
433 U.S. 299 (1977)
HAZELWOOD SCHOOL DISTRICT ET AL.
v.
UNITED STATES
No. 76-255.
Supreme Court of the United States.
Argued April 27, 1977.
Decided June 27, 1977.
CERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE EIGHTH CIRCUIT.
*300 William H. Allen argued the cause for petitioners. With him on the briefs were Coleman S. Hicks and Don O. Russell.
Deputy Solicitor General Wallace argued the cause for the United States. With him on the brief were Solicitor General McCree, Assistant Attorney General Days, Thomas S. Martin, Brian K. Landsberg, Walter W. Barnett, and Cynthia L. Attwood.[*]
*301 MR. JUSTICE STEWART delivered the opinion of the Court.
The petitioner Hazelwood School District covers 78 square miles in the northern part of St. Louis County, Mo. In 1973 the Attorney General brought this lawsuit against Hazelwood and various of its officials, alleging that they were engaged in a "pattern or practice" of employment discrimination in violation of Title VII of the Civil Rights Act of 1964, 78 Stat. 253, as amended, 42 U. S. C. § 2000e et seq. (1970 ed. and Supp. V).[1] The complaint asked for an injunction requiring Hazelwood to cease its discriminatory practices, to take affirmative steps to obtain qualified Negro faculty members, and to offer employment and give backpay to victims of past illegal discrimination.
Hazelwood was formed from 13 rural school districts between 1949 and 1951 by a process of annexation. By the 1967-1968 school year, 17,550 students were enrolled in the district, of whom only 59 were Negro; the number of Negro pupils increased to 576 of 25,166 in 1972-1973, a total of just over 2%.
From the beginning, Hazelwood followed relatively unstructured procedures in hiring its teachers. Every person requesting an application for a teaching position was sent one, and completed applications were submitted to a central personnel *302 office, where they were kept on file.[2] During the early 1960's the personnel office notified all applicants whenever a teaching position became available, but as the number of applications on file increased in the late 1960's and early 1970's, this practice was no longer considered feasible. The personnel office thus began the practice of selecting anywhere from 3 to 10 applicants for interviews at the school where the vacancy existed. The personnel office did not substantively screen the applicants in determining which of them to send for interviews, other than to ascertain that each applicant, if selected, would be eligible for state certification by the time he began the job. Generally, those who had most recently submitted applications were most likely to be chosen for interviews.[3]
Interviews were conducted by a department chairman, program coordinator, or the principal at the school where the teaching vacancy existed. Although those conducting the interviews did fill out forms rating the applicants in a number of respects, it is undisputed that each school principal possessed virtually unlimited discretion in hiring teachers for his school. The only general guidance given to the principals was to hire the "most competent" person available, and such intangibles as "personality, disposition, appearance, poise, voice, articulation, and ability to deal with people" counted heavily. The principal's choice was routinely honored by Hazelwood's Superintendent and the Board of Education.
In the early 1960's Hazelwood found it necessary to recruit new teachers, and for that purpose members of its staff visited a number of colleges and universities in Missouri and bordering States. All the institutions visited were predominantly white, and Hazelwood did not seriously recruit at either of the *303 two predominantly Negro four-year colleges in Missouri.[4] As a buyer's market began to develop for public school teachers, Hazelwood curtailed its recruiting efforts. For the 1971-1972 school year, 3,127 persons applied for only 234 teaching vacancies; for the 1972-1973 school year, there were 2,373 applications for 282 vacancies. A number of the applicants who were not hired were Negroes.[5]
Hazelwood hired its first Negro teacher in 1969. The number of Negro faculty members gradually increased in successive years: 6 of 957 in the 1970 school year; 16 of 1,107 by the end of the 1972 school year; 22 of 1,231 in the 1973 school year. By comparison, according to 1970 census figures, of more than 19,000 teachers employed in that year in the St. Louis area, 15.4% were Negro. That percentage figure included the St. Louis City School District, which in recent years has followed a policy of attempting to maintain a 50% Negro teaching staff. Apart from that school district, 5.7% of the teachers in the county were Negro in 1970.
Drawing upon these historic facts, the Government mounted its "pattern or practice" attack in the District Court upon four different fronts. It adduced evidence of (1) a history of alleged racially discriminatory practices, (2) statistical disparities in hiring, (3) the standardless and largely subjective hiring procedures, and (4) specific instances of alleged discrimination against 55 unsuccessful Negro applicants for teaching jobs. Hazelwood offered virtually no additional evidence in response, relying instead on evidence introduced by the Government, perceived deficiencies in the Government's case, and its own officially promulgated policy "to hire all *304 teachers on the basis of training, preparation and recommendations, regardless of race, color or creed."[6]
The District Court ruled that the Government had failed to establish a pattern or practice of discrimination. The court was unpersuaded by the alleged history of discrimination, noting that no dual school system had ever existed in Hazelwood. The statistics showing that relatively small numbers of Negroes were employed as teachers were found nonprobative, on the ground that the percentage of Negro pupils in Hazelwood was similarly small. The court found nothing illegal or suspect in the teacher-hiring procedures that Hazelwood had followed. Finally, the court reviewed the evidence in the 55 cases of alleged individual discrimination, and after stating that the burden of proving intentional discrimination was on the Government, it found that this burden had not been sustained in a single instance. Hence, the court entered judgment for the defendants. 392 F. Supp. 1276 (ED Mo.).
The Court of Appeals for the Eighth Circuit reversed. 534 F. 2d 805. After suggesting that the District Court had assigned inadequate weight to evidence of discriminatory conduct on the part of Hazelwood before the effective date of Title VII,[7] the Court of Appeals rejected the trial court's *305 analysis of the statistical data as resting on an irrelevant comparison of Negro teachers to Negro pupils in Hazelwood. The proper comparison, in the appellate court's view, was one between Negro teachers in Hazelwood and Negro teachers in the relevant labor market area. Selecting St. Louis County and St. Louis City as the relevant area,[8] the Court of Appeals compared the 1970 census figures, showing that 15.4% of teachers in that area were Negro, to the racial composition of Hazelwood's teaching staff. In the 1972-1973 and 1973-1974 school years, only 1.4% and 1.8%, respectively, of Hazelwood's teachers were Negroes. This statistical disparity, particularly when viewed against the background of the teacher-hiring procedures that Hazelwood had followed, was held to constitute a prima facie case of a pattern or practice of racial discrimination.
In addition, the Court of Appeals reasoned that the trial court had erred in failing to measure the 55 instances in which Negro applicants were denied jobs against the four-part standard for establishing a prima facie case of individual discrimination set out in this Court's opinion in McDonnell Douglas Corp. v. Green, 411 U. S. 792, 802.[9] Applying that *306 standard, the appellate court found 16 cases of individual discrimination,[10] which "buttressed" the statistical proof. Because Hazelwood had not rebutted the Government's prima facie case of a pattern or practice of racial discrimination, the Court of Appeals directed judgment for the Government and prescribed the remedial order to be entered.[11]
We granted certiorari, 429 U. S. 1037, to consider a substantial question affecting the enforcement of a pervasive federal law.
The petitioners primarily attack the judgment of the Court of Appeals for its reliance on "undifferentiated work force statistics to find an unrebutted prima facie case of employment discrimination."[12] The question they raise, in short, is *307 whether a basic component in the Court of Appeals' finding of a pattern or practice of discriminationthe comparatively small percentage of Negro employees on Hazelwood's teaching staffwas lacking in probative force.
This Court's recent consideration in Teamsters v. United States, 431 U. S. 324, of the role of statistics in pattern-or-practice suits under Title VII provides substantial guidance in evaluating the arguments advanced by the petitioners. In that case we stated that it is the Government's burden to "establish by a preponderance of the evidence that racial discrimination was the [employer's] standard operating procedurethe regular rather than the unusual practice." Id., at 336. We also noted that statistics can be an important source of proof in employment discrimination cases, since
"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 even though § 703 (j) makes clear that Title VII imposes no requirement that a work force mirror the general population." Id., at 340 n. 20.
See also Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 266; Washington v. Davis, 426 U. S. 229, 241-242. Where gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof *308 of a pattern or practice of discrimination. Teamsters, supra, at 339.
There can be no doubt, in light of the Teamsters case, that the District Court's comparison of Hazelwood's teacher work force to its student population fundamentally misconceived the role of statistics in employment discrimination cases. The Court of Appeals was correct in the view that a proper comparison was 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.[13] See Teamsters, supra, at 337-338, and n. 17. The percentage of Negroes on Hazelwood's teaching staff in 1972-1973 was 1.4%, and in 1973-1974 it was 1.8%. By contrast, the percentage of qualified Negro teachers in the area was, according to the 1970 census, at least 5.7%.[14] Although these differences *309 were on their face substantial, the Court of Appeals erred in substituting its judgment for that of the District Court and holding that the Government had conclusively proved its "pattern or practice" lawsuit.
The Court of Appeals totally disregarded the possibility that this prima facie statistical proof in the record might at the trial court level be rebutted by statistics dealing with Hazelwood's hiring after it became subject to Title VII. Racial discrimination by public employers was not made illegal under Title VII until March 24, 1972. A public employer who from that date forward made all its employment decisions in a wholly nondiscriminatory way would not violate Title VII even if it had formerly maintained an all-white work force by purposefully excluding Negroes.[15] For this reason, *310 the Court cautioned in the Teamsters opinion that once a prima facie case has been established by statistical work-force disparities, the employer must be given an opportunity to show that "the claimed discriminatory pattern is a product of pre-Act hiring rather than unlawful post-Act discrimination." 431 U. S., at 360.
The record in this case showed that for the 1972-1973 school year, Hazelwood hired 282 new teachers, 10 of whom (3:5%) were Negroes; for the following school year it hired 123 new teachers, 5 of whom (4.1%) were Negroes. Over the two-year period, Negroes constituted a total of 15 of the 405 new teachers hired (3.7%). Although the Court of Appeals briefly mentioned these data in reciting the facts, it wholly ignored them in discussing whether the Government had shown a pattern or practice of discrimination. And it gave no consideration at all to the possibility that post-Act data as to the number of Negroes hired compared to the total number of Negro applicants might tell a totally different story.[16]
What the hiring figures prove obviously depends upon the figures to which they are compared. The Court of Appeals accepted the Government's argument that the relevant comparison was to the labor market area of St. Louis County and the city of St. Louis, in which, according to the 1970 census, 15.4% of all teachers were Negro. The propriety of that comparison was vigorously disputed by the petitioners, who urged that because the city of St. Louis has made special attempts to maintain a 50% Negro teaching staff, inclusion of *311 that school district in the relevant market area distorts the comparison. Were that argument accepted, the percentage of Negro teachers in the relevant labor market area (St. Louis County alone) as shown in the 1970 census would be 5.7% rather than 15.4%.
The difference between these figures may well be important; the disparity between 3.7% (the percentage of Negro teachers hired by Hazelwood in 1972-1973 and 1973-1974) and 5.7% may be sufficiently small to weaken the Government's other proof, while the disparity between 3.7% and 15.4% may be sufficiently large to reinforce it.[17] In determining *312 which of the two figuresor, very possibly, what intermediate figureprovides the most accurate basis for comparison to the hiring figures at Hazelwood, it will be necessary to evaluate such considerations as (i) whether the racially based hiring policies of the St. Louis City School District were in effect as far back as 1970, the year in which the census figures were taken;[18] (ii) to what extent those policies have changed the racial composition of that district's teaching staff from what it would otherwise have been; (iii) to what extent St. Louis' recruitment policies have diverted to the city, teachers who might otherwise have applied to Hazelwood;[19] (iv) to what extent Negro teachers employed by the city would prefer employment in other districts such as Hazelwood; and (v) what the experience in other school districts in St. Louis County indicates about the validity of excluding the City School District from the relevant labor market.
It is thus clear that a determination of the appropriate comparative figures in this case will depend upon further evaluation by the trial court. As this Court admonished in Teamsters: "[S]tatistics . . . come in infinite variety . . . . [T]heir usefulness depends on all of the surrounding facts and circumstances." 431 U. S., at 340. Only the trial court is in a position to make the appropriate determination after further findings. And only after such a determination is made can a foundation be established for deciding whether or not Hazelwood engaged in a pattern or practice of racial *313 discrimination in its employment practices in violation of the law.[20]
We hold, therefore, that the Court of Appeals erred in disregarding the post-Act hiring statistics in the record, and that it should have remanded the case to the District Court for further findings as to the relevant labor market area and for an ultimate determination of whether Hazelwood engaged in a pattern or practice of employment discrimination after March 24, 1972.[21] Accordingly, the judgment is vacated, and the case is remanded to the District Court for further proceedings consistent with this opinion.
It is so ordered.
[For concurring opinion of MR. JUSTICE WHITE, see post, p. 347.]
MR. JUSTICE BRENNAN, concurring.
I join the Court's opinion. Similarly to our decision in Dayton Board of Education v. Brinkman, post, p. 406, today's opinion revolves around the relative factfinding roles of district courts and courts of appeals. It should be plain, however, that the liberal substantive standards for establishing a Title VII violation, including the usefulness of statistical proof, are reconfirmed.
In the present case, the District Court had adopted a wholly inappropriate legal standard of discrimination, and therefore *314 did not evaluate the factual record before it in a meaningful way. This remand in effect orders it to do so. It is my understanding, as apparently it is MR. JUSTICE STEVENS', post, at 318 n. 5, that the statistical inquiry mentioned by the Court, ante, at 311 n. 17, and accompanying text, can be of no help to the Hazelwood School Board in rebutting the Government's evidence of discrimination. Indeed, even if the relative comparison market is found to be 5.7% rather than 15.4% black, the applicable statistical analysis at most will not serve to bolster the Government's case. This obviously is of no aid to Hazelwood in meeting its burden of proof. Nonetheless I think that the remand directed by the Court is appropriate and will allow the parties to address these figures and calculations with greater care and precision. I also agree that given the misapplication of governing legal principles by the District Court, Hazelwood reasonably should be given the opportunity to come forward with more focused and specific applicant-flow data in the hope of answering the Government's prima facie case. If, as presently seems likely, reliable applicant data are found to be lacking, the conclusion reached by my Brother STEVENS will inevitably be forthcoming.
MR. JUSTICE STEVENS, dissenting.
The basic framework in a pattern-or-practice suit brought by the Government under Title VII of the Civil Rights Act of 1964 is the same as that in any other lawsuit. The plaintiff has the burden of proving a prima facie case; if he does so, the burden of rebutting that case shifts to the defendant.[1] In this *315 case, since neither party complains that any relevant evidence was excluded, our task is to decide (1) whether the Government's evidence established a prima facie case; and (2), if so, whether the remaining evidence is sufficient to carry Hazelwood's burden of rebutting that prima facie case.

I
The first question is clearly answered by the Government's statistical evidence, its historical evidence, and its evidence relating to specific acts of discrimination.
One-third of the teachers hired by Hazelwood resided in the city of St. Louis at the time of their initial employment. As Mr. Justice Clark explained in his opinion for the Court of Appeals, it was therefore appropriate to treat the city, as well as the county, as part of the relevant labor market.[2]*316 In that market, 15% of the teachers were black. In the Hazelwood District at the time of trial less than 2% of the teachers were black. An even more telling statistic is that after Title VII became applicable to it, only 3.7% of the new teachers hired by Hazelwood were black. Proof of these gross disparities was in itself sufficient to make out a prima facie case of discrimination. See Teamsters v. United States, 431 U. S. 324, 339; Castaneda v. Partida, 430 U. S. 482, 494-498.
As a matter of history, Hazelwood employed no black teachers until 1969. Both before and after the 1972 amendment making the statute applicable to public school districts, Hazelwood used a standardless and largely subjective hiring procedure. Since "relevant aspects of the decisionmaking process had undergone little change," it is proper to infer that the pre-Act policy of preferring white teachers continued to influence Hazelwood's hiring practices.[3]
The inference of discrimination was corroborated by post-Act evidence that Hazelwood had refused to hire 16 qualified black applicants for racial reasons. Taking the Government's evidence as a whole, there can be no doubt about the sufficiency of its prima facie case.


*317 II
Hazelwood "offered virtually no additional evidence in response," ante, at 303. It challenges the Government's statistical analysis by claiming that the city of St. Louis should be excluded from the relevant market and pointing out that only 5.7% of the teachers in the county (excluding the city) were black. It further argues that the city's policy of trying to maintain a 50% black teaching staff diverted teachers from the county to the city. There are two separate reasons why these arguments are insufficient: they are not supported by the evidence; even if true, they do not overcome the Government's case.
The petitioners offered no evidence concerning wage differentials, commuting problems, or the relative advantages of teaching in an inner-city school as opposed to a suburban school. Without any such evidence in the record, it is difficult to understand why the simple fact that the city was the source of a third of Hazelwood's faculty should not be sufficient to demonstrate that it is a part of the relevant market. The city's policy of attempting to maintain a 50/50 ratio clearly does not undermine that conclusion, particularly when the record reveals no shortage of qualified black applicants in either Hazelwood or other suburban school districts.[4] Surely not all of the 2,000 black teachers employed by the city were unavailable for employment in Hazelwood at the time of their initial hire.
But even if it were proper to exclude the city of St. Louis from the market, the statistical evidence would still tend to prove discrimination. With the city excluded, 5.7% of the teachers in the remaining market were black. On the basis of a random selection, one would therefore expect 5.7% of *318 the 405 teachers hired by Hazelwood in the 1972-1973 and 1973-1974 school years to have been black. But instead of 23 black teachers, Hazelwood hired only 15, less than two-thirds of the expected number. Without the benefit of expert testimony, I would hesitate to infer that the disparity between 23 and 15 is great enough, in itself, to prove discrimination.[5] It is perfectly clear, however, that whatever probative force this disparity has, it tends to prove discrimination and does absolutely nothing in the way of carrying Hazelwood's burden of overcoming the Government's prima facie case.
Absolute precision in the analysis of market data is too much to expect. We may fairly assume that a nondiscriminatory selection process would have resulted in the hiring of somewhere between the 15% suggested by the Government and the 5.7% suggested by petitioners, or perhaps 30 or 40 black teachers, instead of the 15 actually hired.[6] On that assumption, the Court of Appeals' determination that there were 16 individual cases of discriminatory refusal to hire black applicants in the post-1972 period seems remarkably accurate.
In sum, the Government is entitled to prevail on the present record. It proved a prima facie case, which Hazelwood failed to rebut. Why, then, should we burden a busy federal court with another trial? Hazelwood had an opportunity to offer evidence to dispute the 16 examples of racially motivated refusals to hire; but as the Court notes, the Court of Appeals has already "held that none of the 16 prima facie cases of *319 individual discrimination had been rebutted by the petitioners. See 534 F. 2d 805, 814 (CA8)." Ante, at 306 n. 10. Hazelwood also had an opportunity to offer any evidence it could muster to show a change in hiring practices or to contradict the fair inference to be drawn from the statistical evidence. Instead, it "offered virtually no additional evidence in response," ante, at 303.
Perhaps "a totally different story" might be told by other statistical evidence that was never presented, ante, at 310. No lawsuit has ever been tried in which the losing party could not have pointed to a similar possibility.[7] It is always possible to imagine more evidence which could have been offered, but at some point litigation must come to an end.[8]
*320 Rather than depart from well-established rules of procedure, I would affirm the judgment of the Court of Appeals.[9] Since that judgment reflected a correct appraisal of the record, I see no reason to prolong this litigation with a remand neither side requested.[10]
NOTES
[*]  Briefs of amici curiae urging affirmance were filed by Robert Allen Sedler and Joel M. Gora for the American Civil Liberties Union; by Robert A. Murphy, Richard S. Kohn, and Richard T. Seymour for the Lawyers' Committee for Civil Rights Under Law; by Jack Greenberg, James C. Gray, Jr., Patrick O. Patterson, Eric Schnapper, and Louis Gilden for the NAACP Legal Defense and Educational Fund, Inc.; and by Stephen J. Pollak, Richard M. Sharp, and David Rubin for the National Education Assn.
[1]  Under 42 U. S. C. § 2000e-6 (a), the Attorney General was authorized to bring a civil action "[w]henever [he] has reasonable cause to believe that any person or group of persons is engaged in a pattern or practice of resistance to the full enjoyment of any of the rights secured by [Title VII], and that the pattern or practice is of such a nature and is intended to deny the full exercise of [those rights]." The 1972 amendments to Title VII directed that this function be transferred as of March 24, 1974, to the Equal Employment Opportunity Commission, at least with respect to private employers. § 2000e-6 (c) (1970 ed., Supp. V); see also § 2000e-5 (f) (1) (1970 ed., Supp. V). The present lawsuit was instituted more than seven months before that transfer.
[2]  Before 1954 Hazelwood's application forms required designation of race, and those forms were in use as late as the 1962-1963 school year.
[3]  Applicants with student or substitute teaching experience at Hazelwood were given preference if their performance had been satisfactory.
[4]  One of those two schools was never visited even though it was located in nearby St. Louis. The second was briefly visited on one occasion, but no potential applicant was interviewed.
[5]  The parties disagree whether it is possible to determine from the present record exactly how many of the job applicants in each of the school years were Negroes.
[6]  The defendants offered only one witness, who testified to the total number of teachers who had applied and were hired for jobs in the 1971-1972 and 1972-1973 school years. They introduced several exhibits consisting of a policy manual, policy book, staff handbook, and historical summary of Hazelwood's formation and relatively brief existence.
[7]  As originally enacted, Title VII of the Civil Rights Act of 1964 applied only to private employers. The Act was expanded to include state and local governmental employers by the Equal Employment Opportunity Act of 1972, 86 Stat. 103, whose effective date was March 24, 1972. See 42 U. S. C. §§ 2000e (a), (b), (f), (h) (1970 ed., Supp. V).

The evidence of pre-Act discrimination relied upon by the Court of Appeals included the failure to hire any Negro teachers until 1969, the failure to recruit at predominantly Negro colleges in Missouri, and somewhat inconclusive evidence that Hazelwood was responsible for a 1962 Mississippi newspaper advertisement for teacher applicants that specified "white only."
[8]  The city of St. Louis is surrounded by, but not included in, St. Louis County. Mo. Ann. Stat. § 46.145 (1966).
[9]  Under McDonnell Douglas, a prima facie case of illegal employment discrimination is established by showing

"(i) that [an individual] 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." 411 U. S., at 802.
Upon proof of these four elements, "[t]he burden then must shift to the employer to articulate some legitimate, nondiscriminatory reason for the employee's rejection." Ibid.
[10]  The Court of Appeals held that none of the 16 prima facie cases of individual discrimination had been rebutted by the petitioners. See 534 F. 2d, at 814.
[11]  The District Court was directed to order that the petitioners cease from discriminating on the basis of race or color in the hiring of teachers, promulgate accurate job descriptions and hiring criteria, recruit Negro and white applicants on an equal basis, give preference in filling vacancies to the 16 discriminatorily rejected applicants, make appropriate backpay awards, and submit periodic reports to the Government on its progress in hiring qualified Negro teachers. Id., at 819-820.
[12]  In their petition for certiorari and brief on the merits, the petitioners have phrased the question as follows:

"Whether a court may disregard evidence that an employer has treated actual job applicants in a nondiscriminatory manner and rely on undifferentiated workforce statistics to find an unrebutted prima facie case of employment discrimination in violation of Title VII of the Civil Rights Act of 1964."
Their petition for certiorari and brief on the merits did raise a second question: "Whether Congress has authority under Section 5 of the Fourteenth Amendment to prohibit by Title VII of the Civil Rights Act of 1964 employment practices of an agency of a state government in the absence of proof that the agency purposefully discriminated against applicants on the basis of race." That issue, however, is not presented by the facts in this case. The Government's opening statement in the trial court explained that its evidence was designed to show that the scarcity of Negro teachers at Hazelwood "is the result of purpose" and is attributable to "deliberately continued employment policies." Thus here, as in Teamsters v. United States, 431 U. S. 324, "[t]he Government's theory of discrimination was simply that the [employer], in violation of § 703 (a) of Title VII, regularly and purposefully treated Negroes . . . less favorably than white persons." Id., at 335 (footnote omitted).
[13]  In Teamsters, 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. When special qualifications are required to fill particular jobs, comparisons to the general population (rather than to the smaller group of individuals who possess the necessary qualifications) may have little probative value. The comparative statistics introduced by the Government in the District Court, however, were properly limited to public school teachers, and therefore this is not a case like Mayor v. Educational Equality League, 415 U. S. 605, in which the racial-composition comparisons failed to take into account special qualifications for the position in question. Id., at 620-621.

Although the petitioners concede as a general matter the probative force of the comparative work-force statistics, they object to the Court of Appeals' heavy reliance on these data on the ground that applicant-flow data, showing the actual percentage of white and Negro applicants for teaching positions at Hazelwood, would be firmer proof. As we have noted, see n. 5, supra, there was no clear evidence of such statistics. We leave it to the District Court on remand to determine whether competent proof of those data can be adduced. If so, it would, of course, be very relevant. Cf. Dothard v. Rawlinson, post, at 330.
[14]  As is discussed below, the Government contends that a comparative figure of 15.4%, rather than 5.7%, is the appropriate one. See infra, at 310-312. But even assuming, arguendo, that the 5.7% figure urged by the petitioners is correct, the disparity between that figure and the percentage of Negroes on Hazelwood's teaching staff would be more than fourfold for the 1972-1973 school year, and threefold for the 1973-1974 school year. A precise method of measuring the significance of such statistical disparities was explained in Castaneda v. Partida, 430 U. S. 482, 496-497, n. 17. It involves calculation of the "standard deviation" as a measure of predicted fluctuations from the expected value of a sample. Using the 5.7% figure as the basis for calculating the expected value, the expected number of Negroes on the Hazelwood teaching staff would be roughly 63 in 1972-1973 and 70 in 1973-1974. The observed number in those years was 16 and 22, respectively. The difference between the observed and expected values was more than six standard deviations in 1972-1973 and more than five standard deviations in 1973-1974. The Court in Castaneda noted that "[a]s 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 teachers were hired without regard to race would be suspect. 430 U. S., at 497 n. 17.
[15]  This is not to say that evidence of pre-Act discrimination can never have any probative force. Proof that an employer engaged in racial discrimination prior to the effective date of Title VII might in some circumstances support the inference that such discrimination continued, particularly where relevant aspects of the decisionmaking process had undergone little change. Cf. Fed. Rule Evid. 406; Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 267; 1 J. Wigmore, Evidence § 92 (3d ed. 1940); 2 id., §§ 302-305, 371, 375. And, of course, a public employer even before the extension of Title VII in 1972 was subject to the command of the Fourteenth Amendment not to engage in purposeful racial discrimination.
[16]  See n. 13, supra, and n. 21, infra. But cf. Teamsters, 431 U. S., at 364-367.
[17]  Indeed, under the statistical methodology explained in Castaneda v. Partida, supra, at 496-497, n. 17, involving the calculation of the standard deviation as a measure of predicted fluctuations, the difference between using 15.4% and 5.7% as the areawide figure would be significant. If the 15.4% figure is taken as the basis for comparison, the expected number of Negro teachers hired by Hazelwood in 1972-1973 would be 43 (rather than the actual figure of 10) of a total of 282, a difference of more than five standard deviations; the expected number in 1973-1974 would be 19 (rather than the actual figure 5) of a total of 123, a difference of more than three standard deviations. For the two years combined, the difference between the observed number of 15 Negro teachers hired (of a total of 405) would vary from the expected number of 62 by more than six standard deviations. 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, each of these statistical comparisons would reinforce rather than rebut the Government's other proof. If, however, the 5.7% areawide figure is used, the expected number of Negro teachers hired in 1972-1973 would be roughly 16, less than two standard deviations from the observed number of 10; for 1973-1974, the expected value would be roughly seven, less than one standard deviation from the observed value of 5; and for the two years combined, the expected value of 23 would be less than two standard deviations from the observed total of 15. A more precise method of analyzing these statistics confirms the results of the standard deviation analysis. See F. Mosteller, R. Rourke, & G. Thomas, Probability with Statistical Applications 494 (2d ed. 1970).

These observations are not intended to suggest that precise calculations of statistical significance are necessary in employing statistical proof, but merely to highlight the importance of the choice of the relevant labor market area.
[18]  In 1970 Negroes consituted only 42% of the faculty in St. Louis city schools, which could indicate either that the city's policy was not yet in effect or simply that its goal had not yet been achieved.
[19]  The petitioners observe, for example, that Harris Teachers College in St. Louis, whose 1973 graduating class was 60% Negro, is operated by the city. It is the petitioners' contention that the city's public elementary and secondary schools occupy an advantageous position in the recruitment of Harris graduates.
[20]  Because the District Court focused on a comparison between the percentage of Negro teachers and Negro pupils in Hazelwood, it did not undertake an evaluation of the relevant labor market, and its casual dictum that the inclusion of the city of St. Louis "distorted" the labor market statistics was not based upon valid criteria. 392 F. Supp. 1276, 1287 (ED Mo.).
[21]  It will also be open to the District Court on remand to determine whether sufficiently reliable applicant-flow data are available to permit consideration of the petitioners' argument that those data may undercut a statistical analysis dependent upon hirings alone.
[1]  "At the initial, `liability' stage of a pattern-or-practice suit the Government is not required to offer evidence that each person for whom it will ultimately seek relief was a victim of the employer's discriminatory policy. Its burden is to establish a prima facie case that such a policy existed. The burden then shifts to the employer to defeat the prima facie showing of a pattern or practice by demonstrating that the Government's proof is either inaccurate or insignificant. An employer might show, for example, that the claimed discriminatory pattern is a product of pre-Act hiring rather than unlawful post-Act discrimination, or that during the period it is alleged to have pursued a discriminatory policy it made too few employment decisions to justify the inference that it had engaged in a regular practice of discrimination." Teamsters v. United States, 431 U. S. 324, 360.
[2]  "We accept the Government's contention that St. Louis City and County is the relevant labor market area for our consideration. The relevant labor market area is that area from which the employer draws its employees. United States v. Ironworkers Local 86, 443 F. 2d 544, 551 n. 19 (9th Cir. 1971). Of the 176 teachers hired by Hazelwood between October, 1972, and September, 1973, approximately 80 percent resided in St. Louis City and County at the time of their initial employment. Approximately one-third of the teachers hired during this period resided in the City of St. Louis and 40 percent resided in areas of St. Louis County other than the Hazelwood District." 534 F. 2d 805, 811-812, n. 7 (1976).

It is noteworthy that in the Court of Appeals, Chief Judge Gibson, in dissent, though urgingas Hazelwood had in the District Courtthat the labor market was even broader than the Government contended, id., at 821, did not question the propriety of including the city in the same market as the county, see Defendants' Brief and Memorandum in Support of Its Proposed Findings of Fact and Conclusions of Law, filed on Aug. 21, 1974, in Civ. Act. No. 73-C-553 (A) (ED Mo.), p. 24. In this Court, petitioners had abandoned any argument similar to that made below.
[3]  Proof that an employer engaged in racial discrimination prior to the effective date of the Act creates the inference that such discrimination continued "particularly where relevant aspects of the decisionmaking process [have] undergone little change. Cf. Fed. Rule Evid. 406; Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, 267; 1 J. Wigmore, Evidence § 92 (3d ed. 1940); 2 id., §§ 302-305, 371, 375. And, of course, a public employer even before the extension of Title VII in 1972 was subject to the command of the Fourteenth Amendment not to engage in purposeful racial discrimination." Ante, at 309-310, n. 15.

Since Hazelwood's hiring before 1972 was so clearly discriminatory, there is some irony in its claim that "Hazelwood continued [after 1972] to select its teachers on the same careful basis that it had relied on before in staffing its growing system." Brief for Petitioners 29-30.
[4]  "Had there been evidence obtainable to contradict and disprove the testimony offered by [the Government], it cannot be assumed that the State would have refrained from introducing it." Pierre v. Louisiana, 306 U. S. 354, 361-362.
[5]  After I had drafted this opinion, one of my law clerks advised me that, given the size of the two-year sample, there is only about a 5% likelihood that a disparity this large would be produced by a random selection from the labor pool. If his calculation (which was made using the method described in H. Blalock, Social Statistics 151-173 (1972)) is correct, it is easy to understand why Hazelwood offered no expert testimony.
[6]  Some of the other school districts in the county have a 10% ratio of blacks on their faculties. See Plaintiff's Exhibit 54 in Civ. Act. No. 73-C-553 (A) (ED Mo. 1975); Brief for United States 30 n. 30.
[7]  Since Hazelwood failed to offer any "applicant-flow data" at the trial, and since it does not now claim to have any newly discovered evidence, I am puzzled by MR. JUSTICE BRENNAN'S explanation of the justification for a remand. Indeed, after the first trial was concluded, Hazelwood emphasized the fact that no evidence of this kind had been presented; it introduced no such evidence itself. It stated:

"There is absolutely no evidence in this case that provides any basis for making a comparison between black applicants and white applicants and their treatment by the Hazelwood School District relative to hiring or not being hired for a teaching position." Defendants' Brief and Memorandum in Support of Its Proposed Findings of Fact and Conclusions of Law, supra, n. 2, at 22.
[8]  My analysis of this case is somewhat similar to MR. JUSTICE REHNQUIST's analysis in Dothard v. Rawlinson:

"If the defendants in a Title VII suit believe there to be any reason to discredit plaintiffs' statistics that does not appear on their face, the opportunity to challenge them is available to the defendants just as in any other lawsuit. They may endeavor to impeach the reliability of the statistical evidence, they may offer rebutting evidence, they may disparage in arguments or in briefs the probative weight which the plaintiffs' evidence should be accorded. Since I agree with the Court that appellants made virtually no such effort, . . . I also agree with it that the District Court cannot be said to have erred as a matter of law in finding that a prima facie case had been made out in the instant case." Post, at 338-339 (concurring opinion).
[9]  It is interesting to compare the disposition in this case with that in Castaneda v. Partida, 430 U. S. 482. In Castaneda, as in this case, "[i]nexplicably, the State introduced practically no evidence," id., at 498. But in Castaneda, unlike the present case, the Court affirmed the finding of discrimination, rather than giving the State a second chance at trying its case. (It should be noted that the Castaneda Court expressly stated that it was possible that the statistical discrepancy could have been explained by the State. Id., at 499.)
[10]  Hazelwood's brief asks only for a remand "for reconsideration of the alleged individual cases of discrimination . . . ." Brief for Petitioners 78. Hazelwood explains: "[The question raised in its petition for certiorari is] a question of law. It is a question of what sort of evidentiary showing satisfies Title VII. . . . The question is whether on the evidence of record an unrebutted prima facie case was established." Reply Brief for Petitioners 2.
