665 F.2d 531
27 Fair Empl.Prac.Cas.  1352,28 Empl. Prac. Dec. P 32,413Placido RIVERA, et al., Plaintiffs-Appellants,Richard Gonzales, Intervenors-Appellants,v.The CITY OF WICHITA FALLS, et al., Defendants-Appellees.
No. 80-1332.
United States Court of Appeals,Fifth Circuit.
Unit A*Jan. 11, 1982.

Crampton & Crampton, Holly Crampton, Wichita Falls, Tex., for appellants.
Sherrill, Pace, Rogers, Crosnoe & Morrison, Lonny D. Morrison, Wichita Falls, Tex., for defendants-appellees.
Appeal from the United States District Court for the Northern District of Texas.
Before REAVLEY, RANDALL and SAM D. JOHNSON, Circuit Judges.
SAM D. JOHNSON, Circuit Judge:


1
This is an appeal from those portions of a judgment rendered in favor of the employer in a class action brought under Title VII, 42 U.S.C. § 2000e et seq. Named plaintiffs Placido Rivera, Ernest Ceballos, Ernest Castillo, Pete Arthur Gonzales, Richard Gonzales, and David Maldonado are former employees of, or rejected applicants for employment with, the City of Wichita Falls, Texas.  They represent a class defined as all Spanish surnamed Americans of Mexican descent who were discriminated against by the defendants, the City of Wichita Falls, Texas and certain of its officials,1 through the establishment and application of various employment policies and practices.  The claims asserted on behalf of the class challenged the full range of the City's employment practices.  After trial without a jury, however, the district court found discrimination only in the recruitment practices of the City's Fire Department.2  It rejected the plaintiffs' contentions that screening procedures used by the City's Police Department had a discriminatory impact on members of the class which could not be justified as job-related, that plaintiffs were unlawfully excluded from employment in the upper three levels of general City government, and that plaintiffs were discriminatorily denied promotions and training in the various divisions and levels of the City government.  The plaintiffs appeal these rulings and the district court's award of only $4,000 in attorney's fees.  We affirm the judgment of the district court.

I.

2
The plaintiffs' attack was, at inception, a broad one.  On behalf of the class they charged that the City was engaged in a pattern and practice of discrimination against Mexican-Americans which manifested itself in the entire range of the City's employment practices, throughout all divisions of the City government.  In addition, individual relief was pursued by three named plaintiffs and three intervenors who claimed to have been victimized by specific acts of discrimination.  The action as now presented, however, is of considerably narrower dimensions.  Through a series of waivers and self-initiated constrictions in the scope of the challenges pressed,3 the plaintiffs have limited the issues on appeal to these:


3
1. Did the district court err in holding that the City had successfully shown that the one element of its police recruit selection process which the court found to have a discriminatory impact is necessary for the performance of the job?


4
2. Did named plaintiff Ernest Ceballos present a prima facie case of discrimination by the City in its refusal to accept him in its police recruit training program?


5
3. Did the plaintiffs present a prima facie case of discrimination in hiring in regard to the upper three levels of the City government?


6
4. Did the plaintiffs present a prima facie case of discrimination in the training and promotion of class members employed by the City?


7
The class-wide claims charged the City with engaging in a "pattern and practice" of employment discrimination in violation of section 707(a) of the Civil Rights Act of 1964, 42 U.S.C. § 2000e-6(a).4 The pattern or practice branch of employment discrimination law is designed to reach and to remedy pervasive resistance to the principles of equality of treatment and opportunity in the workplace articulated in Title VII.  Accordingly, the threshold inquiry in a pattern or practice discrimination action is whether there is evidence of a correlation between employment decisions and the, inter alia, race, sex, or national origin of employees or job applicants.  The plaintiffs' initial responsibility of establishing a prima facie case of pattern and practice discrimination in hiring or promotion may, then, satisfied by a showing that "there is a significant statistical disparity between the racial, sexual, or ethnic balance and composition of an employer's work force and that of the community from which the workers are hired," United States v. City of Alexandria, 614 F.2d 1358, 1364 (5th Cir. 1980) (citations omitted).


8
The degree of the observed statistical disparity is, however, of critical importance.  An absolute disparity between these percentages of representation is not enough.  To be legally cognizable, the pattern revealed must be at least "significantly discriminatory," Dothard v. Rawlinson, 433 U.S. 321, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977); at minimum, the percentages must be "markedly disproportionate," Griggs v. Duke Power Company, 401 U.S. 424, 91 S.Ct. 849, 852, 28 L.Ed.2d 158 (1971).5  Once made, however, a showing of significant disparity raises an inference that employment decisions are tainted by intrusion of illegitimate concerns.  The logical foundation of this inference rests on the observation that, "absent explanation, it is ordinarily to be expected that nondiscriminatory (employment) practices will in time result in a work force more or less representative of the racial and ethnic composition of the population in the community from which employees are hired."  Teamsters, 97 S.Ct. at 1856 n.20.  Organization-wide disparities tend to support the thesis that discriminatory acts are not "isolated or 'accidental' or sporadic .... (but are, rather,) the company's standard operating procedure-the regular rather than the unusual practice," 97 S.Ct. at 1855.


9
Only upon the plaintiffs' establishment of a prima facie case of pattern or practice discrimination would the defendants have either to discredit the plaintiff's case, or to show that, despite the adverse impact, the challenged practices are necessary for the performance of the job.  Griggs, 91 S.Ct. at 853-54; Ensley Branch of the N.A.A.C.P. v. Siebels, 616 F.2d 812, 816 (5th Cir. 1980), cert. denied, 449 U.S. 1061, 101 S.Ct. 783, 66 L.Ed.2d 603 (1981).  A successful rebuttal, however, does not necessarily settle the matter.  If the defendant rebuts by showing the challenged practices to be job-related, the plaintiff may still prevail by showing less discriminatory alternatives.  Albemarle Paper Company v. Moody, 422 U.S. 405, 95 S.Ct. 2362, 2375, 45 L.Ed.2d 280 (1975).


10
District court determinations of the adequacy of these showings are reviewed under the variable standard appropriate to Title VII cases.  Under this standard, as in the usual case, the district court's findings of subsidiary facts would be overturned only if found to be clearly erroneous.  The ultimate factual question, however, of whether the subsidiary findings of fact point to the defendants' unlawful discrimination against the plaintiffs, is subject to an independent redetermination on appeal.  Danner v. United States Civil Service Commission, 635 F.2d 427, 430-31 (5th Cir. 1981).

II.
A. Police Recruit Selection Procedures
1. The Class Claims

11
In the district court, the plaintiffs challenged the entirety of the City's police recruit selection procedures.  The police recruit selection process employed by the City of Wichita Falls consists of four successive screening devices.  First, applicants take the Basic Occupational Language for Police Officers (BOLPO) test.  BOLPO, a test of the ability of an applicant to comprehend the type of reading material encountered in a police training academy, is used to predict the likelihood of the applicant's successful completion of the police academy curriculum.  An applicant passing BOLPO next takes a physical agility test.  This test focuses on the applicant's ability to perform those feats typically required of Wichita Falls police officers.  Applicants clearing the first two hurdles are then the subjects of background investigations.  A background investigation consists primarily of an inquiry into the applicant's work history, a determination of whether he has a criminal record, and a check into whether he habitually associates with "police characters."  This step is considered by the City to be crucial in the selection of people suited to the highly sensitive, demanding and public position of a police officer.  The final review of the applicant's qualifications is made at an assessment center, where applicants, under the direction of police officers trained as "assessors," engage in role playing, participate in simulated work experiences, and answer standard questions designed to measure their abilities to communicate effectively.  Applicants passing all four tests are ranked by their cumulative scores and are offered positions with the police department in accordance with their rankings as openings occur.


12
Each of the four selection procedures were challenged by the plaintiffs as having a disparate impact on Spanish surnamed Americans of Mexican descent.  The district court found, however, that the plaintiffs succeeded in adducing a prima facie case only in support of their challenge to the BOLPO test.  The plaintiffs' statistical proof on the comparative failure rates of whites and Mexican-Americans on the BOLPO test is indeed adequate to support a prima facie case of BOLPO's discriminatory impact on Mexican-Americans.  In the relevant period of December 1974 to May 1978,6 5.4 percent of all white applicants, twenty-one out of 387, failed BOLPO.  During the same period, 40 percent of all Mexican-Americans, fourteen out of thirty-five, failed BOLPO.  This substantially higher failure rate for class members is clearly statistically significant.7


13
The plaintiffs' success was, however, short-lived.  The district court held that the City had proved the test to be properly validated under the validation standards of the Uniform Guidelines on Employee Selection Procedures, 29 C.F.R. § 1607.  See Albemarle, 95 S.Ct. at 2378; Griggs, 91 S.Ct. at 854-55.  The district court based its determination on the United States Civil Service Commission's technical report on BOLPO, which concluded that the tests of BOLPO established both its "content validity" and its "criterion-related validity."


14
A test's degree of content validity is defined as the degree to which the subject matter of the test relates to those significant parts of the curriculum for which the test is intended to predict the applicants' capability.  To put it more clearly, an Early American history test which has content validity might well cover the Boston Tea Party, but would not cover the bombing of Pearl Harbor.  The content validity of BOLPO was established in conformity with an August 1972 discussion draft of the Uniform Guidelines on Employee Selection Procedures by the Equal Employment Opportunity Coordinating Council.  As the guidelines suggested, a "comprehensive job analysis" was performed to identify the cognitive skills required of police recruits.  That analysis arrived at the unremarkable conclusion that the ability to comprehend and effectively use materials such as those presented in training was a critical requirement for successful performance in the basic course at the academy.  Accordingly, the test consisted of reading selections excerpted directly from standard training materials used in police academies in Texas.


15
After the test was designed, a "reliability estimate" was computed to determine the reliability of BOLPO test scores.  Testing a representative sample of thirty incumbent police officers in Wichita Falls,8 a reliability coefficient of .92 was obtained.  The Civil Service Commission's report concluded that this coefficient comfortably exceeds the minimum requirements which a test must satisfy in order to be considered to be content validated.


16
In addition to content validation of the test, the BOLPO test was measured for "criterion-related validity."  Criterion-related validity establishes a correlation between test scores and an independently determined measure of successful job performance.  A "predictive" validity study, i.e., using knowledge of test performance to predict future performance at the police academy, was conducted with a group of trainee police candidates chosen from two academies in Texas prior to training.9 There was a strong correlation of .66 between the BOLPO test scores and the final grades at the training academies.10


17
The strength of the correlations established by the content validity and predictive criterion-related validity studies amply supports the district court's conclusion that BOLPO was properly validated.  Further inquiry would be necessary only if the plaintiffs offered an alternative to BOLPO which has a less discriminatory effect on the class.  They did not.  The district court's judgment that the City's use of BOLPO in its selection of police recruits does not violate Title VII is accordingly affirmed.


18
The district court determined that plaintiffs failed to make a prima facie showing that any of the other three elements of the selection process, that is, the physical agility test, the background investigation and the job performance assessment, had a discriminatory impact.  The plaintiffs do not argue that the subsidiary factual findings supporting these determinations are clearly erroneous, nor do they argue that the district court erred in failing to draw an inference of an absence of discrimination from the subsidiary findings.11  Rather, they contend that these tests must nonetheless be properly validated.  The duty to validate, however, arises only when the test has a disparate impact.  Albemarle, 95 S.Ct. at 2375.  This is so even if, as plaintiffs contend to be the case with regard to the background investigations and the job performance assessments, the investigation is without written guidelines and is totally subjective.  See Eubanks v. Pickens-Bond Construction Co., 635 F.2d 1341, 1347 (8th Cir. 1980); accord Hamilton v. General Motors Corp., 606 F.2d 576, 580 (5th Cir. 1979), cert. denied, 447 U.S. 907, 100 S.Ct. 2990, 64 L.Ed.2d 856 (1980).


19
Finally, plaintiffs argue that the district court should not have considered separately the individual tests for the selection of police recruits.  Instead, they assert, the entire selection process should have been analyzed as a whole.  Noting that 17.62 percent of white applicants completed the selection process while only 3.33 percent of class applicants did so, the plaintiffs argue that the process as a whole had a discriminatory effect on the class, and that therefore the process in its entirety must be validated.


20
Such an approach might be appropriate if the effect of the individual elements in the selection process cannot be isolated, but a disparate impact can be shown to arise from the procedures' completion.  Applied, however, to situations in which the source of the disparate impact can be identified, the plaintiffs' approach would allow the disparate impact of one element to require validation of other elements having no adverse effects.  The burden of determining the validity of a screening procedure, weighing not only on the employer but also on the limited resources of the district court, will not be imposed where proof of an absence of discriminatory effect attributable to the procedure shows it to be unwarranted.  The plaintiffs' invitation to adopt this approach must be declined.

2. The Individual Claim

21
Ernest Ceballos, one of the named plaintiffs, appeals the district court's holding that the City's refusal to admit him to the police academy was for reasons other than his national origin.  Ceballos originally complained that the City's claim that he failed the background investigation was a subterfuge.12  At trial, however, he testified:


22
Q. Don't you think that it's fair to say that your employment history at that time would cause considerable concern to someone who was considering you as a police officer?


23
A. Yes.


24
Q. Then, of course, Officer Winn told you that that's the reason that you weren't being considered; isn't that right?


25
A. Right....


26
Q. In fact, you testified in connection with this proceeding that whatever the reasons may have been for you not being employed as a police officer, you didn't think it had anything to do with the fact that you were a Mexican American person; isn't that right? ...


27
A.  Yes.


28
The district court is affirmed.

B. The City's General Workforce

29
1. Administrative, Professional and Technical Employment


30
The plaintiffs' efforts at trial concentrated on their allegation that the City has engaged in a pattern and practice of discrimination against class members in filling its upper level positions.  To establish their prima facie case, the plaintiffs relied on evidence of an "underrepresentation" of class members in the City's top three job categories and an "overrepresentation" of class members in the City's lower four job categories.13  They contended, first, that the lower four job categories constituted the labor pool from which the City selected people to fill positions in its upper three job categories, and that, therefore, the disparity between Mexican-American representation in the upper and lower levels indicated that the City discriminated against class members in training and promotions.14  In the alternative, they argued that the frequency of appearance of Mexican-Americans in the top three categories was significantly lower than that which would be expected in consideration of the number of Mexican-Americans in the relevant external labor pools, indicating discrimination by the City against Mexican-Americans in hiring.  The district court concluded that comparison of the percentage of class members employed in the upper three job categories with the percentage of class members employed in the lower four job categories was inappropriate, and that the underrepresentation of class members in the upper three job categories was, when compared to an external labor pool, statistically insignificant.  This determination led it to hold that the plaintiffs had failed to establish a prima facie case of pattern or practice discrimination.


31
A review of the statistical evidence found wanting by the district court must begin with a definition of the labor pools against whose composition the adequacy of class members' representation in the City's ranks is measured.  There is perhaps no determination more critical to the ultimate resolution of a pattern and practice discrimination action than definition of that labor pool from which positions allegedly discriminatorily assigned would properly be filled.  See Wilkins at 395-99.  Only in rare instances can an exact definition of the size and characteristics of the relevant labor market be attained.  Id. at 398 n.13.  However, a heightened sensitivity to the often-decisive effect of labor pool definition has led the courts to scrutinize carefully the definitions offered, and to require a reasonable semblance of accuracy in the definition ultimately accepted.


32
Of the many factors considered in definition of relevant labor pools, few have received more judicial attention than that of applicant qualifications.  Although there are several variations on the approach to incorporation of applicant qualifications in labor pool definitions, the fundamental premise uniting all of the variations was articulated in Hazelwood School District v. United States, 433 U.S. 299, 97 S.Ct. 2736, 2741-42, 53 L.Ed.2d 768 (1977).  Confronted with allegations that Hazelwood School District discriminated against blacks in hiring faculty members, the Supreme Court held that a determination of underrepresentation could rest only on a comparison of the school district's minority hiring record to a population of blacks who were qualified to teach in elementary and secondary classrooms.  Id. at 2742.  The Hazelwood rule requires that the relevant labor pool be tailored to eliminate those whose exclusion from the positions in issue could be attributed to want of the requisite skills.


33
One of the more significant refinements to the Hazelwood rule requires identification not only of the population having the requisite qualifications for the positions in question, but also identification of the source of qualified applicants to which the employer normally looks.15  The source is almost always defined in part in geographical terms, Hazelwood, 97 S.Ct. at 2743-44.  It is also often defined by distinction between the employer's existing workforce, and external labor markets.  Use of the employer's existing workforce as the source of applicants for positions in question may be appropriate when the employer fills these positions by promotion.  James at 341-43; Robinson v. Union Carbide Corp., 538 F.2d 652, 659 (5th Cir. 1976), cert. denied, 434 U.S. 822, 98 S.Ct. 65, 54 L.Ed.2d 78 (1977).  Proof of a policy favoring promotion does not, however, automatically invoke this "internal comparison" variant of labor pool definition.  Plaintiffs seeking to use this approach are, no less than those applying external comparison methodologies, required by Hazelwood to identify those segments of the existing workforce qualified, by reason of training or experience, to assume the higher level positions at issue.16  In other words, the percentage of minority workers in all lower level positions combined will not, without more, be considered to be the relevant labor market from which upper level positions would be filled.  Rather, the lower level positions must be differentiated by degree of ability in order to identify those which are the resource from which promotions to the positions in issue would be made.  Wilkins at 398 n.13, 409 n.37.


34
The plaintiffs have vigorously contended that their statistical evidence should be evaluated by the "internal comparison" approach.  Pointing to undisputed evidence of a small percentage of class members in the City's upper three job categories, a large percentage of class members in the City's lower four job categories, and to the City's ready concession that its policies favor filling positions by promotion, plaintiffs maintain that the labor pool from which candidates for upper level jobs are drawn is the City's existing, lower level workforce.  There is, admittedly, some superficial appeal to this argument.  Evidence adduced at trial indicated that the percentages of Spanish-surnamed Mexican-Americans employed in the City's various job categories in 1976 and 1977 were:17


35
The discrepancy is obvious.18  That a discrepancy is obvious, however, does not necessarily lead to the conclusion that something is amiss.  In this case, a closer scrutiny of the data leads only to the conclusion that no conclusions can be drawn from it.


36
The eight job categories listed above are titled:

I  Official/Administrative
II  Professionals
III  Technicians
IV  Protective Service

37
(including fire and police)

V  Para-Professional
VI  Office/Clerical
VII  Skilled Craft
VIII  Service/Maintenance

38
The plaintiffs' contention that Categories V through VIII provide the standard against which representation of class members in Categories I through III should be measured necessarily assumes, as discussed above, that employees presently classified in the former categories are eligible for promotion into the latter categories.  As such an assumption would imply, the City does arrange its workforce into a hierarchical structure.  It is first divided into departments, whose directors report to the City Manager, and then into divisions, whose superintendents report to department directors.  Further distinctions exist within the divisions as is appropriate to the type of work the division performs.  In the divisions of Utility Systems and Street Maintenance, on which the plaintiffs' evidence focused, the bulk of the workforce is stratified as supervisors, foremen, crew leaders, senior laborers, and laborers.


39
The City's eight job categories do not, however, represent sequential steps in that hierarchy.  Category I, including the City Manager, department directors, and division superintendents, may properly be considered to contain "higher level" jobs.  Categories II, III, V, VI, VII, and VIII, however, as their titles indicate, are distinguished from each other by the kind and function of jobs which they include, rather than by degree of responsibility within a particular function.  Positions of greater responsibility within a particular function, up to and including what would commonly be considered middle management positions, are classified within that category which includes the entry level position subject to the higher level employees' supervision.  The Utilities Systems Division provides an example.  Five of its six levels, from system worker through supervisor, are classified as category VIII jobs.  Only the sixth level, Utility Systems Division Superintendent, is found in a "higher" category, i. e., Category I.


40
Against this background, the plaintiffs' contention that the considerable proportion of Mexican-Americans observed in the lower categories of V through VIII should, then, be reflected in Category I, must be rejected.  This argument fails to recognize that Category I positions, as the top rungs on the several ladders beginning in Categories V through VIII, would not be available to all employees classified in Categories V through VIII.  Rather, they would be available only to those employees in Categories V through VIII who had reached within their respective divisions the highest level of progression encompassed within those "lower" categories.  The entire employment of Categories V through VIII does not define the labor pool from which all Category I positions might be filled.  At most, only a subset of Category V through VIII positions furnishes candidates for Category I jobs.


41
The plaintiffs produced no evidence which defined the number of jobs within this subset of positions immediately below Category I, they did not identify the number of Mexican-Americans in these positions, and they did not identify the number of openings which have occurred in Category I superintendent positions since 1972, when the City became subject to Title VII.  They provided only evidence of the total numbers and percentages of class members within Categories V through VIII.  Compare Wilkins at 398 n.13.  In light of the plaintiffs' failure to produce evidence properly identifying this subset, the district court's conclusion that the City's lower job categories do not provide the basis against which class members' representation in Category I should be evaluated, must be affirmed.


42
The plaintiffs similarly urge that the adequacy of class members' representation in Categories II and III is properly ascertained by an internal comparison to their rate of employment in Categories V through VIII.  However, there is no support in the record for a finding that employees of Categories V through VIII would, in a normal course of progression, move into Categories II and III.  Category II, Professionals, is primarily composed of data processing systems analysts, city planners, attorneys, public health nurses, sanitarians, and nutritionists.  Category III, Technicians, includes data processing programmers, coders and system operators, engineers, surveyors, construction inspectors, and laboratory technicians.  These are, as the district court observed, "positions which require special training for acquiring skills which persons in the general labor market do not possess or cannot readily acquire through minimal on-the-job training."


43
Categories VI through VIII, by comparison, are primarily composed of, respectively, records clerks and typists, mechanics, and heavy equipment operators, and maintenance and construction workers.  Category V, Para-Professionals, does appear to include employees whose skills are in the same areas as those of some Category II and III employees: it is composed of health aides, engineering aides and legal investigators.  The plaintiffs, however, introduced no evidence whatsoever bearing on the qualifications required of, or actually held by, the City's para-professionals, technicians and professionals.  Id.  There is in the record no basis for a determination of whether Category V employees would be eligible for Category II or III positions.


44
The plaintiffs, in an attempt to bridge the gap between the level of skills required of employees in Category II and III positions and of employees in Categories V through VIII, have adduced evidence that the City does make available some employee training.  Company training programs, coupled with a corporate policy favoring promotion over recruitment, have in several cases made appropriate a comparison of minority representation in the organization's higher echelons to minority employment among its rank and file.  See Fisher at 544; James at 341; and Robinson at 659.  In those cases, however, it was the employer's policy and practice to hire unskilled workers into entry-level positions and to provide them with all training necessary for advancement into higher-level positions.  As stated in Fisher, "(W)here skills are commensurate with the company training, we will approve statistical comparisons between (minority) make-up in key positions and (minority) composition in the total work force," 613 F.2d at 544 (emphasis added).


45
The City readily concedes that its policy favors promotion over recruitment of new employees, and that it supports this policy by offering both opportunities for formal training and on-the-job training to its employees.  Such facts do not, however, support the inference that plaintiffs would have us draw, that positions in Categories II and III would, by the City's policy and design, be filled by employees in the lower four job categories.  All evidence of the nature of the training made available by the City indicates that its purpose is to improve the employee's skill at the type of job in which he is presently engaged, and not to train him in a different skill or qualify him for certification in a professional field.  City-offered training teaches street maintenance workers to operate graders, and utility systems workers to read maps so that they may become utility systems foremen.  It does not, nor is it required to, teach a utility systems foreman to be a surveyor or civil engineer.  In the absence of the latter type of training, it cannot be said that professional and technical employees are drawn from the para-professional, clerical, mechanical, and maintenance workforces.  The district court's conclusion that an internal comparison would be here, too, inappropriate, is affirmed.


46
The conclusion that an internal comparison is inappropriate does not, however, resolve the ultimate issue of whether discrimination exists in the City's upper ranks.  Such a conclusion means only that another, external labor market must be identified as the relevant comparative basis.  Accordingly, the plaintiffs offered expert statistical testimony, in which the defendants concurred, that the external labor pools from which employees qualified for the first three job categories would be drawn could be either state, regional, or national pools.


47
Neither party, however, offered evidence of the number and minority compositions of persons in the regional or state labor pools which would supply applicants for the top three job categories.  The court, therefore, on the concerted recommendation of both parties' experts, used 1970 United States census data to derive the percentage of Spanish surnamed persons in the Wichita Falls Standard Metropolitan Statistical Area (SMSA) labor pool and the nationwide labor pool qualified for positions encompassed in the top three job categories.19  Limitations inhering in the 1970 census data, however, required that the City's job categories II and III, Professional and Technical employees, be analyzed in combination: the census reports cumulated census data on professionals and technicians into a single category.  The court's analysis was further limited by the plaintiffs' failure to adduce, in any of the voluminous data and extended testimony which plaintiffs presented at trial, data on the total number of people and the number of Spanish surnamed Americans of Mexican descent hired by the City in the first eight months of 1978, in all of 1973, and in the last four months of 1972.  This omission effectively withdrew from the court's consideration the issue of the City's hiring performance in two of the six years which it had determined the action properly to encompass.20


48
Working within these constraints, the district court made the following findings upon comparison of employment in the City's upper three categories with the relevant qualified labor pools:


49
36. The following table sets forth (a) the percentage of Spanish surnamed persons employed by the City in 1977 in EEOC job categories 1, 2, and 3; (b) the percentage of Spanish surnamed persons employed in the Wichita Falls SMSA in 1970 in EEOC job categories 1, 2, and 3; and, (c) the percentage of Spanish surnamed persons employed nationwide in 1970 in EEOC job categories 1, 2, and 3:


50
Job       (a) City work  (b) Wichita Falls
Category      force            SMSA         (c) Nationwide
--------  -------------  -----------------  --------------
1             4.5%              3.0%              2.0%
2             1.9%               )                )
3             1.4%              )2.0%             )2.0%


51
38. The following table sets forth the expected and observed numbers of Spanish surnamed persons hired by the City from 1974 through 1977 in EEOC job categories 1, 2, and 3. The expected numbers and the standard deviations are computed using 3% as the percentage of Spanish surnamed persons in the labor pool for EEOC job category 1 and 2% as the percentage of Spanish surnamed persons in the labor pool for EEOC job categories 2 and 3 combined.


52
Job       Total  Observed        Expected        Standard
Category  Hires  Sp.-sur. Hires  Sp.-sur. Hires  Deviation
--------  -----  --------------  --------------  ---------
  1         14         0               .42          .64
2 & 3      146         1              2.92         1.69


53
On this basis, the district court concluded that plaintiffs failed to make out a prima facie case of discrimination.


54
The plaintiffs attack these findings with the single argument that the court erred in utilizing standard deviation analysis in its determination of the significance in the variation between the expected and the observed numbers of Spanish surnamed Americans of Mexican descent employed in the City's top three job categories.  The plaintiffs vigorously contend that any discrepancy unfavorable to the class emerging from a simple comparison of the percentages is evidence of discrimination adequate to support a prima facie case.  This argument flies in the face of rudimentary principles of sound statistical analysis.  It is axiomatic that statistical significance may be attributed to an observed discrepancy only upon reduction to an acceptable level of the possibility that such a variation would, in the normal course of events, reasonably be expected to occur simply by random chance.  Sullivan, Zimmer & Richards, supra n.7 at 71-80.  Standard deviation analysis quantifies the likelihood of a benign explanation for an observed discrepancy; its use is essential where, as here, the discrepancy apparent upon a simple comparison of expected and observed occurrences is slight.21


55
Nor does the plaintiffs' argument find a basis in the case law defining the standard by which the adequacy of statistical proof of discrimination is to be measured.  Judicial insistence on proper qualification of statistical proof is by no means new.  The Supreme Court's sophisticated statistical analysis in Hazelwood, 97 S.Ct. at 2741-2744 and Castaneda, 97 S.Ct. at 1281 n.17, both of which decisions were rendered prior to trial of this action, clearly articulated the measure by which the adequacy of statistical proof is to be determined.22  Its endorsement of standard deviation analysis as an acceptable method by which the competency of statistical proof may be shown has been reflected in the decisions of this Court.  See Wilkins at 398 n.12.  This argument must, accordingly, be dismissed as without foundation.


56
The district court's conclusion that the plaintiffs failed to establish a prima facie case of discrimination against class members in the City's upper three job categories is supported by the evidence.  Only statistical proof was offered, and comparison between the expected and the observed numbers of class members in those positions cannot be said to evidence a "marked disproportion," Griggs 91 S.Ct. at 852.  This conclusion is affirmed.

2. Promotion and Training

57
The plaintiffs alleged that the City's job qualifications and employee assessment practices operated discriminatorily to deny promotions to class members.  They produced, however, no statistical evidence on the progression-or lack thereof-of Spanish surnamed Americans of Mexican descent through the hierarchies of the divisions into which these class members were hired.  They offered no evidence whatsoever, either statistical or testimonial, regarding the promotion of office and clerical workers, virtually all craft workers, and most service/maintenance employees.  The only personal testimony produced regarding the City's promotion practices related to the progression of Utilities Systems and Street Maintenance employees; with a single exception, this testimony was to the effect that Mexican-Americans received no fewer promotions than did any other class of employees.  That exception was the testimony by Raul Vasquez, one of two Mexican-American utility systems supervisors,23 to his belief that the City looked more favorably on promoting minorities after Placido Rivera filed charges of discrimination with the Equal Opportunity Employment Commission in early 1973.  Vasquez did not elaborate on his beliefs, nor did the plaintiffs pursue this avenue by either presenting evidence of specific instances of failure to promote, or introducing statistical evidence supporting an inference of an increased rate of promotion of class members after the EEOC charge was filed.  Vasquez' single bit of testimony, standing alone, is not sufficient to make out a prima facie case of failure to promote.  The district court's finding of an absence of evidence that the City's promotion practices had a discriminatory impact is affirmed.


58
The same failure to present evidence dooms the plaintiffs' attack on the district court's finding of an absence of discrimination by the City in training its employees.  What evidence there was of City-provided training indicated that on-the-job training was given to laborers, mechanics, equipment operators, and clerical employees; that technical, professional, and administrative employees were offered the opportunity to attend training seminars relating to the fields in which they worked; that the City made a college tuition subsidy program available to all employees; and that the City encouraged all utilities systems workers to obtain various certifications, but did not itself offer or subsidize related courses.  All testimony, including that by the plaintiffs' witnesses, indicated that this training was made equally available to all employees who by virtue of their position were qualified for it.


59
The plaintiffs did offer documentary evidence which indicated that only three percent of all City employees participating in seminars offered from the time of the City's inclusion under Title VII in 1972 until trial in August 1978 were class members.  The plaintiffs failed, however, to put this information into context.  They did not show to which fields of employment the seminars were relevant, for which levels of employees the seminars were designed, or the proportion of class members in these fields and at the appropriate levels.  Standing alone, this statistic has no probative value.


60
The plaintiffs contend that the City discriminates by offering seminars to its professional and technical employees while offering only on-the-job training to laborers, equipment operators, and clerical employees.  There is, however, no requirement that the City offer any particular form of training-or, for that matter any training at all-to its employees.  It is required only to offer what training it chooses to make available on an even-handed, nondiscriminatory basis.  This, it appears, it does.  There is no basis on which a finding of discrimination in training could be rested.  The district court is affirmed.

III.

61
The district court concluded that the only claim upon which plaintiffs prevailed was their class action claim that the City Fire Department discriminated in hiring class members.  After analyzing and balancing the factors identified as guidelines in Johnson v. Georgia Highway Express, Inc., 488 F.2d 714, 717-19 (5th Cir. 1974), the district court found that the services and expenses necessarily and reasonably required to establish this claim entitled plaintiffs' attorneys to the sum of $4,000.  The court did not abuse its discretion in determining the amount of the award relating to the Fire Department hiring claims.  This award is affirmed.

IV.

62
We add in closing an echo of an observation well taken by a recent panel of this Court.  Private enforcement of the employment discrimination laws is an essential component in the collective effort to rid our society of the debilitating effects of racial, ethnic, and sexual prejudice.  When used in conjunction with a class action, the power of the laws is magnified many times over-but therein lies the danger, as well as the good.  These actions determine the rights of untold numbers; frequently, those affected are wholly unaware of even the existence of the proceeding.  The burden borne by those who would assert these interests has grown heavier in recent years, as the forms in which discrimination appears become more varied, and more subtly interrelated.  The days-if they ever existed-of casual renditions of "broad conclusions from crude and incomplete statistics," Wilkins at 410, are indeed long since past.  The successful prosecution of class-wide employment discrimination claims demands considered and refined statistical analysis by counsel as well versed in the learning of mathematicians as in their own.  The legal principles we apply today are familiar ones.  Their invocation, particularly where the sought-after adjudication determines, for better or for worse, the interests of an undetermined count of unidentified people, must be with care and caution, unless the citizen's sword against discrimination in the workplace would be turned unwittingly against the citizen.


63
The judgment of the district court is affirmed.


64
AFFIRMED.



*
 Former Fifth Circuit case, Section 9(1) of Public Law 96-452-October 14, 1980


1
 The City officials named as defendants are the City Manager, Mayor, Board of Aldermen, Chief of Police, and Personnel Director.  All individual defendants are sued in their official capacity.  The City Manager, Gerald G. Fox, and the Chief of Police, Curtis Harrelson, are sued as well in their individual capacity.  Plaintiffs, however, seek only injunctive relief against them individually.  All claims for exemplary damages, and all claims for back pay except those against the City itself, were waived before trial


2
 The district court found that the Fire Department's hiring practices had a discriminatory impact on Spanish surnamed Americans of Mexican descent, in that they discouraged class members' applications for positions with the Fire Department.  The plaintiffs did not challenge the actual qualifications which the City required of its firemen.  The court ordered the City to develop a program for recruitment of Mexican-American applicants for the Fire Department and to publicize in the newspaper, on radio, and on television a notice to all Spanish surnamed persons in the Wichita Falls area that they may be
entitled to a cash award and/or employment based on your successfully making the following showing:


1
 That you would have applied for a job as a fireman with the Wichita Falls Fire Department since September 10, 1972, but for its discrimination against Spanish-surnamed persons;


2
 That you were qualified for a job as a fireman with the Wichita Falls Fire Department at the time you would have applied
The City fulfilled this notice requirement.  No class member applied for relief.


3
 The class claims originally included charges of harassment and retaliation by the City against class members who filed EEOC claims against it, and of discriminatory termination.  These claims were abandoned, leaving as the class-wide issues discrimination in the City's general recruiting, hiring, training, and promotion practices, and in its hiring practices for supervisory and administrative positions
Of the six original individual plaintiffs and intervenors, only one actually tried his claim before the district court.  Plaintiff-intervenors Rivera, Castillo, Pete Gonzales, and Maldonado through their attorneys "waived" all claims, and Ceballos and Richard Gonzales "waived" their claims for monetary relief during the course of the trial.  These "waivers" reduced Richard Gonzales' claim for relief to a demand for reinstatement, and Ceballos' claim for relief to a demand for admission to the police academy and seniority.  Gonzales later stated, however, under questioning by his attorney, that he preferred his current job to his old job with the City.  The court thereupon granted his request for a "waiver" of his claim to reinstatement.  He thus effectively "waived" the entirety of his claim.  Only Ceballos' claim was tried.


4
 The plaintiffs also alleged violations of § 1981 of the Civil Rights Act of 1866, 42 U.S.C. § 1981, and § 1983 of the Civil Rights Act of 1871, 42 U.S.C. § 1983.  Consideration of these alternative remedies for employment discrimination is necessary only if their violation can be made out on grounds different from those available under Title VII.  The plaintiffs have not argued that such distinctions exist.  Moreover, the case law controlling in this Circuit indicates that the elements of substantive claims of employment discrimination brought under § 1981 and § 1983 parallel those of claims brought under Title VII
In Williams v. DeKalb County, 582 F.2d 2 (5th Cir. 1978) this Court interpreted the Supreme Court's holding in Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976) as requiring that claims of discriminatory impact brought under § 1981 be supported by proof of purposeful discrimination.  Such actions thus appear to parallel those alleging disparate treatment through discriminatory patterns and practices under Title VII.  See Vasquez v. McAllen Bag & Supply Co., 660 F.2d 686, at 688 (5th Cir. 1981); note 5, infra.  It is, in any case, possible that § 1981 would not apply to this action.  Section 1981, though reaching claims of racial discrimination, may not address discrimination on the grounds of national origin.  See Runyon v. McCrary, 427 U.S. 160, 96 S.Ct. 2586, 49 L.Ed.2d 415 (1976); Jones v. Alfred H. Mayer Co., 392 U.S. 409, 88 S.Ct. 2186, 20 L.Ed.2d 1189 (1968); Patel v. Holley House Motels, 483 F.Supp. 374 (S.D.Ala.1979).
Neither in this instance would § 1983 appear to provide an avenue for the prosecution of discrimination claims different from that available under Title VII.  This Court has held that when § 1983 is used as a parallel remedy with Title VII in a discrimination suit, the elements of the substantive cause of action are the same under both statutes.  Whiting v. Jackson State University, 616 F.2d 116 (5th Cir. 1980).


5
 A showing of "marked disproportion" between the representation of the allegedly disfavored group in the employer's workforce and its representation in the labor market from which the employer hires suffices to establish a prima facie case of "disparate impact" discrimination.  Dothard, 97 S.Ct. at 2727; Griggs, 91 S.Ct. at 852.  The disparate impact branch of pattern and practice discrimination law is concerned exclusively with the actual effect of the challenged employment practices.  Whether the observed result occurred by design or merely by happenstance is irrelevant.  International Brotherhood of Teamsters v. United States, 431 U.S. 324, 97 S.Ct. 1843, 1854 n.15. 52 L.Ed.2d 396 (1977)
Throughout this action, the plaintiffs have insisted that they allege, as well, a theory of "disparate treatment" arising from the City's challenged patterns and practices.  "Disparate treatment" denotes, in many contexts, an alternative approach to proof of employment discrimination.  It may, but need not be, used in conjunction with allegations of pattern or practice discrimination, id. at 1854 n.15 (noting in the context of a "pattern or practice" discrimination case that either theory, of disparate impact or disparate treatment, may be applicable to a particular set of facts).  Where it is not, it may be used to reach "isolated ... or sporadic discriminatory acts," id. at 1854 n.15, 1855, 1855 n.16.  The crux of it in all cases, however, is that the discriminatory act was purposeful.  When it is used in an action alleging pattern or practice discrimination, it reflects the plaintiff's contention that the employer intended that its employment practices have the observed discriminatory effect.  Allegations under a "disparate treatment" theory thus serve either to require direct proof of the employer's intent through testimony to vignettes of discriminatory acts, see Teamsters, 97 S.Ct. at 1856; James v. Stockham Valves & Fittings Co., 559 F.2d 310, 329 (5th Cir. 1977), cert. denied, 434 U.S. 1084, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978), or to enhance the degree of disparity which must be shown.  In the absence of testimony of victims of discrimination, discriminatory treatment may be shown only by statistical evidence of "gross disparities," Teamsters, 97 S.Ct. at 1856 n.20, giving rise to a "compelling" inference of purposeful discrimination, James at 329 (5th Cir. 1977).
In this case, the plaintiffs have relied wholly on statistical proof.  Accordingly, in determining whether they have made out a prima facie case of discrimination, it is appropriate in the first instance to review the evidence for the lesser degree of statistical disparity adequate to support a disparate impact action.  Statistical proof failing to show a "marked disproportion," Griggs, 91 S.Ct. at 852, by definition cannot show the "gross disparity," Teamsters at 1856 n.20, necessary to sustain allegations of disparate treatment.


6
 The City began using BOLPO in conjunction with the other three elements of its police recruit selection procedure in December 1974.  The plaintiffs' statistical evidence of the class members' comparative performance on the several elements of the selection process extended through May 1978, rather than through the time of trial.  The district court properly considered May 1978 to define the close of the period under examination


7
 In the evaluation of a testing procedure, the absence of discriminatory impact is defined as the occurrence of a uniform failure rate across all racial and ethnic groups.  If the BOLPO failure rate experienced by white applicants, 5.4 percent, is assumed to be the designed failure rate and is, accordingly, applied as the norm, 1.89 of 35 Mexican-American applicants, with a standard deviation of 1.345, would be expected to fail BOLPO.  The difference between the expected value of 1.89 failures and the observed value of 14 failures is approximately nine standard deviations.  A difference of more than two or three standard deviations is generally considered to raise a compelling inference of discrimination.  Casteneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 1281 n.17, 51 L.Ed.2d 498 (1977)
We recognize that the application of probability theories to samples as limited as 35 is, of itself, problematic.  Cf. Wilkins v. University of Houston, 654 F.2d 388, 409 n.37 (5th Cir. 1981) (reserving the issue of applicability of statistical proof to small numbers of positions, in that case 14, requiring diverse and specialized qualifications).  We do not believe, however, that the limited size of the population in question precludes us from recognizing a decisive pattern emerging from a history of experiences.  Where, as here, the observed disparity is so great, we do not hesitate to conclude that a prima facie case has been established.


8
 Because only one class member both completed the selection process and accepted employment as a police recruit, the sample of applicants with which to revalidate BOLPO was too small up to the time of trial.  While lack of an adequate applicant pool in Wichita Falls at the time of validation may justify using incumbent police officers when validating BOLPO for purposes of its adoption, once an adequate applicant pool has developed, revalidation should be undertaken for purposes of continued use of BOLPO.  See 18 C.F.R. § 1607.5(K)


9
 The report also reviewed a "concurrent" criterion-related validity study which attempted to measure the correlation of success on the tests with success as a police officer.  The criterion against which BOLPO scores were here compared was a ranking of police officers by their immediate supervisor from best qualified to least qualified.  The correlation between the supervisory ranking and test scores was modest, only .38, but still statistically significant.  The report concluded on the strength of this correlation that BOLPO was a useful measure of police performance
This study was conducted with a sample of incumbent police officers from Wichita Falls.  A differential validity study, in which the results of tests compared with job performance are separately reported for minority and nonminority groups, was not feasible and therefore not undertaken because there was not a sufficient sample size for protected classes.
Plaintiffs attack this aspect of the "criterion-related validity" study because it gives no indication if any guidelines were given for ranking by the supervisors, if the supervisors had the test scores or had access to them, or what if any controls were used to protect the accuracy of the evaluation process.  This raises the danger of "criterion contamination": the criterion measure is not independent of, but is influenced by, the test score or supervisor bias.  See Albemarle, 95 S.Ct. at 2379; League of United Latin American Citizens v. City of Santa Ana, 410 F.Supp. 873, 905-06 (C.D.Cal.1976); 29 C.F.R. § 1607.14B(2); C. Sullivan, M. Zimmer, R. Richards, Federal Statutory Law of Employment Discrimination 111-12 (1980).  These criticisms need not be addressed.  It is sufficient that the test validly predicts performance at the police academy.  It need not also bear a positive correlation to satisfactory performance as a police officer.  Washington, 96 S.Ct. at 2052-53.


10
 Plaintiffs argue that the correlation established at other academies cannot be used to validate the test for use at the Wichita Falls Police Academy.  However, validity studies conducted by one test user will justify use of that test by others when the jobs of the two users are substantially similar and the test was clearly validated by the first user.  29 C.F.R. § 1607.7


11
 The physical agility test had no disparate adverse impact on class members.  By plaintiffs' own reckoning 2.85% of class member applicants failed the physical agility test from December 1974 to May 1978, while 19.9% of white applicants failed the agility test during the same period
The background investigation resulted in the elimination of 21.8% of the white applicants from December 1974 to May 1978.  During that same period, 25% of the class member applicants were eliminated on the basis of the background investigation.  We cannot say that the district court erred in holding that the investigation did not have a disparate impact on employment discrimination of class members as police recruits.
The assessment center evaluation resulted in the rejection of 15% of the white applicants, and 20% of the class member applicants between December 1974 and May 1978.  The district court held that this did not have a disparate impact on the employment of class members as police recruits.  We affirm.


12
 Ceballos was twice refused admission to the police academy.  Both times he filed charges with the EEOC.  The first charge, filed in March 1974, alleged that the department's height requirement, under which Ceballos had been rejected, had a discriminatory impact on Mexican-Americans.  In due course, a right to sue letter issued on this charge.  However, the charge became moot before it was tried, because when the City lifted the height requirement in February 1974, Ceballos reapplied, and was again rejected.  In April 1974 he filed a second charge with the EEOC, alleging that his second rejection was attributable to a discriminatory impact which the City's screening devices, particularly the BOLPO test and the background investigation, had on Mexican-Americans


13
 The plaintiffs characterized the rate of employment of class members in the City's lower job categories as "overrepresentative" by comparison of these rates not only to the rate of employment in the higher job categories but also to the percentage of class members residing in the City of Wichita Falls.  The district court found that 5.7% of the population in the Wichita Falls Standard Metropolitan Statistical Area is Spanish surnamed


14
 In making these comparisons the plaintiffs disregarded Category IV, Protective Services.  Their reasons for doing so were not articulated in either their brief on appeal or in the record below.  It may be that they believed that their particularized attacks on the recruiting and screening processes of Category IV's component parts, the Police and Fire Departments, adequately aired all mechanisms of discriminatory practices operating in that category.  Or they may have recognized that the general employment of Category IV bears, at best, a very limited relationship to employment in Category I, and no apparent relationship at all to employment in Categories II and III.  If the latter is the case, the plaintiffs' reasons for omission of Category IV from their "internal comparison" presaged our own analysis of the relationship of Categories V through VIII to Categories I, II, and III


15
 An employer cannot, of course, limit the number of minorities in his employ simply by recruiting and hiring from predominantly white areas.  In such a case, the relevant labor market would be considered to be that from which the employer, in the absence of discriminatory bias, would be expected to draw.  Markey v. Tenneco Oil Co., 635 F.2d 497, 500 (5th Cir. 1981)


16
 A prima facie case may, of course, be shown without evidence of qualifications where the inference of discrimination is supported by a compelling level of minority underrepresentation in a sizeable workforce.  In such a case, the burden of proving lack of qualifications is on the company.  United States v. Hayes International Corp., 456 F.2d 112 (5th Cir. 1972).  Where, however, this exception to the Hazelwood rule is sought to be invoked to establish a prima facie case based on an internal comparison of the minority composition of high-ranking positions to the percentage of minority workers in low-level positions, it is necessary to show not only a compelling level of comparative underrepresentation, but also a policy of filling upper level positions through promotion of employees hired at entry-level and trained by the company in the requisite skills.  Fisher v. Procter & Gamble Manufacturing Co., 613 F.2d 527, 544 (5th Cir. 1980), cert. denied, 449 U.S. 1115, 101 S.Ct. 929, 66 L.Ed.2d 845 (1981).  As will be discussed in the text, infra, the plaintiffs failed to show that the City engages in such a practice


17
 The number of Spanish-surnamed Americans of Mexican descent in each job category, as compared to the total number of employees in each job category, for the two years in question was:
       I     II    III    IV     V      VI    VII      VIII
1976  0/22  2/107  1/64  5/213  4/13  14/133  12/110  58/282
1977  1/22  2/107  1/69  5/206  5/16  16/134  12/98   56/274
The plaintiffs presented data on the number of class members employed in each job category and the total number of employees in each job category for each of the years from 1973 through 1977.  The latter two years are representative of the pattern of Mexican-American employment seen in the City's workforce throughout the five-year period.
       I     II   III    IV     V     VI     VII   VIII
1976  0     1.87  1.56  2.47  30.76  10.53  10.90  20.44
1977  4.54  1.87  1.45  2.43  31.25  11.94  12.24  20.44


18
 The change in the first category was occasioned by the employment of one class member in that category, apparently by promotion, out of a total employment of 22 persons in that category


19
 The plaintiffs did not advocate without reservation the use of the 1970 census data.  Their statistical expert testified to several weaknesses in the data.  One was that separate statistics on Mexican-Americans were not cumulated in the 1970 census; rather, Mexican-Americans, Cubans, Puerto Ricans, and all others with Spanish surnames were counted together as "Hispanics."  Another was that Government investigations into the accuracy of the 1970 census indicated that Mexican-Americans, like most minorities, were substantially undercounted.  Yet another was that the census statistics analyzing the population by job skill included in each skill category only people actually employed in those skill categories.  People qualified for, but not employed in, such positions were omitted from the statistics quantifying the proportion of the population eligible for the type of employment in question
These are not insignificant defects.  The plaintiffs did not, however, produce any other, more reliable, statistics on the number and qualifications of Mexican-Americans in either the state or national labor markets.  Particularly in the absence of their suggestion of a reasonable alternative, they will not be heard to disparage the probative value of evidence which they presented in their case-in-chief, and which was offered for precisely the purpose to which it was put by the court.


20
 The district court certified the named plaintiffs to represent the class for the period beginning "180 days prior to the date of the earliest filing of a named Plaintiff's EEOC charge (March 9, 1973) to the present (time of trial)."  So defined, the period relevant to determination of the class-wide claims ran from September 10, 1972 through trial in mid-August of 1978


21
 Of course, where the disparity apparent upon simple comparison of percentages is compelling, c. f. Hazelwood, 97 S.Ct. at 2742 n.14, 2743, such analysis may serve only to confirm the strong inference of discrimination already raised.  We do not mean to imply that in such clear cases a ritual of calculating the standard deviation must rigidly be observed


22
 Castaneda and Hazelwood were both cases in which the plaintiffs sought to establish through statistical evidence that they had been the victims of purposeful discrimination.  Castaneda arose directly under the equal protection clause of the fourteenth amendment; Hazelwood alleged purposeful discrimination in violation of Title VII.  These cases indicated that an inference of purposeful discrimination fairly could be drawn "(a)s a general rule for such a large sample, if the difference between the expected value and the observed number is greater than two or three standard deviations," Hazelwood, 97 S.Ct. at 2742 n.14 quoting Castenada 97 S.Ct. at 1281 n.7.  A variation of two standard deviations would indicate that the probability of the observed outcome occurring purely by chance would be approximately five out of 100; that is, it could be said with a 95% certainty that the outcome was not merely a fluke.  Sullivan, Zimmer & Richards, supra n.9 at 74
Where the issue is of the existence of a disparate impact, without regard to whether the adverse effect was actively sought, it is possible that a lesser disparity may lend support to an inference that the challenged practice tends to exclude the defined class of persons at a rate higher than the norm.  Statistics such as those here presented, exhibiting a disparity of less than, and slightly more than, one standard deviation, do not, however, exhibit a "marked disproportion," Griggs 91 S.Ct. at 852, between the allegedly favored and disadvantaged groups.  Standing alone, they do not raise the requisite inference.  They may, however, in conjunction with testimony of discriminatory incidents, in the proper case suffice to establish a prima facie case.  Such evidence was not presented here.


23
 Of five Utility Systems Supervisors employed by the City at time of trial, two were Mexican-American, one was American Indian, and two were white


