JERRE S. WILLIAMS, Circuit Judge:
John D. Page and Don Thomas, black citizens of the United States, brought suit against U.S. Industries, Inc.,1 contending that defendant engaged in individual and classwide discrimination in violation of Title VII, 42 U.S.C. § 2000e et seq. and 42 U.S.C. § 1981.2 The named plaintiffs represent a class of black and Mexican-American, past, present and future employees of U.S. Industries, Inc., seeking redress for alleged violations stemming from defendant’s employment policies relating to promotion, progression, job placement, initial [1042]*1042work assignments and pay.3 After a bench trial the district court determined that plaintiffs failed to demonstrate that defendant had engaged in unlawful discrimination in violation of Title VII and § 1981.
We have reviewed the anecdotal, documentary, and statistical evidence presented by both parties, and we affirm the judgment of the district court.
I. PROCEDURAL HISTORY
At the time this suit was filed, plaintiffs were employed in Houston, Texas, at the Kansas Street facility of U.S. Industries, Inc., Wyatt Division. Wyatt is a Texas corporation which owns and operates the Kansas Street plant as a wholly owned subsidiary of U.S. Industries, Inc. The Kansas Street plant is engaged in the fabrication of heavy gauge steel for use primarily in the manufacture of pressure vessels for oil refineries and petrochemical plants.
During the period covered by plaintiffs’ claims, Wyatt employed a large number of hourly paid production and maintenance workers at the Kansas Street facility. These employees performed their job duties within one of several departments. Within each department were various levels of welders, fitters, crane operators and helpers. The employees were assigned to various job classifications established by the collective bargaining agreement executed by Wyatt and the Boilermakers Union and its affiliate, Local 561. Job descriptions for each classification and rates of pay were also established by the collective bargaining agreement. Within each job classification employees were designated at one of three levels of skill and experience — A, B, or C. A was the highest level, and C was a learner classification.
The large majority of new hires at the plant were hired into the entry level position of helper although some experienced or qualified new hires entered at other levels. During the hiring process, a prospective employee was interviewed and his or her application for employment was reviewed to determine if the individual possessed any pri- or experience. When an individual was hired, a form was prepared reflecting any prior experience that the new hire had. This form was transmitted to the new employee’s foreman for use in making initial work assignments. The department to which a newly hired helper was assigned depended upon the needs of the various departments at the time and on any related experience the individual may have had. The majority of those hired as helpers were assigned to one of the assembly departments. Once a person was hired and assigned to a department, the foreman designated the task the helper was required to perform. These tasks included grinding welds on vessels, sweeping and cleaning the department, helping move parts of vessels within the department, or working as an assistant to an employee in a higher classification.
Once assigned to a department, an employee had the opportunity to develop his skills and thus increase his chances of progression to the extent that he was permitted to assist a craftsman. Although the company from time to time maintained welder and fitter training classes, an important factor in obtaining the skills required for promotion was an assignment to work as a helper to a craftsman. Whether an employee was assigned to assist a craftsman depended wholly upon the decision of his foreman.
The job descriptions for helper found in the collective bargaining agreement did not specify what steps a Helper B had to take in order to qualify himself to be promoted to Helper A. Whether a particular employee progressed to Helper A or had the opportunity to learn a trade or occupation depended primarily on the discretion of the employee’s foreman. The foreman evaluated the ability of an employee to perform [1043]*1043new tasks on the basis of his own prior experience at the plant and observation of the employee.
The collective bargaining agreement contained more specific guidelines on the qualifications necessary for promotion into Wyatt’s higher level job classifications. For example, the collective bargaining agreement effective November 18, 1977, supplied the following job descriptions:
Fitter A —assembles all types of complicated products according to drawings. Interprets and works from drawings or prints to assemble fabricated or prefabricated parts. Is skilled in the fabrication and working of materials with knowledge of tolerances and allowances. Must use applied mathematics. Is responsible for proper fitup of the product without supervision.
Welder, Electric Automatic A — Sets up and operates automatic fusion electric welding machines. Adjusts speeds and controls operation, including feed of electrode, flux and speed of travel. Knows proper fit-up and positions work properly. Does normal maintenance and adjustments of equipment. Selects proper size and types of flux and rod. Adjusts controls, operates, and maintains incidental equipment and appurtenances. Performs arc-air grooving operations when required. Performs work without supervision.
Job vacancies were not posted at the Kansas Street plant. Employees made known their preference for a position within a certain job classification by signing a job preference log maintained in the personnel office.
In order to progress from helper into one of the upper level welder classifications an employee had to pass standard tests set out in the American Society of Mechanical Engineers Boiler and Pressure Vessel (“ASME”) Code Manual. The foreman of the department determined when an employee could take such a test based on the foreman’s personal experience at the plant and his personal observation of the employee. The foreman could also consult with a leadman to determine whether an employee was ready to take such a test. Promotions were not, however, entirely dependent upon an employee’s skill. The collective bargaining agreement stated that seniority, as well as ability and qualifications, was to be evaluated when considering eligibility for promotion.
In order to obtain certification to weld on portions of the pressure vessels under the ASME Code, welders had to pass welding tests which consisted of welding steel plates in various welding positions (horizontal, vertical or overhead). The test plates had to be x-rayed and show no flaws before a welder could be certified for a particular welding position. Welders also were required to pass tests before welding on different types of steel alloys. If a foreman decided that a particular employee could not take a test, that employee could obtain the assistance of a welding instructor or speak to the plant manager. Additionally, an employee could file a grievance pursuant to the collective bargaining agreement.
In order to progress within the fitter classification, an employee was required to demonstrate certain mathematical skills. Unlike the ASME Code test for welders, no test was used to measure an employee’s applied mathematical skills. Accordingly, the foremen had to observe each employee to decide whether he had the requisite skills required for promotion under the collective bargaining agreement.
The collective bargaining agreement provided for wage rate ranges within each job classification. As employees developed skill and ability, they were awarded merit increases within the wage rate ranges in each classification. It was the foreman’s initial decision as to whether an employee received a merit increase. The amount of the merit increase was determined by the ranges set out in the collective bargaining agreement subject to the approval of the shop superintendent. The foreman was not required to submit any written justification for the granting or withholding of a merit increase or for the amount of an increase. There was no fixed period of time during which a [1044]*1044performance review had to be made or an increase granted.
On August 13, 1974, Page and Thomas filed a complaint in the U.S. District Court for the Southern District of Texas alleging that defendant had discriminated against them and the class they purported to represent in violation of Title VII and 42 U.S.C. § 1981 with respect to hiring and layoff policies, entry level wages, job assignments, wage rate increases, transfers, overtime, and lines of progression. At trial, plaintiffs abandoned their claims with respect to hiring and layoff policies.4 They ultimately characterized this case as “basically a promotion-progression case” and limited the issues to allegations that defendant had discriminated against plaintiffs with respect to entry-level wage rates, initial job assignments, promotion to higher-paying job classifications and merit increases.
The district court certified the following class on September 8, 1978:
All Blacks and Mexican-Americans who are, or have been, or have applied to be, or may apply to be employed by Wyatt Division, U.S. Industries, Inc., Texas and/or in the bargaining unit represented by Defendant International Brotherhood of Boilermakers, Iron Shipbuilders, Blacksmiths, Forgers and Helpers, AFL-CIO and its affiliate, Local Union No. 561, at anytime since April 23, 1967.
The date of class membership was subsequently revised from April 1967, to January 23, 1969.
The evidence presented by plaintiffs at trial was directed at showing that class members suffered statistically significant wage disparities, were disproportionately relegated to lower level jobs, were underrepresented in leadmen and foremen positions, and took significantly longer to promote to craft positions than similarly situated white employees. To establish their prima facie case of discrimination, plaintiffs presented testimony from the named plaintiffs and other class members regarding defendant’s employment practices. Plaintiffs also presented raw data on the numbers of employees in particular job classifications and testimony from an expert witness regarding plaintiffs’ statistical evidence. This statistical evidence compared the average hourly wage rates of class members with the average hourly wage rates of white employees. Statistical evidence regarding selection of class members and white employees for the position of leadman was also presented.
Wyatt responded with testimonial and documentary evidence on its affirmative action efforts, and its employment practices regarding hiring, initial job assignments, training, and promotions-to higher job classifications. Wyatt also presented statistical evidence relating to the composition of its workforce, comparisons of the annual earnings of class members and white employees in the same job classifications, numbers of merit increases and promotions awarded to class members and white employees, and a comparison of the length of time for class members and white employees to progress from an entry-level helper position into any one of the highest-paying craft positions. On rebuttal, plaintiffs presented their own statistical evidence comparing progression rates of class members and white employees.
The district court rejected plaintiffs’ individual and classwide claims of discrimination. The court concluded that plaintiffs’ evidence, both statistical and otherwise, failed to show that the.plaintiffs had suffered discrimination as a result of the defendant’s promotion and progression policies. Plaintiffs appeal from that judgment.
Before turning to a discussion of the class claims, we note that the ultimate question of the existence of discrimination is a question of fact. Thus, the district court’s findings of fact, including its ultimate finding on the existence of discrimination, may not be overturned unless clearly erroneous. Pullman-Standard v. Swint, 456 [1045]*1045U.S. 273,102 S.Ct. 1781,1788, 72 L.Ed.2d 66 (1982).
II. CLASS CLAIMS
A plaintiff may bring a cause of action under Title VII under either the disparate treatment or the disparate impact theory of recovery. Under the disparate treatment theory, the Title VII plaintiff must prove the existence of a pattern and practice of race discrimination. International Brotherhood of Teamsters v. United States, 431 U.S. 324, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977). To succeed in a disparate treatment case, a plaintiff must “prove more than the mere occurrence of isolated or ‘accidental’ or sporadic discriminatory acts.” Id. at 336 & n. 16, 97 S.Ct. at 1855 & n. 16. He or she must “establish by a preponderance of the evidence that racial discrimination was the company’s standard operating procedure — the regular rather than the unusual practice.” Ibid. In a disparate treatment ease discriminatory intent must be established by either direct or circumstantial evidence. Teamsters, supra, 431 U.S. at 335 n. 15, 97 S.Ct. at 1854 n. 15; Wheeler v. City of Columbus, Miss., 686 F.2d 1144, 1150 (5th Cir.1982).
By contrast, in a disparate impact case a Title VII plaintiff need not show discriminatory intent. Rather, he or she must show that a facially neutral employment practice has the result of producing a significantly adverse impact on one race. Ibid.; Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 2726, 53 L.Ed.2d 786 (1977). The district court analyzed the class claims under the disparate impact theory, concluding that the evidence presented by plaintiffs clearly related to the impact caused by defendant’s promotional system on a class of employees. The court accordingly rejected defendant’s suggestion that this case be viewed as “merely an accumulation of disparate treatment cases.”
Citing Teamsters, the court noted that either theory may be applicable to the same set of facts and that the facts of this case were conducive to analysis under either model. See 431 U.S. at 335 n. 15, 97 S.Ct. at 1854 n. 15. Consequently, the court chose to analyze the plaintiffs’ claims also under the disparate treatment theory. The court concluded that the plaintiffs had failed to prove discrimination under this theory as well.
Plaintiffs argue that their case is correctly viewed as a disparate impact case but that the court erred in deciding that plaintiffs failed to sustain their burden of proof under this theory. Wyatt argues that the district court should have analyzed the plaintiffs’ claims solely under the disparate treatment theory. The defendant bases this contention on our recent decisions in Pouncy v. Prudential Ins. Co., 668 F.2d 795 (5th Cir.1982) and Pegues v. Mississippi State Employment Service, 699 F.2d 760 (5th Cir.), cert, denied,-U.S.-, 104 S.Ct. 482, 78 L.Ed.2d 679 (1983). In both of these decisions we concluded that employment practices which rely on subjective selection criteria should be analyzed under the disparate treatment theory. In Pegues we stated:
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. Zim-mer 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.
699 F.2d at 765. See also Carroll v. Sears Roebuck & Co., 708 F.2d 183, 188 (5th Cir. 1983) (“The use of subjective criteria to evaluate employees in hiring and job placement decisions is not within the category of facially neutral procedures to which the disparate impact model is applied.”).
In light of our recent decisions in Pouncy and Pegues, we conclude that this [1046]*1046case properly can be analyzed under the disparate treatment theory. However, we note, as did the district court, that either theory may be applied to the same set of facts. Pegues, supra, 699 F.2d at 763; Wheeler v. City of Columbus, Miss., supra, 686 F.2d at 1150.
It is clear that a promotional system which is based upon subjective selection criteria is not discriminatory per se. Consequently, such a system can be facially neutral but yet be discriminatorily applied so that it impacts adversely on one group. In using a disparate impact analysis, the district court pointed out that many of this Court’s decisions examine the classwide impact of a subjective promotional system. See, eg., James v. Stockham Valves & Fittings Co., 559 F.2d 310 (5th Cir.1977), cert, denied, 434 U.S. 1034, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978); Rowe v. General Motors Corp., 457 F.2d 348 (5th Cir.1972). We agrée with the district court’s assessment that the subjective promotional system in this case indeed may have had a classwide impact. Thus, we examine the defendant’s promotional system under the disparate impact model as well.
A. Disparate Treatment
Under the disparate treatment analysis, a Title VII plaintiff may establish a prima facie case of disparate treatment using statistics alone if the statistics show a “gross disparity” in the treatment of workers based on discriminatory factors such as race. Hazelwood School District v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977); Carroll v. Sears Roebuck & Co., supra, 708 F.2d at 190; Payne v. Travenol Laboratories, Inc., 673 F.2d 798, 817 (5th Cir.), cert, denied, 459 U.S. 1038, 103 S.Ct. 451, 74 L.Ed.2d 605 (1982). However, if the statistical disparity shown by the plaintiffs’ evidence is insufficient alone to establish a prima facie case of disparate treatment, we have held that a Title VII plaintiff “may get over his or her hurdle by combining statistics with historical, individual, or circumstantial evidence.!’ Payne, supra, 673 F.2d at 817; Carroll, supra, 708 F.2d at 190. In order to rebut a prima facie case of disparate treatment, the defendant must discredit the plaintiff’s evidence or provide a non-discriminatory explanation for the apparently discriminatory result. Ibid.
Plaintiffs maintain that Wyatt employed a totally subjective system of awarding job assignments, promotions and wage increases which served as a ready mechanism for discriminatory conduct by the predominantly white supervisory staff responsible for employment decisions at the plant. They argue that because decisions regarding job assignments and promotions were based upon the subjective judgments of company foremen, minority employees were subject to a number of discriminatory employment practices:
(1) Company foremen assigned white employees hired in as helpers to assist craftsmen and assigned to minority employees the more menial tasks of sweeping and grinding. Plaintiffs contend that this practice delayed the progress of minority employees because the initial assignment in the helper classification was determinative of how quickly an employee acquired the necessary skills to progress to a welder or fitter classification.
(2) In order to progress from helper to a welder classification, or to progress to the various levels within the welder classification, an employee was required to pass standard ASME Code tests. Plaintiffs contend that company foremen selected white employees to take the ASME Code tests before similarly situated minority employees were permitted to take the tests.
(3) In order to progress to a fitter classification, employees were required to demonstrate certain mathematical skills. However, no tests were administered to determine whether an employee possessed the requisite mathematical ability to be promoted to a fitter position. Only the foreman’s subjective evaluation of an employee’s skills determined whether an employee moved from helper to a fitter classification or from a lower fitter classification to a higher one. Plaintiffs maintain that the foremen al[1047]*1047lowed white employees to advance to the fitter classification and within that classification more rapidly than minority employees.
(4) Lastly, plaintiffs complain because Wyatt allowed company foremen to decide when an employee was entitled to a merit increase. The foremen also determined the size of the increase subject to the wage ranges provided in the union contract and the approval of shop and plant supervisors. As previously noted, foremen were not required to submit written justification for the granting or withholding of a merit increase or for the amount of the increase. Moreover, there was no fixed period of time during which a performance review had to be made or an increase granted. Plaintiffs argue that this employment policy was dis-criminatorily applied because foremen granted more and larger merit increases to white employees.
1. Statistical Evidence
It is undisputed that defendant selected employees to fill the A classification jobs from the pool of employees in the lower and intermediate level jobs. In the absence of discriminatory factors, the proportion of employees in the higher level jobs should be generally reflective of the proportion of minorities available for promotion from lower level jobs. Thus, as plaintiffs correctly contend, an appropriate statistical analysis should determine whether the number of minority employees found in Wyatt’s higher level jobs is proportionate to the number of minority employees in the lower level jobs. Plaintiffs contend that the information contained in the following chart demonstrates that minorities were in Wyatt’s during the significantly underrepresented higher level job classifications class period.
% Minority "A" % Minority Helper % Minority “B”
10% 1969 54% 44%
14% 1970 69% 33%
15% 1971 61% 44%
18% 1972 78% 47%
18% 1973 ' 67% 59%
16% 1974 52% 43%
26% 1975 59% 47%
31% 1976 50% 61%
35% 1977 50% 58%
38% 1978 74% 50%
As seen below, plaintiffs presented a number of analyses designed to prove that the disparities depicted in the above chart were statistically significant. Rather than concentrating solely on refuting plaintiffs’ statistical evidence, Wyatt presented a strong statistical case of its own. The parties’ reliance on statistical evidence requires us to judge the statistical significance of the disparities shown by the parties’ respective analyses.5
Plaintiffs offered statistical evidence through the testimony of Dr. Robert Thrall to show that the discriminatory application of Wyatt’s employment policies resulted in significant statistical disparities in the treatment of white and minority workers. In the first of a series of statistical analyses conducted by Dr. Thrall, he calculated the average white wage and the average minority wage for defendant’s total workforce as of July 31 of each year of the class period. Dr. Thrall found that in each year the average white wage exceeded the average minority wage and that the differential was statistically significant.6
Dr. Thrall conducted a similar analysis of average white wages and average minority [1048]*1048wages for all craftsmen employed during the class period. This analysis also revealed that the average white wage for craftsmen exceeded the average minority wage. Dr. Thrall found that this differential also was statistically significant.7
Dr. Thrall conducted an additional analysis which compared the average white wage to the average minority wage for employees hired in 1965 or after and still employed as of July 31 of the years 1969 through 1978. Plaintiffs argue that this analysis was designed to offset any biases which resulted from the presence of white employees who were a part of defendant’s workforce prior to 1965, the year defendant became subject to the mandates of Title VII.8 The results of this analysis showed differentials which were statistically significant for the years 1969-1975, and 1978. In 1976 and 1977, the differential was below two standard deviations. In 1978, the differential again was statistically significant. Plaintiffs argue that the analysis of post-65 hires demonstrates that the wage disparities were due to concentration of minorities in defendant’s lower job classifications.
Plaintiffs concede that an analysis of post-1965 hires shows no significant differentials in the wages paid to white and minority employees who had reached craftsman status. Plaintiffs argue, however, that minority employees, though eventually promoted, progressed to the A classification at a much slower rate than did white employees. To support this contention, Dr. Thrall compared the average wages of minority and white cohorts who were craftsmen by 1, 2, 3, and 4 years after hire. The results of this analysis showed that for employees hired in the same year who became craftsmen one year after hire, white employees received an average salary which was 2.9% higher than the average salary of their minority cohorts. For employees who reached craftsman status two years after hire, the salary advantage of white employees was 3.4%; for three years, the advantage was 5.7%; for four years, the advantage was 3%; and for five years, the advantage was 2.4%. Plaintiffs maintain that the lower salaries of minority employees, especially during their first three years as craftsmen, indicate that minorities advanced more slowly than white employees into the higher paying craft classifications.
Plaintiffs’ expert also conducted an analysis to determine whether whites and minorities were treated equally in assignment to leadmen.9 Using an expectation level based upon the percentage of minorities in defendant’s total workforce, Dr. Thrall found that the actual number of minority leadmen was lower than the expected number and that the difference was statistically significant.10
The district court faulted the plaintiffs’ statistical wage evidence for several rea[1049]*1049sons. The court pointed out that wage evidence is usually used in a corroborative, almost illustrative role, see, e.g., James v. Stockham Valves & Fittings Co., supra, 559 F.2d at 327; Watkins v. Scott Paper Co., 530 F.2d 1159, 1165 (5th Cir.), cert, denied, 429 U.S. 861, 97 S.Ct. 163, 50 L.Ed.2d 139 (1976), but that in this case the plaintiffs used evidence of average wage disparities as the primary indicator of discrimination without other evidence of underutilization of minorities. Of critical importance to the court was the fact that plaintiffs presented no statistical evidence which directly addressed the issues of promotion and length of time to progress. The court, therefore, concluded that the statistical wage evidence alone was insufficient to determine that minorities were underutilized in the various departments.
To illustrate the inadequacy of average wage rates as the sole indicator of underutilization, the court noted that the union contract provided for different wages for various A classification jobs. Thus, an A classification crane operator might earn less than an A classification welder. As the district court acknowledged, this fact would not significantly diminish the value of plaintiffs’ aggregated average wage comparisons if the evidence showed that Wyatt maintained segregated job classifications or if. minority employees were directed away from the higher paying classifications. There was, however, no evidence or assertion that minority employees were encouraged to become, for example, crane operators instead of welders. Thus, we find no error in the conclusion of the district court that because there were multiple lines of progression within the various jobs, each with a different wage scale, with minorities dispersed throughout the jobs, and no evidence that minority employees were directed towards the lines of progression with lower pay scales, the plaintiffs’ average wage comparisons were insufficient alone to establish a prima facie case of discrimination. Such evidence “failfed] to take into account the fact that a number of factors operate[d] simultaneously to influence the amount of salary [the employees] receive[d].” Wilkins v. University of Houston, 654 F.2d 388, 402 (5th Cir.1981), vacated and remanded, 459 U.S. 809, 103 S.Ct. 34, 74 L.Ed.2d 47, aff’d in relevant part on remand, 695 F.2d 134 (5th Cir.1983).11
We also find persuasive the statistical evidence presented by defendant through the expert testimony of Dr. Michael Parks to rebut the results shown by plaintiffs’ statistical evidence. First, defendant concedes that if we lump all employees together in one comparison, the average hourly wage for class members is lower than the average hourly wage for white employees. Wyatt argues, however, that it was inappropriate to lump all employees together to determine whether race was a discriminatory factor because such an analysis failed to take into account other significant factors such as the differences in the various job classifications, the disproportionately high percentage of class members being hired by defendant at that time, and the experience and qualifications of the employees being compared.
In conducting his statistical analyses, defendant’s expert witness properly emphasized the disparity between the actual and expected number of minorities who received promotions and merit increases during the [1050]*1050class period. As pointed out above, these figures are more valid statistically than mere wage comparisons which do not take job classifications and job progressions into account. Dr. Parks based his expectation of promotions upon the internal composition of defendant’s workforce.
Defendants’ statistical evidence revealed that during the years 1969 through 1978, defendant implemented 1,250 promotions, 582 (46.6%) of which were to class members. Defendant’s evidence also showed that the number of promotions received by class members was not significantly different statistically from the percentage of class members employed in each six-month period during the years 1969 through 1978. Plaintiffs correctly point out that this evidence loses some of its probative value because the figures do not reflect the types of promotions given to minority employees as opposed to white employees. Plaintiffs’ point is that if minorities were given smaller promotions, it would logically follow that minorities would have to receive more promotions to reach the same level as white employees who were given one substantial promotion.
. In response to plaintiffs’ assertion that class members were assigned menial jobs as helper and thus took longer to progress to the A classifications, defendant’s expert compared the length of time required for class members and white employees to progress from helper to A classifications.12 This comparison revealed that as of December 3, 1979, there were a total of 193 employees employed by Wyatt in the various A classifications who had originally been hired as helpers and had progressed to one of the A classifications (other than Helper A). Of those 193, 77 (39.9%) were minority employees who, on the average, progressed from helper to one of the A classifications in 40.41 months of employment as compared to an average of 51.77 months of employment for the 116 white employees who had so advanced. This difference in length of time to progress shows a statistically significant difference in favor of minority employees.13 As of December 3, 1979, there [1051]*1051were 86 employees employed by Wyatt in an A classification who had originally been hired in 1969 or after as helpers and had progressed to one of the A classifications-(other than Helper A). Of those 86, 47 (54.6%) were minority employees who, on the average, progressed from helper to an A classification in 28.85 months of employment as compared to an average of 25.05 months of employment for the 39 similarly situated white employees who had so advanced. This small difference in length of time to progress is not statistically significant.
On rebuttal, plaintiffs’ expert conducted a similar statistical analysis measuring the length of time required to progress from helper to the A classifications. Plaintiffs’ analysis, however, included only employees who had been hired in 1965 or after and who were still employed as of August 27, 1974, and December 3, 1979. Plaintiffs’ analysis reflected a statistically significant difference in length of time to progress between white and minority employees as of August 1974 in favor of white employees, but no such difference was shown as of December 1979.14
In sum, the evidence shows that while 51% of the employees hired by Wyatt during the years 1969 through 1978 were class members, over 54% had progressed to skilled A classifications by December 1979.15 It is obvious that no disparity exists between the number of minority employees expected to progress to upper level jobs and the number which actually progressed. Plaintiffs argue that even though these figures show that class members are not underrepresented in Wyatt’s upper level jobs, minorities, nonetheless, took a disproportionately longer time to reach these upper level classifications than did white employees. However, plaintiffs offered no statistical evidence to support this contention or to show that the alleged longer progression rate for minorities was the result of race discrimination.
On the basis of this evidence, we do not find error in the conclusion of the district court that plaintiffs failed to prove a gross disparity in the treatment of minority and white employees. The court was not in error in concluding that the statistical evidence was insufficient alone to establish a prima facie case of disparate treatment.
2. Employee Testimony
To buttress the statistical evidence which alone is not enough, plaintiffs also presented testimony from class members regarding individual instances of discrimination. We look next to this testimonial evidence to determine whether in combination with the statistical evidence, a prima facie case of disparate treatment is established.
The class members who were called to testify presented various comparisons between themselves and white employees indicating that the white employees progressed to higher job classifications at a faster rate than did class members. Viewed in isolation this testimony tends to support plaintiffs’ claims of discrimination. However, this testimony loses weight when it is infused into Wyatt’s overall promotion and progression history. When the individual case histories of minority employees are compared with those of other non-minority employees, the evidence shows that other [1052]*1052non-minority employees took just as long to progress as the class members, and in some instances class members progressed faster than white employees. Moreover, in many instances an employee was promoted at a faster rate because he possessed prior job related experience. Plaintiffs, however, offered no evidence on the comparative qualifications of white and minority hires.16
To support their contention that minorities were assigned the menial jobs in the helper classification, plaintiffs called several witnesses who testified that when they first came to work at Wyatt as helpers, they were assigned less desirable jobs such as sweeping and grinding while white employees were immediately assigned to assist fitters. However, S. Wardsworth, a black employee who was a witness for plaintiffs, testified that when he was hired in 1967, white and black employees were assigned to perform the same type of work. Additionally, Joe Lee Wardsworth, a black employee called by defendant as a witness, testified that since 1968 or 1969 the job duties assigned to whites and minorities have been the same. Another black witness for plaintiffs, Raymond Harris, testified that he was not assigned to perform sweeping and grinding duties but rather was assigned to assist a fitter because of his previous experience and skill as a tack welder.
Lemond Edwards, a class member, testified that he progressed from helper to the Welder A classification in approximately five and one-half years, while Keith Gilmore, a white employee progressed to the Welder A classification in approximately two years. The evidence shows, however, that Gilmore was initially hired as a welder rather than a helper because of his prior welding experience.
Elbert Ferguson, also a class member, testified that he progressed from helper to a Machine Operator C classification in five years, while Karl Frenzel, a white employee, progressed to the Machine Operator C classification in approximately one year. Although the evidence shows that employee Ferguson progressed slower than most machine operators, it also shows ■ that some minority employees progressed faster than both Ferguson and the white employees to whom he compared himself, and some white employees progressed more slowly than did Ferguson.
The record is replete with such instances where class members complained of discriminatory treatment by comparing themselves to selected white employees, where upon further comparison the evidence shows that while the class member advanced more slowly than the selected white employees, he advanced more quickly than others. In other instances,- the record shows that white employees who advanced more quickly than the class members began the job with more job related experience than the testifying class member.
The district court concluded that the plaintiffs’ testimonial evidence did not bolster their statistical evidence enough to establish a prima facie case of disparate treatment. This conclusion is subject at least to some doubt when we view the evidence of individual instances of discrimination as yet unanswered by the defendant’s rebuttal evidence. As the Supreme Court has noted, “[t]he burden of establishing a prima facie case of disparate treatment is not onerous.” Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 253, 101 S.Ct. 1089, 1093, 67 L.Ed.2d 207 (1981). The prima facie case merely “raises an inference of discrimination ... because we presume [that the alleged discriminatory] acts, if otherwise unexplained, are more likely than not based on the consideration of impermissible factors.” Furn-co Construction Corp. v. Waters, 438 U.S. [1053]*1053567, 577, 98 S.Ct. 2943, 2949, 57 L.Ed.2d 957 (1978). Even though plaintiffs’ testimonial evidence of discrimination when “unexplained” might have established a prima facie case of discrimination, it is clear that the district court properly concluded that the evidence presented by the defendant adequately rebutted any inferences of discrimination raised by plaintiffs’ evidence. Moreover, as discussed below, plaintiffs failed to sustain their burden of proving that the defendant acted with discriminatory intent.
3. Discriminatory Intent
As previously noted, in order to sustain their burden of proof in a disparate treatment case, plaintiffs had to prove that the defendant acted with discriminatory intent. The district court’s finding as to whether the defendant engaged in intentional discrimination here also is subject to review under the clearly erroneous standard set forth in Rule 52(a) Fed.R.Civ.P. Pullman Standard v. Swint, supra, 456 U.S. 273, 102 S.Ct. at 1790-91.
In Boykin v. Georgia-Pacific Corp., 706 F.2d 1384, 1390 (5th Cir.1983), cert, denied, — U.S. -, 104 S.Ct. 999, 79 L.Ed.2d 231 (1984), we stated that “[although proof of discriminatory motive is generally required in disparate treatment cases, the evidence of subjective standard-less decision-making by company officials, which is a convenient mechanism for discrimination, satisfies this requirement.” Relying upon this language, plaintiffs argue that they have satisfied the intent requirement by showing that defendants maintained a subjective promotional system. This contention is not persuasive, however. The record clearly shows that defendant did not maintain the type of standardless subjective system envisioned by the Court in Boykin. The employment system at issue in Boykin was devoid of any objective bases for judging possible applicants. Moreover, the statistics presented by the Boykin plaintiffs supported their claims of discrimination. On the contrary, the record in. the instant case indicates that Wyatt’s supervisory personnel, although permitted wide discretion in promotion and wage decisions, were required to make those decisions in accordance with the standards set out in the union contract. Moreover, unlike the statistical evidence in Boy-kin, the statistics presented by plaintiffs fall far short of supporting their claims of. discrimination. We cannot hold that the type of discretionary system at issue is automatic proof of discriminatory motive.
“The ultimate burden of persuading the trier of fact that the defendant intentionally discriminated against the plaintiff remains at all times with the plaintiff.” Texas Department of Community Affairs v. Burdine, supra, 450 U.S. at 253,101 S.Ct. at 1093. The district court’s finding that plaintiffs failed to sustain this burden is not clearly erroneous.
B. Disparate Impact
We need deal only briefly with the issue of disparate impact. A prima facie case of disparate impact must be shown by identification of a neutral employment practice coupled with proof of its discriminatory impact on one class of employees in the employer’s workforce. Johnson v. Uncle Ben’s, Inc., 657 F.2d 750, 753 (5th Cir.1981), cert, denied, 459 U.S. 967, 103 S.Ct. 293, 74 L.Ed.2d 277 (1982). If a plaintiff succeeds in making such a showing, the defendant to be free of liability must then demonstrate that the challenged practice is justified by business necessity. Ibid; Albemarle Paper Co. v. Moody, 422 U.S. 405, 425,95 S.Ct. 2362, 2375,45 L.Ed.2d 280 (1975); Griggs v. Duke Power Co., 401 U.S. 424, 431-32, 91 S.Ct. 849, 853-54, 28 L.Ed.2d 158 (1971). If the defendant rebuts the prima facie case by showing the challenged practices to be job-related, the plaintiff may still prevail by showing less discriminatory alternatives. Ibid.
A plaintiff may use statistical as well as non-statistical evidence in establishing a prima facie case of disparate impact. In judging the sufficiency of the statistical proof presented, we have held that a showing of a “marked disproportion” between the representation of the allegedly disfa[1054]*1054vored group in the employer’s workforce and its representation in the labor pool from which employees are selected suffices to establish a prima facie case of disparate impact. Rivera v. City of Wichita Falls, 665 F.2d 531, 535 n. 5 (1982).
The “marked disproportion” standard requires a lesser showing of statistical disparity than the “gross disparity” standard required in a disparate treatment action. Ibid. Nonetheless, we find no error in the district court’s conclusion that plaintiffs’ statistical evidence does not show a marked disproportion in the number of minority employees in Wyatt’s lower level classifications as compared with the number of minority employees in its upper level positions. Indeed, as noted, the record shows that from an internal workpool consisting of approximately 51% minorities, Wyatt promoted 54% minorities to A classification positions.
Thus, although plaintiffs successfully identified a facially neutral employment practice, they failed to meet the second prong of the disparate impact prima facie case — they failed to show that the challenged practice impacted adversely upon class members.
C. Class Action Summary
In affirming the district court’s conclusion that no classwide race discrimination existed in this case, we are mindful that employment practices which are based upon the subjective judgments of predominantly white supervisory personnel should be viewed with caution. As we noted in Rowe v. General Motors Corp., supra, 457 F.2d at 359, promotional systems which depend upon the subjective evaluation and favorable recommendation of immediate supervisors provide a ready vehicle for discrimination. In Rowe, we invalidated a subjective promotion system shown to result in discrimination which embodied the following mechanisms: (1) the foreman’s recommendation was the single most important factor in the promotion process; (2) foremen were given no written instructions pertaining to the qualifications necessary for promotion; (3) the standards determined to be controlling were vague and subjective; (4) hourly employees were not notified of promotion opportunities or of the qualifications necessary to get jobs; and (5) there were no safeguards in the procedure designed to avert discriminatory practices. Id. at 358-59.
The plaintiffs claim that the promotion process employed by Wyatt is precisely the type of promotion system found in Rowe. As the district court noted, however, there áre several significant differences between the promotion system employed by Wyatt and that found in Rowe. Unlike in Rowe, the defendant in this case used job classifications which were a product of collective bargaining and set out in the collective bargaining agreement. We stated in 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), that qualifications required by collective bargaining agreements provide valid criteria which inject an element of objectivity into the promotion process. Thus, we note that although inclusion of objective standards in the collective bargaining agreement does not eliminate the subjectiveness of an employment practice, it does aid in reducing the possibility that employees will be subjected to discriminatory treatment as a result of discretionary decision making. Moreover, the fact that employees were able to seek review of a foreman’s testing or promotion decision by speaking with the plant manager indicates that defendant employed some safeguards to avert discriminatory practices. Indeed, the record shows that class members were successful in seeking review of decisions made by company foremen.
The most important consideration in our decision to affirm the district court is the fact that the statistics presented by the plaintiffs simply do not show that class members were discriminated against in regard to promotion, progression, and pay during the class period. In fact, the rebuttal statistics presented by defendant reveal that the numbers of minorities employed in [1055]*1055Wyatt’s higher level jobs has increased gradually but steadily over the years.
Thus, “[w]hile subjective criteria and discretionary promotion procedures may present a situation conducive to invidious discrimination,” Hill v. K-Mart Corp., 699 F.2d 776, 781 (5th Cir.1983), we conclude the record reveals no such classwide discrimination in this case.
III. INDIVIDUAL CLAIMS
The individual claims are to be analyzed as alleged disparate treatment violations. A plaintiff may use statistics alone or in combination with historical and individual evidence to establish a prima facie case of disparate treatment, Payne, supra, 673 F.2d at 817. Using such evidence, a plaintiff must show: (1) membership in a minority group; (2) an application for an open job or promotion for which he was qualified; (3) rejection; and (4) the employer promoted or hired a non-minority for the job or continued to seek non-minority applicants for the position applied for by the plaintiff. McDonnell Douglas v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817,1824, 36 L.Ed.2d 668 (1973). Once the plaintiff establishes a prima facie case, the defendant must show non-discriminatory reasons for its employment decision. If the defendant succeeds in rebutting the prima facie case, the plaintiff is then given an opportunity to show that defendant’s espoused reasons for the rejection were pretextual. Texas Department of Community Affairs v. Burdine, supra, 450 U.S. at 254-56, 101 S.Ct. at 1094-95.
It is clear the individual plaintiffs Page and Thomas succeeded in establishing a prima facie case of discrimination. It is equally clear, as indicated by the facts set out below, that the district court properly concluded that defendant successfully rebutted plaintiffs’ prima facie case.
A. John Page
Page asserts in his individual claim that despite the fact that he had prior experience as a tack welder, he was initially assigned to work as a grinder in the helper classification, while white employees with no prior experience were assigned to assist fitters. Page complains that the only time he was assigned to assist a fitter was when a white helper was absent or unable to perform the task at hand. He claims that his initial assignment as a grinder in the helper classification delayed his promotional progress. The district court noted, however, that Page failed to note or indicate any prior welding experience on his application for employment.
In his trial testimony, Page compared his progress to that of Charles Lott, a white employee. Page testified that it took him approximately fifty-five months to promote from helper to Welder A, while Lott advanced to the Welder A classification approximately thirty-eight months after his initial hire date. The district court noted that while it is clear that Lott progressed faster than plaintiff Page, the record shows that other white employees hired at the same time or after Page required a longer period of time to progress to the Welder A classification than did Page. For example, J.L. Jackson, a white employee hired as a Helper C, required seventy-five months to progress to Welder A, and K.G. Bailey, another white employee, required sixty-one months to progress to Welder A. Moreover, the district court noted that some minority employees progressed from helper to Welder A faster than Page and Lott. J. Garcia, a Mexican-American employee, was hired as a Helper C and progressed to Welder A within thirty-two months of the initial hire date. R.C. Santee, a black employee, was hired as a Helper C and progressed to the Welder A classification within thirty-six months of the initial hire date.
Page also compared his progress to that of Clarence Cole, a white employee, who was hired as a Helper C. Page complains that it took him two years after hire to be promoted to Helper C but that within two months of hire, Cole was promoted from Helper C to the learner welder position, a promotion Page did not obtain for another eight months. Upon further comparison, the evidence shows that while it took Page longer to advance to the learner welder [1056]*1056position, he progressed to the Welder A classification faster than did Cole.
Page additionally claims that throughout the course of his employment he performed work outside his job classification without having been properly reclassified or adequately paid. During the time he was classified as a helper, Page performed some work as a painter. He was never classified as a painter nor was he paid a painter’s wages. Page also claims he continuously performed Welder A type work throughout 1969 without being properly reclassified. The district court noted that under Wyatt’s employment policies, a less skilled employee may improve his skill by working with and under the close supervision of a more skilled employee. Thus, it was not uncommon at Wyatt for a welder with a lower classification to be assigned to work with an A classification employee and to perform tasks included in the job description of the higher classification. The court found no evidence that white and minority employees were treated differently in this context. We conclude that the district court’s findings on this issue are supported by the record, and thus reject Page’s claims of discrimination on this issue.
Lastly, Page claims that he resigned from employment at defendant’s plant due to the company’s failure to appoint him as an assistant welding instructor. The district court found that Page was not denied a promotion to that position because of his race, but rather that he voluntarily resigned from his employment with the company. We conclude that this finding too is supported by substantial evidence in the record.
B. Don Thomas
Plaintiff Don Thomas was hired by defendant as a Helper B and was initially assigned to do sweeping and grinding. At the time Thomas was hired, there were approximately four other blacks on the. second shift of Thomas’ department, all of whom were assigned to sweep and grind with the exception of LaSalle Phymes who was occasionally assigned to assist a fitter. Thomas complains that white. employees who were hired at the same time were permitted to practice for the welding ASME Code tests during working hours with the help of the welding instructor while he was permitted to practice welding only during his lunch break and without the aid of the welding instructor. Thomas also contends that he was repeatedly denied an opportunity to take the welding test and that even after he was finally permitted to take the test and was promoted from Helper B to Welder C, he was still required to perform sweeping and grinding duties. He complains that he was permitted to assist a skilled fitter only for brief periods when a white employee was absent.
Thomas asserts that once he was finally allowed to assist A Welders he continuously performed the same job assignments as an A Welder, but was retained in the lower C classification. Thomas complains that despite his numerous requests to take the Welder A test, he was refused the opportunity to do so. He was finally allowed to take the test for promotion from Welder C to B, which he passed, but he was still retained in the C classification for several months. He contends that he obtained his A classification only after speaking with the plant manager.
The district court found that Thomas was assigned to assist welders in the A classification in accordance with company policy and in order to allow Thomas to increase his own skill and ability by working with the A classification workers. We conclude that the record supports the district court’s finding that Thomas’ progression rate was comparable to that of other employees at the plant, and that he was promoted on the basis of his skill and ability, and that his progress was not delayed because of his race.
We accordingly reject Thomas’ individual claim that Wyatt discriminated against him in violation of Title VII and § 1981.
IV. CONCLUSION
Plaintiffs’ evidence has failed to establish that Wyatt intentionally discriminated against class members or that Wyatt’s employment practices disparately impacted [1057]*1057upon the class. In addition, Page and Thomas have not met the burden of establishing their individual claims. There having been no showing of discrimination against minorities in the promotion policies of defendant during the period at issue, we find no error in the judgment rendered for defendant by the district court.
AFFIRMED.
T represents the statistical disparity in the progression rates of white and minority workers. A negative number indicates a disparity in favor of class members.