
489 F.Supp. 282 (1980)
James GAY, Leonard Whitman, Frederick McDowell, Douglas Lee, and Gary Dennis, on behalf of themselves and all persons similarly situated, Plaintiffs,
and
Loyal Graham, Intervenor,
v.
WAITERS' AND DAIRY LUNCHMEN'S UNION, LOCAL NO. 30; Dining Room Employees Union, Local No. 9; Hotel and Restaurant Employees & Bartenders Union, Local No. 2; The St. Francis Hotel Corporation, a Delaware Corporation; Alioto Fish Co., Ltd., a California Corporation d/b/a Alioto's No. 8 Restaurant; Clift Hotel; Hilton Hotels Corp., a Delaware Corporation d/b/a San Francisco Hilton & Tower; Holiday Inns, Inc.; Hyatt Corp., a Delaware Corporation d/b/a Hyatt on Union Square and Hyatt Regency; Mark Hopkins, Inc., a Hawaii Corporation d/b/a Mark Hopkins; Sheraton Palace Corp. and Kyo-Ya Co., Ltd. d/b/a Sheraton Palace; and Westbury Hotel of California and Grosvenor Sutter Associates d/b/a Westbury Hotel, Defendants.
No. C-73-0489-WWS.
United States District Court, N. D. California.
February 6, 1980.
*283 William H. Carder, Michael H. Weiss, Marjorie Gelb, Employment Law Center, San Francisco, Cal., for plaintiffs.
*284 Donald D. Connors, Jr., Cecily A. Waterman, Brobeck, Phleger & Harrison for defendant The St. Francis Hotel Corporation; Barbara Ashley Phillips, Paul Burns, San Francisco, Cal., for defendant Hilton Hotels Corp.

FINDINGS OF FACT, CONCLUSIONS OF LAW AND MEMORANDUM OF OPINION
SCHWARZER, District Judge.


                                           Contents
                                                                                           Page
       I. Introductory Statement ..........................................................   285
      II. Background of this Action .......................................................   285
     III. Findings of Fact ................................................................   286
            St. Francis ...................................................................   286
            Hilton ........................................................................   287
            Union .........................................................................   288
            Individual Claimants ..........................................................   290
            Class Members .................................................................   291
      IV. Discussion.......................................................................   292
          A. Statute of Limitations .......................................................   292
          B. Liability of Hotels for Discriminatory Acts of Union .........................   293
             1. Vicarious Liability .......................................................   293
             2. Conspiracy ................................................................   294
             3. Violation of Collective Bargaining Agreement ..............................   294
          C. Liability of Hotels on Individual Claims .....................................   295
             1. St. Francis ...............................................................   295
             2. Hilton ....................................................................   296
          D. Liability of Hotels on Class Claim ...........................................   296
             1. Standard of Proof under Section 1981 ......................................   296
             2. Elements of Prima Facie Case ..............................................   300
                a. Relevant Labor Market ..................................................   301
                    i. Geographic Area ....................................................   302
                   ii. Age Bracket ........................................................   303
                  iii. Population Segment .................................................   303
                   iv. Time ............................................................... - 304
                    v. Earnings bracket ...................................................   304
                   vi. Employment Qualifications ..........................................   306
                  vii. Finding and Conclusion Respecting Black Male Availability ..........   307
                b. Comparison of Defendants' Data .........................................   307
                   i. Hiring Transfer and Promotion Data ..................................   307
                  ii. Statistical AnalysisPrima Facie Case .............................   310
             3. Defendants' Rebuttal Evidence .............................................   311
                a. Applicant Flow Data ....................................................   312
                b. Experience Requirement .................................................   312
       V. Conclusion ......................................................................   315



*285 I. Introductory Statement

This is an action for alleged discrimination by defendants in hiring, promoting and transferring black males into waiter positions. Plaintiffs sue on behalf of themselves and a class consisting of black males who were denied employment as waiters. The only defendants remaining in the case are The St. Francis Hotel Corporation ("St. Francis") and Hilton Hotels Corporation ("Hilton"). Plaintiffs' principal claim is based on 42 U.S.C. § 1981[1], but they also charge that defendants conspired with the labor union representing waiters in violation of 42 U.S.C. § 1985(3) and breached the collective bargaining agreement in violation of 29 U.S.C. § 185.

II. The Background of this Action

This case has had a long and tortuous history; only so much as is relevant to this disposition is summarized here. The original complaint was filed on March 28, 1973. Of the original defendants only the St. Francis remains. On June 27, 1973, its motion to dismiss the Section 1981 claim was denied. On March 19, 1975, plaintiffs' motion for class certification was denied. On March 11, 1977, the Court of Appeals reversed the class order and remanded the case which meanwhile had been reassigned to another judge. 549 F.2d 1330 (9th Cir.). On May 31, 1977, an amended and supplemental complaint was filed against the original defendants. On August 23, 1977, the Court tentatively determined that the action could be maintained as a class action against the defendant labor unions but not against the St. Francis.
On February 8, 1978, plaintiffs with leave of Court filed a second amended and supplemental complaint adding several new defendants, including the Hilton, and alleging claims under Sections 1981 and 1985 against all defendants and under Title VII against all but the St. Francis. On August 8, 1978, the Court ruled on a number of motions. So far as is relevant here, the Court's order struck the claim of plaintiff McDowell against the St. Francis, denied the motion for summary judgment against plaintiff Dennis, dismissed the claims against the Hilton arising under Title VII, except for prospective relief, and those claims predating February 8, 1975.
On June 22, 1979, the Court entered a second amended order permitting the action to proceed on behalf of a class defined, so far as is now relevant, as follows:
A. All black males working, or seeking to work as waiters who, after March 28, 1970, were or are being or are in the future, on account of their race,
* * * * * *
(3) denied employment by defendant Saint Francis Hotel Corporation; or
(4) terminated by defendant Saint Francis Hotel Corporation; or
(5) denied promotions by defendant Saint Francis Hotel Corporation; or
(6) denied equal treatment with white waiters with respect to assignment or compensation by defendant Saint Francis Hotel Corporation.
B. All black males working, or seeking to work as waiters who, after February 8, 1974, were or are being or are in the future, on account of their race,
(1) denied employment by . . . Hilton Hotels Corporation; or
(2) terminated by any of said defendants; or
(3) denied promotions by any of said defendants; or
(4) denied equal treatment with white waiters with respect to assignment or compensation by any of said defendants.
The action went to trial before the Court on October 29, 1979, on the claims of the foregoing class and the individual claims of *286 Whitman, Dennis and Gay against the St. Francis and Whitman, Dennis and McDowell against the Hilton. After seven trial days, and extended oral argument heard on November 21, 1979, the action was submitted.

III. Findings of Fact[2]

Findings of Fact Respecting the St. Francis
The St. Francis is a large, class A luxury hotel at Powell and Geary Streets in San Francisco. It operates four restaurants, in addition to banquet and room service departments. All employ waiters, captains and bus persons.
Victor's is a French restaurant located in the St. Francis Tower. It offers only French service, i. e., food is brought from the kitchen on platters and served onto plates at the table. Service is performed by teams consisting of a captain, a waiter and a bus person. Orders are taken by the captain or the waiter. Waiters bring the food to the side of the table where the captain performs whatever carving, boning or flaming is necessary and then serves the plates, assisted by the waiter. Bus persons assist in serving water, bread and butter. Both waiters and bus persons set up and clear tables. Captains assist whenever needed. Each team is responsible for six or seven tables. The English Grill is an a la carte restaurant specializing in seafood. No French service is performed but waiters bone fish. The Dutch Kitchen is a coffee shop which offers simple a la carte items prepared in the kitchen and served directly to the patron by plate service only, no French service being involved. The Terrace Room offers similar items at lunch only. Food service at the latter three restaurants is performed by the waiters. Two other restaurants, the Medallion Room and the Penthouse, were closed in 1972 and 1978, respectively.
The banquet department provides food and service for special functions. It maintains a staff of so-called steady extra (permanent) waiters. The number of functions and their size determines the number of waiters needed at any particular time. Generally one waiter is required for every 15 guests at lunch and for every ten guests at dinner. Extra banquet waiters are hired when needed by referral from the union hiring hall. French service has been performed at some banquets since about 1974; for the most part, however, banquet waiters only bring the served plates from the kitchen to the tables. The menu is fixed and orders are taken only for wine.
Room service is provided from the regular room service menu. Orders are taken by cashiers and picked up by the waiter who then delivers the food from the kitchen. He assembles the necessary utensils and other items needed to fill the order and sets the table. With limited exceptions, the menu does not involve French service.
Whenever a food service position opens up, the restaurant or department manager submits a requisition to the personnel department. Prior to 1976, managers occasionally hired directly without personnel department action. A notice of the vacancy is posted on the employee bulletin board and managers inform employees considered to be eligible for transfer or promotion, inviting them to apply.
Unless the vacancy is filled by promotion or transfer from within, the personnel department notifies the union of the vacancy. Since 1977 requests for referrals have been sent to the union for all vacancies. Prior to that time requests were regularly sent only for extra or temporary positions. Vacancies for permanent jobs were referred to the union only intermittently and few referrals were received from the union.
Depending on its needs at the time of a vacancy, the personnel department may also solicit applicants from state and private agencies and minority organizations, or from among persons whose applications are *287 on file in the office. It also receives applications from walk-in applicants.
An outside applicant must first make an appointment, usually by telephone, with the personnel department. Generally no appointment is made for persons seeking a position for which no opening then exists. The office is open to applicants from Monday through Thursday, 9 a.m. to noon. When the applicant appears for his appointment, he is asked to complete a form which calls for, among other things, a listing of prior jobs. Applications may be submitted even if there is no job opening, although at various times during the relevant period no applications were accepted when no vacancies existed. The St. Francis receives a total of between 5,000 and 7,500 applications a year, at least a dozen for each food server position vacancy. Applications are retained in an active file for six months. An informal log of applicants was maintained until 1977 when the interviewers began to maintain a more comprehensive record of applicants.
After completing the application, outside applicants receive a screening interview by the personnel department which determines on the basis of factors such as prior experience and job stability whether to refer the applicant for a further interview with the manager of the department or restaurant having the opening. That manager selects the applicants he wishes to interview and makes the hiring decision based on the interviews.
In the hiring of waiters, persons employed by the St. Francis, in particular bus persons, are given preference over outside applicants. Bus persons are evaluated on the basis of their work record for the St. Francis, including such factors as diligence, reliability, organizational and language ability and familiarity with hotel operations. They are not required to have had prior experience as a waiter but will often have had opportunities as bus persons to perform some of the duties of a waiter. Although there is no fixed time which a bus person must serve before being eligible for promotion, it generally runs from six months to two years, with on the job training continuing after promotion. Over the years, approximately one third of the permanent waiters have been promoted from bus persons. In addition, a number of permanent banquet waiters have been hired from among extra banquet waiters.
Persons hired as waiters from the outside are required to have had some prior experience as a waiter. This requirement is not contained in any job description or other document and its implementation is left to the discretion of the individual restaurant or department managers who make the hiring decisions. Applicants for Victor's must have had prior experience as a la carte waiters. In the English Grill, some dining room experience is desired. In the Dutch Kitchen, any food service experience is accepted. Banquet waiters are expected to have some French service experience. Room service requires a year's experience as a food server.
All applicants for waiter positions must be twenty-one years of age and present a neat and clean appearance. Other factors considered are job stability and attitude. Room service waiters must be willing to work flexible hours and part-time, and have reliable transportation.
The St. Francis has no training program for new waiters. On the job training is provided by having new waiters work with more experienced waiters and through general supervision. Opinions differ among management over how long it takes before a newly hired waiter can be expected to be proficient. The time will vary with the person's ability, and with the complexity of the duties required of him in the particular restaurant or department, and may range from several weeks to over a year.

Findings of Fact Respecting the Hilton
The Hilton also operates a large luxury hotel in downtown San Francisco. Its methods of operation are similar to those of the St. Francis.
The Hilton operates three restaurants. The Gazebo is a coffee shop which employs *288 about nine to ten waiters at breakfast and lunch and four or five at dinner, in addition to captains and bus persons. Henri's Room at the Top serves a buffet lunch and a la carte dinner. It employs about eight waiters in addition to captains and bus persons. Prior to 1978, it served only buffet style and employed only captains and busboys. No French service is performed at either the Gazebo or Henri's Room. The Chef's Table is a first class restaurant serving a la carte lunches and dinner. It employs about five or six waiters, and captains and bus persons. French service is performed at dinner by the waiters and captains.
The banquet department employs a permanent staff of approximately ten steady banquet waiters. In addition, it hires extra banquet waiters through the union hiring hall for particular functions. Banquets range from functions for a few persons to well over a thousand. Banquet waiters are not required to know French service or to be able to flame dishes.
The room service department employs a permanent staff of about fourteen waiters. It provides food service in the hotel rooms at all hours.
When a food server position becomes vacant, the restaurant or department manager notifies the personnel department which gives notice to the union. In filling the position, preference is given to bus persons and other employees of the Hilton desiring a promotion or transfer. Among outside applicants, those referred by the union are given preference, other things being equal. Until 1977, few union referrals were received for permanent positions. Since then the hiring hall has been reorganized and the Hilton now allows the union 72 hours to refer applicants before it fills a position from the outside.
Notices of vacancy are posted in the hotel and at the hiring hall. Notice may also be given to various outside agencies, and at times advertisements are placed in newspapers and previously filed applications reviewed for prospects.
All applicants must file an application which is maintained in an active file for one year. No log of applications was maintained until November, 1978. About 6,000 applications are filed annually. Applications are accepted at the personnel office only when a vacancy exists. After completing the application, the applicant is given a screening interview at the personnel office. That office may then refer him for a further interview to the department or restaurant manager who makes the hiring decision. Generally managers have required some unspecified amount of prior food service experience. The Hilton provides no training program; waiters are expected to become proficient in a matter of days or weeks.

Findings of Fact Respecting the Union
Both the St. Francis and Hilton at all relevant times were members of the Hotel Employers Association, an employers' association which represented these and other hotels in collective bargaining.[3] Through their membership in the association, the St. Francis and Hilton were at all relevant times parties to collective bargaining agreements covering waiters and others engaged in food service.
Until 1974, the union representing waiters in San Francisco was the Waiters' and Dairy Lunchmen's Union Local No. 30. In that year, it merged into Dining Room Employees Union Local No. 9 and in 1975, that union merged into Hotel and Restaurant Employees and Bartenders Union Local No. 2, the present collective bargaining representative. These unions, at the respective times, were the collective bargaining representatives of waiters, bus persons and captains employed by the St. Francis and the Hilton. They will be referred to here collectively as "the union."
At all relevant times, the union operated a hiring hall in San Francisco for waiters, bus persons and captains, among others. The collective bargaining agreement required employers to apply to the union for *289 referrals to fill any vacancy, and the union to refer applicants on a non-discriminatory basis.[4] Section 3(g) provided for an adjustment board to hear any appeals based on a failure to comply with the referral provisions of the agreement. No appeals to the adjustment board were ever made.
In the early 1970's the union maintained a classification board which interviewed members and determined whether to rate them as experienced waiters. When requests for experienced a la carte waiters were received at the hiring hall, the dispatcher would select from among available members those whom he considered qualified for the position. This practice, as well as the classification board, was discontinued sometime after the filing of this action. There was in any event a shortage of experienced a la carte waiters and few were in the hiring hall available for referral. The hotels, unable to meet their needs for experienced waiters through the hiring hall, generally hired directly, subject only to the requirement that the new waiter be or become a union member.
For the most part, referrals were limited to temporary extra banquet waiters for which the hotels depended on the hiring hall. Men were dispatched to these jobs on rotation designed to give each of them as nearly the same number of jobs as feasible.
In the early 1970's, about 150 members would generally be in the hiring hall available for some type of waiter work. In later years, the number increased to about 300. In 1977, Local 2 reorganized the operation of the hiring hall and undertook to persuade the hotels to make regular use of it.
When the union referred a waiter to a hotel in response to a request for help, it issued a so-called work slip. The slip was taken by the waiter to the hotel and evidenced his good standing as a union member. When a hotel requested applicants for permanent positions, the union on occasion issued an interview slip. More frequently, the hotel would select the person it wished to hire for a particular permanent position from among applicants from various sources and, before hiring, send him to the union to obtain a work slip evidencing his good standing. When this procedure was followed, the notation "by request" was made on the slip.
The union maintained copies of these slips in its records. However, there is only an informal and incomplete record of requests for referrals received by the union *290 and none which reflects requests to which the union was unable to respond.
Until 1972, the union had fewer than 100 black male members. In 1973 it had 127. In 1976, when membership information was computerized, 8,000 of its 18,000 members were coded as waiters (which included waitresses and bus persons). Of these 8,000 names, 5,343 (66%) were race coded. Blacks totaled 4.5%. The union did not encourage membership by those who did not hold jobs, generally urging a person to find a job before applying.
Based on the available records, plaintiffs computed the rate at which black waiters were referred to jobs by the hiring hall as follows:


          UNION REFERRALS TO ST.
              FRANCIS HOTEL    
                1970 - 1977
                Black      Total     % Blacks
By Request       10         187        5.3
Others            9         106        8.5
All Referrals    19         293        6.5
          UNION REFERRALS TO ALL
                EMPLOYERS      
                1970 - 1977
                Black      Total     % Blacks
By Request       85         3020       2.8
Others          555         7177       7.7
All Referrals   640       10,197       6.3
    UNION REFERRALS TO HILTON HOTEL
               1974 - 1977
               Black      Total     % Blacks
By Request       4        112         3.6
Others           5         53         9.4
All Referrals    9        165         5.4
          UNION REFERRALS TO ALL
                EMPLOYERS      
                1974 - 1977
               Black      Total     % Blacks
By Request       47       1396        3.4
Others          453       5418        8.4
All Referrals   500       6814        7.3

The union's Equal Employment Opportunity (EEO 3) reports show referrals of black males for all jobs in proportion to total referrals for the respective periods of August and September as follows:


August/September     1970      1971    1972
Total referrals      2551      2467    3550
Black males           263       252     320
                    10.3%     10.2%      9%


Findings of Fact Respecting the Individual Claimants

Leonard Whitman
Whitman was an experienced a la carte waiter when he came to San Francisco in 1961. The union issued him an a la carte card and dispatched him to banquets at various hotels including the St. Francis. He held a variety of jobs, in and out of the food business, and in and out of San Francisco, until 1973. From time to time he worked as a banquet and part-time a la carte waiter at hotels and restaurants.
During 1973, while working as an extra banquet waiter at the St. Francis, he asked the banquet manager for a permanent job on several occasions. He also claims to have filed a written application at the time but was never interviewed.
In 1975, he again asked about a permanent position at the St. Francis. He was told that he would have to get clearance from the union first, but the union's business agent told him that the hotel would have to call to request the clearance. The banquet manager, however, declined to call until he had obtained a work or referral slip from the union.
During 1975, he also made oral job requests to the Hilton's banquet manager but received no offer.

Gary Dennis
Dennis first became a waiter about 1975 when he began to be referred to extra banquet and club jobs by the union. Among other places, he worked banquets at the St. Francis and the Hilton. He made several attempts to file an application at the St. Francis in 1975 but was told there *291 were no openings and was not given an application. He also made oral inquiries.
In 1976 or 1977, he was referred by the union and was hired as an extra room service waiter by the St. Francis. In 1977, he filed a written application for a permanent waiter position with the St. Francis but was not interviewed. In 1978, he saw a position posted and inquired about it but received no response.
Beginning in October 1975, Dennis repeatedly inquired at the Hilton about a permanent position but was never able to file an application. The union referred him to the Hilton as an extra banquet waiter between 1975 and 1978, but for a time the Hilton did not accept him because of a dispute between him and a captain.

James Gay
Gay is presently employed as the restaurant manager at the Double Tree Inn in Pacific Grove. He began to work as an a la carte waiter in 1961 and came to San Francisco in 1968. He worked as a banquet, extra and club a la carte waiter on referral by the union. He was unable to obtain union referrals to permanent jobs. Whenever he was referred to the St. Francis he asked about a permanent job. He may have filed a written application about 1969 or 1970 and possibly in 1973, but received no response.

Frederick D. McDowell
McDowell has been a waiter for nearly forty years. He came to San Francisco in 1964 and began to work as an extra banquet waiter out of the union hall in 1972. While working at the Hilton, he repeatedly inquired about a permanent job but received no interview. He did not file an application.
It is not disputed that all four men were experienced waiters qualified for employment at either the St. Francis or the Hilton.

Findings of Fact Respecting Class Members

Thomas Wainwright
Wainwright has been employed as a permanent banquet waiter by the Hilton since 1978. He has been a waiter for 23 years, in San Francisco since 1976.
In 1976, he tried to apply at the St. Francis but was at first told by the guard that applications were not being accepted. After a number of attempts, he was able to file several applications but was never interviewed. He also inquired about a position while working as an extra banquet waiter at the St. Francis.
He obtained his job at the Hilton in May, 1978, while working as an extra banquet waiter, when the banquet captain asked him if he would like a permanent job.

Levoi St. Louis
St. Louis has been employed as a room service waiter at the Fairmont Hotel. He has worked as a waiter since 1962 and moved to San Francisco in 1977.
He filed an application with the St. Francis and was asked to come for an interview. When he arrived, his application was lost and he was told to come back next week. When he returned, he was told there were no openings. He never heard again from the St. Francis.
He also filed an application with the Hilton and was interviewed by a maitre d'. He was told to come back and when he returned was told that his hiring had been approved. He was later told that, although the manager wanted to, he could not give him the job.

Richard L. Mason
Mason was employed as a permanent banquet waiter by the St. Francis in October, 1979. He had some experience as a food server before he came to San Francisco in 1975. He then became a banquet waiter at the Fairmont.
He first applied at the St. Francis early in 1979. He was given a referral slip by the union and went to the personnel office where he was told he was too late and given an appointment for the next day. He returned the next day, was given an application after some difficulty over whether he had an appointment, and was interviewed by the personnel manager. When he called the next day, he was told the job was filled. *292 In October, he called the personnel office again. He was interviewed by the banquet manager and, when he called the next day, was offered the job.

Stephen Outlaw
Outlaw has been a waiter in San Francisco since 1973. In 1972, he went to work as a bus person at Victor's in the St. Francis. He was promoted to waiter in 1973, without previous waiter experience. While he was at Victor's, French service was performed by the captain with the waiter serving the finished plates. He left Victor's in 1977. When he returned and reapplied, there were no openings, but he was given a position as temporary room service waiter.
In July, 1976, he filed an application with the Hilton but was not called.

Aubrey Blackburn
Blackburn worked as a waiter for nine years in Jamaica before coming to San Francisco in 1976. He applied three times to the Hilton during 1977. The first time, in response to an advertisement, he filed an application and was interviewed but heard nothing further. Twice thereafter he was referred by the union, filed applications, was interviewed but did not hear. While working as an extra waiter at the Hilton, he also asked about a permanent job but was told there were no openings.
During 1977 and 1978, he also filled out applications at the St. Francis on three occasions, once as a walk-in, once on referral from the union, and once at the banquet manager's instance. He was once interviewed by the personnel office but did not hear again.

IV. Discussion


A. Statute of Limitations

The St. Francis contends that the claims against it should be limited to a period of three years preceding the filing of the first amended and supplemental complaint on May 31, 1977. Its argument rests on a reading of the original 1973 complaint. Insofar as that complaint alleged a claim against the St. Francis, it contends, that claim arose solely out of the alleged wrongful discharge of McDowell. The claim of hiring discrimination, according to the St. Francis, was first raised in the 1978 second amended complaint, or, at the earliest, in the 1977 amended complaint.
Examination of the fourth claim of the original 1973 complaint discloses that it was brought against the St. Francis by McDowell on behalf of a class of black persons qualified to be waiters who have been or are now employed by the St. Francis, have sought or are seeking such employment or have been or are discouraged from seeking such employment by discriminatory practices. The claim alleges that in addition to race-based harassment and intimidation leading to McDowell's involuntary termination, the St. Francis "regularly engages in other similar acts, practices and policies denying equal employment opportunity to Plaintiffs and their class . . ." Those acts are further described in the complaint's preliminary statement, charging that "a system of racially discriminatory employment practices [is] maintained" by the union, the employer associations which bargain for the hotels and most of the hotels. It further charges each defendant with being a major participant in the system and liable for all of the transactions complained of. Discovery of the St. Francis's employment practices, including hiring, commenced with the filing of the complaint.
Accordingly, the addition in 1978 of specific hiring discrimination claims by plaintiffs Gay and Whitman, who were parties to the original complaint, did not expand the substantive scope of plaintiffs' claims against the St. Francis. The recent claims are merely specifications of the general employment discrimination claim asserted against it in 1973.
Inasmuch as the claims asserted in 1973 must be construed as including hiring discrimination claims of a class, the statute of limitations on them was tolled until the denial of the class action motion as to the St. Francis in August 1977. Those claims were reasserted by the filing of the second amended complaint in 1978. The statute has therefore not run on them. See American Pipe and Construction Co. v. Utah, 414 *293 U.S. 538, 554, 94 S.Ct. 756, 766, 38 L.Ed.2d 713 (1974); see also United Air Lines v. McDonald, 432 U.S. 385, 97 S.Ct. 2464, 53 L.Ed.2d 423 (1977).
In any event, the 1978 claims against the St. Francis are sufficiently closely related to the 1973 claims to come within the relation back doctrine under Rule 15(c), Fed.R. Civ.P. The St. Francis had adequate notice from the original pleading to avoid any prejudice by the later amendment. 6 Wright & Miller, Federal Practice and Procedure, § 1501, at 523-24, 526-27 (1971).
The Hilton was first named as a defendant in the second amended complaint filed on February 8, 1978. By order of August 8, 1978, the Court held all claims against it arising more than three years prior to the filing of that complaint to be time barred. Cal.Civ.Proc.Code § 338, subd. 1; Smith v. Cremins, 308 F.2d 187 (9th Cir. 1962).[5]
Accordingly, the claims are limited as to the St. Francis to those arising after March 28, 1970; as to the Hilton, to those arising after February 8, 1975.

B. Liability of Defendant Hotels For Discriminatory Acts of the Union


1. Vicarious Liability

Plaintiffs contend that even though they have settled with the union, they may still hold the hotels liable "for relying on the unions as a recruitment and hiring agent for their waiter employees." Reliance is placed on the decision in Commonwealth of Pennsylvania v. Local 542, International Union of Operating Engineers, 469 F.Supp. 329 (E.D.Pa.1978), in which Judge Higginbotham reviewed and analyzed at length the law bearing on vicarious liability of employers for a union's discriminatory operation of a hiring hall. The court concluded that, although the issue is not free from doubt in the light of other decisions, the employer may be held liable where it has in effect delegated to the union the hiring of its employees.
That decision does not sustain plaintiffs' argument here. In the first place, the record does not present a prima facie case of discriminatory treatment of blacks by the union. Overall union referrals of blacks ranged from about 6 to 10 percent during the period. But these numbers must be evaluated in light of black membership which in the early 1970's was insignificant in numbers and, even after it grew, appears not to have exceeded 4.5 percent. Even taking into account the union's use of subjective criteria in making referrals to permanent jobs, one cannot draw an inference of discriminatory treatment from the referral rates.[6]
*294 Whether black membership in the union may, however, be accepted as a neutrally composed availability pool for comparison purposes depends on whether there is evidence supporting an inference of race-based exclusionary membership practices by the unions. There is evidence indicating that blacks experienced difficulties in securing food server positions in San Francisco in the early 1970's. To the extent that was true, blacks would have been deterred from joining the union, and, being without jobs, would have been unwelcome. Whether the union's past practice of discouraging membership by unemployed waiters had a sufficiently disparate impact to warrant a finding of discrimination, however, cannot be determined on this record, especially without the union as a party.
Moreover, it cannot be found here that the hotels delegated to the union the selection of persons to be hired for permanent positions. While the collective bargaining agreement obligated the hotels to request and the union to make referrals for all vacancies, it specifically reserved the determination of suitability and competence to the employer.[7] In practice, moreover, the union made few referrals and the hotels hired few permanent employees from among referrals. With the union unable to supply the needs of the hotels for experienced waiters, the hotels obtained applicants through their own efforts. By tacit consent the hiring hall provisions of the collective bargaining agreement largely fell into disuse with respect to permanent employees until the fall of 1977.[8]

2. Conspiracy in Violation of 42 U.S.C. § 1985(3)

Plaintiffs also contend that defendants violated 42 U.S.C. § 1985(3) by conspiring with the union to evade the hiring hall provisions of the agreement, thus permitting the hotels to engage in racially discriminatory hiring practices. The elements of a violation in the context of an employment discrimination case are stated in Bethel v. Jendoco Construction Co., 570 F.2d 1168, 1172-73 (3rd Cir. 1978), as follows:
(1) a conspiracy;
(2) for the purposes of depriving another . . . of equal protection or equal privileges and immunities;
(3) any act in furtherance of the conspiracy committed or caused to be committed by a conspirator;
(4) whereby another . . . was injured in his or her person or property or deprived of a right or privilege as a United States citizen.

See Griffin v. Breckenridge, 403 U.S. 88, 102-103, 91 S.Ct. 1790, 1798-99, 29 L.Ed.2d 338 (1971).
Inasmuch as the record here, as discussed in the preceding section, does not warrant a finding of discrimination by the union, there is no basis for imposing conspirator liability on the hotels even if there were evidence of an unlawful agreement, which there is not. See Commonwealth of Pennsylvania v. Local 542, I.U.O.E., supra, 469 F.Supp. at 413-14; Croker v. Boeing Co., 437 F.Supp. 1138, 1178 (E.D.Pa.1977).

3. Violation of the Collective Bargaining Agreement

Plaintiffs further contend that defendants are liable under 29 U.S.C. § 185 for violating the terms of the collective bargaining agreement. They argue first that by engaging in discriminatory hiring practices defendants violated Section 8 of the collective bargaining agreement which states:

*295 There shall be no discrimination against any employee on account of membership in, or activity on behalf of the Union or because of race, color, creed, sex, age, religion or national origin as defined by law.
This provision, on its face, applies only to employees. Plaintiffs, however, are asserting hiring claims. They have offered no evidence that the parties to the collective bargaining agreement intended by this provision to confer rights and benefits on job applicants and, in the absence of such evidence, the Court will not make that assumption.
Plaintiffs also contend that defendants' failure to adhere to the exclusive hiring hall provisions of the contract is a violation. Section 3(b) provides, however, that "[i]n the event that the Union . . . is not able to provide competent help suitable for the position [the employer] shall be at liberty to hire persons not referred by the Union." There is no evidence that the union ever grieved the hotels' use of the by request system. Indeed, there was undisputed testimony by union representatives of a shortage of qualified a la carte waiters and of the union's inability to meet the hotels' needs for permanent employees. It must be concluded that the union considered the by request system to be authorized under the contract. This interpretation was implicitly approved by the membership's ratification of renewal agreements, with Section 3(b) unchanged in 1971 and 1975.

C. Liability of Defendant Hotels on Individual Claims


1. Individual Claims Against the St. Francis

Both Whitman and Gay claimed to have submitted written applications to the St. Francis in or before 1973; if they did, neither the applications nor evidence of the dates on which they were submitted is before the Court. Nor is there evidence permitting a finding as to the date of any oral application or request for employment by either of them or Dennis. It is therefore not possible for the Court to determine whether openings existed at the time when any of them applied.
The hiring of waiters, both white and black, during each year of the period beginning 1971 and continuing to the present, establishes that openings did exist. But plaintiffs' Exhibit 28, based on those applications which could be found during trial preparation, shows that no black applied at or about the time a non-black was hired. In one case, a black applicant other than a named plaintiff submitted an application about a week before a non-black was hired, in three cases, the time lapse was two to three weeks. In all other cases, it was one or more months.
The elements of a prima facie case of race-based disparate treatment are the same, whether the action is maintained under 42 U.S.C. § 1981 or Title VII, 42 U.S.C. § 2000e et seq.:
The complainant in a Title VII trial must carry the initial burden under the statute of establishing a prima facie case of racial discrimination. This may be done by showing (i) that he belongs to a racial minority; (ii) that he applied and was qualified for a job for which the employer was seeking applicants; (iii) that, despite his qualifications, he was rejected; and (iv) that, after his rejection, the position remained open and the employer continued to seek applicants from persons of complainant's qualifications.
McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973) (footnote omitted). If a prima facie case is proved, "[t]he burden then must shift to the employer to articulate some legitimate, nondiscriminatory reason for the employee's rejection." Id. The evidence is insufficient to establish that at the time the individual plaintiffs may have applied, the *296 St. Francis was seeking applicants for the positions they sought.[9]
There is evidence that applications were retained for a time and sporadically referred to when openings occurred soon after their submission. However, such reference was rare because it was considered time consuming and inefficient; not only were large numbers of applications received, but applicants frequently moved, were difficult to locate or had taken other jobs. Proof that a person's application may have been on file when a later opening occurred, therefore, does not satisfy, as a practical matter, the requirements of a prima facie case of disparate treatment. Even if it did, it would be sufficiently rebutted by defendants' legitimate and nondiscriminatory business reasons for not regularly considering retained applications. Cf. Furnco Construction Corp. v. Waters, 438 U.S. 567, 576-78, 98 S.Ct. 2943, 2949-50, 57 L.Ed.2d 957 (1978). Inasmuch as these plaintiffs have failed to prove a prima facie case, their individual claims must be denied.

2. Individual Claims Against the Hilton

There is no record that Whitman, McDowell or Dennis ever filed written applications with the Hilton. Nor does the evidence permit a determination of the date on which any of them may have made an oral application or request. Hence, the requisite finding cannot be made that at the specific time when they sought employment as waiters at the Hilton an opening existed and their claims must be rejected for the reasons discussed above.
It is true, of course, that in the general period when the individual claimants were interested in employment at the Hilton, waiters were being hired. But plaintiffs' own evidence shows that, with only a few exceptions, waiters were hired within a few days of the date of their application.[10] No explanation was given why that should have been the practice; presumably, the need to fill a waiter vacancy promptly played a part. Whatever the reason, there is no evidence that any of the individual plaintiffs sought employment at any time when a position was open for which another person was hired.
Moreover, plaintiffs' Exhibit 30, based on applications still available, shows that other rejected black applicants had not applied at the same time as the successful non-black applicants. With only two exceptions, their applications had been submitted over a month before the successful application. There is no record of a black applicant submitting an application between the submission of the successful applicant's applications and the date of his hiring, except in two cases of internal promotions.

D. Liability of Defendant Hotels on the Class Claim


1. The Standard of Proof Under Section 1981

At the threshold lies the question of the quantum of proof required of plaintiffs. *297 This case is brought under Section 1981, not Title VII of the Civil Rights Act of 1964 (42 U.S.C. § 2000e et seq.). Plaintiffs chose to present it as a case of intentional racial discrimination, contending that their proof of disparate impact on blacks is sufficient to support an inference of purposeful disparate treatment. If this were so, this Court would not reach the question whether Section 1981 requires that the defendants' intent to discriminate be proved. However, because plaintiffs' proof may not support such an inference, the Court must address this issue.[11]
Until the decision in Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), it was generally assumed that the same standard of proof applied under Section 1981 and Title VII. Employment practices having a disparate racial impact were held unlawful, regardless of intent, unless justified as a business necessity. See Boston Chapter, NAACP Inc. v. Beecher, 504 F.2d 1017, 1021 (1st Cir. 1974), cert. denied, 421 U.S. 910, 95 S.Ct. 1561, 43 L.Ed.2d 775 (1975); Carter v. Gallagher, 452 F.2d 315, 323 (8th Cir. 1971), cert. denied, 406 U.S. 950, 92 S.Ct. 2045, 32 L.Ed.2d 338 (1972).
In Washington v. Davis, plaintiffs alleged, among others, a claim under Section 1981 that the District of Columbia's examination for police applicants violated the Fifth Amendment. The examination was alleged to have resulted in the exclusion of disproportionately high numbers of black applicants. There was no allegation of intentional discrimination. The District Court granted summary judgment for defendants on this claim; the Court of Appeals reversed; and the Supreme Court, in turn, reversed the judgment of the Court of Appeals. The Court held, in part, that, in the absence of a racially discriminatory purpose, official action does not violate the equal protection guarantees of the Fifth and Fourteenth Amendments simply because it has a racially disproportionate impact.
Washington v. Davis did not decide whether in actions under Section 1981 plaintiffs must prove discriminatory purpose. The Court's discussion focused on proof requirements under the Fifth and Fourteenth Amendments; Section 1981 was not mentioned in this context. The Court's order that summary judgment be granted for defendants has nevertheless been taken to imply that Section 1981 requires proof of intent to discriminate. See, e. g., Arnold v. Ballard, 448 F.Supp. 1025, 1027-28 (N.D. Ohio 1978). However, such a reading of the opinion is not required; summary judgment on the Section 1981 claim is adequately supported by the Court's additional holding that the defendant had proved the examination to be job related.[12] Moreover, the focus on the constitutional flaw in the decision under review may have been dictated by the Court's action in raising the intent issue sua sponte.[13]
*298 The conclusion that Washington v. Davis left open the issue under Section 1981 was also reached by the entire panel in Davis v. County of Los Angeles, 566 F.2d 1334, 1340, 1350 n.10 (9th Cir. 1977), vacated as moot, 440 U.S. 625, 99 S.Ct. 1379, 59 L.Ed.2d 642 (1979). Indeed, Justice Powell observed, in dissenting from the holding that Davis v. County of Los Angeles had become moot, that the case presented "the important questionheretofore unresolved by this Courtwhether cases brought under 42 U.S.C. § 1981, like those brought directly under the Fourteenth Amendment, require proof of racially discriminatory intent or purpose." 440 U.S. at 637, 99 S.Ct. at 1386.
In Davis v. County of Los Angeles, supra, the majority of the Court of Appeals panel held that proof of liability under Section 1981 should track the requirements of Title VIIthat is, that no proof of intent is required. 566 F.2d at 1340. In vacating that case as moot, however, the Supreme Court expressly noted that its action deprived the opinion of the Court of Appeals of precedential effect. 440 U.S. at 634 n.6, 99 S.Ct. at 1384 n.6. Thus, the question must be considered as open in the Ninth Circuit. Its disposition turns on several factors discussed in the opinions in Davis v. County of Los Angeles and in other recent lower court decisions.
The legislative history of Section 1981 shows that although it rests in part upon the Thirteenth Amendment,[14] its origin was closely tied to the Fourteenth Amendment.[15] A number of courts have relied on this connection in finding the same intent requirement as under the Fourteenth Amendment.[16] The legislative history also shows that Congress in enacting the first precurser of Section 1981 meant it "to deal with the most egregious forms of reactionary white conduct; . . . not . . . to fashion an evidentiary presumption designed to root out more subtle forms of discrimination." Note, Racially Disproportionate Impact of Facially Neutral PracticesWhat Approach under 42 U.S.C. Section 1981 and 1982?, 1977 Duke L.J. 1267, 1279-80.[17]
Legislative history is not conclusive; the present day interpretation of Section 1981 is not rigidly bound by "the sentiments of the Reconstruction Congress." Runyon v. McCrary, 427 U.S. 160, 191, 96 S.Ct. 2586, *299 2604, 49 L.Ed.2d 415 (1976) (Stevens, J., concurring). However, the policy concerns which led the Supreme Court in Washington v. Davis to hold that the Fourteenth Amendment requires proof of intent support a similar interpretation of Section 1981. The Court there thought if appropriate to "await legislative prescription" before extending to new areas the rule that facially neutral action is illegal if in practice it benefits or burdens one race more than another. Washington v. Davis, 426 U.S. at 248, 96 S.Ct. at 2051.
Title VII of the Civil Rights Act of 1964 was such a legislative prescription in the field of employment. Title VII proscribes conduct based on proof of its racially discriminatory impact alone, Griggs v. Duke Power Co., 401 U.S. 424, 432, 91 S.Ct. 849, 854, 28 L.Ed.2d 158 (1971), but it does so in the context of a procedural scheme which subjects claims to a prior administrative screening investigation and a uniform short statute of limitations. Section 1981 cases may be filed without prior screening and within the varying time limits provided by state laws. The absence of mechanisms to control the filing of what may be baseless claims, or claims which have been rendered more difficult to defend by the passage of time warrants, as a matter of policy, judicial adherence to a higher standard of proof under Section 1981, at least until further legislative action.
Moreover, Section 1981 applies to a whole range of public and private contractual relationships other than employment. As discussed above, the legislative history of Section 1981 lacks any indication of intent to outlaw conduct on the basis of racially disparate impact alone. Section 1981 therefore does not supply the "legislative prescription" that the Supreme Court regarded as necessary before expanding the rule into new areas.
These considerations lead the Court to agree with the majority of courts that have decided the issue[18] that proof of discriminatory *300 intent is required in actions brought under Section 1981. This conclusion has important implications, discussed below, regarding the requisites of a prima facie case based, as in this action, primarily on statistics.

2. Elements of the Prima Facie Case

Plaintiffs contend that the defendant hotels engaged in a pattern or practice of purposeful discrimination against black male applicants for positions as waiters. The record is devoid of any direct evidence of intent to discriminate. It does, however, reflect a series of employment practices which may have tended to exclude blacks.
The record shows that both defendants preferred to promote or transfer from within rather than to hire from the outside. Both had experience requirements which, however, were vague, unwritten, and left entirely to the discretion of the various room or service managers to administer. Aside from experience, hiring criteria used were subjective, turning on such matters as appearance, demeanor and job stability. Until recently, the hotels hired permanent waiters largely without resort to the union hiring hall. Thus there was no established procedure for giving public notice of all job openings. The defendants also had in effect rules and practices which caused some prospective applicants to encounter difficulties in their attempts to make application; their employment offices were open to the public only for limited periods, applications were not always accepted, and there was no regular procedure for interviewing all applicants. Finally, some apparently qualified black applicants were rejected without explanation.
The aggregate impact of these practices might well have been felt more severely by blacks seeking waiter positions than by whites. Whether it is sufficient to constitute a prima facie case of purposeful discrimination turns on the analysis of defendants' hiring and work force statistics in the following sections.
Teamsters v. United States, 431 U.S. 324, 339, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396 (1977), established that purposeful employment discrimination may be proved by statistical evidence. The Court said:
Statistics showing racial or ethnic imbalance are probative in a case such as this one only because such imbalance is often a telltale sign of purposeful discrimination; absent explanation, it is ordinarily to be expected that nondiscriminatory hiring practices will in time result in a work force more or less representative of the racial and ethnic composition of the population in the community from which employees are hired. Evidence of longlasting and gross disparity between the composition of a work force and that of the general population thus may be significant . . .
431 U.S. at 340 n.20, 97 S.Ct. at 1857 n.20. The Court agreed that the government had made out a prima facie case under Title VII by proving, in addition to individual instances of discrimination, that in communities where 10 to 50 percent of the population was black, defendant employed not a single black line driver before the suit was commenced.[19] In Hazelwood School District *301 v. United States, 433 U.S. 299, 307, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977), also a Title VII case, the Court again stated:
Where gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination.
Statistical evidence of racial disparity may therefore be probative of purposeful discrimination. See Washington v. Davis, 426 U.S. at 242, 96 S.Ct. at 2048; Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 266, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977); Personnel Administrator of Massachusetts v. Feeney, 442 U.S. 256, 99 S.Ct. 2282, 2295 n.23, 60 L.Ed.2d 870 (1979). Justice Stevens, concurring in Washington v. Davis, explained the evidentiary connection as follows: "Frequently the most probative evidence of intent will be objective evidence of what actually happened rather than evidence describing the subjective state of mind of the actor. For normally the actor is presumed to have intended the natural consequences of his deeds." Id., 426 U.S. at 253, 96 S.Ct. at 2054. He added that "the line between discriminatory purpose and discriminatory impact is not nearly as bright, and perhaps not quite as critical, as the reader of the Court's opinion might assume." Id., 426 U.S. at 254, 96 S.Ct. at 2054.
While perhaps not bright, the line between impact and intent is critical in this case. If the intent requirement is to have meaning in a statistics-based case, the evidence must show more than that the defendant could or should have known that its actions had a disparate impact on blacks. As the Court said in Personnel Administrator of Massachusetts v. Feeney, supra, 99 S.Ct. at 2296 "`[d]iscriminatory purpose,' however, implies more than intent as volition or intent as awareness of consequences. [citation omitted] It implies that the decisionmaker . . . selected . . . a particular course of action at least in part `because of,' not merely `in spite of,' its adverse effects upon an identifiable group." (footnotes omitted). Feeney upheld a veterans' preference law against a claim of unconstitutional sex discrimination. The Court found that where adverse impact was an unavoidable consequence of a legitimate legislative policy untainted by evidence of a prohibited purpose, no inference of discriminatory intent arose. Id., 99 S.Ct. at 2296 n.25. Whether such an inference may be drawn from evidence of disparate impact turns on a sensitive and practical evaluation of the full factual context. Id., 99 S.Ct. at 2296 n.24. In cases of employment discrimination, where proof of intent rests on statistical evidence of impact, that impact must be "longlasting and gross" to sustain the inference that the defendant acted for the purpose of creating or maintaining it. Teamsters, supra, 431 U.S. at 340, n.20, 97 S.Ct. at 1856 n.20.
Another feature of statistical evidence that must be borne in mind is that, contrary to the illusion of certainty which it may create, it does not afford a mathematically precise basis for decision. Hazelwood recognizes this fact, directing the district court to evaluate not simply a single set of employment statistics but the entire range of available data, including work force, applicant flow and hiring rates. 433 U.S. at 308 n.13, 97 S.Ct. at 2742 n.13. Inferences drawn from the statistical proof must, moreover, be tempered by the other evidence which brings "the cold numbers convincingly to life." Teamsters, 431 U.S. at 339, 97 S.Ct. at 1856. As the Supreme Court noted in Hazelwood, quoting from Teamsters, "[S]tatistics . . . come in infinite variety . . . [T]heir usefulness depends on all of the surrounding facts and circumstances." 433 U.S. at 312, 97 S.Ct. at 2744.

a. The Relevant Labor Market

The statistical analysis must begin with a determination of the pool of individuals available and qualified to become waiters for the defendant hotels and the percentage *302 of black males in that pool. Whether or not an inference of discriminatory impact and purpose arises from the percentage of blacks hired or promoted by the defendants depends on the choice of the proper labor market for statistical comparison. See Hazelwood, supra, 433 U.S. at 311 n.17, 97 S.Ct. at 2743 n.17. The parties are in fundamental disagreement on this issue, and have presented largely contradictory expert opinions.
In the opinion of plaintiffs' expert, Dr. John H. Pencavel, the relative availability of black waiters should be measured by reference to the percentage of black males, 21 to 64 years of age, living in the San Francisco/Oakland Standard Metropolitan Statistical Area (SMSA), weighted in accordance with the frequency of applications from within and without San Francisco, and earning less than the 1975 median earnings of permanent banquet waiters at defendant hotels, adjusted to 1970 dollars. Applying these factors, Dr. Pencavel arrived at a black availability range of 15.1% to 17.9%, varying with the median earnings at the two hotels. Each of these factors will be discussed in the following sections.

i. The relevant geographic area

Because the percentage of black residents varies among the counties in the SMSA, the percentage of blacks in the relevant labor market will vary depending on the geographic definition of the market. Dr. Pencavel chose to use data from the San Francisco/Oakland SMSA, weighted in accordance with the ratio of applications for all waiter positions received from within and without San Francisco, respectively. Of all waiter applications which were retained by the St. Francis and the Hilton, approximately 85 percent came from residents of the City and County of San Francisco, 13% came from other counties in the SMSA, and 2% came from outside the SMSA. Thus, Dr. Pencavel weighted the San Francisco data by a factor of 85/98 and the data from other counties in the SMSA by 13/98.
Dr. Pencavel's approach is sound. It is reasonable to estimate the geographic composition of the available labor pool by reference to the distribution of residence of the actual applicants.[20] Plaintiffs concede that the applications Dr. Pencavel relied on do not document the residence of all actual applicants. Not all written applications were retained, nor were all applications in writing. However, there is no reason to suppose that the residential distribution of the group whose applications were retained does not approximate that of the actual applicant pool as a whole.[21]
Defendants contend that weighting results in double-counting. That would be true if San Francisco figures were averaged with SMSA figures. However, the procedure used by Dr. Pencavel was to back out the San Francisco figures from the SMSA aggregates before applying the weighting factors. This method avoids double counting.
Defendants' expert, Dr. Seymour L. Wolfbein, argued that the judgment of the Bureau of the Census to aggregate the counties of the SMSA as an economically integrated unit should be accepted without modification. This judgment, however, does not preclude an attempt to arrive at a more precise measure of the percentage of blacks in the work force available for the *303 particular jobs at issue here. Refinement of SMSA data by weighting is therefore not inconsistent with their design. Inasmuch as 85% of waiter applications submitted to defendants came from San Francisco residents, it is reasonable to conclude (in the absence of contrary evidence) that approximately the same proportion of all those available to become waiters for defendants resided in San Francisco. See United States v. Ironworkers Local 86, 443 F.2d 544, 551 n.19 (9th Cir.), cert. denied 404 U.S. 984, 92 S.Ct. 447, 30 L.Ed.2d 367 (1971); Smith v. Union Oil Co., 17 Fair Empl. Prac. Cas. 960, 968, 17 Empl.Prac.Dec. ¶ 8411 (N.D.Cal.1977); Markey v. Tenneco Oil Co., 439 F.Supp. 219, 234-235 (E.D.La.1977).

ii. The relevant age bracket

Waiters employed in establishments serving alcoholic beverages are required by state law to be 21 years of age. No waiter over 64 years old appears to have been hired by defendants. Accordingly, Dr. Pencavel used an age bracket of 21 to 64 years, inclusive. The choice is not seriously disputed by defendants and is reasonable.

iii. The relevant population segment

Dr. Pencavel favored the use of general population, rather than the more restricted civilian labor force data, although he acknowledged that both should be considered. Labor force data include all persons who, at the time of the census, are either employed or actively seeking employment.[22]
Census data have been criticized for tending to undercount certain segments of the population such as the poor or disadvantaged, and hence proportionately undercounting blacks more than whites. Dr. Pencavel argued that this phenomenon is aggravated in the labor force statistics by the phenomenon of discouraged workers, i. e., those who have given up seeking work actively. Pencavel's opinion was that discouraged workers are more prevalent among black males than white males. Dr. Wolfbein countered by citing findings that the rate of participation in the labor force is the same among black and white males.
The criticisms of the census data appear to the Court to be too speculative and imprecise to warrant rejection of the work force data for present purposes. That conclusion is supported by the arguments against the use of general population data in place of work force data. The former include children, students, inmates of institutions, military personnel, the disabled and those not actively seeking work. The percentage of blacks in each of these categories differs from the percentage of nonblacks.[23] The birthrate for blacks, for example, is higher than for whites and may therefore explain the higher percentage of blacks among students not in the labor force and among those under 65 years old. Illness and disability may have a higher incidence among blacks than others. Similarly, racial discrimination may have led to *304 a relatively higher percentage of black persons not actively seeking work. The exclusion of those population segments not likely to supply applicants for waiter positions makes the civilian work force data a more reliable indication of the available labor pool.

iv. The relevant time

The last available complete census data come from the 1970 Census. Plaintiffs contend that the percentage of blacks in the population has significantly increased since that time. Data from the 1975 Current Population Survey (CPS), offered by plaintiffs, tend to refute this assertion. Comparison of these data with the 1970 San Francisco SMSA Census shows that the percentage of blacks in the population, as well as their percentage in the civilian labor force, rose by only a fraction of one percent in the higher earnings bracket and declined in the lower earnings bracket.[24]
Plaintiffs claimed that projections prepared by the California Employment Development Department for current years for which no census data are available show an increase in the percentage of blacks in the population and work force in San Francisco. The projections appear to be prepared from various public health data and are conceded by plaintiffs to be considerably less reliable than census or CPS data; they certainly afford no basis for comparison with earlier census or CPS data and must therefore be rejected. The Court accepts the 1970 census and the 1975 CPS data as the most recent reliable data.[25]

v. The relevant earnings brackets

Dr. Pencavel contended that the availability of workers for particular jobs depends on the terms of employment offered, the most obvious aspect of which is pay. Normally persons will not be interested in a job paying less than they are currently earning. Dr. Pencavel therefore narrowed the available population further to that segment "whose earnings are less than those they can expect to earn if employed as waiters by the defendant hotels." Plaintiffs' Exhibit 66 at page 10. The black percentage of that segment is claimed to be the closest estimate of actual black availability for the jobs at issue.
Dr. Pencavel's analysis was based on what defendants' records showed to be the median earnings of permanent banquet waiters in 1975. There are obvious difficulties involved in reliance on those figures.
The premise for the use of earnings brackets is that prospective applicants make a choice based on information concerning *305 the earnings in the job. There is no evidence to show what prospective applicants knew, believed, or were told (by published notices, interviewers or other means) about the earnings of defendants' waiters. There is certainly no reason to believe that any applicants would be influenced by the figures computed by plaintiffs for purposes of the trial, i. e., the 1975 median earnings of permanent banquet waiters at the St. Francis and the Hilton, respectively. A median earnings figure is a construct that would not be known by anyone who did not know the whole range and distribution of waiters' actual incomes.[26] Banquet waiter earnings are used because other waiters probably under-report their tips; however, for this reason the Court can only speculate about the range of earnings of other waiters. In any event, there is no evidence to show what potential applicants expected banquet or other waiters at the hotels to earn, other than vague references to the St. Francis being the best paying hotel.[27]
Even if potential applicants had more complete information than is before the Court, their expectations about waiter earnings would inevitably be uncertain. Lack of predictability of the number of hours he will work and the amount of tips he will receive preclude an applicant from accurately forecasting his future earnings. Even among banquet waiters, who receive a fixed percentage in lieu of tips, the spread in earnings is wide. An expected earnings cutoff, although it may be useful in estimating the available labor pool for certain other occupations, is of doubtful validity for hotel waiters.
The record discloses other reasons militating against use of the earnings cutoff. The position of waiter has strong non-monetary incentives and disincentives. For example, the irregular working times may, regardless of the compensation, make the job attractive to certain persons but unattractive to those seeking normal hours. Personal service positions appeal to some but repel others. Whether the impact of considerations such as these is random without regard to race is not known. Dr. Wolfbein also questioned whether, in light of recent evidence concerning the aspirations of young blacks, it can be assumed that interest in becoming a waiter is equal among racial groups. Cf. United States v. Commonwealth of Virginia, 454 F.Supp. 1077, 1097 (E.D.Va.1978). These factors, although not subject to being quantified, inject further uncertainty into the use of an earnings cutoff; if nothing else, they illustrate the significant role of subjective elements in determining availability.
For these reasons, the Court rejects as too speculative the use of an earnings cutoff to define the availability of black males.[28]


*306 vi. The relevant employment qualifications

In Hazelwood, the Supreme Court stated that "a proper comparison [is] between the racial composition of Hazelwood's teaching staff and the racial composition of the qualified public school teacher population in the relevant labor market." 433 U.S. at 308, 97 S.Ct. at 2742.[29] In a footnote following this statement, the Court distinguished Teamsters, saying that "the comparison between the percentage of Negroes on the employer's work force and the percentage in the general areawide population was highly probative, because the job skill there involved the ability to drive a truckis one that many persons possess or can fairly readily acquire." 433 U.S. at 308 n.13, 97 S.Ct. at 2742 n.13.
Plaintiffs contend that the job skill involved in the position of waiter is readily attainable by members of the general population with normal intelligence and physical capabilities. That contention is amply supported by the evidence. Plaintiffs' witnesses as well as various employees of defendants


                   Percentage of Black Workers by Occupational Group
                              (In order of Median Earnings)
                                         Annual Median     Total
      Industry                           Earnings            # Workers     % Blacks
     Other Craftsmen and Kindred
       Workers                             $9697.00         23,098        11.5%
     Other Mechanics and Repairmen          9679.00         15,429         5.7%
     Transport Equipment Operatives         9482.00         43,579        12.5%
     Cabinet Makers                         9406.00          1,127         4.9%
     Bakers                                 8672.00          1,784         8.9%
     Operatives Except Transport            8644.00         72,492        13.1%
     Clerical and Kindred Workers           8629.00         77,933         9.7%
     SalesclerkRetail Trade                8096.00         14,400         5.0%
     Laborers Exc. Farm                     8073.00         49,991        21.3%
     Apparel Craftsmen and Upholsterers     7994.00          1,808         6.5%
     Service Workers
         Exc. Private Household             7657.00         80,540        14.5%
     Farmers and Farm Managers              7214.00          1,706         6.1%
     Religious Workers                      6845.00          2,447         8.7%
     Farm Laborers and Farm Foreman         5429.00          3,241        12.7%
     Private Household Workers              4409.00            978        24.4%
     Source: 1970 Census of Population, Vol. 1, General Social and Economic Characteristics,
             Part 6: California at 1823-26 (Table 175) (April 1973).

*307 testified that the necessary skills can be acquired on the job in a matter of days or weeks. The requisite skills vary, of course, between restaurants offering a complex menu with French service and those offering simple fare directly served out of the kitchen. Moreover a waiter's competence is undoubtedly enhanced by experience. Nevertheless, the skills required to work as a waiter in these hotels are those that many persons possess or can readily acquire. Accordingly, general population and civilian work force data are the proper frame of reference. Cf. EEOC v. Sheet Metal Workers Intern. Association, Local No. 122, 463 F.Supp. 388, 404-409 (D.Md. 1978).
Defendants respond that as a matter of policy they hire only experienced waiters in order to maintain the standards they have set for themselves as luxury hotels. This argument is properly considered as a part of their rebuttal case, discussed below. Prior work experience is not so manifestly a job-related qualification for waiters that plaintiffs should bear the burden of proving, as part of their prima facie case, the percentage of blacks among experienced waiters.[30]

vii. Finding and Conclusion Respecting Black Male Availability

As the Court observed in Hazelwood, "what the hiring figures prove obviously depends upon the figures to which they are compared." 433 U.S. at 310, 97 S.Ct. at 2743. The "determination of the appropriate comparative figures" was held by the Court to require evaluation and findings by the district court respecting the relevant factors and considerations.
Based on the record and the considerations discussed and evaluated in the foregoing paragraphs, the Court finds the appropriate comparison is with a labor market consisting of all males, aged 21 to 64, in the civilian labor force in the weighted San Francisco/Oakland SMSA as shown in the 1970 census.
The statistical data offered by plaintiffs produce a black availability figure of 11.1% in that market, or availability pool. Exhibit 66, Table 3. The choice of a particular figure should, however, not be permitted to create the illusion of certainty or precision. As Dr. Pencavel observed, no single figure provides a reliable estimate of availability. The entire process is perhaps more calculated to exclude gross error than to lead to precise answers. The Court concludes that the analysis producing an availability figure of 11.1% is the one which, in the circumstances of this case, appears to be the most rational and valid.[31]

b. Comparison of Defendants' Hiring Data


i. Hiring, transfer and promotion data

Inasmuch as the question to be decided is whether defendants engaged in purposeful discrimination during the years at issue, comparisons must be based on defendants' employment practiceshiring, transfer and promotion of black males into waiter positions during that period. Because of the nature of the statistical tests applied, the question arises whether to use aggregate *308 figures for the whole period or to divide it into parts. This choice necessarily has an effect on the outcome of the analysis. The same percentage of blacks actually hired could be statistically significant or not, depending on the number of hires; the more years grouped together, the larger the number, the more significant statistically is a given percentage variation from the number of black hires expected.
Use only of data for the entire period for either defendant, however, would be questionable. Statistical testing of the type used here assumes that the employment practices being evaluated remained the same over the whole period. Material differences in the way selection practices within a single period affected black applicants would lead to invalid or misleading test results for that period. Plaintiffs argued that the hotels changed their practices so as to increase their rate of hiring and promoting blacks during the course of this lawsuit. Plaintiffs did not attempt to support this argument with statistical tests comparing the rates before and after any alleged change in defendants' practices. The test statistics below suggest that the hiring practices of the St. Francis may have changed after 1975 and those of the Hilton after 1977. These years end the periods of the statistically most significant divergence between actual and expected hiring of blacks by the respective hotels. But in the absence of direct evidence of a change in hiring practices, the Court cannot rely on these periods to the exclusion of data for later years.[32]
Reliance on one test of a single time period would be especially inappropriate, moreover, where the issue is intent and the test is whether the disparities were so "longlasting and gross" that an inference of purposeful discrimination arises. A more satisfactory indication of intent is the pattern of cumulative results. The racial makeup of progressively increasing numbers of hires, year by year, is relevant to what the defendants might have known about the racial impact of their hiring practices over time. The tables below organize the annual data into consecutive periods, each starting with the earliest year for which figures are in evidence.
The data are as follows:


                                    St. Francis Hotel
                           Hire, Promotion and Transfer Data
                 Positions                %      Expected No. of      Z[33]
      Period     Filled       Blacks    Black    Blacks at 11.1%    Statistic
      1970           12          0      0%                1           -1.22
      1970-71        35          1      2.9%              4           -1.55
      1970-72       111          6      5.4%             12           -1.91
      1970-73       153          9      5.9%             17           -2.05
      1970-74       193         11      5.7%             21           -2.39
      1970-75       256         13      5.1%             28           -3.07
      1970-76       293         17      5.8%             33           -2.89
      1970-77       329         21      6.4%             37           -2.72
      1970-78       371         25      6.7%             41           -2.67
      1970-79       390         38      7.2%             43           -2.46



*309
                                    Hilton Hotel
                           Hire, Promotion and Transfer Data[34]
                   Positions                %     Expected No. of       Z
    Period         Filled       Blacks    Black   Blacks at 11.1%    Statistic
    1974[35]        42          3      7.1%            5           -0.82
    1974-75            59          3      5.1%            7           -1.47
    1974-76            77          3      3.9%            9           -2.01
    1974-77           125          6      4.8%           14           -2.24
    1974-78           179         11      6.1%           20           -2.11
    1974-79           206         17      8.3%           23           -1.30



*310 ii. Statistical AnalysisPrima Facie Case

Having determined the pool of available workers, the percentage of blacks in that pool, and the rate at which blacks were hired by defendants, it is possible to draw certain statistical conclusions. The statistical test employed estimates the likelihood that the variation between the observed data (i. e., the actual number of blacks hired) and the expected (based on the percentage of blacks in the availability pool) is consistent with random selection, given the total number hired.[36]
The Supreme Court first discussed this kind of statistical analysis in Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977), in the context of alleged discrimination in the selection of grand jurors. In that case it held proof that over an 11 year period only 39% of the persons summoned were Mexican-Americans where Mexican-Americans constituted 79.1% of the county's population to be sufficient to establish a prima facie case of purposeful discrimination. In a footnote, the Court explained the statistical analysis and concluded:
As a general rule for such large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that the jury drawing was random would be suspect to a social scientist. The 11-year data here reflect a difference between the expected and observed number of Mexican-Americans of approximately 29 standard deviations. A detailed calculation reveals that the likelihood that such a substantial departure from the expected value would occur by chance is less than 1 in 10140.
The data for the 2½-year period during which the State District Judge supervised the selection process similarly support the inference that the exclusion of Mexican-Americans did not occur by chance. Of 220 persons called to serve as grand jurors, only 100 were Mexican-Americans. The expected Mexican-American representation is approximately 174 and the standard deviation, as calculated from the binomial model, is approximately six. The discrepancy between the expected and observed values is more than 12 standard deviations. Again, a detailed calculation shows that the likelihood of drawing not more than 100 Mexican-Americans by chance is negligible, being less than 1 in 1025. 430 U.S. at 497 n.17, 97 S.Ct. at 1281 n.17.
The Court cited the foregoing statement in Hazelwood, where it found the observed and the expected values in two time periods to differ by more than five and six standard deviations, respectively. 433 U.S. 309 n.14, 97 S.Ct. at 2742 n.14. It went on to observe:
Because a fluctuation of more than two or three standard deviations would undercut the hypothesis that decisions were being made randomly with respect to race, 430 U.S. at 497 n.17, 97 S.Ct. at 1281 n.17, each of these statistical comparisons would reinforce rather than rebut the Government's other proof.
433 U.S. at 311 n.17, 97 S.Ct. at 2743 n.17.
Having previously concluded that plaintiffs are required to prove purposeful discrimination in this case, the Court must determine whether the statistical disparities here are sufficient to allow such an inference. Although, as the Supreme Court has observed, fluctuations of more than two or three standard deviations "would undercut the hypothesis that decisions were being made randomly", it does not follow that an inference of purposeful discrimination must arise. Where as here, the plaintiffs' proof rests essentially on comparisons with an availability percentage constructed for trial purposes, the disparity must be so gross as not to be dependent on defendants' contemporary knowledge of that rate. The weight to be given the Z statistic must, moreover, take into account the strength of the underlying data. In this case, the availability percentage, as previously discussed, is the product of numerous choices by the Court among alternatives and is at best a reasonable estimate, not a precise calculation derived from scientific observation.
*311 To evaluate the statistical evidence in an intent case, one must also, insofar as possible, consider the data in the light in which they appeared to the defendant at the time. In the case of the St. Francis, after hiring no blacks in 1970 and only one in 1971, the rate of hiring increased to over five percent on a cumulative basis. Only for the entire 1970-75 period does the disparity exceed three standard deviations. In the case of the Hilton, the cumulative rate of hiring ranged between 3.9% and 7.1% during the precomplaint period; the Z statistic did not exceed 2.24.
Thus, even though a Z statistic of three indicates a probability of random occurrence of only .22%,[37] viewing the data as a whole the Court cannot conclude that they raise an inference of purposeful discrimination. "The mathematical conclusion that the disparity between . . . two figures is `statistically significant' does not, however, require an a priori finding that these deviations are `legally significant.'" United States v. Test, 550 F.2d 577, 584 (10th Cir. 1976) (jury selection case). The Supreme Court, while noting that disparities "greater than two or three standard deviations" would be suspect to a social scientist, has never accepted that level as sufficient to raise an inference of intent.[38] In the cases in which it has applied this analysis to determine the presence of purposeful discrimination, it has relied on disparities ranging from five to 29 standard deviations. See Castaneda, supra, 430 U.S. at 497, 97 S.Ct. at 1281; Hazelwood, supra, 433 U.S. at 311, 97 S.Ct. at 2743.[39] Statistical disparities considerably more gross and long-lasting than those found here being required to support an inference of purposeful discrimination, the Court finds and concludes that plaintiffs have failed to establish a prima facie case as to their class claims under Section 1981.

3. Defendants' Rebuttal Evidence

Although the foregoing findings make it unnecessary to consider defendants' rebuttal evidence, the interest in a complete and final disposition of the case leads the Court nevertheless to deal with it.


*312 a. Applicant Flow Data

In rebuttal of plaintiffs' case, defendants offered a variety of applicant flow statistics. They purported to show that the percentage of successful black applicants was not significantly different from that of white applicants.
In cases where general population or labor force data may not accurately reflect the segment of the work force available for the job, applicant data may be a more accurate frame of reference. Hazelwood, 433 U.S. at 308 n.13, 313, 97 S.Ct. at 2742 n.13, 2744. Such data may itself be skewed, however, by discriminatory practices which discourage or deflect potential applicants. Dothard v. Rowlinson, 433 U.S. 321, 330, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977).
In this case, the record shows the applicant data of each defendant to be seriously flawed. In the case of the St. Francis, no record purporting to be an accurate and complete list of applicants and their race was maintained in the ordinary course of business. The St. Francis's data were derived from a walk-in log which contains only sporadic and fragmentary entries, from records kept only in recent years by interviewers and from an analysis of 600 applications by persons not on the walk-in logs or interviewer records.
The deficiencies of these records include the following:
(1) The race coding of the walk-in log is speculative and unreliable and may understate black applicants. Persons counted as black were only those whose names appeared on a list of black waiters prepared by plaintiffs for purposes of this lawsuit; black applicants not on plaintiffs' list were assumed to be non-black.
(2) The walk-in logs were kept only intermittently and the information on them was incomplete.
(3) The application procedures used may have discouraged black applicants at a stage prior to sign-in.
(4) The records did not include oral applications made to managers by temporary banquet waiters or employees seeking transfer or promotion.
(5) The impact of the internal promotion policy on the applicant data cannot be ascertained.
These deficiencies in the applicant flow data render any comparison between the rate at which black and non-black applicants were hired meaningless.
In the case of the Hilton, data were derived only from applications specifically for waiter positions during the period 1976-1978. The data were based not on records kept in the ordinary course of business but on a review of those applications for the period 1976-1978 which were retained. Their deficiencies include the following:
(1) The count of blacks was inaccurate and unreliable; persons were counted as blacks only if their names appeared on plaintiffs' list of black waiters. The Hilton itself noted two persons wrongly race coded by this method. Note to Hilton's Ex. A-1.
(2) Oral applications were not recorded.
(3) Application procedures may have deterred black applicants.
(4) Applications for internal promotions and transfers are not recorded.
(5) Only applications specifying waiter as the position sought and those not specifying a position but listing prior waiter experience were counted; applicants who specified captain or bus person but were qualified as waiters were not counted.
These data also are insufficient to permit one to make a meaningful comparison between the rates at which blacks and non-blacks were hired.

b. The Experience Requirement

Had the plaintiffs established a prima facie case, the issue would arise whether the inference of discriminatory intent could be rebutted by proof that defendants consistently imposed an experience requirement that accounted for the rate at which they hired and promoted blacks to be waiters. Both defendants contended and offered evidence to show that they did not hire as waiters persons without prior waiter *313 experience. Plaintiffs disputed the evidence that any waiter experience, much less any minimum length, was consistently required.[40] Because, as the following discussion shows, defendants failed to prove that the proportion of blacks among experienced waiters was smaller than among the labor force as a whole, the evidence that an experience requirement may have been imposed, consistently or not, is irrelevant. And because the low rate of hiring blacks cannot be attributed to the experience requirement, the Court need not reach the legal issue whether experience was a legitimate qualification.[41]
Defendants' contention was addressed to the plaintiffs' statistical case. Arguing that waiter experience is a requisite element of the appropriate labor pool definition, defendants attempted to show that there was no disparity between the percentage of blacks they hired and the percentage in the pool of experienced waiters. Dr. Wolfbein, defendants' labor economist, urged the use of census occupational data for the SMSA to establish this percentage. Those data report as waiters persons who were employed as waiters at the time of the taking of the census or, if then unemployed, whose last job had been as waiter.[42] The percentage of blacks among those shown as waiter in this census was 6.98% in the San Francisco/Oakland SMSA in 1970; the corresponding national figure was 15.7%.[43]
*314 The occupational census does not purport to reflect the total number of persons who are experienced or qualified in a particular occupation. Each person who has worked since 1960 is counted as experienced in only one job: his current job or, if unemployed at the time of the census, his immediately preceding job. The occupational census "presents a picture of occupational background rather than qualification." Smith v. Union Oil Co. of California, 17 Fair Empl. Prac.Cas. 960, 967-968, 17 Empl.Prac.Dec. ¶ 8411 (N.D.Cal.1977). Thus an experienced waiter who is working at another job or is unemployed after having had another job does not show up as a waiter. Conversely, an inexperienced waiter newly hired at the time of the census would be counted as a waiter.
The significance of the occupational data varies with the degree of mobility in and out of the particular occupation. Persons engaged in professional or other relatively highly skilled occupations, such as engineers or scientists, are less likely to be found in jobs outside their occupations than those who, like waiters, are engaged in lower paid and more easily learned occupations. The occupational census is therefore a more accurate index of availability of the former than the latter. For purposes of showing the percentage of black males in the pool of experienced waiters, it is of limited utility. The method used does not produce an accurate count of the number of experienced waiters in the population.
If these shortcomings were racially neutral if there were reason to believe that approximately the same percentage of whites as blacks were experienced waiters employed in another job at the time of the censusthe census occupational data would have some persuasive force. The evidence, however, is to the contrary. The evidence previously discussed suggests race-based barriers to entry into the occupation in the San Francisco SMSA. In 1970, black males represented only 6.98% of all male waiters in the San Francisco SMSA, while representing 15.7% nationally. The local waiters union which had 4100 members in 1970 had only 78 black members; as late as 1976, no more than 4.5% of its members were blacks. It may be inferred that an experienced black waiter trying to change jobs within this area, or having moved here from elsewhere,[44] had more difficulty obtaining a waiter job than a comparably experienced white. As a result it is likely that experienced black waiters had to take other jobs more often than did whites. Thus, blacks may well have comprised a disproportionately large fraction of the experienced waiters omitted by the method used in compiling occupational census figures. The possibility of such a racial bias is strong enough to warrant rejecting, as a measure of availability, the percentage of blacks among those counted in the occupational census as waiters.
The Court therefore finds the 1970 census occupational figure for experienced black waiters in this area too unreliable an indication of actual prior experience to define the available labor pool, even if experience were a valid qualification. That is not to say that census occupational data may not in the proper case serve as a useful guideline for availability. In this case, however, conditions prevailing in the labor market cause them, and the statistical calculations they underlie, to be entitled to little weight.
The nonstatistical evidence gives no more support to the contention that the experience requirement explains why fewer blacks were hired than otherwise. Defendants did not claim that any of the named plaintiffs or class members who testified were unqualified. There is no evidence *315 that any particular black was rejected by the defendants for lack of experience. Counsel for the St. Francis argued that experienced black waiters were scarce, citing union membership data for the early 1970's. However, union membership was a consequence of getting a waiter job, not of seeking one. The testimony of the individual and class plaintiffs shows, moreover, that many experienced black waiters sought work at the St. Francis and Hilton without success.
The Court finds that on this record, the experience requirement cannot be regarded as having placed a significant limitation on the number of blacks available for employment as waiters. Hence, it could not be accepted as an explanation for any disparity in the rate at which blacks were hired.

V. Conclusion

For the reasons stated, the complaint must be dismissed and judgment entered for defendants, the parties to bear their own costs.
IT IS SO ORDERED.
NOTES
[1]  Section 1981 provides:

All persons within the jurisdiction of the United States shall have the same right in every State and Territory to make and enforce contracts, to sue, be parties, give evidence, and to the full and equal benefit of all laws and proceedings for the security of persons and property as is enjoyed by white citizens, and shall be subject to like punishment, pains, penalties, taxes, licenses, and exactions of every kind, and to no other.
[2]  The findings of fact are based on exhibits and the Court's notes of testimony. The Court had the benefit of a reporter's transcript only of the testimony of Dr. John Pencavel, Dr. Shanna Swann, and Dr. Seymour Wolfbein.
[3]  The association is a party for purposes of relief only, pursuant to Rule 19(a), Fed.R.Civ.P.
[4]  Section 3. HIRING:

(a) In the hiring and discharging of employees, the Employer shall determine the suitability and competence of the employees within the provisions of this Section, and provided that such determination shall not be used for the purpose of discriminating against members of the Union, or to circumvent the spirit and intent of this Agreement.
(b) In filling all vacancies and hiring additional or new help, the individual hotels signatory hereto shall apply to the Union having jurisdiction over the particular classification involved and it shall have the right to choose from among all applicants for referral and, except as otherwise provided in this Section, to reject any job applicant referred by the Union. In the event that the Union claiming jurisdiction is not able to provide competent help suitable for the position shall be at liberty to hire persons not referred by the Union. [sic]
(c) Any person hired by a hotel who is not a member of the Union having jurisdiction of the classification in which such person is employed shall, within 30 days after such hiring, make application for membership in the Union.
* * * * * *
(g) Selection by the Union of applicants for referral to jobs shall be on a nondiscriminatory basis and shall not be based on, or in any way affected by Union membership, by-laws, rules, regulations, constitutional provisions or any other aspect or obligation of Union membership, policies, or requirements. In carrying out this provision, the Unions shall maintain lists of applicants for referral for the various classifications of jobs covered by this Agreement. Eligibility for registration on said lists shall be determined solely upon the basis of each applicant's experience and qualifications for the particular classification of work involved. When an employer applies to the Union as provided in Subsection (b) hereof, eligible applicants will be referred to the Employer in the order of their registration on said lists unless the Employer requests referral of a particular applicant or group of applicants for specified job openings. Said lists of eligible applicants shall be available to the Employer at the Union offices upon request.
[5]  The period of recovery is limited to three years prior to the filing of the second amended complaint on February 8, 1978, notwithstanding that the class definition encompasses persons who suffered discrimination by the Hilton after February 8, 1974.

This Court's order dated August 8, 1978, left open the possibility of injunctive relief under Title VII against a defendant class of hotels, including the Hilton and several hotels named in the original 1973 complaint, the St. Francis having been excluded by earlier stipulation. Inasmuch as the claims against other defendants have now been dismissed, the question arises whether a claim for injunctive relief under Title VII may be asserted against the Hilton alone. A suit under Title VII must be filed within 90 days of the issuance of a right to sue letter by the EEOC. Wong v. Bon Marche, 508 F.2d 1249 (9th Cir. 1975). The Title VII claim against the Hilton is predicated on an EEOC charge by James Gay against the Hotel Employers Association of San Francisco as to which the EEOC issued a right to sue letter on February 14, 1973. The original complaint in this action based on that charge was filed on March 28, 1973, but the Hilton was not named a defendant until the second amended complaint, filed on February 8, 1978. Almost five years passed between issuance of the right to sue letter and the filing of claims in this action against the Hilton; these claims are therefore barred by the statutory time limit. The doctrine of relation back does not apply to these claims. Fed.R.Civ.P. 15(c)(2). Nor did the 1973 complaint toll the running of the time for members of the class to bring suit against the Hilton. See Johnson v. Railway Express Agency, 421 U.S. 454, 467-68 n.14, 95 S.Ct. 1716, 1724 n.14, 44 L.Ed.2d 295 (1975).
[6]  The rate at which blacks were referred by request to the St. Francis and Hilton was some-what lower than the general referral rate of blacks. As discussed elsewhere, by request referrals were in response to employment action of the particular hotel (see Findings of Fact Respecting the Union, supra), and therefore cannot be attributed to the union.
[7]  See note 4, supra.
[8]  Plaintiffs' argument has changed substantially in the course of the litigation. At one time they claimed that the St. Francis was guilty of discrimination by relying on the union hiring hall rather than using the by request system which permits it to hire outside the hiring hall from non-discriminatory sources. See plaintiffs' July, 1977 memorandum re class action determination at 20-21. At the time of trial, they argued that the defendants and the union conspired to circumvent the hiring hall provisions of the contract in favor of the discriminatory by request system.
[9]  Statistical evidence, discussed below in the context of the class claims, may be probative of individual claims, see Senter v. General Motors Corp., 532 F.2d 511, 528 (6th Cir. 1976), cert. denied, 429 U.S. 870, 97 S.Ct. 182, 50 L.Ed.2d 150 (1977). Inasmuch as the statistical proof in this case fails to establish a prima facie case on behalf of the class, however, it is of no help to the individual claimants.
[10]   Name         Applied     Hired
  Shadden      5/14/76     5/17/76
  Pusawong     9/15/76     9/20/76
  Hartnett     10/2/76     10/2/76
  Roach        12/27/76    12/28/76
  Bowes        2/20/77     2/21/77
  Allen        3/14/77     3/15/77
  Dion         4/22/77     4/26/77
  Tuthill      4/4/77      5/6/77
  Algozino     6/6/77      6/8/77
  Rose         6/16/77     6/16/77
  Graver       9/14/77     9/17/77
  Coronella    11/22/77    11/23/77
  Coppini      2/27/78     2/28/78
  Rabb         3/3/78      3/13/78
  Muth         4/26/78     5/12/78
  Loi          6/6/78      6/8/78
  Moreno       7/7/78      7/7/78
  Fernandez    5/24/78     8/28/78 (Bus person
                                    promotion)
  Lemus        4/24/78    10/23/78 (Bus person
                                    promotion)
  Clelland     8/17/78     11/1/78 (Waiter
                                    promotion)
  Miller       11/15/78    11/28/78
  Capapas      8/17/78     11/1/78 (Bus person
                                    promotion)
Source: Plfs. Ex. 30.

[11]  This case is now seven years old. Should this decision be appealed, a decade may have passed since its filing before it is decided. The parties are entitled to a final resolution as soon as possible. Accordingly, to reduce the risk of a remand for a new trial, the Court has undertaken to make findings and conclusions on a number of issues which, though not essential to the present disposition, may be regarded as critical by the Court of Appeals.
[12]  Judge Tuttle has noted that:

The fact that the Court [in Washington v. Davis] found it necessary to decide the adequacy of the validation [of the employment test] in order to resolve the statutory claims demonstrates that the infirmity of the plaintiffs' constitutional ground did not control the outcome of their statutory claims.
Williams v. De Kalb County, 577 F.2d 248, 257 n.5, vacated on rehearing, 582 F.2d 2 (5th Cir. 1978).
[13]  The constitutional issue was raised by the Supreme Court sua sponte under its rule allowing notice of "a plain error not presented." 426 U.S. at 238, 96 S.Ct. at 2046. Such notice is reserved for errors "of a fundamental nature", Sibbach v. Wilson & Co., 312 U.S. 1, 16, 61 S.Ct. 422, 427, 85 L.Ed. 479 (1941), cited at 426 U.S. at 238 n.9, 96 S.Ct. at 2047 n.9. The Court regarded the constitutional requirement that intent to discriminate be proved as deserving of sua sponte notice; the statutory issue under Section 1981 may not have been mentioned because it was regarded as not sufficiently compelling to be considered "plain error." See Note, Racially Disproportionate Impact of Facially Neutral PracticesWhat Approach Under 42 U.S.C. Sections 1981 and 1982?, 1977 Duke L.J. 1267, 1283.
[14]  See Runyon v. McCrary, 427 U.S. 160, 168 n.8, 96 S.Ct. 2586, 2593 n.8, 49 L.Ed.2d 415 (1976). Indeed, the decision that Section 1981 applies in the absence of state action was grounded upon the statute's relation to the Thirteenth Amendment. Id.; Johnson v. Railway Express Agency, 421 U.S. 454, 459-460, 95 S.Ct. 1716, 1719-20, 44 L.Ed.2d 295 (1975); cf. Jones v. Alfred H. Mayer Co., 392 U.S. 409, 441-443 n.78, 88 S.Ct. 2186, 2204-05 n.78, 20 L.Ed.2d 1189 (1968). However, the Supreme Court's reasons for requiring proof of intent in cases under the Fourteenth Amendment may also be applicable to cases under the Thirteenth Amendment. As Judge Wallace has noted, uncertainty about whether the Thirteenth Amendment requires proof of discriminatory purpose underscore the arguments against removal of the requirement in Section 1981 cases by judicial interpretation. Davis v. County of Los Angeles, supra, 566 F.2d at 1349 n.8 (dissenting opinion).
[15]  See Judge Wallace's discussion of the links between the Fourteenth Amendment and the Civil Rights Acts of 1866 and 1870, Davis v. County of Los Angeles, supra, 566 F.2d at 1349. He finds the 1870 Act to have been a statute enacted to implement the Fourteenth Amendment, one purpose of which was to remove uncertainty concerning the constitutionality of the 1866 Act.
[16]  E. g., Mescall v. Burrus, 603 F.2d 1266, 1270 (7th Cir. 1979); Johnson v. Hoffman, 424 F.Supp. 490, 494 (E.D.Mo.1977), aff'd 572 F.2d 1219, 1223 (8th Cir.), cert. denied, 439 U.S. 986, 99 S.Ct. 579, 58 L.Ed.2d 658 (1978); Arnold v. Ballard, 448 F.Supp. 1025, 1028 (N.D.Ohio 1978); Lewis v. Bethlehem Steel Corp., 440 F.Supp. 949, 964 (D.Md.1977).
[17]  This interpretation is consistent with the Supreme Court's characterization of the precurser of Section 1982, from which Section 1981 was also derived, as "meant to prohibit all racially motivated deprivations of the rights enumerated in the statute," Jones v. Alfred H. Mayer Co., 392 U.S. 409, 426, 88 S.Ct. 2186, 2196, 20 L.Ed.2d 1189 (1968) (emphasis added to "racially motivated"). See Davis v. County of Los Angeles, supra, 566 F.2d at 1350 (Wallace, J., dissenting); Lewis v. Bethlehem Steel Corp., supra, 440 F.Supp. at 964-65.
[18]  Section 1981 was found to require proof of discriminatory purpose in Mescall v. Burrus, 603 F.2d 1266, 1269-1271 (7th Cir. 1979); Williams v. De Kalb County, 582 F.2d 2 (5th Cir. 1978); Grigsby v. North Mississippi Medical Center, Inc., 586 F.2d 457 (5th Cir. 1978); Johnson v. Hoffman, 424 F.Supp. 490, 494 (E.D.Mo. 1977), aff'd 572 F.2d 1219, 1223 (8th Cir.) cert. denied, 439 U.S. 986, 99 S.Ct. 579, 58 L.Ed.2d 658 (1978); Donnell v. General Motors Corp., 576 F.2d 1292, 1300 (8th Cir. 1978); Chicano Police Officer's Assn. v. Stover, 552 F.2d 918, 920 (10th Cir. 1977); City of Milwaukee v. Saxbe, 546 F.2d 693, 705 (7th Cir. 1976); Drayton v. City of St. Petersburg, 477 F.Supp. 846, 855 (M.D.Fla.1979); Stewart v. Hannon, 469 F.Supp. 1142 (N.D.Ill.1979); Rich v. Martin Marietta, 467 F.Supp. 587, 617 (D.Colo.1979); Walker v. Robbins Hose Co. No. 1, Inc., 465 F.Supp. 1023, 1044 (D.Del.1979) (dictum); Flora v. Moore, 461 F.Supp. 1104, 1116 (N.D.Miss. 1978); Stewart v. City of Pontotoc, Mississippi, 461 F.Supp. 767, 777 (N.D.Miss.1978); National Organization for Women v. Waterfront Commission of New York, 460 F.Supp. 84, 87 (S.D. N.Y.1978) (1981 and 1983); United States v. City of Buffalo, 457 F.Supp. 612, 618 (W.D.N.Y. 1978) (dictum); Queen v. Dresser Industries, Inc., 456 F.Supp. 257, 261 n.8 (D.Md.1978) (dictum); Arnold v. Ballard, 448 F.Supp. 1025, 1027-28 (N.D.Ohio 1978); Milburn v. Girard, 441 F.Supp. 184 (E.D.Pa.1977) (dictum); Lewis v. Bethlehem Steel Corp., 440 F.Supp. 949, 964-966 (D.Md.1977); Croker v. Boeing Co., 437 F.Supp. 1138, 1181-1182 (E.D.Pa.1977); Guardians Association of New York City v. Civil Service Commission, 431 F.Supp. 526, 534 (S.D.N.Y.) vacated without opinion 562 F.2d 38 (2d Cir.), reinstated, 466 F.Supp. 1273, 1275 (S.D.N.Y.1977); Ortiz v. Bach, 14 FEP 1019, 1020 (D.Colo.1977); Williams v. City and County of San Francisco, 483 F.Supp. 335 (N.D.Cal.1979).

Section 1981 was found not to require proof of discriminatory purpose in these cases since Washington v. Davis, supra; Williams v. De Kalb County, 577 F.2d 248 vacated on rehearing, 582 F.2d 2 (5th Cir. 1978); Davis v. County of Los Angeles, 566 F.2d 1334 (9th Cir. 1977), vacated as moot, 440 U.S. 625, 99 S.Ct. 1379, 59 L.Ed.2d 642 (1979); Kinsey v. First Regional Securities, Inc., 181 U.S.App.D.C. 207, 215 n.22, 557 F.2d 830, 838 n.22 (1977) (dictum noting that in a suit under Title VII and § 1981, intent need not be proven); Commonwealth of Pennsylvania v. Local 542, International Union of Operating Engineers, 469 F.Supp. 329, 398-400 (E.D.Pa.1978) follows the majority in Davis v. Los Angeles, after finding intent was proven by high statistical significance of results; Movement for Opportunity v. Detroit Diesel, 18 F.E.P. Cas. 557, 568-569 (S.D.Ind.1978); Dawson v. Pastrick, 441 F.Supp. 133, 140 (N.D.Ind. 1977) aff'd, 600 F.2d 70 (7th Cir. 1979) (the Court of Appeals noted that the finding of liability under § 1981 was not appealed); Winston v. Smithsonian Science Information Exchange, 437 F.Supp. 456, 473 (D.D.C.1977) (dictum, since the court found plaintiff failed to show even discriminatory impact; the court did not cite Washington v. Davis and relied only on earlier cases for the equivalence of 1981 proof burdens to Title VII) aff'd without opinion, 194 U.S.App.D.C. 81, 595 F.2d 888 (1979); Gutierrez v. Aero Mayflower Transit Co., No. C-78-1863-SC (N.D.Cal., April 27, 1979).
At least one Circuit has expressly reserved the question: United Black Firefighters of Norfolk v. Hirst, 604 F.2d 844, 848 (4th Cir. 1979); see also Richardson v. Pennsylvania Department of Health, 561 F.2d 489 (3d Cir. 1977); but see Resident Advisory Board v. Rizzo, 564 F.2d 126, 140-145 (3d Cir. 1977), aff'g 425 F.Supp. 987, 1024 (E.D.Pa.1976), cert. denied, 435 U.S. 908, 98 S.Ct. 1457, 55 L.Ed.2d 499 (1978).
[19]  It should be noted that Teamsters was presented as a disparate treatment case, in which intent to discriminate was proved by inference from a statistical showing of racially disparate effects buttressed, as in the present case, by individual accounts of the employees' treatment. Teamsters, 431 U.S. at 335, 339-40, 97 S.Ct. at 1856; cf. Hazelwood, 433 U.S. at 306-307 n.12, 97 S.Ct. at 2741 n.12; see also Arlington Heights v. Metropolitan Housing Development Corp., supra, 429 U.S. at 266, 97 S.Ct. at 563; Washington v. Davis, supra, 426 U.S. at 241-242, 96 S.Ct. at 2048.
[20]  It might be argued that blacks were under-represented among the applicants, having been discouraged from applying by the discriminatory practices complained of, and that actual applicant data are therefore unreliable. See Teamsters, supra, 431 U.S. at 365-67, 97 S.Ct. at 1869-70; Dothard v. Rawlinson, 433 U.S. 321, 330, 97 S.Ct. 2720, 2727, 53 L.Ed.2d 786 (1977). But this is no reason to reject weighting in favor of San Francisco since the data indicate that a higher percentage of blacks reside there than in the other counties in the SMSA.
[21]  Although the Court finds no reason to suspect a geographic bias as a result of omissions from the actual applicant data, the same omissions do suggest a possible racial bias in the data, as discussed in Section 3a infra. These conclusions are not inconsistent. There are imperfections in the applicant flow data, such as speculative race coding, which may have excluded black applicants or mischaracterized them as nonblack. But the imperfections do not suggest any similar persistent tendency to misstate the residence of applicants.
[22]  Labor force figures are determined by survey questioning. Those answering that they are currently employed or were either employed or actively seeking work within four weeks before the survey are treated as within the labor force. The civilian labor force equals the total labor force less those in the armed forces.
[23]  The differences are shown in the following table, computed from 1970 Census data for San Francisco/Oakland SMSA, weighted in the same manner as plaintiffs' data:



--------------------------------------------------------
                                        Weighted SMSA
-------------------------------------------------------
                             Nonblacks  Blacks
-------------------------------------------------------
Males, 16 years and over      100 %     100 %
Civilian labor force           70.0      71.0
Armed Forces                    3.9       2.6
Not in labor force             26.1      26.4
  Inmates of institutions       1.0       1.6
  Enrolled in school            6.2       6.7
  OtherUnder 65 years old      7.6      12.5
          65 years and over    11.3       5.5
-------------------------------------------------------
Source of data: 1970 Census of Population, Vol. 1
                Characteristics of the Population, Part
                6 California at 499 (Table 85), 611
                (Table 92) (April 1973).
-------------------------------------------------------

[24]  The figures presented by Dr. Pencavel reflect the percentage of black males, aged 21 to 65, in the San Francisco/Oakland SMSA within different earnings brackets. Using the 1975 median earnings of banquet waiters employed by the St. Francis ($16,267) and the Hilton ($11,970), respectively, and adjusting for inflation to compute the median earnings in 1970, the following comparison may reasonably be made, based on the earnings brackets available from census data:



          1970                         1975
 Earning $11,000 or less      Earning $17,000 or less
    Population       13.4%          13.5%
    Labor Force      12.4%          12.9%
 Earning $8,500 or less       Earning $12,000 or less
    Population       16.4%          15.8%
    Labor Force      15.7%          15.2%

Any comparison of black representation within particular earnings brackets over time must, however, be viewed with caution. It is likely to be affected by the relative rise in the income of black workers and the relative improvement in their status, as shown by the increase in the black percentage of white collar and craft workers and the decrease in the black percentage of laborers.
[25]  The absence of data reflecting black representation in the population which are more recent than the 1970 Census and are readily accessible and reliable has additional significance. No inference concerning defendants' state of mind respecting the ratio of black hires can be drawn on the basis of data which were not both readily accessible and considered reliable. Neither the CPS data about blacks in the SMSA, available only on computer tapes, nor the EDD data, which are not reliable for this purpose, satisfy these requirements. Thus, in determining whether the evidence supports an inference of intentional discrimination, reference must be limited to the 1970 Census data.
[26]  Plaintiffs also offered data on entry level and maximum earnings of banquet waiters. But the use of brackets based on these figures depends equally on the presence of evidence that they were known to potential applicants. Moreover, the subjective elements involved make them questionable criteria. A person may take a cut in starting pay in anticipation of future advantages. Or he may discredit the maximum earnings as a measure of his likely compensation.
[27]  The collective bargaining agreement does reflect shift and meal pay scales, as well as overtime and premium pay provisions, but would not enable a prospective applicant to compute his probable earnings in any particular job.

Information about earnings may have been available from the permanent banquet waiters themselves. They regularly worked with extra waiters, some of whom applied for permanent jobs. There is no evidence, however, that any prospective applicant received earnings information from another banquet waiter.
[28]  The Court has, in any event, considerable doubt concerning the validity of the earnings cutoff method. Census data show no correlation between median earnings and black participation in particular job categories, as shown by the following summary for the San Francisco SMSA:
[29]  The requirement under Hazelwood that the "qualified" labor pool be defined as an element of the prima facie case raises questions concerning the burden on plaintiff to produce evidence of the requisite job skills as well as evidence of the skills possessed by persons in the pool before the burden shifts to defendant to rebut the prima facie case. The issue arises in cases such as this where the parties are in disagreement over the requisite job qualifications and the court faces the question whether to treat the issue as a part of plaintiff's prima facie case or defendant's rebuttal. To the extent the court finds certain qualifications to be so manifestly job-related as to constitute a presumptively valid business necessity, plaintiff's proof of availability (whether individual or statistical) must be premised on the possession of the requisite qualifications. See, Smith v. Olin Chemical Corp., 555 F.2d 1283, 1286-88 (5th Cir. 1977) (en banc) (requirement that manual laborers have good back was so manifestly job related, notwithstanding disparate racial impact, that employer did not need to make evidentiary showing of business necessity). Any statistical definition of the available labor pool offered by plaintiff as part of the prima facie case must therefore take into account such manifestly job-related qualifications. The defendant may then, as a part of the rebuttal case, offer evidence to justify additional requirements. See note 41, infra.
[30]  See note 29, supra.
[31]  The Court notes that although at trial plaintiffs' expert advocated a market having a range of 15.1% to 17.9% black males, in his pretrial deposition, taken before he had refined his analysis for trial, he estimated the range of availability of black males to be between 11% and 20%.

Additional support is provided by occupational census data. Although the Court concludes below that the occupational census data reflecting the percentage of black waiters in the San Francisco SMSA are unacceptable as a measure of availability, the range between the San Francisco (6.98%) and the national figure (15.7%) nevertheless provides a useful reference. Exhibit 77. The national figure corresponds more closely to the overall percentage of blacks in the population, suggesting the absence of pervasive racial bars to access to waiter jobs. It is therefore reasonable to expect that the true San Francisco availability figure would fall somewhere above the actual San Francisco figure of 6.98% and below a maximum of 15.7%. For the reasons discussed above in connection with the definition of the relevant labor market, however, the 15.7% figure cannot simply be adopted as the measure of local availability. See also note 43, infra.
[32]  Plaintiffs point out that post-complaint evidence has little probative value on the issue whether defendants discriminated. See Teamsters v. United States, supra, 431 U.S. at 341-42, 97 S.Ct. at 1857-58; Rich v. Martin Marietta Corp., 522 F.2d 333, 346 (10th Cir. 1975). In this case, however, the bulk of the evidence presented by both sides related to events following the filing in 1973 of the original complaint naming the St. Francis. This was largely due to the amount of time that passed before trial and the fragmentary nature of available records. The Court must therefore base its findings on all available data, regardless of whether they predate the complaint.
[33]  The Z statistic is computed as a part of a statistical test, the so-called Z test. It is based on an assumed normal distribution of observed values around any expected value. The variation between observed values and the expected value (here the percentage of blacks in the availability pool) is measured in terms of standard deviation (or standard error). The Z statistic reflects the number of standard deviations by which the observed value differs from the expected value. By reference to tables based on the normal distribution curve, the Z statistic can be used to determine the probability that the observed value is the product of random selection or occurrence.

The formula for calculating the standard deviation is derived from an equation which mathematically describes the normal distribution. This formula was set out by the Supreme Court in Hazelwood, supra, 433 U.S. at 311 n.17, 97 S.Ct. at 2743 n.17 and in another context in Castaneda v. Partida, 430 U.S. 482, 496-97 n.17, 97 S.Ct. 1272, 1281, 51 L.Ed.2d 498 (1977); other courts have applied the formula in employment discrimination cases. See note 39 infra. The standard deviation is equal, in this case, to the square root of the product of the probability of drawing a nonblack (.889) and the probability of drawing a black (.111), multiplied by the square root of the sample size. Given a sample size of 100, for example, the formula in this case would be:
      .111 × 889      ×    100  =  3.14
The standard deviation (or standard error) for this sample would therefore be approximately 3. Statistical theory tells us that if 100 samples were drawn independently and at random from the same population group, in 95 of the draws the observed number of blacks would be within two standard deviations of the expected number of blacks, i. e., approximately between 17 and 5. To put it differently, if there were fewer than 5 or more than 17 blacks in a sample of 100, the probability of obtaining that number as a result of random selection is less than five percent.
The Z statistic is equal to the difference between the expected number (11.1% of the sample) and the actual number of blacks hired divided by the standard deviation:
             (Actual         (Expected
   Z   =      Number)  -      Number)
            __________________________
                    (Standard
                     Deviation)
The Z statistic thus reflects the number of standard deviations between expected and actual hires. Under the formulae stated above, the standard deviation tends to decrease as the sample size increases; as a necessary corollary, the Z statistic tends to increase as the standard deviation decreases.
The probability that a particular observed value would occur by chance can be estimated by consulting a table that shows the probability, in a normal distribution, of a random variation equal to the Z statistic. A Z statistic of 2.00, for example, indicates a less than 5% likelihood that the observed value would occur by chance. Such a result is described as being significant at the .05 level. See F. Mosteller, R. Rourke, & G. Thomas, Probability with Statistical Applications 130-46, 270-91, 292-98, 304-307 (2d ed. 1970).
Plaintiffs used the same statistical method to calculate Z statistics, based on an expected rate of black hires of 15.1%.
[34]  The parties disagree whether persons hired as captains in the Hilton's Henri's Room should be included among waiters. Until 1977, Henri's Room served buffet style and therefore employed no waiters. The captains seated patrons, served drinks, collected checks and occasionally helped patrons at the buffet. Thus their duties were somewhat different from those normally performed by waiters but no more demanding. Inasmuch as there is no reason to suppose that persons applying for waiter positions at the Hilton would not have been qualified to work as Henri's Room captains, the Court has included the latter in the statistical analysis.
[35]  The record includes data from 1974, which preceded the liability period for the Hilton. Data from that year are relevant, nonetheless, to show the effects of employment practices if there is proof that the same practices continued during the liability period. See Hazelwood School District v. United States, supra, 433 U.S. at 309-10 n.15, 97 S.Ct. at 2742-43 n.15.
[36]  See note 33, supra.
[37]  The probability that the other observed values were the result of random selection is approximately as follows:



              Period    Z       % Probability
                                of Chance
                                Occurrence
St. Francis:  1970      1.22      22.24%
              1970-71   1.55      12.12%
              1970-72   1.91       5.62%
              1970-73   2.05       4.04%
              1970-74   2.39       1.68%
              1970-75   3.07        .22%
              1970-76   2.89        .38%
              1970-77   2.72        .66%
              1970-78   2.67        .76%
              1970-79   2.46       1.38%
Hilton:       1974      0.82      41.22%
              1974-75   1.47      14.16%
              1974-76   2.01       4.44%
              1974-77   2.24       2.50%
              1974-78   2.11       3.48%
              1974-79   1.30      19.36%

Source of probabilities: P. Hoel, Introduction to Mathematical Statistics 391 (Table II) (4th ed. 1971). Probabilities given are for a two-sided test. Mosteller, supra, at 302-307.
[38]  It must be borne in mind that the probability of random occurrence of a value is not the obverse of the probability that it is the result of deliberate action. The mathematical theory underlying the Z test is that values of considerable disparity from the expected value will occur, although based on the normal bell-shaped distribution curve the chance of their occurrence lessens sharply the greater the disparity. But the fact that a particular value having a Z statistic of 2 will occur at random only once in twenty does not mean that there is a 95% chance that it was the product of deliberate action. See Mosteller, Rourke & Thomas, supra, at 308-11.
[39]  See, also, Younger v. Glamorgan Pipe & Foundry Co., 20 Fair Empl.Prac.Cas. 776, 782 n.8 (W.D.Va.1979) (differences of 2.3 and 1.47 standard deviations found not to provide basis for "inferring that such . . . decisions were made or influenced because of race"). Cf. Thomas v. Parker, 19 Fair Empl.Prac.Cas. 49, 51 (D.D.C.1979) (prima facie case of racially motivated adverse treatment of an individual was established by nonstatistical evidence plus statistics showing less than one chance in 10,000 that the observed value occurred by chance [a comparable Z statistic, in the terms discussed above, would be at least 3.90]).
[40]  The evidence bearing on the experience requirement was inconsistent and inconclusive, largely because the requirement was unwritten and imposed by the personnel offices and, in varying degrees, by the room and department managers who made final hiring decisions each in their individual fashion.

In the case of the St. Francis, all persons hired as waiters were required to have some food service experience. But the amount of experience required was nowhere specified and varied with the room or department for which the waiter was hired and the particular manager doing the hiring. In some instances, a year was required; in some less; and in others, attendance at a college hotel and restaurant management program was accepted. Similarly, the quality of the required experience varied, from French service to simple plate service or any kind of food serving. Where bus persons were promoted to waiter, their food service experience was frequently minimal.
In the case of the Hilton, a less stringent but equally subjective experience requirement was imposed. Generally, there was no particular minimum time and little regard for the quality of the experience.
[41]  The Court's conclusion, supra, that Section 1981 requires proof of discriminatory purpose, calls into question the legal standard for rebuttal proof. Although the precise question appears not to have been decided under Section 1981, a prima facie case of purposeful discriminatory treatment under Title VII may be rebutted by evidence that the challenged hiring procedures were "reasonably related to the achievement of some legitimate, non-discriminatory purpose", Furnco Construction Co. v. Waters, 438 U.S. 567, 576, 98 S.Ct. 2943, 2950, 57 L.Ed.2d 957 (1978); see Board of Trustees of Keene State College v. Sweeney, 439 U.S. 24, 99 S.Ct. 295, 58 L.Ed.2d 216 (1978); McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973). A prima facie case under Title VII based on disparate impact without proof of intent may be rebutted only by proof that business necessity justified the challenged practice. Griggs v. Duke Power Co., 401 U.S. 424, 431, 91 S.Ct. 849, 853, 28 L.Ed.2d 158 (1971); Dothard v. Rawlinson, 433 U.S. 321, 331-32, 97 S.Ct. 2720, 2727-28, 53 L.Ed.2d 786 (1977). The latter, more stringent standard was applied to invalidate experience requirements in cases decided under Section 1981 before Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976). See, e. g., Crockett v. Green, 388 F.Supp. 912 (E.D.Wis.1975), aff'd, 534 F.2d 715 (7th Cir. 1976).
[42]  The relevant portion of the 1970 Census questionnaire read:

33-35. Current or most recent job activity
Describe clearly this person's chief job activity or business last week, if any. If he had more than one job, describe the one at which he worked the most hours.
If this person had no job or business last week, give information for last job or business since 1960.
Source: 1970 United States Census of Population, Vol. 2, Subject Reports 7A: Occupational Characteristics at IX (June 1973).
[43]  It is perhaps noteworthy that in another case in which Dr. Wolfbein appeared as an expert witness to perform a similar analysis of 90% of the workforce of a helicopter manufacturing plant in Philadelphia, he utilized a different approach:

In terms of geographic areas Dr. Wolfbein used the Philadelphia SMSA or the entire United States, whichever had the highest percentage of blacks for the particular occupation. Croker v. Boeing Co., 437 F.Supp. 1138, 1156 (E.D.Pa.1977) (emphasis added). Dr. Wolfbein did not explain why this approach would not have been appropriate here, especially in light of the evidence showing that black males with prior waiter experience frequently moved to San Francisco from other areas. Had it been used by defendants, they presumably would not have urged adoption of the occupational census data.
[44]  Most of the plaintiffs' witnesses testified that they encountered difficulties finding work as waiters upon arriving in San Francisco, despite having previous waiter experience. Several testified that they accepted other kinds of work after failing to get a waiter job.
