This case presents several significant issues concerning the order and allocation of proof, the proper role of statistical evidence, and the appropriate standard of appellate review in employment discrimination actions brought pursuant to 42 U.S.C. § 1981. Plaintiff-appellant Gay, along with three other black male waiters (the waiters),1 filed the original complaint in this action on March 28, 1973, alleging discrimination on the basis of race in the hiring, promotion, and transfer of black male waiters and applicants by the Waiters’ & Dairy Lunchmen’s Union (the union) and several well-known San Francisco hotels and restaurants. The waiters sued individually and on behalf of a class of all similarly situated persons, seeking monetary and equitable relief under Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq. Over five years ago we addressed the question whether this case could be maintained as a class action under Fed.R.Civ.P. 23(b)(2), reversing the district court’s denial of the waiters’ motion for class certification.2 549 F.2d 1330 (9th Cir. 1977). Following our remand to the district court, the waiters filed an amended complaint adding the Hilton Hotels Corporation (the Hilton) as a defendant and alleging new claims under section 1981. Subsequently, all Title VII claims were dismissed by the district court and all defendants except the Hilton and the St. Francis Hotels Corporation (the St. Francis) settled. The remaining claims were tried before the district court in October of 1979. On February 6, 1980, the district court entered judgment for the hotels on the waiters’ individual and class claims, filing exhaustive findings of fact and conclusions of law in a thoughtful 30-page opinion. 489 F.Supp. 282 (N.D.Cal. 1980).3 The waiters appeal pursuant to 28 U.S.C. § 1291, and we affirm.

*535I

The facts are well-summarized in the district court’s opinion. We repeat only those which are relevant to the legal issues raised in this appeal.

The St. Francis and the Hilton are large, luxury hotels in downtown San Francisco. Each operates several restaurants, ranging in nature from simple coffee shops to elegant dinner restaurants, as well as banquet departments that provide food services for a variety of special functions and offer room service. The hiring practices of both hotels are similar. Preference is given to those currently employed as buspersons in filling waiter vacancies in any of the hotels’ restaurants. When a vacancy is not filled by promotion, the personnel department notifies the union of the vacancy and posts a notice of opening in the hotel. Only occasionally, if at all, has the general public been notified of the existence of open waiter positions, either through newspaper advertisements or solicitations to employment agencies.

Both hotels insist that a person seeking employment as a waiter first file a written application with the personnel department. The St. Francis, however, generally refuses to schedule appointments with the personnel office for persons seeking waiter positions when no opening then exists. The district court found that applicants appearing for appointments with the St. Francis’s personnel department were asked to complete written application forms, although written applications were accepted even when no waiter vacancies existed. 489 F.Supp. at 287. The Hilton ostensibly requires all applicants to file written applications with the personnel office prior to being considered for waiter positions. The record, however, clearly reveals that many applicants for waiter positions were hired by the Hilton’s restaurant managers before the personnel department was notified of the vacancy, and that several were hired without being required to file written applications.

The hotels each receive approximately 6,000 applications per year, an average of between 12 and 15 applications for every waiter position which becomes open. Both retain written applications in an active file for a period between six months and one year. These retained applications, however, are only sporadically referred to when vacancies occur, 489 F.Supp. at 296, because the hotels consider reference to previously filed applications time-consuming and inefficient, and typically fill open waiter positions very quickly. With few exceptions, applicants are hired only if a vacancy occurs within one to three days of their application. Id. n.10. All applicants are interviewed by the manager of the hotel restaurant seeking to fill a vacancy. The restaurant managers make the final hiring decisions based upon the interviews and their resulting impressions of such factors as pri- or job experience and job stability, appearance and demeanor. These criteria are not contained in any job description or other document, and their implementation is left entirely to the discretion of the individual restaurant managers. Id. at 300.

The waiters consist of four individual plaintiffs and four class plaintiffs. All the individual plaintiffs “were experienced waiters qualified for employment at either the St. Francis or the Hilton.” Id. at 291. Three of the four individual plaintiffs worked at various times as banquet or extra banquet waiters at the St. Francis, one worked in a similar position at the Hilton, and one of the four worked at both hotels. The district court found that only one of the individual plaintiffs ever filed a written application for a permanent waiter position with either hotel. All made periodic oral requests for permanent positions; the district court expressly found that in some of the years in question, two of the individual plaintiffs made such oral requests repeatedly. However, the district court determined that with respect to both hotels, the evidence was insufficient to permit a finding as to the date of any of these oral job *536requests; therefore, the district court found that it was not possible to determine from the record whether vacancies existed at the time that any of the individual plaintiffs orally requested permanent positions. Id. at 295-96. Accordingly, the district court held that the waiters had failed to establish a prima facie case of intentional discrimination on their individual claims. Id.

Concluding that proof of intentional discrimination is required for section 1981 claims, id. at 299-300, the district court held that the class had failed to prove a prima facie case of an alleged pattern or practice of purposeful discrimination against black male waiter applicants. The district judge concluded that the circumstantial evidence was wanting and that the statistical presentation was insufficient to raise a prima facie case, id. at 311, and entered judgment for the hotels on the class claims.

The waiters appeal the district court’s judgment only with respect to their claims arising under 42 U.S.C. § 1981. Although their attack on the district court’s judgment is limited to these claims, it is vigorous and extremely wide in scope. Among other things, the waiters contend that the district court erred in concluding that discrimination actions brought pursuant to section 1981 require proof of discriminatory intent. Assuming that proof of discriminatory intent is a requisite element in a prima facie section 1981 case, they then argue that their statistical evidence of racially-imbalanced hiring decisions, standing alone, was sufficient to establish a prima facie case of discriminatory intent. Alternatively, they argue that the district court erred by failing to consider, with respect to their individual claims, relevant testimonial and other circumstantial evidence of discrimination introduced during trial. Finally, the waiters insist that their statistical and circumstantial evidence of discrimination, viewed together, established a prima facie case of intentional discrimination as a matter of law on both the individual and class claims, and that this prima facie case was never rebutted by either of the hotels. They therefore ask us to reverse the district court’s judgment and direct entry of judgment in their favor.

The waiters’ first argument, that a prima facie case of discrimination under section 1981 should not require proof of a discriminatory purpose, can be disposed of summarily. We held nearly two years ago that section 1981 is limited to claims of intentional discrimination. Craig v. County of Los Angeles, 626 F.2d 659 (9th Cir. 1980), cert. denied, 450 U.S. 919,101 S.Ct. 1364, 67 L.Ed.2d 345 (1981) (Craig). We have since followed Craig repeatedly. See, e.g., Williams v. Owens-Illinois, Inc., 665 F.2d 918, 928 (9th Cir. 1982). The Second Circuit recently reached the same result, Guardians Ass’n v. Civil Service Comm’n, 633 F.2d 232, 268 (2d Cir. 1980), cert. granted, 454 U.S. 1140, 102 S.Ct. 997, 71 L.Ed.2d 291 (1982), as did the Third Circuit en banc, Croker v. Boeing Co., 662 F.2d 975, 989 (3d Cir. 1981). The Supreme Court has now taken this position. General Building Contractors Ass’n v. Pennsylvania, - U.S. -, 102 S.Ct. 3141, 73 L.Ed.2d 835 (1982).

II

In order to decide the remaining issues, we must first focus briefly on the relationship, and differences, between Title- VII and section 1981. Title VII prohibits employment discrimination on account of race, sex, religion, and national origin. 42 U.S.C. § 2000e-2(a). Section 1981, which provides that all persons “shall have the same right ... to make and enforce contracts ... as is enjoyed by white citizens,” is limited to a prohibition of racial discrimination. Runyon v. McCrary, 427 U.S. 160, 167-68, 96 S.Ct. 2586, 2592-2593, 49 L.Ed.2d 415 (1976). Title VII and section 1981 are thus overlapping, but independent remedies for racial discrimination in employment. Johnson v. Railway Express Agency, 421 U.S. 454, 461, 95 S.Ct. 1716, 1720, 44 L.Ed.2d 295 (1975). While some of the difficult issues the courts have faced recently could have been avoided had Congress repealed section 1981, at least as applied to employment, when it enacted Title VII in 1964, Congress chose not to do so. Id. at 459, 95 S.Ct. at 1719. It *537is therefore the duty of the federal courts to apply these statutes in light of their separate language and legislative histories, promoting consistency between the two only to the extent that doing so does not conflict with the language or purpose of either.

Our decision in Craig reflects the major differences between section 1981 and Title VII. The latter is an ambitious, prophylactic measure designed to outlaw artificial, unnecessary barriers to employment which act as “built-in head winds” against the progress of minority groups. Title VII was designed to bar not only overt employment discrimination, “but also practices that are fair in form, but discriminatory in operation.” Griggs v. Duke Power Co., 401 U.S. 424, 431, 91 S.Ct. 849, 853, 28 L.Ed.2d 158 (1971). A prima facie “disparate impact” ease under Title VII may therefore be established without any proof of intentional discrimination: where a business practice, neutral on its face, is shown to have a substantial, adverse impact on some group protected by Title VII, the plaintiff has made out a prima facie case, and the burden4 shifts to the defendant to establish that the practice is justified by “business necessity.” Contreras v. City of Los Angeles, 656 F.2d 1267, 1275-80 (9th Cir. 1981). Good intent or absence of intent is no defense to such disparate impact Title VII claims. International Bhd. of Teamsters v. United States, 431 U.S. 324, 349, 97 S.Ct. 1843, 1861, 52 L.Ed.2d 396 (1977) (Teamsters); Griggs v. Duke Power Co., supra, 401 U.S. at 432, 91 S.Ct. at 854.

Section 1981, on the other hand, does not embody the same broad, prophylactic purpose as does Title VII. There are very real historical and practical differences between the two statutes. Davis v. County of Los Angeles, 566 F.2d 1334, 1348-51 (9th Cir. 1977) (Wallace, J., dissenting), vacated as moot, 440 U.S. 625, 99 S.Ct. 1379, 59 L.Ed.2d 642 (1979); see General Building Contractors Ass’n v. Pennsylvania, supra, 102 S.Ct. at 3146-48. We therefore held in Craig that a prima facie case of racial discrimination in cases brought under section 1981, like cases brought under the equal protection clause and 42 U.S.C. § 1983, see Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), requires proof of intentional discrimination. Craig, supra, 626 F.2d at 668. A plaintiff suing under section 1981 may not avail himself of the more liberal Griggs standard for establishing a prima facie case of employment discrimination upon a showing of disparate impact alone.

A Title VII violation, of course, can be established by means other than an unrebutted showing of disproportionate impact. See Teamsters, supra, 431 U.S. at 335-36 n.15, 97 S.Ct. at 1854 n.15. An alternative, equally valid theory of liability is that of “disparate treatment”: that an individual was singled out and treated less favorably than others similarly situated on account of race or any other criterion impermissible under the statute. By their very nature, these claims require proof of intentional discrimination. Id. (“[p]roof of discriminatory motive is critical”). Whether brought under Title VII, the equal protection clause or section 1981, therefore, claims of disparate racial treatment require proof of intentional racial discrimination. The district court correctly recognized this parallel between these otherwise dissimilar constitutional and statutory provisions. See 489 F.Supp. at 295.

The plaintiff in a Title VII disparate treatment case, like most civil plaintiffs, bears the ultimate burden of persuasion on the issue of discriminatory intent. *538Texas Dep’t of Community Affairs v. Burdine, 450 U.S. 248, 253, 101 S.Ct. 1089,1093, 67 L.Ed.2d 207 (1981) (Burdine). But the burden of production, sometimes referred to as the burden of going forward with evidence sufficient to avoid a directed verdict or judgment as a matter of law, shifts. Id. at 253-56, 101 S.Ct. at 1093-95. A prima facie case of disparate treatment under Title VII is established by proof of facts supporting an inference of intentional discrimination. Furnco Construction Corp. v. Waters, 438 U.S. 567, 576, 98 S.Ct. 2943, 2949, 57 L.Ed.2d 957 (1978) (Furnco). This initial burden of production is “not onerous,” Burdine, supra, 450 U.S. at 253, 101 S.Ct. at 1093, and is met upon a “showing of actions taken by the employer from which one can infer, if such actions remain unexplained, that it is more likely than not that such action was based upon” race or another impermissible criterion. Furnco, supra, 438 U.S. at 576, 98 S.Ct. at 2949. The plaintiff’s immediate burden of production may be discharged by proof of the four elements articulated in McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973) (McDonnell Douglas),5 or by an alternative presentation of evidence supporting an inference of discrimination. The Supreme Court has consistently emphasized that the McDonnell Douglas criteria are not the only mode of establishing a prima facie case of intentional discrimination under Title VII. See Burdine, supra, 450 U.S. at 253-54 n.6, 101 S.Ct. at 1093-94 n.6; Furnco, supra, 438 U.S. at 577, 98 S.Ct. at 2949; Teamsters, supra, 431 U.S. at 358, 97 S.Ct. at 1866; McDonnell Douglas, supra, 411 U.S. at 802 n.13, 93 S.Ct. at 1824 n.13.

While Title VII disparate impact cases are of little help to us in this case, the reasoning used to analyze the required prima facie showing in a Title VII disparate treatment case is of great assistance because it is nearly identical to the inquiry necessary in a section 1981 case. Since a prima facie section 1981 case, like a prima facie disparate treatment case under Title VII, requires proof of intentional discrimination, the focus of the judicial inquiry must be whether the plaintiff has proven by a preponderance of evidence facts from which the court must infer, absent rebuttal, that the defendant was more likely than not motivated by a discriminatory animus. Under both statutes, the court must make a sensitive inquiry into the direct and circumstantial evidence of discrimination offered by the plaintiff in order to determine if the facts so proved allow a legally-permissible inference of discriminatory intent. Accordingly, it is not inappropriate to allow section 1981 claimants to avail themselves of Title VII discriminatory treatment standards in proving a prima facie case. See Hudson v. IBM Corp., 620 F.2d 351, 354 (2d Cir.), cert. denied, 449 U.S. 1066, 101 S.Ct. 794, 66 L.Ed.2d 611 (1980).

Our statement in Craig that “equal protection rather than Title VII standards apply to employment discrimination claims brought under § 1981,” Craig, supra, 626 F.2d at 668, is not to the contrary. The comment was part of our reasoning that discriminatory intent is required in a section 1981 case. Thus in Craig, we were distinguishing the Title VII standards set down in Griggs, a disparate impact case, from the equal protection requirement of proving a discriminatory purpose established in Washington v. Davis, supra, 426 U.S. at 238-42, 96 S.Ct. at 2046-2048. We have since clearly stated that “the McDonnell Douglas criteria provide a useful guide to a plaintiff’s burden in a section 1981 .. . non-class employment discrimination suit.” Tagupa v. Board of Directors, 633 F.2d *5391309, 1312 (9th Cir. 1980) (footnotes omitted). We hold, therefore, that a plaintiff may establish a prima facie case of intentional discrimination in employment under section 1981 upon proof of facts which would establish a prima facie case of disparate treatment under Title VII, pursuant to the four McDonnell Douglas elements or. otherwise.

Yet we expressly do not hold that Bur-dine, Furnco and McDonnell Douglas must be blindly followed in all aspects of section 1981 cases. “[A] plaintiff’s burden in a 1981 ... action may differ in some respects from that of a plaintiff in an action brought under Title VII .... ” Tagupa v. Board of Directors, supra, 633 F.2d at 1312. The two statutes, as we stated earlier, are markedly dissimilar in several important respects. We here deal only with a plaintiff’s burden to demonstrate a prima facie case under section 1981, and need go no further.

Ill

Before turning to the waiters’ arguments on the merits we are confronted with the question of the appropriate standard of review for the issues raised in this appeal. Applying the criteria articulated in McDonnell Douglas, supra, 411 U.S. at 802 & n.13, and Hazelwood School Dist. v. United States, 433 U.S. 299, 307, 97 S.Ct. 2736, 2741, 53 L.Ed.2d 768 (1977), the district court determined that the waiters failed to establish a prima facie case of intentional discrimination. 489 F.Supp. at 295-96 (individual claims); id. at 311 (class claims). The St. Francis characterizes this determination as a finding of fact, and argues that we may therefore reverse the district court’s judgment consistent with Fed.R. Civ.P. 52(a) only if we conclude that this so-called finding was clearly erroneous.6 The waiters, on the other hand, argue that the clearly erroneous standard properly applies to questions of fact resolved by the district court by reference to the credibility of conflicting documentary, testimonial or circumstantial evidence, but that the determination whether an employment discrimination plaintiff has established a prima facie case of intentional discrimination under McDonnell Douglas is a question of law for the district court, reviewable on appeal free of the clearly erroneous standard. Thus, the question squarely presented is whether, in a section 1981 case alleging disparate treatment in employment, the district court’s determination that the plaintiff failed to establish a prima facie case of intentional discrimination under McDonnell Douglas and its progeny is a finding of fact within the meaning of Fed.R.Civ.P. 52(a). If so, such a finding may be set aside or reversed on appeal only if the appellate court determines that the finding is clearly erroneous. A finding of fact is clearly erroneous only when, although there is evidence in the record to support it, the court of appeals is left with the “definite and firm conviction” that a mistake has been committed. United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 541, 92 L.Ed. 746 (1948); Edinburgh Assurance Co. v. R. L. Burns Corp., 669 F.2d 1259, 1261 (9th Cir. 1982).

The answer to this inquiry is not crystal clear. There is some language in two cases which can be perceived as suggesting a rule different from that established by our earlier precedent. To see whether the conflict is real or only apparent, we must review our decisions on this issue.

In a series of cases beginning in 1977, we have applied the clearly erroneous standard to the district court’s findings on the facts supporting the four McDonnell Douglas elements, as well as the factual question of the extent of any adverse impact demonstrated by the plaintiff’s statistical evidence. E.g., Chavez v. Tempe Union High School Dist., 565 F.2d 1087 (9th Cir. 1977); White v. City of San Diego, 605 F.2d 455 (9th Cir. 1979); *540McLean v. Phillips-Ramsey, Inc., 624 F.2d 70 (9th Cir. 1980) (per curiam); Hagans v. Andrus, 651 F.2d 622 (9th Cir.), cert. denied, 454 U.S. 859, 102 S.Ct. 313, 70 L.Ed.2d 157 (1981); Fernandez v. Wynn Oil Co., 653 F.2d 1273 (9th Cir. 1981). These factual findings include the four McDonnell Douglas elements themselves, which are, after all, factual determinations.7 These cases lead to the conclusion that the district court’s findings on what facts were established by a preponderance of the evidence must be accepted on appeal unless clearly erroneous, but that the court’s determination whether the facts so proved were sufficient to establish an inference of discrimination, in other words whether the plaintiff’s proof established a prima facie case thus shifting the burden of production to the defendant, is a legal conclusion freely reviewable on appeal.

In these cases we applied the clearly erroneous standard of review to the facts found by the district court by reference to the credibility of conflicting documentary, testimonial and circumstantial evidence. In Chavez v. Tempe Union High School Dist., supra, a high school English teacher alleged that she was denied the position of language department chairperson on account of national origin in violation of Title VII. She raised both disparate treatment and disparate impact claims. 565 F.2d at 1090. The district judge determined that the plaintiff had failed to establish a prima facie case of disparate treatment based upon his finding that at the time of the plaintiff’s application, the position had already been filled. Id. We affirmed. After concluding as a matter of law that “the failure to prove the existence of a job opening is a fatal defect in a prima facie case of overt discrimination,” id. at 1091, we addressed the district court’s findings of fact. We held that the district court “was not clearly erroneous in determining as a factual matter” that the principal’s selections of department chairpersons were automatically approved. Id. We further held that the district court’s finding of fact “as to the actual date of Chavez’ application” was clearly erroneous, but that “the district judge’s factual determination that at the time of Chavez’ application, the position was already filled ... was not clearly erroneous.” Id. at 1092. In view of our earlier holding that a prima facie disparate treatment case requires a showing of job availability, therefore, we held that Chavez had failed to establish a prima facie case. Id.

We did not, however, hold or imply that the district court’s determination that the facts proved by the plaintiff were insufficient to establish a prima facie case was a finding of fact reversible only if clearly erroneous. Indeed, we distinguished between the district court’s finding on the factual question of job availability and the court’s “conelu[sion] as a matter of law that the [school] district had not violated Chavez’ civil rights.” Id. at 1090. We applied this same distinction to Chavez’ disparate impact claim. Chavez argued that the neutral practices employed by the district, specifically the failure to advertise chairperson positions and the district’s failure to follow its own standards for qualifications, had a disproportionate adverse impact on minorities. We pointed out that the facts showed that Chavez “had a fair opportunity to obtain a position as acting department head,” and that “Chavez ha[d] not shown that the failure of the district to follow its own standards had a disproportionately unfavorable impact on minorities.” Id. at 1094. Accordingly, we “conclude[d] that Chavez ha[d] failed to establish a prima facie ease of discrimination under Title VII .... ” Id. at 1095. Thus, nothing in Chavez suggests that the determination whether the amount of disproportionate impact established by a Griggs plaintiff is sufficient to raise a prima facie case is a finding of fact subject to the clearly erroneous standard of review.

In White v. City of San Diego, supra, a female city accountant alleged that the city’s failure to promote her violated Title VII on both disparate treatment and disparate impact theories of sexual discrimination. While addressing her disparate treat*541ment claim we again distinguished between the four factual McDonnell Douglas elements and the subsequent conclusion whether the plaintiff’s proof of those or alternative facts was sufficient to permit an inference of intentional discrimination under Furnco. “Thus, however we view the City’s subsequent ... hirings, they cannot, on these facts, raise an inference of discrimination on the basis of sex.” 605 F.2d at 459 (emphasis added).

In our analysis of her Griggs disparate impact claim, we addressed the standard of review issue expressly. White argued that the clearly erroneous standard did not apply because her claim was that the trial court improperly applied the law to undisputed facts. Id. at 459. We concluded, however, that her claim was actually that the district court erred in weighing her statistical proof. The district court found that her statistics were unreliable and the sample sizes she offered were too small. Id. at 460. We appropriately deferred to the district court’s fact-finding function with respect to this statistical evidence. Id. at 460-61. Thus, although we applied the clearly erroneous standard to the district court’s “factual assessment” of statistical data, id., we did not apply that standard to the district court’s determination that the data failed to establish a prima facie case. See also Frausto v. Legal Aid Society, 563 F.2d 1324, 1328-29 (9th Cir. 1977) (concluding that the district court did not clearly err in finding that plaintiff’s statistical data showed higher proportion of minority employees than in qualified, available population). We followed both White and Chavez in Hagans v. Andrus, supra, where we reviewed the district court’s determination that the plaintiff failed to establish a prima facie case as a freely reviewable conclusion of law, 651 F.2d at 624, but separately reviewed the court’s findings of fact under the clearly erroneous standard. Id. at 626-27.

In two other cases we made the Chavez distinction clearly and expressly. In McLean v. Phillips-Ramsey, Inc., supra, a disparate treatment case, the district court dismissed the action at the close of the plaintiff’s case-in-chief. “In support of its conclusion that McLean had not established a prima facie case, the district court found that” McLean had failed to prove several of the four factual McDonnell Douglas criteria. 624 F.2d at 71 (emphasis added). We reversed. We wrote that “[tjhese findings may not be disturbed unless clearly erroneous,” id., but “conclude[d] that the district court’s findings [were] clearly erroneous.” Id. In Fernandez v. Wynn Oil Co., supra, 653 F.2d at 1275, the district court found that the plaintiff had failed to demonstrate she was qualified for the position in question and, alternatively, that the individual eventually chosen for the job had superior qualifications. Citing McLean, we held that “[u]nless these findings are clearly erroneous, they must not be disturbed on appeal.” Id. See also Pack v. Energy Research & Development Adm’n, 566 F.2d 1111, 1113 (9th Cir. 1977) (per curiam) (clearly erroneous standard applied to district court finding that plaintiff was considered for position sought). We then held that the record supported both findings. We did not, however, apply the clearly erroneous standard to the question whether these findings supported the district court’s conclusion that no prima facie case had been made out. We deferred to the trial court’s ability to resolve disputed issues of fact, but analyzed the legal issue without any reference to the clearly erroneous standard.

Fernandez has therefore failed to demonstrate that the district court clearly erred in failing to find her qualified for the DIO position. If an applicant is not qualified for the job in question, she has failed to establish a prima facie case.

Fernandez v. Wynn Oil Co., supra, 653 F.2d at 1275 (citations omitted).

In sum, these cases establish that the district court’s factual assessment of the plaintiff’s evidence, including the court’s findings as to whether the plaintiff has proved any or all of the four factual McDonnell Douglas criteria, may not be upset on appeal unless clearly erroneous. They do not support the proposition that the district court’s determination that the *542plaintiff failed to establish a prima facie case is a finding of fact subject to the clearly erroneous standard of review.8

The first case which presents us with some difficulty is Golden v. Local 55, Int’l Ass’n of Firefighters, 633 F.2d 817 (9th Cir. 1980). Four rulings by the district court were contested on appeal. The third was that the union did not breach its duty of fair representation and, in the fourth, “the court found that the union had not violated Title VII.” Id. at 820. Without citation of authority, we stated that “[t]he standard for reviewing rulings three and four is whether the findings are consistent with Fed.R.Civ.P. 52(a).” Id. Notwithstanding this statement, however, we appear to have applied a substantial evidence standard of review. “We find substantial evidence to support the conclusion of ‘no Title VII violation’ under both [disparate impact and disparate treatment] theories.” Id. at 821. See also id. at 823 (“We find substantial evidence, however, to support the conclusion that no disparate impact was shown.”). At any rate, Golden can be harmonized in part with our earlier cases. The district court found that the promotion examination in question “did not have a discriminatory impact on minorities.” Id. at 823. Under White v. City of San Diego, supra, 605 F.2d at 460, this is a factual assessment of the weight of statistical data, subject to the clearly erroneous standard of review. In addition, the fact that two of our cases decided subsequent to Golden have followed the earlier holdings, see Hagans v. Andrus, supra, 651 F.2d at 622; Fernandez v. Wynn Oil Co., supra, 653 F.2d at 1273, demonstrates that this case does not present a complete departure from the weight of our precedent.

The only other case found in our circuit which may be read to apply the clearly erroneous standard to the district court’s conclusion that the plaintiff has proved facts sufficient to establish a prima facie case of intentional discrimination is Piva v. Xerox Corp., 654 F.2d 591 (9th Cir. 1981), which involved an allegation of disparate treatment based upon sex.9 There, we first briefly summarized the shifting burdens of production involved in McDonnell Douglas lawsuits, and then wrote:

In this circuit, the trial court’s conclusions regarding the success or failure of the plaintiff and defendant in meeting these burdens are reviewed under the clearly erroneous test. Golden v. Local 55, [supra ]. This standard of review is particularly appropriate where, as in this case, the underlying facts are in dispute and the validity of the proffered statistical evidence is in question. See White v. City of San Diego, [supra ].

Id. at 594 (footnote omitted). On its face, this language appears to be inconsistent with our prior line of cases from Chavez to Fernandez. Two authorities are cited: Golden, which as indicated earlier may be questionable precedent, and White, which is consistent with our holdings from Chavez to Fernandez. To attempt to harmonize in part, we could point to portions of Piva in which the clearly erroneous test was properly applied to the district court’s findings on the McDonnell Douglas factual criteria. See id. at 595, 598. To this extent, Piva would be consistent with our earlier precedent. Nevertheless, there is an inconsistency in our cases, leaving us the burden to determine which to follow.

In order to decide this case, we choose to follow the longer and more estab*543lished line of cases. Applying the clearly erroneous standard to the district court’s determination that an employment discrimination plaintiff failed to establish a prima faeie case of disparate treatment appears to us to be inconsistent with the theoretical10 and functional11 role of the McDonnell Douglas burden-shifting procedure, with *544the Supreme Court’s analysis and holding in Furnco,12 and with the purpose of Rule 52(a).13. For these reasons, it could be argued that the vitality of Golden and Piva *545are largely undercut by the reasoning of Supreme Court decisions and the logical application of a governing rule.14 In addition, while we recognize the apparent conflict, it is unnecessary for our court to resolve the issue en banc to decide this ease. If we freely review the district judge’s conelusion that no prima facie case has been demonstrated and conclude that he was conrect, we would, obviously, come to the same *546conclusion if we followed the more restrictive clearly erroneous standard of review. Since the Supreme Court has stated that “[a] McDonnell Douglas prima facie showing is not the equivalent of a factual finding of discrimination,” Furnco, supra, 438 U.S. at 579, 98 S.Ct. 2950, we are content in this case to apply the de novo standard of review.

IY

The waiters characterize this case as “emblematic of the ‘modern’ employment discrimination lawsuit.” It is clear from the record that the waiters were unable to produce any “smoking gun” evidence of overt discrimination: they did not establish the existence of “all-white” departments, come forward with testimony of racial epithets or other clear indications of discriminatory motivation, or produce any direct evidence of intentional discrimination. This failure was not fatal to their case, however, since it is settled that a prima facie showing of disparate treatment may be made without any direct proof of discriminatory motivation. Yet we disagree with the waiters’ basic argument on appeal: that the facts they did prove were sufficient to establish a prima facie case of disparate treatment as a matter of law. The waiters insist that their evidence demonstrated a “significant underrepresentation” of blacks by both hotels over the course of nearly a decade; the application of numerous “subjective employment practices” that “inevitably invite” discrimination; the treatment of black applicants in a way “that could only lead . .. to discouragement and surrender”; and a “resolute refusal” by the hotels to “give a damn about the situation or to take any steps of a remedial nature.” Yet the waiters have failed to meet their burden of demonstrating that any of the district court’s material findings of fact were clearly erroneous, and have failed to convince us that the district court erred when it concluded from these facts that they failed to establish a prima facie case.

The district court found that the waiters were qualified for the positions sought, that they worked as banquet or extra banquet waiters at both hotels on a temporary or part-time basis and frequently made oral inquiries concerning permanent positions, but that they did not produce sufficient evidence to permit a finding as to the date when they orally applied. It was therefore “not possible ... to determine whether openings existed at the time when any of [the waiters] applied.” 489 F.Supp. at 295. Based upon the waiters’ own exhibits, the court found that the vast majority of black applicants did not apply for a waiter position at or about the time a non-black was hired. Id. In almost all cases, no black had applied for a waiter position ultimately filled by a non-black within one month of the successful non-black applicant. Id. at 295, 296.

These findings of fact are not disputed by the waiters. They argue that the district court erred in concluding from these facts that they failed to establish a prima facie case of intentional discrimination. As an initial matter, the waiters argue that the district court incorrectly required them to establish that they had filed written applications. This argument is unpersuasive. The district court’s opinion in no way relied upon the waiters’ failure to prove that they had filed written applications. Somewhat similarly, the waiters argue that under Teamsters they need not have applied for the positions at all, in writing or otherwise, because they were deterred from doing so. This argument is also unpersuasive. Teamsters, a class action, provides a limited exception to the rule that the plaintiff in a disparate treatment lawsuit must demonstrate that he or she applied for the position sought. The necessary prerequisite to such a claim is proof of a “consistently enforced discriminatory policy” which discourages applicants from even attempting to apply. Teamsters, supra, 431 U.S. at 365, 97 S.Ct. at 1869. See Tagupa v. Board of Directors, supra, 633 F.2d at 1312 n.2. There was no such proof in this case.

The waiters’ major argument is that their evidence was sufficient to satisfy McDonnell Douglas. They argue correctly that *547the district court found that job openings did, in fact, exist. See 489 F.Supp. at 296 (“in the general period in which the individual claimants were interested in employment ... waiters were being hired”). The district court was not clearly erroneous in making this finding. In view of the fact that the St. Francis hired 390 waiters between 1970 and 1979, see id. at 308, and the Hilton hired 206 waiters between 1974 and 1979, see id. at 309, it would belie reality to find that there were no vacancies in waiter positions at the hotels. The waiters, however, insist that such a “general availability” of jobs is sufficient to satisfy the second McDonnell Douglas criterion — that the plaintiff “applied and was qualified for a job for which the employer was seeking applicants.” They contend that where, as here, knowledge of job vacancies is not made generally available, applicants cannot be expected to make carefully-timed applications.

The waiters have cited some cases from other circuits which may support their position. In East v. Romine, Inc., 518 F.2d 332, 338 (5th Cir. 1975), the court held that the plaintiff had established a prima facie case of intentional sex discrimination under McDonnell Douglas upon proof that (1) she was qualified for a position, (2) she applied for the job, and (3) openings were filled “within six months” after application. Although the waiters were unable to establish the exact day upon which they applied, their proof clearly established the years in which they applied and that waiters were being hired regularly during those years. Two other cases upon which they rely contain language supporting their position, but are clearly distinguishable on the facts. In Grant v. Bethlehem Steel Corp., 635 F.2d 1007, 1016-17 (2d Cir. 1980), cert. denied, 452 U.S. 940, 101 S.Ct. 3083, 69 L.Ed.2d 954 (1981), the Second Circuit reversed a judgment of the district court that the plaintiffs had failed to establish a prima facie case since no jobs were available when they applied. The court wrote that it was irrelevant that the plaintiffs “failed to apply often enough or at the correct times,” id., but only because the employer admitted routinely hiring persons for specific openings before they became available and were announced. In Rich v. Martin Marietta Corp., 522 F.2d 333, 347-48 (10th Cir. 1975), the court held that to establish a prima facie case, a plaintiff need not “point to a specific opening.” However, the court expressly limited its holding to promotion cases. “Clearly this [job opening requirement] applies to new employment and is different from an employee who is seeking promotion. The former takes place on a particular day, whereas in the promotion area it invariably arises during a lengthy period of time.” Id. at 348. Finally, a brief dictum in the Supreme Court’s opinion in Furnco might appear to indicate that proof of “general job availability” is sufficient to establish a prima facie McDonnell Douglas case. The Court stated that the plaintiffs had established a prima facie case upon proof of, among other things, that they were “qualified in every respect for jobs which were about to be open.” Furnco, supra, 438 U.S. at 576, 98 S.Ct. at 2949 (emphasis added).

These cases do not persuade us to dispense with the “job opening” requirement. Chavez v. Tempe Union High School Dist., supra, 565 F.2d at 1087. The function of the McDonnell Douglas prima facie case is to eliminate the two most common reasons why an applicant may be rejected: an absolute or relative lack of qualifications, or lack of an open position. Teamsters, supra, 431 U.S. at 358 n.44, 97 S.Ct. at 1866 n.44; see also Burdine, supra, 450 U.S. at 253-54, 101 S.Ct. at 1093-94. Upon proof of facts sufficient to disprove these two most common reasons for a rejection, courts infer, in light of their experience, that the employment decision was “more likely than not” based upon racé. Furnco, supra, 438 U.S. at 577, 98 S.Ct. at 2949. If we were to permit a prima facie case to be established solely upon proof that jobs, in general, were available within some unspecified time from the unspecified date at which a plaintiff applied for a position, we would be permitting a plaintiff to raise an inference of discrimination where he or she has failed *548to disprove one of the two common and neutral reasons for a rejection. Thus, we would be permitting an inference of discrimination in situations in which it was not “more likely than not” that the employment decision was based upon race.

Our cases are not to the contrary. In Chavez v. Tempe Union High School Dist., supra, 565 F.2d at 1087, where the position in question had already been filled when the plaintiff applied, we held that “the failure to prove the existence of a job opening” is a failure as a matter of law to make out a prima facie case of disparate treatment under McDonnell Douglas. Id. at 1091. In a failure to promote case, we observed that requiring the job to remain open in the same sense as in a failure to hire case would frustrate the McDonnell Douglas test. Hagans v. Andrus, supra, 651 F.2d at 625. We emphasized the “flexibility” of the McDonnell Douglas test and held that a position need not necessarily “remain open” under McDonnell Douglas when several applicants apply for a job that will necessarily be filled by one of them at a predetermined time. In one job application ease, we did hold that there may be circumstances where, due to the specific facts involved, some flexibility is required in determining whether, as a practical matter, a job opening occurring after an application is made is an open position under McDonnell Douglas. See McLean v. Phillips-Ramsey, Inc., supra, 624 F.2d at 70. Nevertheless, absent this very narrow and specific exception, the job opening requirement of Chavez is the law of this circuit.

In this case, the waiters’ own evidence demonstrated that “with only a few exceptions, waiters were hired within a few days of the date of their application.” 489 F.Supp. at 296 (footnote omitted). Their own evidence showed that with even fewer exceptions, no black applicant applied at either of the hotels within a month of the date that a non-black was hired. Yet on direct examination, none of the individual plaintiffs was able to recall when he applied for permanent positions at either of the hotels. Having failed to establish the date upon which they applied,, and having failed to establish that any black applicant applied at the time a job was open or, if the McLean exception were to apply, that a job vacancy occurred within a reasonable time, the plaintiffs failed to establish a prima facie case of intentional discrimination. The district court correctly concluded that the waiters failed to prove that their inability to secure jobs at either hotel was “more likely than not” based upon racial discrimination.

With respect to the Hilton, this conclusion is reinforced by the evidence showing that none of the individual plaintiffs ever applied for waiter positions which were subsequently filled by non-blacks. This does not mean, however, as the Hilton argues, that the waiters failed to raise a prima facie case under our decision in Tagupa v. Board of Directors, supra, in which we held that the plaintiff had not applied for the position in question because he had failed to “complete the application process.” 633 F.2d at 1312. There, the application materials the plaintiff furnished, in response to an advertisement, did not include any reference to the job qualifications sought by the employer and requested clearly in the advertisement. The Hilton argues that the individual plaintiffs failed to complete the application process under Tagupa simply because they failed to submit written applications. It is true that the district court found that “[a]ll applicants [at the Hilton] must file an application.” 489 F.Supp. at 288. Insofar as this finding implies that the Hilton refused to consider a person for any waiter position in the absence of a written application, however, it is clearly erroneous. The Hilton’s own witnesses testified that restaurant managers or department heads often sent prospective hirees to the personnel department before the personnel department ever learned of the existence of a job opening. Indeed, they even testified that the hotel’s banquet department managers frequently hired waiters for permanent positions without ever notifying the personnel department of the existence of a job opening. Three of the *549individual plaintiffs worked on a part-time basis in the Hilton’s banquet department and, significantly, the Hilton does not challenge the district court’s finding that all were qualified for permanent employment. Combined with the district court’s finding that these individuals repeatedly inquired about permanent positions, this is sufficient to demonstrate that they applied for the job within the meaning of Tagupa.

Even had the waiters established a prima facie case, however, the evidence was sufficient to support the conclusion that the Hilton rebutted any inference of discrimination. Appellant Whitman “made oral job requests to the Hilton’s banquet manager” during 1975, but received no offer. 489 F.Supp. at 290. This was his sole effort to gain employment at the Hilton. Yet the plaintiffs’ own evidence shows that no waiters were hired by the Hilton’s banquet department in 1975. Appellant McDowell made repeated inquiries about a permanent job at the Hilton while working there as an extra banquet waiter during 1974. However, the banquet department hired only one new waiter during 1974, a black man.15 Finally, appellant Dennis made oral inquiries at the Hilton beginning in October 1975, while working there as an extra banquet waiter. He also testified that he “was never able to file an application.” 489 F.Supp. at 291. Yet the record shows that the Hilton refused to consider him for any further employment because of a dispute between him and a captain during a banquet. Id. Even more striking is the testimony of appellant McDowell that he was “treated wonderful” while working at the Hilton. This corroborates the testimony of the Hilton’s own witnesses, including a black waiter and another black man (presently the manager of the Hilton’s largest restaurant), that the Hilton had never discriminated against black applicants and had, in fact, been singled out for praise by black groups for its work in integration.

Nonetheless, even if we were to assume that the waiters applied for positions at both hotels which subsequently became vacant and were filled by non-blacks, Chavez establishes that a job opening must exist at the time of the application. In addition, even if this were an exception allowed by McLean, a job opening would need to be proven to exist at least within a reasonable time of the date of the application. The district court found that the hotels routinely filled open positions extremely quickly by hiring waiters from among those who had applied within the previous several days, but that no black applicant applied within a month of the hiring of a non-black. These findings establish that the waiters failed to prove the necessary link of timeliness between an application and a vacancy, and thus failed to establish a prima facie case.

The district court also concluded that, assuming a prima facie case were established, the hotels had articulated a legitimate, nondiscriminatory reason for their conduct. As we hold that no prima facie case was proven, we need not address this issue in any detail.

V

The waiters’ two remaining arguments pertain to both the individual and class claims. They maintain that (1) their statistical evidence, standing alone, was sufficient to establish a prima facie case of disparate treatment; and (2) even if not, the statistical proof in conjunction with the circumstantial evidence of discrimination presented was sufficient to establish such a prima facie case. As part of their second argument, the waiters contend that the district judge erred in failing to consider their statistical data with respect to their individual claims. As to this final challenge, the waiters are correct; the district judge erred.

*550The district judge closely scrutinized the statistical evidence introduced by the waiters and credited the testimony of their expert witness, but did so only with respect to the class claims. With respect to the individual claims, the district court observed that the statistical proof “may be probative,” but refused to consider it: “Inasmuch as the statistical proof in this case fails to establish a prima facie case on behalf of the class ... it is of no help to the individual claimants.” 489 F.Supp. at 296 n.9. This was incorrect. We have repeatedly emphasized that proof of the four McDonnell Douglas criteria is not the only way to establish a prima facie case of disparate treatment, and that the McDonnell Douglas approach is to be applied flexibly. In addition, we have clearly held that, if reliable, generalized statistical data is relevant and admissible at the prima facie case stage of a disparate treatment employment discrimination lawsuit. See, e.g., O'Brien v. Sky Chefs, Inc., 670 F.2d 864, 866 (9th Cir. 1982); Lynn v. Regents of the University of California, 656 F.2d 1337, 1342-43 & 1342 n.3 (9th Cir. 1981); Heagney v. University of Washington, 642 F.2d 1157, 1164 (9th Cir. 1981); Reed v. Lockheed Aircraft Corp., 613 F.2d 757, 762 & n.10 (9th Cir. 1980); White v. City of San Diego, supra, 605 F.2d at 459-60. This is true whether or not the statistical data introduced is sufficient of itself to establish a prima facie case. Since the question is one of inferring discriminatory intent, the district court should make a “sensitive inquiry into such circumstantial and direct evidence of intent as may be available,” Village of Arlington Heights v. Metropolitan Housing Corp., 429 U.S. 252, 266, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977) (Arlington Heights), including any reliable statistical data offered by the plaintiff, in order to determine whether the facts so proved constitute prima facie evidence of discriminatory intent. The legal standard to be applied is simply whether the facts proved are sufficient to permit the court to infer, absent explanation, that the employment decision was more likely than not the product of intentional discrimination. Furnco, supra, 438 U.S. at 576, 98 S.Ct. at 2949; White v. City of San Diego, supra, 605 F.2d at 458. Of course, if the claim analyzed is individual rather than class, the statistics must be relevant to the particular plaintiff’s claim. But all evidence, both direct and circumstantial, statistical and nonstatistical, relevant to that question should be assessed on a cumulative basis. EEOC v. American National Bank, 652 F.2d 1176, 1189 (4th Cir. 1981). This error does not, however, require reversal and remand for the district judge to determine whether adding the statistical data would demonstrate a prima facie case. The district judge has already passed upon the factual aspects of the statistical data. A legal question remains. On this record, we conclude that the district court’s error was harmless. With respect to both the individual and class claims, neither the statistical data standing alone, nor in combination with the circumstantial evidence of discrimination offered by the waiters, was sufficient as a matter of law to establish a prima facie case of disparate treatment.

The district judge undertook an exhaustive analysis of the statistical evidence introduced by the waiters. He determined that the appropriate comparison was between the percentage of blacks hired by the hotels and the percentage of blacks in “a labor market consisting of all males, aged 21 to 64, in the civil labor force in the weighted San Francisco/Oakland SMSA as shown in the 1970 census.” 489 F.Supp. at 307. The district judge appropriately focused on the reliability of this statistical data, and his factual assessment of the data was not clearly erroneous. See White v. City of San Diego, supra, 605 F.2d at 460-61. The district judge found that the relevant labor “pool” produced a black “availability figure” of 11.1%. 489 F.Supp. at 307. Because the waiters failed to support their claim that the hotels changed their hiring practices during the course of the lawsuit so as to increase the proportion of blacks hired as waiters, id. at 308, and because the bulk of the evidence presented by both sides related to events following the filing of the complaint, id. at 308 n.32, the district judge *551analyzed the statistical data for the entire relevant period.16 Based upon a comparison of the actual number of blacks hired and the expected number which would have been hired had the hotels hired at a rate equivalent to the proportion of blacks in the relevant labor pool, the district judge computed the so-called “Z statistic,” which measures the degree to which the expected results differ from the actual results. Id. at 308-09 & n.33.

This comparison revealed that the actual percentage of blacks hired by the St. Francis between 1970 and 1979 was 7.2%, while the percentage of blacks hired by the Hilton between 1974 and 1979 was 8.3%. Expressed in terms of standard deviations or the Z statistic, the variance between the percentage of blacks hired by the St. Francis and the black availability figure of 11.1% was 2.46; the correlative figure for the Hilton was 1.30. Expressed in terms of the probability of a random or chance occurrence, these standard deviations translate into a chance probability of 1.38% for the St. Francis, and 19.36% for the Hilton. Id.17

The district court concluded that these statistical disparities were not sufficiently “gross and long-lasting” to support an inference of purposeful discrimination. 489 F.Supp. at 311. The waiters, however, argue that the court erred by looking for a single, fixed Z statistic as a “cut-off point” clearly delineating intentional from unintentional discrimination. This is correct only insofar as it is a statement of the law relating to statistical proof. It would be improper to posit a quantitative threshold above which statistical evidence of disparate racial impact is sufficient as a matter of law to infer discriminatory intent, and below which it is insufficient as a matter of law. Indeed, if any rule of law can be isolated from the Supreme Court’s decisions in Castaneda v. Partida, 430 U.S. 482, 496 n.17, 97 S.Ct. 1272, 1281 n.17, 51 L.Ed.2d 498 (1977), and Hazelwood School Dist. v. United States, supra, 433 U.S. at 307, 308 n.14, 97 S.Ct. at 2741 n.14, it is that for sufficiently large samples, a variance between expected and observed results of greater than 2 or 3 standard deviations is sufficient to make the data “suspect” for a social scientist. However, the statistical differences which the Court in these cases held were sufficient to support an inference of intentional discrimination, respectively 12 and 5 to 6 standard deviations, are far greater than those which would be “suspect” to the social scientist, and significantly greater than the 2.46 and 1.30 standard deviations found in this case. We agree with the Fourth Circuit that courts should be “extremely cautious” of drawing any inferences from standard deviations in the range of 1 to 3. EEOC v. American National Bank, supra, 652 F.2d at 1192. Indeed, the difference in this case between the expected result of 11.1% and the actual results of 7.2% and 8.3% “may be sufficient*552ly small to weaken the [waiters’] other proof.” Hazelwood School Dist. v. United States, supra, 433 U.S. at 311, 97 S.Ct. at 2743. The district court, therefore, properly concluded that the degree of disparate impact shown by the waiters’ statistical data was insufficient to establish a prima facie case of intentional discrimination. Although statistical data may, in a proper case, be sufficient alone to raise a prima facie case, the statistics must be considerably more stark than those involved here.

Nonetheless, the waiters insist that a prima facie case is established if the statistical evidence introduced “rejects the random hypothesis.” They argue that there are only three possible explanations for any specific rejection of a minority applicant: lack of qualifications, racial discrimination, or chance. Therefore, the waiters contend that since data indicating standard deviations of between 2 and 3 is “statistically significant,” and reflects probabilities of random occurrence declining from 5% at 2 standard deviations to less than 1% at 3, such data is sufficient to reject chance as a possible explanation. Since the district court found that they were qualified, and rejected the hotels’ attempts to impeach the waiters’ statistical evidence by demonstrating a lack of qualified blacks in the general labor pool and a relative lack of blacks in the “applicant flow,” see 489 F.Supp. at 312-15, the waiters argue that race — the only remaining explanation — has been shown to be “more likely than not.”

We disagree. It must always be remembered that “[r]egardless of how devastating or reliable the statistics may look, the issue remains in [disparate treatment] cases whether a particular isolated historical event was discriminatory.” Ward v. Westland Plastics, Inc., 651 F.2d 1266, 1270 (9th Cir. 1980) (per curiam). The waiters make the same error of which they accuse the district court, namely taking a quantitative approach to the question of inferring discriminatory intent from statistical evidence. Their purely statistical analysis would almost completely blur the distinction between “impact” and “intent,” and thus eliminate the legal difference between disparate impact and disparate treatment lawsuits. The latter would be transformed almost exactly into a duplicate of the statistically-oriented prima facie showing allowed under Griggs v. Duke Power Co. See Teamsters, supra, 431 U.S. at 335-36 n.15, 97 S.Ct. at 1854 n.15.

This would be both improper and unwise. The question whether the facts proved are sufficient to permit a legal inference of discriminatory intent cannot properly be reduced into a mere battle of statistics. “Discriminatory impact,” as shown by statistical evidence, is a starting point, and an important starting point, to that inquiry, but is rarely sufficient of itself. Arlington Heights, supra, 429 U.S. at 252, 97 S.Ct. at 556. Whatever the impact demonstrated by a plaintiff’s statistical evidence is in fact, the legal question is whether that impact is sufficiently gross or stark that a court must infer that it was intended by the defendant. That an employer was aware of, or totally indifferent to the racially discriminatory impact of its hiring policies is not of itself sufficient to establish a prima facie case and shift the burden of explanation to the defendant. After all, discriminatory intent “implies more than intent as volition or intent as awareness of consequences.... 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.” Personnel Administrator v. Feeny, 442 U.S. 256, 279, 99 S.Ct. 2282, 2296, 60 L.Ed.2d 870 (1979) (footnotes and citation omitted). See General Building Contractors Ass’n v. Pennsylvania, supra, 102 S.Ct. at 3150.

In order to establish a prima facie case of disparate treatment based solely on statistical evidence, the plaintiff must produce statistics showing “a clear pattern, unexplainable on grounds other than race.” Arlington Heights, supra, 429 U.S. at 252, 97 S.Ct. at 556. “But such cases are rare.” Id. Absent a “stark” pattern, “impact alone is not determinative, and the [c]ourt must look to other evidence.” Id. (foot*553notes omitted). It is vitally important, therefore, to remember that “statistically significant” results are not necessarily “legally significant” results. As the district court recognized, “the probability of random occurrence of a value is not the obverse of the probability that is the result of deliberate action.” 489 F.Supp. at 311 n.38. Simply put, statistics demonstrating that chance is not the more likely explanation are not by themselves sufficient to demonstrate that race is the more likely explanation for an employer’s conduct.

Our review does not end with our conclusion that the waiters’ statistical evidence, standing alone, was insufficient to establish a prima facie case. As we explained earlier, a plaintiff may establish a prima facie case of disparate treatment, even without direct proof of the four McDonnell Douglas elements, with a combination of direct, circumstantial and statistical evidence of discrimination. Indeed, the best prima facie case utilizing statistical data, one allowing the strongest inference of intentional discrimination outside of the McDonnell Douglas framework, is that in which the plaintiff’s statistical proof is “bolstered” by other circumstantial evidence of discrimination bringing “the cold numbers convincingly to life.” Teamsters, supra, 431 U.S. at 339, 97 S.Ct. at 1856. Statistics “come in infinite variety .... [Tjheir usefulness depends on all of the surrounding facts and circumstances.” Hazelwood School Dist. v. United States, supra, 433 U.S. at 312, 97 S.Ct. at 2743, quoting Teamsters, supra, 431 U.S. at 340, 97 S.Ct. at 1856. We therefore turn to the waiters’ final argument on the merits: that their statistical data, in conjunction with the circumstantial evidence of discrimination they produced at trial, was sufficient to establish a prima facie case of disparate treatment.

The waiters’ argument revolves around five discrete types of circumstantial evidence of discrimination. First, the waiters ask us to inquire into the “historical context out of which the challenged practices arise.” As a legal matter, the waiters are correct that such considerations are relevant and should be considered by the trier of fact. See Hazelwood School Dist. v. United States, supra, 433 U.S. at 309 n.15, 97 S.Ct. at 2742 n.15; Arlington Heights, supra, 429 U.S. at 267, 97 S.Ct. at 564. However, nothing in the record supports their contention that since the turn of the century, waiter jobs in San Francisco have been continually reserved for whites. The waiters rely only on secondary sources, probably hearsay, which were never introduced into evidence during trial.

Second, the waiters point to an asserted “series of obstacles” confronting applicants at the hotels, which they characterize as “something out of a Kafka novel.” For instance, they refer to their trial testimony that security guards stationed immediately inside the hotel entrances often refused to let would-be applicants in, or only permitted them through after considerable difficulty. They also cite the testimony of appellant Whitman that he was given the “run-around” by the union and the hotels, each indicating that the other had to refer him before a job could be offered. These references are unpersuasive for several reasons. The district court was not required to, and did not, credit this testimony completely. See 489 F.Supp. at 300 (“some prospective applicants ... encountered] difficulties” in attempting to apply). Moreover, nothing in the record demonstrates that applicants at the Hilton encountered any of the asserted “obstacles”; one of the waiters’ own testimony was that he encountered “no problems” in securing a job there. Finally, such isolated instances of “suspicious circumstances,” even if proved, are of limited probative value. The record does not show any clear pattern of obstacles confronting black applicants as a class or any of the individual plaintiffs. Absent such a pattern, any inference of discrimination drawn from the isolated experiences they testified to is insignificant, and cannot appreciably bolster their weak statistical data.

The waiters, in addition, rely on three considerably more relevant types of circumstantial evidence of discrimination: the variety of “subjective employment practices” *554utilized by the hotels, the “foreseeable adverse impact” of these practices, and the sharp increases in the number of black waiters hired by both hotels, particularly the St. Francis, after the trial date was set in 1976. With respect to the subjective employment practices, the waiters point to the district court’s finding that the hotels employed “vague, unwritten” hiring criteria, including appearance, demeanor and job stability, the implementation of which was left to the discretion of the individual restaurant managers.18 See 489 F.Supp. at 300. They add that by leaving hiring decisions to the restaurant managers, both hotels engaged in “decentralized hiring,” and further that both utilized “word-of-mouth recruitment.” They insist that such subjective employment practices are per se suspect because of their capacity for masking racial bias. See Barnett v. W. T. Grant Co., 518 F.2d 543, 559 (4th Cir. 1975). With respect to the foreseeable adverse impact of these practices, the waiters contend that the hotels maintained the same hiring procedures with the knowledge that they had been challenged as racially discriminatory and had produced percentages of black waiters considerably less than the prevailing national rate. Finally, the waiters contend that the St. Francis’s increased rate of black hires after the case was set for trial, particularly during 1979 in which 13 out of 29, or nearly 45% of those hired, were blacks, suggests that the hotel’s earlier, lower rates were the product of intentional discrimination.

Insofar as the waiters may argue that any of these three types of circumstantial evidence alone compels an inference of intentional discrimination sufficient to establish a prima facie case, we disagree. For example, we have clearly held that the use of “subjective” employment criteria is not per se unlawful. Ward v. Westland Plastics, Inc., supra, 651 F.2d at 1270. On the other hand, we reject the hotels’ argument that this is sufficient to dispose of the waiters’ claims. Even if, standing alone, each of these three types of circumstantial evidence fails to establish a prima facie case, the proper question is whether in combination they are sufficient to support an inference of intentional discrimination. Indeed, we have recently stated that “subjective decision-making strengthens an inference of discrimination from general statistical data ... . ” O’Brien v. Sky Chefs, Inc., supra, 670 F.2d at 867. See also Davis v. Califano, 613 F.2d 957, 965 (D.C.Cir. 1979).

This circumstantial evidence, however, does not appreciably bolster the waiters’ weak statistical proof. The district court stated that the hotels’ “subjective” practices “may have tended to exclude blacks.” 489 F.Supp. at 300. We agree that such subjective practices may provide “ready mechanisms for discrimination,” Smith v. Union Oil Co. of California, 17 Fair Empl.Prac.Cas. 960, 991 (N.D.Cal. 1977), because they may make it “easier for those who are of a mind to discriminate.” Alexander v. Louisiana, 405 U.S. 625, 631, 92 S.Ct. 1221, 1225, 31 L.Ed.2d 536 (1972). Yet it is clear that while each of these practices could magnify whatever racially discriminatory predispositions existed within the hotels, their mere existence does not significantly aid the waiters’ effort to prove facts allowing an inference that the defendants acted with discriminatory intent. The fact that hiring criteria or practices are subjective, and are thus susceptible to discriminatory application, is only marginally relevant to the question of discriminatory intent in the absence of proof that the criteria were, in fact, applied in a discriminatory man*555ner.19 Holding otherwise would be the legal equivalent of the rule, overturned by the Supreme Court, that the foreseeable adverse impact of a neutral employment practice on a particular race is prima facie evidence of intentional discrimination. See Personnel Administrator v. Feeny, supra, 442 U.S. at 279, 99 S.Ct. at 2296. While a court should properly consider whether an employer has adhered to a particular practice with full knowledge of its foreseeable effects upon the racial balance of the work force, see Columbus Bd. of Educ. v. Penick, 443 U.S. 449, 464-65, 99 S.Ct. 2941, 2949-2950, 61 L.Ed.2d 666 (1979), and should also consider especially dramatic increases in minority hiring as circumstantial evidence of prior intentional discrimination, see Rich v. Martin Marietta Corp., supra, 522 F.2d at 346, these are simply factors to be considered in making a “sensitive inquiry into such circumstantial and direct evidence of intent as may be available.” Arlington Heights, supra, 429 U.S. at 266, 97 S.Ct. at 563. Their weight depends upon all of the circumstances involved in the case. Having made such a sensitive inquiry, we conclude that the waiters’ statistical and circumstantial evidence, properly viewed together, was markedly insufficient to establish a prima facie case of disparate treatment. Although it was error for the district court to refuse to review the waiters’ statistical and circumstantial evidence with respect to the individual claims, the error was harmless; the waiters’ evidence does not, as a matter of law, raise an inference that race was the more likely reason for their rejection.

VI

We emphasize that while the requirement of proving a prima facie case of disparate treatment is not an “onerous” burden, it is a burden nonetheless. Sanctioning too low a legal standard for inferring discriminatory motivation would encourage harassing, baseless lawsuits, force employers to justify their conduct upon only the slim reed of the highly speculative inference that an employer did not act “randomly” or utilized practices that were “susceptible” to discriminatory application, and would thrust the federal courts directly into the business of prescribing detailed, objective and mandatory hiring guidelines. This is a step we would not lightly take. See Furnco, supra, 438 U.S. at 578, 98 S.Ct. at 2950. Here, the waiters were unable to prove the four factual McDonnell Douglas criteria and avail themselves of the strong inference of discriminatory intent such proof entails. Their statistical and circumstantial evidence showed that the hotels, in particular the St. Francis, entered the decade of the 1970s with levels of black waiters considerably lower than those common in other cities and in the nation as a whole, hired black waiters through the remainder of the decade at a rate somewhat lower than that which would have reflected a work force balanced according to the racial lines of the surrounding communities, and maintained hiring procedures that could have exacerbated the imbalance. But all this simply demonstrates that the hotels did not quickly embrace the concept of affirmative action for minorities and did not go out of their way to ensure that their hiring practices would maximize the number of black and minority waiters hired. It does not demonstrate circumstances from which a court must infer that the hotels more likely than not intended to discriminate against the individual black claimants or against black applicants *556as a class. Neither Title VII nor section 1981 “impose[s] a duty [upon employers] to adopt a hiring procedure that maximizes hiring of minority employees.” Furnco, supra, 438 U.S. at 577-78, 98 S.Ct. at 2949-2950.

AFFIRMED.