MINER, Circuit Judge:

Plaintiffs-appellees, former and present members of the New York City Transit Police Department and a fraternal organization of black transit police officers, commenced an action in the United States District Court for the Eastern District of New York (Sifton, J.) pursuant to, inter alia, Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq. (1982), and 42 U.S.C. § 1981 (1982). The complaint alleged various claims of intentional employment discrimination against minority transit police officers by defendants-appellants New York City Transit Authority, New York City Transit Police Department, and the two most recent chiefs of the Department (collectively, the "Department" or "NYCTA").

Following a lengthy bench trial, Judge Sifton entered judgment for the Department on all of appellees' claims for individual relief, on all claims of discriminatory retaliation, and on all claims of unlawful discrimination in job assignments and promotions. Finding intentional discrimination in the form of excessive lenience on the part of white officers toward other white officers in the initiation of disciplinary proceedings, the district court enjoined appellants from further discrimination and directed the Department to comply with specified deadlines for the promulgation of new rules and procedures to end racial bias in the disciplinary system. The requirement that appellants promulgate new rules and procedures was stayed pending appeal.

For the reasons set forth below, we conclude that the district judge's finding of intentional discrimination was clearly erroneous. We therefore reverse and direct entry of judgment for appellants.

I. BACKGROUND

Defendant-appellant New York City Transit Police Department is charged with the prevention of crime and the maintenance of public peace in and around mass transit facilities. Officers of the Department carry firearms and possess authority equivalent to that of New York City policemen. As of June 1, 1984, there were 3,475 uniformed Department police officers, 69.2% of whom were white, 21.3% of whom were black, and 8.9% of whom were Hispanic. Of the 397 superior officers included in this total, 82.1% were white, 14.1% were black, and 2.3% were Hispanic. All hiring decisions and virtually all promotions within the Department are determined by performance scores on competitive examinations.

The Department maintains an internal disciplinary process, the administration of which is the focal point of this appeal. NYCTA policies require superior officers to issue disciplinary citations — "derelictions," in departmental parlance — to any officer observed violating the Department's procedure manual. (It appears, however, that supervisors are encouraged to forgo the issuance of citations for "hyper-technical violations.") The issuance of a dereliction triggers an elaborate internal hearing and review process, the initial stages of which require the filing of a written report with the chief of the Department and an investigation by the commanding officer of the unit to determine whether the dereliction was justified.

There is a three-tier system for the adjudication of derelictions, with the level of adjudication corresponding to the seriousness of the sanction available. At the first level, an officer may be "warned and admonished" or issued a "minor violation," unless an election is made to contest the dereliction and request a hearing. A hearing before the departmental hearing officer is provided at the second level, where the maximum penalty available is a ten-day suspension from duty. The most severe penalties are reserved for the third level and include fine, suspension, demotion or dismissal after a hearing before the transit authority trial board.

During the three-year period from January 1, 1978 through December 31, 1980, 1,368 derelictions were issued to transit police officers. Of this total, white officers received 58% of the derelictions, blacks received 35.1%, and Hispanics received 5.3%. Of the derelictions issued by minority superior officers, 40% were received by minority officers.

The individual appellees are eleven present and former minority transit police officers who have been subjected to one or more internal disciplinary proceedings. Joined by the Guardians Association, a fraternal organization of black transit police officers, appellees brought the instant action on April 30, 1980, pursuant to, inter alia, Title VII of the Civil Rights Act of 1964 and 42 U.S.C. § 1981, as a class action on behalf of all present and former black and Hispanic officers of the Department. In characterizing themselves as representatives of the class, appellees claimed to be victims of intentional discrimination in the administration of departmental disciplinary procedures that allegedly resulted in dismissals, suspensions from duty without pay, denial of promotions and preferred job assignments, and retaliation against those appellees outspoken in their criticism of perceived racial discrimination within the Department. The disciplinary proceedings forming the bases of appellees' claims were initiated for various infractions of departmental regulations, including on-the-job drinking, excessive tardiness and absenteeism, sleeping on duty, and various sexual offenses.

Appellees sought, inter alia, a declaratory judgment as to the discriminatory administration of disciplinary procedures, injunctive relief prohibiting further discrimination, and money damages to compensate for lost wages and mental anguish occasioned by the purported discrimination. Judge Sifton certified the class on June 2, 1981; a lengthy bench trial began on July 10, 1985.

In his memorandum decision and order dated December 3, 1986, the district judge was highly complimentary of virtually every aspect of the Department's disciplinary procedures and its affirmative action and minority recruitment programs. His review of the challenged NYCTA disciplinary adjudications "fail[ed] to reveal a single result [that appeared] unfair, much less the product of racial animus." Judge Sifton noted that "[t]he record in total presents a sorry picture of abuse of the Department's sick leave policy, insubordination, absenteeism, alcoholism, and family problems interfering with the performance of the job." He concluded that the sanctions "were amply justified by the witnesses['] own misconduct and that that misconduct was in no sense a pretense for discipline administered on other grounds." Accordingly, Judge Sifton dismissed all claims for individual relief, and all claims of unlawful discrimination in job assignments and discriminatory retaliation. Because no backpay could be recovered in light of the dismissal of these claims, the district court decertified the class.

Judge Sifton concluded, however, that, while "hardly overwhelming," the evidence indicated that intentional discrimination existed within the Department in the initiation of disciplinary proceedings, and that this discrimination took the form of excessive lenience on the part of white superior officers toward other white officers in the issuance of derelictions. Concluding that this perceived lenience violated Title VII and section 1981, the district court enjoined the Department from further discrimination against minority officers in the initiation of disciplinary proceedings. The court directed the NYCTA to promulgate new rules within 45 days addressing racial favoritism in the issuance of derelictions. It also ordered the Department to develop within 60 days a system to monitor the racial distribution of derelictions. Under the terms of the injunction, should quarterly reports reveal a disparity in the racial distribution of derelictions greater than that prescribed by the district court, the Department's EEO officer would investigate the causes thereof and, within 90 days, submit a report to the chief of the Department as to his findings and recommendations. The injunction also directs the NYCTA to take all reasonable steps to implement the EEO officer's recommendations.

On January 30, 1987, the district judge issued the injunction and granted appellants' application for a stay pending appeal to this court. The Department challenges the district court's finding of discrimination in the initiation of disciplinary proceedings and appeals from the judgment granting injunctive relief. Inasmuch as no cross-appeal has been taken, the Department's attack on the injunction is the sole issue before us.

II. DISCUSSION

A finding of discriminatory intent is a factual determination, e.g., United States Postal Serv. Bd. of Governors v. Aikens, 460 U.S. 711, 716-17, 103 S.Ct. 1478, 1482-83, 75 L.Ed.2d 403 (1983); Pullman-Standard v. Swint, 456 U.S. 273, 288, 102 S.Ct. 1781, 1790, 72 L.Ed.2d 66 (1982), that may be set aside only if clearly erroneous, Anderson v. Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985). Where the district court's finding is "plausible in light of the record viewed in its entirety," it may not be overturned even though the reviewing court "would have weighed the evidence differently." Id. at 574, 105 S.Ct. at 1512. A finding may be characterized as clearly erroneous when, upon examination of the entire record, a reviewing court "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, 542, 92 L.Ed. 746 (1948), but "[w]here there are two permissible views of the evidence, the factfinder's choice between them cannot be clearly erroneous," Anderson, 470 U.S. at 574, 105 S.Ct. at 1512 (citing United States v. Yellow Cab Co., 338 U.S. 338, 342, 70 S.Ct. 177, 179, 94 L.Ed. 150 (1949)). We have no difficulty in overturning the district court's findings as clearly erroneous for, as discussed below, they are entirely without support in the record.

Although Judge Sifton failed to identify the legal standard under which injunctive relief was ordered, in light of appellees' allegations, and the district court's finding, of intentional discrimination, we will review this appeal as a Title VII discriminatory treatment case, rather than as a disparate impact claim. The central distinction between these two branches of Title VII analysis is that proof of a discriminatory motive is essential in a discriminatory treatment claim, International Bhd. of Teamsters v. United States, 431 U.S. 324, 335 n. 15, 97 S.Ct. 1843, 1854-55 n. 15, 52 L.Ed.2d 396 (1977); Zahorik v. Cornell Univ., 729 F.2d 85, 91 (2d Cir. 1984), while intentional discrimination is not a prerequisite to a claim of disparate impact, Griggs v. Duke Power Co., 401 U.S. 424, 431-32, 91 S.Ct. 849, 853-54, 28 L.Ed.2d 158 (1971); Grant v. Bethlehem Steel Corp., 635 F.2d 1007, 1014 (2d Cir. 1980), cert. denied, 452 U.S. 940, 101 S.Ct. 3083, 69 L.Ed.2d 954 (1981). A claim of discriminatory treatment is established "by proof that plaintiffs were treated less favorably than others solely because of their race, color, religion, sex or national origin." Zahorik, 729 F.2d at 91.

We evaluate a discriminatory treatment claim under the three-part test enunciated in McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). Initially, plaintiffs must demonstrate a prima facie case of discrimination by a preponderance of the evidence, id. at 802, 93 S.Ct. at 1824, which creates a rebuttable presumption of unlawful discrimination, Texas Dep't of Community Affairs v. Burdine, 450 U.S. 248, 254 n. 7, 101 S.Ct. 1089, 1094 n. 7, 67 L.Ed.2d 207 (1981). The second step of the discriminatory treatment analysis requires the defendant to rebut the presumption by "articulat[ing] some legitimate, nondiscriminatory reason" for the purportedly discriminatory acts. McDonnell Douglas, 411 U.S. at 802, 93 S.Ct. at 1824. The final step of the analysis requires plaintiffs to demonstrate that the reason offered by the defendant is merely pretextual. Id. at 804, 93 S.Ct. at 1825.

In reviewing plaintiffs' prima facie showing of discriminatory treatment, the central inquiry is whether plaintiffs have carried "the initial burden of offering evidence adequate to create an inference that [defendant's challenged acts were] based on a discriminatory criterion." Teamsters, 431 U.S. at 358, 97 S.Ct. at 1866. Plaintiffs' burden in establishing a prima facie case "is not onerous," but the ultimate burden of persuasion on the issue of intentional discrimination "remains at all times with the plaintiff." Burdine, 450 U.S. at 253, 101 S.Ct. at 1093. While we are not unmindful of the Supreme Court's admonition against undue preoccupation with whether a prima facie case has been established, see Aikens, 460 U.S. at 715, 103 S.Ct. at 1481-82, our review of the record compels our conclusion that plaintiffs failed entirely to create a rebuttable presumption of purposeful discrimination.

The district court found that excessive lenience by white superior officers toward other white officers in the initiation of disciplinary proceedings constituted intentional discrimination. It based its conclusion on three factors: (1) the limited statistical evidence; (2) the Department's adjudication of a particular disciplinary matter in 1977 involving a white officer; and (3) the "sincere impressions" of appellees' witnesses that minority officers were treated unfairly.

Regarding the first factor, the district court found that "[t]he only statistical evidence of value introduced at trial was presented by defendants." As a result, to the extent predicated upon statistical evidence, the court's finding of discrimination was based solely on a compilation, prepared by defendants' expert, of the number of white and minority officers who received derelictions in the years 1977 and 1979. Dismissing the minor disparity reflected in the data for 1977 as insignificant, the court focused solely on the statistics for 1979, which indicated that 37.1% of the officers receiving derelictions were black or Hispanic, as opposed to a statistically "expected" rate of 26.6%. The court concluded that the discrepancy between actual and expected rates for that year created "the clear inference that the manner in which blacks and hispanics were treated is not to be explained simply by accident."

While it is "unmistakably clear that `[s]tatistical analyses have served and will continue to serve an important role' in cases in which the existence of discrimination is a disputed issue," Teamsters, 431 U.S. at 339, 97 S.Ct. at 1856 (quoting Mayor of Philadelphia v. Educational Equality League, 415 U.S. 605, 620, 94 S.Ct. 1323, 1333, 39 L.Ed.2d 630 (1974)); see also Hazelwood School Dist. v. United States, 433 U.S. 299, 308 n. 14, 97 S.Ct. 2736, 2742 n. 14, 53 L.Ed.2d 768 (1977) (gross statistical disparities alone may establish prima facie proof of discrimination), we are constrained to point out, as counsel for appellees conceded at oral argument, that the district court misapprehended the information conveyed by the statistical evidence. It is clear from the court's discussion that it construed the 1979 data as setting forth the number of derelictions issued when, in fact, the data set forth the number of officers receiving derelictions. The implications of such a misreading are obvious: Because the statistics do not reflect those officers who may have received more than one dereliction that year, the racial distribution of the actual number of disciplinary proceedings initiated is incapable of discernment. Given the importance placed by the district court on the issuance of derelictions, the court's fundamental misreading of the data is fatal to its finding of intentional discrimination. We also hasten to point out that the 1979 data relied upon by the court does not identify the race of the superior officers who issued the derelictions. Therefore, the court's finding of excessive lenience on the part of white officers to other white officers is wholly unsupported by these statistics.

Moreover, even when properly construed, these statistics are at best of marginal significance. The usefulness of such statistical evidence lies in the "standard deviations" revealed by the data. We previously have recognized the importance of the standard deviation as "a measure of how much the particular results of that data differ from the expected results." Kirkland v. New York Dep't of Correctional Servs., 711 F.2d 1117, 1131 n. 17 (2d Cir. 1983) (quoting Guardians Ass'n v. Civil Serv. Comm'n, 630 F.2d 79, 86 n. 4 (2d Cir. 1980), cert. denied, 452 U.S. 940, 101 S.Ct. 3083, 69 L.Ed.2d 954 (1981)), cert. denied, 465 U.S. 1005, 104 S.Ct. 997, 79 L.Ed.2d 230 (1984). In practical effect, the greater the number of standard deviations, the less likely it is that the statistical disparity is the result of chance. See id.; cf. Alston v. Manson, 791 F.2d 255, 257-58 (2d Cir. 1986) (discussing, in jury selection context, usefulness of statistical analysis in determining likelihood of particular racial distribution resulting solely from chance), cert. denied, ___ U.S. ___, 107 S.Ct. 1285, 94 L.Ed.2d 143 (1987).

Defendants' expert, in testifying as to the proper interpretation of the 1979 statistics he prepared, stated that application of an "aggregation technique" was required to make the raw data meaningful. When aggregated, the standard deviation is 1.29; in the absence of aggregation, the standard deviation is 4.02. In light of its emphasis on the 4.02 standard deviation figure, it is obvious that the district court completely disregarded the testimony of the expert who prepared the data as to its proper interpretation. Correctly analyzed, the standard deviation is well below the level deemed significant by the Supreme Court. See Hazelwood School Dist., 433 U.S. at 308 n. 14, 97 S.Ct. at 2742 n. 14 (as a "general rule," a difference between the expected value and the actual figure greater than two or three standard deviations renders "suspect" a hypothesis of racially neutral criteria) (citing Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977)). Because this data formed the exclusive statistical basis for the district court's conclusion, and because the court clearly misapprehended the nature of the data and disregarded testimony as to its proper interpretation, we do not hesitate to characterize its finding of intentional discrimination as clearly erroneous.

Moreover, we cannot overlook the fact that the district court specifically credited certain expert testimony that virtually precludes a finding of excessive lenience by white superior officers toward other white officers. Defendants' expert testified that during the three-year period from 1978 through 1980, minority officers received 40% of the derelictions issued by minority superior officers. He also testified that when the derelictions issued by non-minority officers for the same period are included in the total, minority officers received 40.4% of the derelictions issued. In crediting this testimony, described as a "puzzling aspect of the proof," the district court concluded that "[i]t thus appears that white officers are not issuing derelictions to white officers with the same regularity that both white and black officers are issuing them to black officers." What appears to us from this testimony, rather, is that white and minority superior officers are not issuing derelictions to white officers with the same frequency that white and minority superior officers are issuing them to black officers. We fail to discern how any discriminatory lenience on the part of white officers toward other white officers can be gleaned from this testimony.

We note also that, in light of its reliance on statistical evidence, the district court failed to appreciate the significance of its finding that decisions to initiate disciplinary proceedings are highly decentralized. Where challenged employment practices are decentralized and uncoordinated — as are the independent, on-the-spot decisions by individual superior officers to issue derelictions — statistics, though relevant, "may be less significant in demonstrating bias than where a single office makes all employment decisions." Coser v. Moore, 739 F.2d 746, 750 (2d Cir. 1984). See also Zahorik, 729 F.2d at 92-93, 95 (discussing limited value of statistical evidence in proving discrimination in decentralized faculty tenure decisions).

The other two factors forming the basis of the district court's finding of intentional discrimination were the manner in which the Department resolved a disciplinary matter involving a white officer in January 1977 and the "sincere impression of witness after witness" that the "disciplinary system deals unequally with the races." The district court apparently construed these factors as anecdotal evidence of discrimination. We have acknowledged the importance of anecdotal evidence in the context of employment discrimination cases to supplement or to rebut statistical evidence. See, e.g., Rossini v. Ogilvy Mather, Inc., 798 F.2d 590, 604 (2d Cir. 1986) (in addition to statistical presentations, "district court may properly consider the quality of any anecdotal evidence or the absence of such evidence"); Coser, 739 F.2d at 752 ("failure to locate and identify a meaningful number of concrete examples of discrimination" constitutes major weakness in employment discrimination case). However, given the complete absence of creditable statistical evidence, we find these two factors inadequate to support a finding of intentional discrimination.

The 1977 incident involved a racially derogatory remark made by a white officer during a roll call. After two separate departmental investigations, the officer received a warning but he was not suspended, as the district court apparently thought was warranted. We conclude that this single incident, occurring some six months prior to the relevant time period described in the class certification order, is insufficient to support a finding of intentionally discriminatory lenience toward white officers. See Ste. Marie v. Eastern R.R. Ass'n, 650 F.2d 395, 405-07 (2d Cir. 1981) (where relevant statistical evidence lacking, seven individual incidents of discrimination insufficient to demonstrate pattern or practice of discrimination).

We also conclude that the "sincere impressions" of plaintiffs' witnesses constitute an equally dubious basis for the district court's finding of discrimination. Counsel for appellees conceded at oral argument that most of the "impressions" credited by the district court were those of individual appellees who, presumably with equal sincerity, asserted individual claims on their own behalf, all of which the district court dismissed as meritless.

Our holding that the district court's finding of discrimination is clearly erroneous is bolstered also by the existence of affirmative action and minority recruitment programs within the Department. Although the district court described these programs as "impressive," the court failed to attribute to them their proper significance. See Coser, 739 F.2d at 751 (existence of comprehensive affirmative action program "directly controverts a claim that discrimination is the `standard operating procedure'") (quoting Teamsters, 431 U.S. at 336, 97 S.Ct. at 1854-55).

III. CONCLUSION

In light of the foregoing, we hold that the district court's finding of intentional discrimination in the initiation of disciplinary proceedings is wholly without support in the record. Accordingly, we reverse the judgment of the district court and remand for entry of judgment for appellants.