
506 F.Supp. 319 (1980)
Kay LITTLE, Plaintiff,
v.
MASTER-BILT PRODUCTS, INC., Defendant.
No. WC 79-3-K-P.
United States District Court, N. D. Mississippi, W. D.
December 31, 1980.
*320 *321 David G. Hill, Oxford, Miss., for plaintiff.
William E. Hester, III, New Orleans, La., for defendant.

MEMORANDUM OF DECISION
KEADY, Chief Judge.
In this Title VII class action,[1] plaintiff Kay Little (Little) sues Master-Bilt Products, a division of Standex International Corporation (Master-Bilt), to redress alleged employment discrimination on the basis of sex. Defendant, a Delaware corporation, previously employed plaintiff at its New Albany, Mississippi, plant, where approximately 250 men and women are employed to manufacture commercial refrigeration equipment. The incident that gave rise to this lawsuit took place on September 5, 1978, when defendant involuntarily discharged Little for alleged violation of company work rules. Plaintiff filed charge of discrimination with EEOC and, upon obtaining notice of right to sue, timely filed her complaint.
Finding that Little had satisfied the requirements of Rule 23, F.R.Civ.P., we subsequently certified this cause as a (b)(2) class action and defined the class to consist of all past, present and future female employees at the New Albany plant of defendant Master-Bilt Products, Inc., who work, have worked, or will work in the production area of the New Albany plant. After extensive discovery and pretrial conference before a United States Magistrate, the court bifurcated the issue of liability and reserved all questions of relief. The court conducted a 3-day evidentiary hearing and, having reviewed the parties' memoranda, the court finds the case is ripe for decision and incorporates herein Rule 52(a) requirements.

I. BACKGROUND
Master-Bilt manufactures commercial refrigeration products of all sizes, ranging from cabinet coolers to walk-in refrigerated buildings, and the cabinet production is housed in buildings separate from the walk-in structures. Each production unit has five departments, i. e., in the cabinet section, sheet metal, assembly, refrigeration, wood shop and shipping, and in the walk-in section, sheet metal, decoil, foam, door assembly and shipping.[2]
Bobby Banks as production manager is in charge of the entire manufacturing process. He maintains an office at the front of the plant but spends 50% of his time in the production areas. The production manager issues instructions to the plant superintendent and to all department supervisors. During the relevant period, insofar as the cabinet section is concerned, Bob Portis and Jerry Robbins were supervisors in the sheet *322 metal department and Woody Hill in the assembly department. Cecil Pannell, who preceded Hill as assembly supervisor, was transferred as supervisor of the paint shop. Since May 1978, Phillip Criswell has been the plant's personnel manager. The entire manufacturing process is accomplished at the plant, and this requires basic skills in metal working, welding, punch press and other machine operations and in electrical, mechanical and metal trades.

II. ISSUES
On September 14, 1978  9 days after her discharge on September 5  Kay Little, the named plaintiff, filed a charge of discrimination against Master-Bilt on the basis of sex.[3] The case presents the following Title VII issues:
1. The discharge of Little and individual members of the plaintiff class.
2. The discharge of female employees on a class-wide basis.
3. The failure to promote or upgrade Little and individual members of the plaintiff class.
4. The failure to promote or upgrade female employees as a class; and
5. Job and/or pay classifications segregated by sex.

A. Discharge.

The uncontradicted evidence shows that Master-Bilt hired Little October 31, 1975, to work in its cleaning department. She worked in this department for approximately two years without incident. Near the end of the two years she left work for six to eight weeks for unspecified surgery. Upon her return, Master-Bilt transferred Little to its sheet metal department.[4] Little began to run afoul of company work rules after she commenced work in the sheet metal department. On November 30, 1977, she received a written incident report citing her for "Abusing bathroom privileges and staying away from work station too long." According to Robbins, her supervisor, Little visited the bathroom too often and stayed too long. Robbins testified that Little abused the bathroom privilege by making trips to the bathroom more often than others in the sheet metal department. For this reason, he stated she did not adequately perform her job. Although Robbins counseled Little about her work performance, Little received a second written incident report on June 14, 1978, this time for "Unsatisfactory work and making too many mistakes." Robbins testified that Little's absence from her work station contributed to her inadequate work performance. Finally, on September 5, 1978, Little received a third incident report, for "Unsatisfactory work and low production." According to Robbins, Little's performance had not improved since her June 14 warning. Pursuant to company work rules, Master-Bilt then terminated Little for receiving three incident reports in fewer than twelve months.
The evidence clearly shows, and we find as a fact, that Robbins cited Little for insufficient production and that her failure to perform was due substantially to her excessive trips to the bathroom. The thrust of Little's grievance, however, lies in her claim that Master-Bilt applied its disciplinary rules more leniently to men than to women, particularly with respect to bathroom privileges, and that this uneven enforcement results in women being unlawfully discharged because of their sex.
Both parties presented extensive evidence on this issue. Little contended that several men had performed poorly on the job or had taken off from work without being reprimanded or dismissed. She stated, for example, that Master-Bilt let John Russell off work to play ball. Little also said that Robbins missed work to attend "horse pullings,"[5]*323 that certain men would come to work after drinking and "sleep it off" in the bathroom, and as far as she knew, they were neither reprimanded nor discharged. Finally, Little said that Bob Portis, a supervisor, told her approximately one and one-half years before her termination that women should not be allowed to work at Master-Bilt and that if it were up to him, none would.
Sherron Grose, a Master-Bilt employee until June 2, 1978, was also fired for receiving three incident reports in a 12-month period. Grose, who did punch-hole work in the sheet metal shop, testified that she was cited once for abusing bathroom privileges, once for not doing enough work, and finally for being late to work. As an example of male-female disparate treatment, Grose said that her former husband had also been late June 2 but Master-Bilt did not discharge him, but Grose failed to say whether this was his third write-up in a 12-month period. Grose testified that Master-Bilt often discriminatorily enforced work rules against women but not against men by requiring written excuses when women had to take their children somewhere but not when men took off work for whatever reason. John Wilson, she said, was off work frequently, especially Saturdays, but was never reprimanded. Grose said she knew that Master-Bilt had not punished Wilson for his absences because he told her he had not been "written up."
Another class member, Kathy Swann, has worked for Master-Bilt for six years and continues to work in the assembly department, where Woody Hill is the foreman. Swann testified that Master-Bilt's female employees are generally more harshly treated than are males. With respect to abuse of bathroom privileges, Swann said that men may visit the bathroom for 15 to 20 minutes at a time, but women are not permitted such lengthy visits. Swann also maintained that men at the plant would engage in idle conversation for 15 to 20 minutes at a time, without reprimand.
Swann also claimed that some men drink on the job or become high on drugs. She named one male employee who missed work because he "partied a lot." According to Swann, this male once missed two to three days of work with the excuse that he had car trouble. Swann also named three other men who she said were intoxicated at work. Finally, Swann testified that Cecil Pannell, her foreman who preceded Woody Hill, repeatedly told her and several other women that Master-Bilt would be a much better place to work if no women were employed there.
David Hill, Little's brother, testified he had worked for Master-Bilt since July 24, 1978. He claimed that in a "man-to-man" talk, Phillip Criswell, Master-Bilt's personnel manager, told Hill that when he was caught up with his work, he could smoke in the bathroom. Hill stated that his conversation with Criswell took place in Criswell's office when Hill requested transfer from day to night shift.
Hill also testified about the male employee Kathy Swann claimed "partied a lot." This male, according to Hill, has been absent as many as three days per week but has received, as far as Hill knows, only one warning and is still working at Master-Bilt. Ruth Dixon, another Master-Bilt employee who testified for plaintiff, corroborated Hill and Swann that this male "stays off about every Monday."
To refute plaintiff's proof on the termination issue, Master-Bilt put three of its employees on the stand. First was Phillip Criswell, the personnel manager, who testified that any employee, male or female, who receives three incident reports within a year is discharged. Criswell said that this rule appears in the employees' handbook which, among other things, lists as forbidden practices taking more than a reasonable amount of time to use the bathroom and *324 smoking in the bathroom. All employees, according to Criswell, receive an employees' handbook when they commence work for Master-Bilt. Little's personnel file shows that she was given one.
With respect to the charge of discriminatory rule enforcement, Criswell testified that sex plays no part in employee discharge and specifically did not play any part in Little's case. Criswell produced at trial a stack of written warnings issued to male employees. He also noted a number of examples of male employees discharged for receiving three written reprimands within a year. Criswell stated that lack of transportation, or automobile trouble, is no excuse for missing work. He said that although he could not recall specific instances, men have asked to be excused for that reason but have been refused.
On the subject of bathroom privileges, Criswell testified that men and women employees are treated equally. He said that no time limit exists for bathroom trips. Instead, management has adopted the rule that employees may take a "reasonable" amount of time to use the bathroom. Criswell also noted that employees may use bath facilities during work breaks, during lunch, and before and after work. Criswell denied that men are allowed to smoke in the bathroom when they are caught up with their work, and he specifically accused David Hill of lying about the alleged smoking conversation with him. Criswell said he has no direct knowledge of whether men frequently smoke in the bathroom because the supervisors, not he, enforce this rule.
Bobby Banks, Master-Bilt's production manager, corroborated Criswell's description of plant bathroom policy. He said that employees are free to use the bathroom whenever they need to use it so long as they do not abuse the privilege. Master-Bilt prefers to refrain from limiting the number of trips. Banks stated that instead Master-Bilt judges whether the privilege is being abused by "seat-of-the-pants" determination. Although Banks is not in charge of enforcing company work rules, during the 50% of his time he spends in Master-Bilt's production areas, he hears of violations from supervisors who are responsible for enforcement. Banks specifically recalled seeing Little away from her work station. Banks said that twice Little's supervisor called him over to wait until Little returned. Measuring from the time Banks arrived and not the time Little left her station, Banks claimed 13 minutes elapsed one time and 15 minutes the other before Little returned.
Banks also testified about alleged unpunished misconduct on the part of male employees. In particular, he denied any knowledge of either abuse of bathroom privileges or intoxication at work by male employees mentioned by plaintiff's witnesses, although Banks did state that one male employee was discharged for coming to work intoxicated.
Finally, defendant offered the testimony of Jerry Robbins, the supervisor who cited Little in her three incident reports. Robbins discussed Little's termination and also the case of Sherron Grose. As with Little, Robbins stated that he counseled Grose but without success. He also stated that no employee received a written citation without at least two oral warnings. Robbins testified that he has never fired a man for bathroom violations, in the sense that abuse of bathroom privileges was closely connected with the three requisite written warnings, but he said that he had cited male employees for abuse of bathroom privileges.
We find as a fact that Master-Bilt does not treat women differently than men with respect to bathroom privileges. Although Little, Grose, and Swann assert that Master-Bilt applies bathroom rules more strictly to women than to men, only Swann and Hill cited specific instances of such conduct. Swann said that two male employees recently stayed in the bathroom too long, but she did not know whether they were disciplined. Banks denied knowledge of the alleged incidents. Hill testified only about his man-to-man smoking conversation with Criswell, which Criswell denied. However, even Hill admitted that bathroom smoking infrequently takes place, and the *325 court must bear in mind that Hill's credibility is suspect because he is Little's brother and because Master-Bilt has repeatedly denied him promotions and raises. Both Criswell and Banks testified that Master-Bilt's policy is to permit employees a reasonable time to visit the bathroom, and Robbins stated that he had issued a male employee one bathroom warning. We conclude that Little and Grose received incident reports based on their abuse of bathroom privileges and not because Master-Bilt treated them or other females more harshly or differently than it treats male employees.
We also find as a fact that in general, Master-Bilt is not more lax in enforcing its intoxication rules against men than women. It is true that Little and Swann named four individuals who they said had been intoxicated at work, but Banks testified, and we find as a fact, that Master-Bilt has fired one of them and issued another a written warning. Banks denied knowledge of transgressions on the part of the other two. Swann's testimony that she did not know of any woman terminated or reprimanded for using drugs or alcohol supports the finding that there was not a dual enforcement standard unfair to women.
We further find as a fact that neither Little nor Grose were discriminatorily discharged because of sex or because of any uneven enforcement of company work rules or disciplinary procedures.
Likewise, we find as a fact that female employees in the production departments have not been subjected to discriminatory discharge because of sex. The uncontradicted evidence shows that only 17 of the 155 discharges during the years 1974 through 1979, or 10.97% of all discharged employees in the production areas, were female workers.[6] Since 14.9% of the plant's work force were females, it is incontrovertible that women are not discharged in numbers significantly greater than their proportionate number in the work force.

B. Promotion.

A serious issue of sex discrimination emerges as to defendant's policy and practice in promotions and upgrades of female employees. Five levels of pay exist at Master-Bilt, G-1 through G-5. Full-time employees are hired at the G-3 grade and may advance through G-4 to the G-5 level. However, these grades attach to the job, not the employee. Thus, a "promotion" takes place when there is a change of job duties. A promotion is usually, but not necessarily, associated with change to a job of higher grade.
In contrast, an "upgrade" occurs in either of two ways. The first may happen when a G-4 or G-5 position becomes vacant. If an outsider is hired to fill the vacancy, he is classified as a probationary G-3. After ninety days, and sometimes within a shorter period if the new employee has proven prior experience, the employee is "upgraded" to G-4 or G-5 pay. The second way an upgrade can take place depends on Master-Bilt's periodic evaluation of jobs. If Master-Bilt finds that a G-3 position, for example, warrants greater pay, it may be "upgraded" to the G-4 level. Criteria for evaluating jobs include skill required, responsibility, complexity, physical effort, job conditions, and planning.
*326 Master-Bilt's promotion policy may be briefly stated: before filling a vacancy, Criswell and Banks meet to decide what qualifications are required for the job; develop a list of job candidates; and sometimes consult supervisors about candidates for promotion. No written guidelines, however, exist for evaluating employees. The company posts neither notices of the job vacancies nor notices of required qualifications, and candidates are usually not interviewed prior to the promotion selection.
Absent written job qualifications, management considers such things as job skills acquired either before or during employment with the company, attitude, and the employee's overall personnel file. Because there are no female supervisors, the job evaluation team, to the extent there is input from department supervisors, is necessarily all male. Significantly, the uncontradicted evidence was that the supervisors' attitudes toward women as expressed by Portis and Pannell, was that Master-Bilt would be a "better place" to work if no women were employed at the plant. At the time suit was filed, Master-Bilt had three G-4 female workers.
Plaintiffs contend that promotions and upgrades are functionally indistinguishable and that Master-Bilt has discriminated with respect to both. Master-Bilt urges the contrary view. Each side called former and present Master-Bilt employees to support its position, and each presented statistical evidence through expert testimony. We examine first the employee testimony, then the expert proof.

i. Master-Bilt Employees

Little testified that Master-Bilt discriminatorily denied her a promotion in October 1977 when she worked in the cleaning department. Little, then a G-3 worker, knew about the vacancy and applied to supervisors Lowell, Robbins and Portis for a G-4 position that entailed marking off panels to be stacked in coolers. James Ferguson, a male G-3 employee who worked in the "jig" department, was awarded the position. Robbins and Portis told Little that the jig and cleaning departments were one and the same, and Ferguson was promoted because of greater seniority. Little believed she was unfairly treated because, as the senior G-3 employee in the cleaning department, she considered herself first in line for promotion, particularly since Ferguson had never worked in the cleaning department.
Grose, who worked at a G-3 job in the sheet metal shop until her 1978 termination, testified that she applied for a G-4 layout position in that shop in 1976. After first trying a new employee to fill the vacancy, Master-Bilt transferred Ricky Bolding, a G-3 foam department employee, to the position. According to Grose, she could have done the job because Robbins and Portis told her that she need only be able to read blueprints to be qualified. Grose maintained that she not only could read blueprints, but knew how to choose and cut the appropriate metals, and in fact she had worked with metals in other jobs prior to being employed by Master-Bilt. Grose did not thereafter seek another position, stating that Master-Bilt did not post notices of job vacancies or advise her of its promotion policy.
Kathy Swann, still employed at Master-Bilt, works at a G-3 position in the seamery department. She testified that she has never had a promotion and does not know how to apply for one since the company does not post notices of vacancies, promotion procedures, or job qualifications. Swann said that nevertheless she knew of several job vacancies that were filled by men rather than by women having greater seniority at Master-Bilt. In the sheet metal shop, for example, Swann said that Greg Coone was made shopman over Joan Chunn who had previously worked in a G-4 set-up department position. Swann also stated that James Edge, a sheet metal employee, obtained a G-4 job over veteran female employees even though he had worked at Master-Bilt for only two or three months. Swann named other men, in the paint shop and assembly departments, who she maintained had been promoted over women.
Ruth Dixon, a G-3 paint shop employee, stated that about one year prior to trial, *327 Master-Bilt promoted James Shepard over Kay Townsend to the leadman's job in the paint shop. Townsend had been with Master-Bilt for six or seven years as compared with Shepard's one year of employment. Although Dixon could not fully articulate leadman job requirements, Dixon maintained that she, with even less experience than Townsend, could have done the job.
To counter the foregoing, Master-Bilt presented the testimony of its personnel manager, Phillip Criswell, and production manager, Bobby Banks. Criswell maintained that sex plays no part in placement, promotion, or upgrading of employees. While admitting that women were under-represented at the G-4, G-5 and supervisory levels, Criswell stated that this is so because, in Master-Bilt's experience, men have a more technical background than women and therefore commonly possess better necessary work skills. He attributed this situation to the fact that men were more likely than women to have taken high school shop courses, done welding, repaired automobiles, painted and the like. Criswell stated that the company implemented an employee self-improvement policy, outlined in the employees' handbook, of paying the total cost of technical courses taught at nearby institutions that relate to Master-Bilt job skills, and that, since 1974, of the thirty-four courses paid for by the company, only one was taken by a female. Reading from an extensive list showing all promotions and persons considered for promotion since 1974, Criswell asserted that Master-Bilt selected each individual for promotion because he or she was the best qualified for the job. Although Criswell outlined the resumes of those promoted, he did not compare them with those of the others who were qualified but not chosen, nor did he say what constituted minimum qualifications for each position which he reviewed.
Bobby Banks, production manager, confirmed Criswell's testimony as to the generalized promotion procedures. He maintained that Master-Bilt selects a pool of minimally qualified applicants for promotion, after which he and Criswell choose the person best qualified for the job. Banks undertook a lengthy detail of job requirements and the qualifications of those chosen for all promotions since 1974.
Banks and Criswell confirmed that they neither posted notices of job vacancies nor job qualifications, and they interview candidates only when there is time to do so or the candidates' qualifications appear approximately equal. Both men admitted that, to a large extent, they relied upon their supervisors' records, but the supervisors have no written guidelines for evaluating individuals and only sometimes have input into filling vacancies through promotion. Banks was of the view that an employee's "attitude," "willingness" and "desire" are important promotional considerations.

ii. Expert Testimony

Dr. Charles Kenney was offered by plaintiff and accepted by the court as an expert in statistics and their use in personnel selection and affirmative action plans. Based on Master-Bilt's answers to interrogatories describing employment, transfer, and promotional policies, Kenney was of the opinion that Master-Bilt utilizes neither systematic personnel procedures nor an objective system of employee evaluation. He specifically condemned reliance on factors such as "appearance," "attitude," and "potential for future development," which he described as "red flags" for subjectivity.
Although this is not a hiring case, the court received, over defendant's objection, Kenney's statistical analysis on the relevant labor pool and job applicants and hirings by Master-Bilt of men and women in proportion to their representation in the applicant pool. Upon the authority of Fisher v. Procter & Gamble Mfg. Co., 613 F.2d 527, 540 (5 Cir. 1980),[7] this evidence is deemed to be of *328 some relevance in ascertaining the effect, if any, it may have on sexual discrimination in upgrades and/or promotions occurring since March 18, 1978.
As related to job grades between men and women, Kenney utilized X2 to ascertain whether an imbalance existed. He compared the number of male and female employees who held G-3 jobs with those employed in G-4, G-5, and supervisory positions; these comparisons were made on a yearly basis, 1974 through 1979, and resulted in X2 values far above the 95% confidence level.[8] In fact, Kenney observed that each year the calculation exceeded the 99% level of confidence. It is important to note that the figures by year and by sex used by Kenney are found to be correct data, based upon information supplied by Master-Bilt during the discovery process. Kenney's analyses also showed that females received, on the average, disproportionately fewer promotions and upgrades, and the female underrepresentation is established by more than a 95% level of confidence. Pltf. Exs. 12 and 16.
On cross-examination, Kenney explained why he used X2 rather than the standard deviation formula the Supreme Court referred to in Hazelwood School District v. United States, 433 U.S. 299, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977). According to Kenney, X2 is more appropriate here because with relatively low numbers of persons, standard deviation is suspect. Also, Kenney stated that X2 is the proper test for frequencies, as here, in comparison with Hazelwood, wherein percentages were compared. However, Kenney emphasized that no matter which statistical test he used, his conclusions would be the same because the numbers were "overwhelming."
Kenney also discussed the Supreme Court's cryptic remark in Castaneda v. Partida, 430 U.S. 482, 496 n.17, 97 S.Ct. 1272, 1281 n.17, 51 L.Ed.2d 498, 512 n.17 (1977), *329 that "[a]s a general rule ..., if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that [the result] was random would be suspect to a social scientist." Kenney testified that the level of confidence associated with two standard deviations is approximately 95% and that for three standard deviations it is considerably higher. To be precise, he continued, the 95% level of confidence is reached at 1.96 standard deviations using a two-tailed test. Kenney said that social scientists use two-tailed tests when they hypothesize that observed numbers of a group will be either above or below the numbers expected. A one-tailed test, in contrast, is appropriate when the prediction is in one direction only  an observed frequency either higher or lower than the frequency predicted. Kenney expressed an opinion that the Supreme Court must have contemplated use of a two-tailed test because the expert believed the parties were interested in determining overrepresentation as well as underrepresentation of a minority group. According to Kenney, the Supreme Court thus approved use of the 95% confidence level since two standard deviations is, to all intents and purposes, the equivalent of 1.96 standard deviations and is commonly so considered among statisticians. Furthermore, using a one-tailed test, the 95% confidence level would be reached at 1.645 standard deviations  a figure the Court would unlikely have rounded off to two standard deviations.[9] Kenney maintained that, had the Court intended to use the one-tailed rather than the two-tailed analysis, the level of confidence associated with two (or 1.96) standard deviations would be 97.5% rather than 95%.
Dr. Arnold Levine, defendant's expert statistician, criticized Kenney's analyses. He had no quarrel with use of X2 or Kenney's data base, but instead differed with certain of Kenney's assumptions. Levine found Kenney's hiring analysis wanting because it did not take into account which applicants were qualified for Master-Bilt jobs and how many job offers were rejected by applicants. More importantly, Levine maintained that Kenney's conclusion with respect to promotions was flawed because he unjustifiably lumped together promotions and upgrades even though upgrades were not pertinent to the analysis of promotions.
Levine presented the results of his own statistical analyses. He calculated X2 at 4.44 for comparison of male with female promotions from G-3 to G-4 in the years 1974 to 1980.[10] Using the one-tailed approach because plaintiff hypothesizes only that women are underrepresented rather than either underrepresented or overrepresented *330 at Master-Bilt, Levine stated that this X2 value amounted to a 97.3% level of confidence. The standard deviation of X2 at 4.44, according to Levine, equals 1.80 units. Because 1.80 does not exceed the two or three standard deviation requirement Levine considered the Supreme Court to have imposed in Castaneda, Levine concluded that the female disparate representation at Master-Bilt is not statistically significant.
Relying on the list of persons promoted that Criswell and Banks used in their testimony, Levine stated that in the years 1974-1979, three females were in fact promoted. Based on female representation in Master-Bilt's work force and availability of qualified females for promotion, Levine opined that the expected number of promotions would be four. Levine concluded that the difference between three observed and four expected promotions was statistically insignificant. But Levine's conclusion, according to Kenney, was suspect because the latter considered the determination of qualifications and availability arbitrary. Levine readily conceded that he had relied upon the company to decide who was and who was not qualified or available for promotion.
Levine then performed further X2 analyses of promotions from G-3 by sex and of promotions and upgrades that occurred only since March 18, 1978, 180 days before plaintiff filed her EEOC charge. Levine's calculation for promotions alone yielded X2 of .564, which equates to .25 standard deviations. See Deft. Ex. 12. Taking into account both promotions and upgrades, X2 equalled 1.58 or .7 standard deviations. See Deft. Ex. 13. It was Levine's opinion that, whether upgrades are considered alone or in common with promotions, no chance existed that the difference in the numbers of males and females promoted or upgraded was attributable to sexual discrimination. Levine's conclusion was criticized by Kenney as based on an artificially short period of time, March 18, 1978, to 1980.
At plaintiff's request, Levine performed an X2 analysis of both promotions and upgrades for the period 1974 through 1978. Computing X2 at 5.01, Levine found the equivalent number of standard deviations to be approximately 1.95. Levine performed a similar analysis for the same period of time, but included only promotions from G-3 to G-4. The result of this calculation was X2 of 6.2, with the equivalent standard deviation at 2.2. Levine made these calculations using the one-tailed test, maintaining that the two-tailed test was inapplicable. Thus, by application of the one-tailed test, Levine was compelled to admit that the significance level associated with these calculations exceeded the 97.72% level of confidence, or a minimum of two standard deviations, which he believed the Supreme Court, in Castaneda, mandated under all circumstances.
Placing the testimony of both experts in proper perspective, we observe that they do not differ as to the raw data of promotions and upgrades among production area workers, but they do differ as to what period of time constitutes the relevant scope of inquiry and whether the Supreme Court, in the Castaneda decision, used the one-tailed or two-tailed test in calculating statistical significance. Since both of these issues pose essentially legal questions, little, if any, weight may be accorded the opinions of either expert on these issues, as it is the judicial function to resolve questions of law, including the interpretation of court decisions.[11]

iii. Factual Findings

The lay testimony clearly shows, and we find as a fact, that Master-Bilt discriminates against women in its promotion policies. Plaintiff's witnesses collectively testified to numerous incidents in which men were promoted over women who had longer tenure at Master-Bilt and who were able to do the job. Master-Bilt attempted to rebut this proof through Criswell and Banks. *331 These witnesses explained that Master-Bilt promoted employees on the basis of who was best qualified, and they cited numerous examples. However, they testified solely on the qualifications of the person promoted, not the other applicants, and only Banks specified any job duties. The undisputed proof at trial was that all production area jobs are easy to learn and in fact some required as little as one day's training. Moreover, the proof showed, and we find as a fact, that female employees have had to teach new male workers in their departments who have been promoted over them how to do their jobs. Finally, we reject Criswell's thesis that the fact that hardly any women take technical courses at local schools is a credible explanation of why few women are promoted. In light of the undisputed proof that many of these jobs require little training, this intimation has no probative value. Even if it did, defendant failed to show that the males who were promoted were those who had completed such educational courses.
As heretofore noted, we hold as a fact from undisputed testimony that Master-Bilt implements no objective promotion policy. The overwhelming evidence is, and we find the fact to be, that promotions and upgrades are made largely on an ad hoc basis, controlled by subjective determination of those qualified for various job vacancies. We also find that Master-Bilt does not post notices of job vacancies, qualifications for jobs, or procedure to apply for promotions. In our view, promotions and upgrades are functionally identical because both denote advancement and increased pay; and this advancement, whether characterized as promotion or upgrade, is not the result of the application of objective evaluation standards. We therefore find that Master-Bilt's promotion and upgrade procedures are arbitrary and operate to the detriment of women employees.
The statistical proof shows, and we find as a fact, that female employees are grossly underrepresented in G-4, G-5, and supervisory positions. Because the relevant calculations reveal that this underrepresentation was statistically significant at a level of confidence exceeding 95%, we find that Master-Bilt's promotion and upgrade policies affect women differently than men to the women's detriment. This level of confidence exists whether or not promotions are analyzed alone or are instead considered with upgrades, and we accordingly find that Master-Bilt treats its female employees in a disparate manner in both promotions and upgrades. Indeed, the level of confidence associated with most, but not all, these calculations is greater than 97.72%.

III. CONCLUSIONS OF LAW
Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e-2, prohibits discrimination on the basis of sex in "compensation, terms, conditions, or privileges of employment" and also in an individual's employment opportunities. Plaintiff contends specifically that Master-Bilt has violated Title VII in two respects.[12] First, she argues that Master-Bilt enforces its disciplinary rules more strictly against women than men, resulting in a disproportionate number of female employees discharged. Second, plaintiff says, Master-Bilt has failed to promote or upgrade qualified and eligible women through use of a highly subjective promotion policy.
Plaintiff seeks to recover under both disparate treatment and disparate impact theories of employment discrimination. Under the former theory, plaintiff must show that "[t]he employer simply treats some people less favorably than others" because of their sex. International Brotherhood of Teamsters v. United States, 431 U.S. 324, 335-36 n.15, 97 S.Ct. 1843, 1854 n.15, 53 L.Ed.2d 396, 415-16 n.15 (1977). Proof of discriminatory intent is necessary *332 in order for a plaintiff to prevail on a disparate treatment case, although such intent may be inferred from the circumstances. Id. In individual disparate treatment cases, the shifting burden of proof established in McDonnell Douglas v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), applies.
The disparate impact theory is normally invoked to attack facially neutral policies which, although applied evenly, impact more heavily on a protected group. Once a significant disparate impact is found, the defendant must show that the questioned policy bears "a manifest relation to the employment in question," and that this business necessity may not be met by other policies which would impact less severely on the protected group. Griggs v. Duke Power Co., 401 U.S. 424, 432, 91 S.Ct. 849, 854, 28 L.Ed.2d 158, 165 (1971). Proof of discriminatory intent is not necessary in disparate impact cases. Id. at 431, 91 S.Ct. at 853; Scott v. City of Anniston, 597 F.2d 897, 898 (5 Cir. 1978), cert. denied, 446 U.S. 917, 100 S.Ct. 1850, 64 L.Ed.2d 271 (1980).
Given this general framework, we now proceed to a legal determination of whether the class or individual claims of discharge and promotion have merit.

A. Discharge.

The evidence clearly shows that plaintiff, both individually and as a class, has failed to prove her prima facie case with respect to the complaint of discriminatory discharge. An adequate foundation for this conclusion lies in Levine's uncontradicted statistical proof that the defendant discharges female employees in numbers not significantly greater than their proportion in Master-Bilt's work force. But even if the statistical proof were inconclusive, the testimony of present and past employees demonstrated that Master-Bilt does not enforce its disciplinary rules in a manner such that women are discharged in greater proportion than men. Hence, the class claims of disparate impact of its policies resulting in discharge must be dismissed.
The individual plaintiffs who were discharged, Little and Grose, fare no better than did the class claims. Under the McDonnell Douglas standard, as adapted to discharge cases by the Fifth Circuit in Marks v. Prattco, Inc., 607 F.2d 1153 (5 Cir. 1979), the elements essential to a prima facie case are:
(1) member of a protected minority;
(2) qualified for the job from which discharged;
(3) discharged; and
(4) position vacated filled by non-protected member.
Id. at 1155. Assuming for the sake of argument that Little and Grose met the first three requirements, their claims would fail for want of the fourth requirement. The record does not reveal the sex of the employee who replaced Grose, and Little was replaced by Marilyn Hunter, another female. Moreover, the proof shows that Master-Bilt discharged both Little and Grose for good cause, and plaintiff did not rebut this proof as pretextual. Therefore, neither the class nor the individual plaintiffs may recover on the claims of unlawful discharge.

B. Promotion.

We hold that plaintiffs have proved that Master-Bilt discriminates against women in its promotion and upgrade policies and practices. In reaching this conclusion, we rely on statistical evidence, expert opinion, and lay testimony. Plaintiff has, in our view, made a prima facie case solely through use of statistics, although we note the holding of the Fifth Circuit in Williams v. Tallahassee Motors, Inc., 607 F.2d 689 (5 Cir. 1979), that often statistics alone are of insufficient force to establish a prima facie case of discrimination. Yet meaningful statistics, when coupled with other evidence, may become adequate to prove a prima facie case. Even if we were to find that the statistical evidence and expert opinion alone failed to show discrimination in promotions and upgrades against female employees, in conjunction with lay testimony, such evidence adequately depicts a pattern of promotion practices discriminatory to female workers.
*333 As a preliminary matter, defendant objects to the admissibility of evidence of discriminatory acts that occurred before 180 days prior to charge-filing. Defendant's position rests on United Air Lines, Inc. v. Evans, 431 U.S. 553, 558, 97 S.Ct. 1885, 1889, 52 L.Ed.2d 571, 578 (1977), which holds that discriminatory acts which took place more than 180 days prior to charge-filing are not actionable. However, under Fisher v. Procter & Gamble Mfg. Co., 613 F.2d 527 (5 Cir. 1980), evidence of past discriminatory acts may be used to prove present discrimination so long as "prior practices [are] considered relevant to show independently actionable conduct occurring within the statutory period." Id. at 540. The testimony of lay witnesses reveals that many specific instances of discrimination occurred during the statutory period. We therefore rule discriminatory acts occurring before 180 days prior to the EEOC charge are admissible to aid in proving present Title VII violations.
As heretofore noted, much of plaintiff's proof on discrimination in promotions and upgrades consisted of statistical evidence. Through use of chi squared (X2) analysis, we found as a fact that Master-Bilt's promotion and upgrade policies impact more severely on female employees than on male employees.[13] Because we also found that most of the X2 calculations exceeded the 97.72% level of confidence, even if the court were to accept defendant's interpretation of Castaneda, plaintiff has nonetheless made out a prima facie case of discrimination against female workers.
Again, if plaintiff has not proved her case at the 97.72% level of confidence which defendant contends is required by Castaneda, plaintiff has nonetheless made out her case using only the 95% level, which we conclude is legally sufficient under the circumstances of this case. We agree with defendant's expert, Dr. Levine, that the one-tailed test is more appropriate than the two-tailed test in Castaneda and in the case sub judice. Dr. Kenney's mistake in advocating the two-tailed test ignores that the Supreme Court, in Castaneda, was solely concerned with underrepresentation  not overrepresentation  of Mexican-Americans on grand juries, and that we are presently concerned only with underrepresentation of female workers at Master-Bilt. It is evident to us, if not to a social scientist, that a one-tailed test applies to the discrimination hypothesis. Nevertheless, it seems equally plain that Castaneda does not stand for an inflexible legal requirement, as maintained by Levine, that a level of confidence of 97.72%, rather than 95%, is essential to make out a prima facie Title VII case based on statistical evidence alone. The generality of the Court's language itself belies such an intent:
"As a general rule ..., if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that [the result] was random would be suspect to a social scientist."
430 U.S. at 496 n.17, 97 S.Ct. at 1281 n.17, 51 L.Ed.2d at 512 n.17.
Later, in Hazelwood, the flexibility of the standard of statistical significance was emphasized by Justice Stewart in the majority opinion and Justice Stevens in dissent. In referring to Castaneda, the Court, in note 17, stated: "These observations are not intended to suggest that precise calculations of statistical significance are necessary in employing statistical proof ...." 433 U.S. at 311 n.17, 97 S.Ct. at 2743 n.17, 53 L.Ed.2d at 779 n.17. Moreover, Justice Stevens, though dissenting on the merits, nevertheless clearly implied that a 95% level of confidence would be adequate in that case to prove discrimination by statistics. See id. at 318 n.5, 97 S.Ct. at 2747 n.5, 53 L.Ed.2d at 783 n.5.
In terms of levels of confidence, the difference between "two or three standard deviations," mentioned in Castaneda, is much greater than the 2.72 percentage point difference between 97.72% and 95%. *334 Castaneda stands only for the general proposition that a level of confidence acceptable to "a social scientist" may serve to prove a prima facie case of employment discrimination under Title VII. As Dr. Kenney stated, without contradiction, 95% is the level of confidence often used among social scientists in statistical analyses. We are persuaded that, given the high degree of subjectivity which infects the promotion selection process, the 95% level is sufficient to prove a prima facie case of discrimination against Master-Bilt.[14]
Laying aside the X2 analysis altogether, plaintiff nonetheless has made out a prima facie case on the basis of raw numbers. See James v. Stockham Valves & Fittings Co., 559 F.2d 310 (5 Cir. 1977), cert. denied, 434 U.S. 1034, 98 S.Ct. 767, 54 L.Ed.2d 781 (1978). At no time from 1974 through 1979 did women constitute more than 5% of G-4, G-5, and supervisory positions. In contrast, throughout these years they represented from approximately 19% to 33% of all G-3 employees even though they constituted only from approximately 13% to 23% of the production area employees, including G-4, G-5, and supervisory positions. We also note that only about 10% of those hired for production jobs are female even though women represent about one-third of all applicants and more than half of Union County's available work force.
We note the efforts of Master-Bilt to rebut plaintiff's prima facie case by contending that Master-Bilt's policy was to promote the employees most qualified and that it carried out this policy without bias toward female workers. The defense evidence at trial was largely conclusory and does not persuade us that the defendant met its burden plainly enunciated by case law. We are compelled to reject defendant's proffered explanations as legitimate, nondiscriminatory reasons for plaintiff's disparate treatment of class members in its promotion policy. Cases such as Fisher v. Procter & Gamble, supra; James v. Stockham Valves & Fittings Co., supra; and Rowe v. General Motors Corp., 457 F.2d 348 (5 Cir. 1972), hold that proffered legitimate rationales for disparate impact on class members are invalid if they rest on subjective evaluations.[15] As noted, Master-Bilt's promotion and upgrade procedures are highly subjective. Job evaluation for purposes of upgrading rests on nebulous factors such as skill required, responsibility, complexity, physical effort, job conditions, and planning. Master-Bilt elucidated no systematic procedure for quantifying and comparing these factors, and, of course, female workers had no voice or participation in such process. A highly significant fact is that Master-Bilt does not post notices of job vacancies, qualifications for jobs, or promotion procedures, so that frequently no employee is aware that a promotion is in the offing until Master-Bilt selects an employee to fill the vacant slot. Indeed, Master-Bilt made no attempt to justify this subjective promotion policy as job related.
Moreover, defendant's proof with respect to specific promotion practices must be deemed unavailing. The record reflects at least two outstanding examples of unconvincing evidence. First, plaintiff showed that many of Master-Bilt's production jobs are easy to learn and require minimal *335 training. In response, defendant adduced testimony in an effort to establish that those best qualified were promoted. Defendant listed a number of qualifications possessed by workers selected for promotion. However, there was no showing that these qualifications were job-related, see Griggs v. Duke Power Co., supra, and even if they were, defendant did not elicit the qualifications of employees passed over to show the court that indeed Master-Bilt promoted only the most qualified workers. Second, defendant attempted to explain the disparity of women in G-4, G-5, and supervisory jobs through its self-improvement education program, in which practically no women have participated. This purportedly legitimate explanation must fail because Master-Bilt neglected to draw a connection between this fact and female employees' disproportionate absence in upper-level jobs. There was simply no showing that Master-Bilt promoted those workers who had taken the technical courses. These and other gaps in Master-Bilt's evidence strip the proffered defense of the persuasiveness essential to overcome the plaintiff's prima facie case.
Our ruling on the promotion issue subsumes the class claims for job and/or pay classifications segregated by sex, and thus renders unnecessary further discussion of such claims.
Although Master-Bilt is liable to the plaintiff class on the promotion and upgrade issue, the individual claims of Kay Little and Sherron Grose must fail on their face. Under United Air Lines v. Evans, supra, discriminatory acts that occurred more than 180 days prior to charge-filing have no present legal consequences. Little's charge-filing took place September 14, 1978, so unlawful discriminatory acts occurring before March 18, 1978 are barred by limitations. Because Master-Bilt denied Little promotion in 1977 and Grose in 1976, neither may recover on their individual claims.

IV. RELIEF
Although the court bifurcated the issues of liability and relief, we found it appropriate that our judgment dismissing individual and class claims for unlawful discharge and uneven enforcement of disciplinary policies and work rules based on sex, and also dismissing the individual claims of Kay Little and Sherron Grose upon disciplinary practices by Master-Bilt in promotion and upgrades because of sex, should nevertheless have incorporated therein declaratory and injunctive relief to the plaintiff class for discriminatory policies, practices and procedures by Master-Bilt in promoting and upgrading female production workers because of sex. Therefore the court will issue a declaratory judgment that the policies, practices and procedures of Master-Bilt in promoting and upgrading female production employees at its New Albany, Mississippi, plant impermissibly discriminate against the plaintiff class because of sex, and will also issue a preliminary and permanent injunction prohibiting the defendant from failing to apply forthwith objective policies and practices in the promotion and upgrading of production workers without discrimination based on sex. This court's order shall also include suitable provisions for the defendant to devise and submit to the court for approval a program of written objective standards to be used by it in the upgrade and promotion of all production area workers, including foremen and supervisors, without regard to sex, and further outlining, since backpay is presumptively awardable to the members of the class upon a finding of class discrimination, provisions for notice to members of the plaintiff class and for filing of backpay claims not inconsistent with the views contained in this opinion.
Let an order issue accordingly.
NOTES
[1]  42 U.S.C. § 2000e et seq.
[2]  The corporate management and office personnel are irrelevant to this case and hence need not be considered.
[3]  Little's EEOC charge reads: "I have been discriminated against because of my sex in my termination from Masterbilt, and also in the terms, conditions, privileges, and opportunities of my employment while I worked at Masterbilt."
[4]  Little has not claimed that the transfer was retaliatory or objectionable in any way.
[5]  The court is reliably informed that a "horse pulling," as it obtains in Northeast Mississippi, involves attaching a sled to a horse with weights incrementally placed on the sled which is pulled by the animal. The purpose of the sport is to find out which horse has the best "pull power."
[6]                                      Discharges by Sex by Year
                      1974     1975    1976    1977    1978    1979   1974-79
Male                  24         11      22      20      40      21      138
Female                 8          2       0       0       6       1       17
% Female              25%     15.38%      0%      0%  13.04%   4.76%   10.97%
% Female in M-B
  Work Force*         21%     15.7%    13.3%   13.3%  11%     15.6%    14.9%
* Includes managers and officials, craft workers, operatives.
Deft. Ex. 10.

[7]  Relying on 1970 census data for Union County, Mississippi, Kenney projected that 962 females, or 52.48% of the available "operatives," were the relevant labor pool. Using the statistic chi squared (hereafter X2), he compared the expected proportion of males and females in a group, based on their proportion in the group from which they were drawn, with the proportion of men and women actually selected to be members of the smaller group. Kenney found a X2 value of 18.21 for labor pool members compared to production job applicants. Pltf. Ex. 3. Of course, the higher the X2 value, the less likely it is that the disproportionate sexual representation is attributable to chance. By the same process, Kenney performed X2 analyses of applicants and actual hires for production jobs. The X2 value for 1977 was 50.95, and for 1978 it was 61.42. Pltf. Exs. 4 and 5. Using standard statistical tables, Kenney determined that all three X2 values represented a confidence level greater than 95%, i. e., chances were better than 95 out of 100 that the disproportionate representation of women in these groups was not attributable to chance, or less than 5 out of 100 that it was attributable to chance. Kenney maintained that the 95% level of confidence, or .05 standard of significance, is the significance standard commonly used by statisticians. Though the .05 standard is most common, Kenney said the second and third most common standards are .01 and .001.
[8]  These data, which are compiled from Pltf. Exs. 6 through 11, are as follows:



1974
                            Male   Female   Total
G-4, G-5, and supervisors     48      0        48
G-3                           81     39       120
                             ___     __       ___
Total                        129     39       168
X2 = 18.52
1975
G-4, G-5, and supervisors     45      2        47
G-3                           72     23        95
                             ___     __       ___
Total                        117     25       142
X2 = 7.31
1976
G-4, G-5, and supervisors     49      1        50
G-3                           84     24       108
                             ___     __       ___
Total                        133     25       158
X2 = 9.02
1977
G-4, G-5, and supervisors     51      1        52
G-3                           91     21       112
                             ___     __       ___
Total                        142     22       164
X2 = 7.28
1978
G-4, G-5, and supervisors     55      1        56
G-3                          107     27       134
                             ___     __       ___
Total                        162     28       190
X2 = 9.19
1979
G-4, G-5, and supervisors     57      2        59
G-3                          125     34       159
                             ___     __       ___
Total                        182     36       218
X2 = 8.83

For these tables, X2 must exceed 3.8 to achieve significance at the 95% level of confidence. As can be seen, the X2 values calculated for each year above are well above 3.8.
[9]  Plaintiff's Ex. 14 provides as follows:



       Standard Deviation Units for One and Two-Tailed Tests
                   and Two Levels of Confidence
           Level of Confidence   95%         97.5%
           One-Tailed Test       1.645       2 or 1.96
           Two-Tailed Test       2 or 1.96   about 2.25

[10]  Deft. Ex. 11 shows:



             Analysis of Promotions from G-3 to G-4 Positions
   Year        G-3 employees         Expected promotions      Total
             % Male     % Female     Male         Female     promotions
   1974      67.50        32.50      3.38         1.63           5
   1975      75.80        24.20      6.82         2.18           9
   1976      77.80        22.20      4.67         1.33           6
   1977      81.25        18.75      3.25          .75           4
   1978      79.85        20.15      9.58         2.42          12
   1979      78.62        21.38      4.72         1.28           6
   1980      77.18        22.82      3.09          .913          4
                                    _____        ______         __
                                    35.50        10.50          46
Actual promotions: 42 male, 4 female.
X2 = 4.44   Equivalent std. dev. = 1.80

[11]  As our survey of the law will later show, both Kenney and Levine, in departing from the area of their expertise, committed legal errors upon entering the domain of law.
[12]  As discussed previously, we find as a fact and here conclude as a matter of law that Master-Bilt's employment policies with regard to bathroom privileges, intoxication at work, and excuses from work were not applied differently to men and women. Hence, this claim will not be discussed further except to the extent that these evenly applied policies might result in disparate impact on females resulting in discharge.
[13]  Defendant contends that upgrades may not be considered together with promotions because the two are dissimilar. We, however, hold otherwise.
[14]  However, this does not mean that a 95% level of confidence should be given blanket approval in all discrimination cases. Indeed, we can perceive of many situations where facially objective methods are either found to exist or are practiced, in which, for example, the 99% level of confidence would be necessary to make out a prima facie case based on statistics alone. Compare Gay v. Waiters' and Dairy Lunchmen's Union, Local No. 30, 489 F.Supp. 282, 311 (N.D.Cal.1980) (even though some statistics exceeded 99% level of confidence, data as whole did not raise inference of purposeful discrimination), with Caulfield v. Board of Education of New York, 486 F.Supp. 862, 903 (E.D.N.Y.1979) (statistics, most with confidence level of 95% and many with much higher level, significant to show disproportionate impact and in conjunction with other evidence, met both "effects" and "intent" standards of proof).
[15]  These cases were recently approved in Johnson v. Uncle Ben's Inc., 628 F.2d 419 (5 Cir. 1980).
