Plaintiffs’ Title VII claims against the state and federal defendants rest on Section 703(b) of the Civil Rights Act of 1964, as amended, 42 U.S.C. § 2000e-2(b). This provision prohibits an employment agency, as defined in Section 701(c), 42 U.S.C. § 2000e(c), from failing or refusing to “refer for employment, or to otherwise discriminate against, any individual because of his race, color, religion, sex, or national origin, or to classify or refer for employment any individual on the basis of his race, color, religion, sex, or national origin.” [3] MSES, a division of the Mississippi Employment Security Commission, is a member of the national network of state employment services established by the Wagner-Peyser Act, as amended, 29 U.S.C. §§ 49 through 49K. Under the Act, federal funds in the form of grants covering operational costs are dispensed by USES to state employment services. Participating state services must adhere to USES policies and procedures, Espinoza v. Stokely-Van Camp, Inc., 641 F. 2d 535 (7th Cir.), cert. denied. 453 U.S. 950, 102 S.Ct. 27, 69 L.Ed.2d 1033 (1981), including those governing the classification, referral and testing of applicants. 20 C.F.R. §§ 653.1-653.13 (1982). During the relevant period many of these policies and procedures were set forth in the federal Employment Security Manual, a U.S. Department of Labor publication. [4] Summary judgment was rendered in favor of the federal defendants on all claims asserted, the court having determined that: (1) Congress’ omission of USES from the 1972 amendments to Title VII, Section 701(c), 42 U.S.C. § 2000e(c), as amended, manifested an intent to exonerate this entity from all potential claims of employment discrimination except those authorized under Section 717, 42 U.S.C. § 2000e-16; (2) plaintiffs had failed to exhaust their administrative remedies as a prelude to assertion of their Title VI claim, 42 U.S.C. § 2000d; (3) the United States was immune from suit under 42 U.S.C. § 1981 and the thirteenth amendment; (4) no allegation of intentional discrimination had been raised, pretermitting maintenance of a cause of action under the fifth amendment; and (5) no private right of action against the federal government could be implied from the terms of the Wagner-Peyser Act, as amended, 49 U.S.C. §§ 49-49K. Only the first determination is challenged on appeal. [5] Evidence bearing on the interrelationship of the federal and state defendants was directed exclusively to the testing issue. Our analysis of the federal defendants’ liability is thus circumscribed by the issues as joined and the evidence adduced. [6] A specific six-digit numerical code (nine digits since 1978) was assigned to each of the 20,000 job definitions incorporated in the DOT. These codes are organized into the following broad occupational categories, or families, symbolized by a single digit: OCCUPATIONAL CATEGORIES 0/1 Professional, technical, and managerial occupations 2 Clerical and sales occupations 3 Service occupations 4 Agricultural, fishery, forestry, and related occupations 5 Processing occupations 6 Machine trades occupations 7 Benchwork occupations 8 Structural work occupations 9 Miscellaneous occupations Subsumed within the nine major job families are more than 82 diverse, two-digit divisions. The families of particular importance in this case, the clerical and sales, service, and agricultural codes, are subdivided into a variety of occupations: CLERICAL AND SALES OCCUPATIONS 20 Stenography, typing, filing, and related occupations 21 Computing and account-recording occupations 22 Production and stock clerks and related occupations 23 Information and message distribution occupations 24 Miscellaneous clerical occupations 25 Sales occupations, services 26 Sales occupations, consumable commodities 27 Sales occupations, commodities, n.e.c. 29 Miscellaneous sales occupations SERVICE OCCUPATIONS 30 Domestic service occupations 31 Food and beverage preparation and service occupations 32 Lodging and related service occupations 33 Bartering, cosmetology, and related service occupations 34 Amusement and recreation service occupations 35 Miscellaneous personal service occupations 36 Apparel and furnishings service occupations 37 Protective service occupations 38 Building and related service occupations AGRICULTURAL, FISHERY, FORESTRY AND RELATED OCCUPATIONS 40 Plant farming occupations 41 Animal farming occupations 42 Miscellaneous agricultural and related occupations 44 Fishery and related occupations 45 Forestry occupations 46 Hunting, trapping and related occupations These subdivisions are in turn broken down into specialized fields. For example, included within the first division under the clerical and sales code, stenography, typing, filing, and related occupations, are: 201 Secretaries 202 Stenographers 203 Typists and typewriting-machine operators 205 Interviewing clerks 206 File clerks 207 Duplicating-machine operators and tenders 208 Mailing and miscellaneous office machine operators [7] There are no findings or conclusions set forth in the district court’s opinion to support its rejection of plaintiffs’ classification and referral claims, other than a detailed recitation of federal policies and regulations governing MSES’s classification and referral functions, a discussion of the limited role of the Cleveland office in placing applicants, the general efforts made by MSES staff to obey the civil rights laws, the excellent relationship between the Cleveland office and the black community, and a conclusionary statement that the state defendants had at all times sought to classify and refer applicants without regard to race or sex. It is nonetheless clear, from the court’s extensive and somewhat laudatory exposition of defendants’ case, that it did not deem plaintiffs’ evidence to be either credible or probative of discrimination. 488 F.Supp. at 243. Handicapped though we are by the dearth of specific factual findings, we proceed, in light of the recent death of the trial judge and the substantial passage of time since the inception of the lawsuit, to decide this case in the interests of justice and judicial economy. See Felder v. United States, 543 F.2d 657 (9th Cir. 1976). Cognizant of the preferred practice of remand, we are loathe to return this voluminous record, including thousands of pages of testimony and myriad exhibits, to another trial judge for a transcript review. We may perform that function under circumstances as here presented, particularly since we find that the record is susceptible of only one resolution of the factual issues presented. United States v. Georgia Power Co., 695 F.2d 890 (5th Cir.1983). [8] Because we conclude that plaintiffs have failed to make out a prima facie case, we need not consider defendants’ rebuttal evidence. See Pouncy v. Prudential Ins. Co. of America. [9] The statistical disparities in this example approach the “inexorable zero” decried by the Supreme Court in International Brotherhood of Teamsters, 431 U.S. at 342 n. 23, 97 S.Ct. at 1858 n. 23. Standard deviation analysis was applied to these disparities to eliminate chance as a likely explanation for the revealed under-representation. Hazelwood School Dist. v. United States; Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977). As defined in Castaneda, the standard deviation quantifies the probability that chance is responsible for any difference between an expected outcome and the observed outcome in a sample comprised of a protected and nonprotected group (a binomial distribution). 430 U.S. at 496 n. 17, 97 S.Ct. at 1281 n. 7. As the number of standard deviations increases, the probability of chance as the cause of any difference between the expected and observed results diminishes. EEOC v. American Nat’l Bank, 652 F.2d 1176 (4th Cir.1981), reh’g denied, 680 F.2d 965 (4th Cir.), cert. denied, - U.S. -, 103 S.Ct. 235, 74 L.Ed.2d 186 (1982). Generally speaking, in a sample equivalent in size to that evaluated in Castaneda, a difference between expected and observed values in excess of two or three standard deviations at the 5% significance level permits an inference of discrimination. See Harrell v. Northern Elec. Co., 672 F.2d 444 (5th Cir.), modified on reh’g, 679 F.2d 31 (5th Cir.), cert. denied, - U.S. -, 103 S.Ct. 449, 74 L.Ed.2d 603 (1982). In Harrell, 672 F.2d at 447 n. 5, we set forth a formula for computing standard deviations based on the Castaneda model. We delete therefrom the .5 correction factor used to compensate for Harrell’s sample size, and specially note a publication error in the reproduction of the formula — the square root sign in the denominator was omitted. The correct formula for determining the number of standard deviations is: Tailored to the facts presented in the case at bar, N = total number of applicants referred; P = percentage of female applicants; X = number of females referred; and Q = percentage of male applicants. Application of the formula to plaintiffs’ data discloses that the difference between the expected and the observed number of women referred to Travenol Laboratories’ material handler jobs exceeded 17 standard deviations. Expected versus observed numbers of women referred to the female-dominated assembler jobs differ by more than 13 standard deviations. Both figures exceed the two or three — 769 — standard deviations considered sufficient to undermine chance as the reason for the disparity. Plaintiffs presented evidence of sex and race segregated referrals during a 14-month interval commencing November 1969, but failed to draw the requisite comparisons between favored and disfavored groups, or to control for divergent qualifications possessed by applicants within either group. Accordingly, this evidence can at best be characterized as inconclusive, and does not function to enhance plaintiffs’ prima facie showing. [10] We have determined that one of the named plaintiffs, Rebecca Gillespie, proved an individual claim of disparate treatment in the context of referral. See p. 775, infra. Under the Teamsters analysis, this proof suggests a qualitative explanation for the prima facie showing heretofore made for 1970 on the basis of statistical and historical evidence. See Phillips v. Joint Legislative Committee, 637 F.2d 1014 (5th Cir.1981). [11] Plaintiffs concentrated much of their effort at trial on statewide data covering an undefined period culminating in March 1976, purportedly showing strong racial and gender disparities in the pay rates of jobs to which referrals were made by each of the 82 branch offices within the MSES system. Dr. Mann testified, based on his performance of an accepted statistical test, that such disparities were statistically significant. Given our approval of limitations im — 771 — posed by the district court on the scope of the class, such data have no relevance to the practices of the Cleveland office. Since the pertinent data have' not been dissected out from those relating to other offices, Dr. Mann’s statewide analyses are without probative value on the issues posited in this litigation. [12] Tests that had been differentially validated or which did not appear to significantly impact upon blacks in a discriminatory manner were removed from the interim policy’s strictures in January 1973. Although the S-28 Tableworker battery had last been validated in 1954, it was considered by USES to exert no adverse racial impact. [13] Despite the district court’s finding that Rebecca Gillespie, an experienced nurse’s aide, had erroneously been required to undergo testing, there was no evidence that other experienced candidates for referral to the nurse aide training program, whether white or black, were similarly treated. We therefore attach no significance to this isolated incident in analyzing plaintiffs’ classwide data pertaining to nurse aide referrals. [14] Because we affirm the district court’s determination that the disputed tests produced no disparate impact upon black referral candidates during the years involved in plaintiffs’ studies, we do not address plaintiffs’ averment that the state defendants transgressed USES’s interim policy in administering the nurse aide and licensed practical nurse examinations beginning in September 1972, or the challenge to expert testimony on the job-validation issue. Nor is it necessary for us to reach the question whether the district court erred in construing the 1972 amendment to Section 701(c) of the 1964 Civil Rights Act, 42 U.S.C. § 2000e(c), to relieve USES of putative liability for discriminatory testing. That question remains for another day. [15] Consistent with Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982), we may reverse a district court’s finding on the question of discriminatory intent only if we are satisfied that this finding is clearly erroneous. Chaline v. KCOH, Inc., 693 F.2d 477 (5th Cir. 1982). We are not prepared to say that the district court’s factual findings with respect to the claims of Pegues, Williams and Boyd are clearly erroneous.