
    INMATES OF the NEBRASKA PENAL AND CORRECTIONAL COMPLEX, Appellants, v. John B. GREENHOLTZ et al., Appellees.
    No. 77-1031.
    United States Court of Appeals, Eighth Circuit.
    Submitted Sept. 16, 1977.
    Decided Dec. 2, 1977.
    Rehearing and Rehearing En Banc Denied Feb. 1, 1978.
    See also, 8 Cir., 567 F.2d 1381.
    
      Roy Haber, Native American Rights Fund (argued and on rebuttal) Boulder, Colo., Walter R. EchoHawk and Arlinda F. Locklear, Boulder, Colo., on briefs and appendix, for appellants.
    Ralph H. Gillan, Asst. Atty. Gen., Lincoln, Neb. (argued), and Paul L. Douglas, Atty. Gen., Lincoln, Neb., on brief, for appellees.
    Before VAN OOSTERHOUT and MATTHES, Senior Circuit Judges, and STEPHENSON, Circuit Judge.
   VAN OOSTERHOUT, Senior Circuit Judge.

On this appeal a subclass of plaintiffs-appellants consisting of native American and Mexican-American inmates of the Nebraska Penal and Correctional Complex renew their claim that defendant members of the Nebraska Board of Parole have denied discretionary parole to subclass members on grounds which are racially and ethnically discriminatory, in violation of the fourteenth amendment. The claim is asserted under 42 U.S.C. § 1983 and its jurisdictional counterpart 28 U.S.C. § 1343(3). On appeal only injunctive relief is sought. Our jurisdiction rests on 28 U.S.C. § 1291 and Rule 54(b), Fed.R.Civ.P.

The Nebraska Board of Parole (the Board) is comprised of five persons appointed by the Governor and confirmed by the Legislature. Neb.Rev.Stat. § 83-189 (Reissue 1976). At the time of trial it consisted of three white men, one black man and one white woman. The statutory framework in which the Board operates is set out in some detail in the district court’s opinion and may be summarized only briefly here.

The authority to grant parole to eligible Nebraska inmates prior to the time of mandatory parole or discharge is vested in the Board. Neb.Rev.Stat. § 83-192(1) (Reissue 1976). Each inmate is eligible for parole upon completion of his or her minimum term less good time and is eligible for parole prior to completion of the minimum term with the approval of the sentencing judge. Neb.Rev.Stat. § 83-1,110(1) (Reissue 1976). The precise determination of initial eligibility under this statute is somewhat complicated and is the subject of a lengthy stipulation between the parties.

Each inmate is entitled to a review of his or her parole status at least once a year. Neb.Rev.Stat. § 83-192(9). Whenever the Board considers the release of an inmate who is eligible for parole, it must grant such parole unless it is of the opinion that parole should be deferred for one or more of four enumerated reasons. Neb.Rev.Stat. § 83-1,114(1) (Reissue 1976). In its deci-sionmaking process the Board is required to consider a comprehensive list of factors bearing upon the inmate’s suitability for parole. Neb.Rev.Stat. §§ 83-1,114(2) & 83-1,115 (Reissue 1976). The Board’s decision, determined by majority vote, must be based upon the entire record before the Board. Neb.Rev.Stat. § 83-1,111(2) (Reissue 1976). It is clear from these statutes that the Board has considerable discretion in reaching a decision and that many of the factors which it considers are subjective in nature. The use of the term “discretionary” parole is accordingly an apt one.

As noted by the district court the plaintiff subclass does not contend its members are entitled to immediate release on parole. Rather it claims that defendants have denied parole to eligible subclass members on constitutionally impermissible racial and ethnic grounds. The cause was tried in segmented portions in May, July and December 1975 and February-March 1976. The district court held that plaintiffs had failed to prove a prima facie case of invidious racial and ethnic discrimination. 436 F.Supp. at 442. A review of the evidence adduced by plaintiffs is essential to our disposition of the appeal.

I.

Plaintiffs’ case at trial consisted of four primary components: (1) a statistical analysis and expert testimony in support thereof; (2) testimony elicited from Board members and from expert witnesses concerning the differences in norms and values of white and minority cultures; (3) a number of individual cases of alleged discrimination; and (4) a number of alleged racial slurs or epithets by Board members.

1. Plaintiffs’ Exhibit 18, introduced and received in the rebuttal portion of plaintiffs’ case, is a statistical analysis of data extracted from Board records of essentially all of the approximately twenty-two hundred male inmates confined in the penal complex in 1972 and 1973. It purports to demonstrate that in those years native American and Mexican-American inmates who were eligible for discretionary parole received a substantially lower percentage of discretionary paroles than did eligible white and black inmates. The exhibit contains the following breakdown, by racial and ethnic group, of the number of inmates eligible for discretionary parole and the number of discretionary paroles received:

White Black Native Mexican- Total American American .
Eligible for release by discretionary parole 590 235 59 18 902
Received discretionary parole 358 148 24 5 535
Per cent that received discretionary parole 60.7 63.0 40.7 27.8 59.3

Exhibit 18, prepared by a witness whom the district court accepted as an expert, recited that the data utilized in arriving at the above statistics were gathered in a manner generally recognized in the field of statistics and that the results were statistically accurate. The witness corroborated this recitation at trial. He concluded: “The data indicate that there is a substantial relationship between race and whether or not an eligible inmate receives a discretionary parole.”

2. Plaintiffs’ counsel expended considerable effort in probing the manner in which Board members interpret and apply the statutory criteria which bear upon an inmate’s suitability for parole. This testimony was developed largely for the purpose of demonstrating that defendants do not recognize and consider various racial and cultural characteristics which plaintiffs contend must be recognized and considered in a nondiscriminatory and otherwise constitutional evaluation process. Essentially, the methodology employed by plaintiffs’ counsel was first to elicit testimony from the defendant Board members, particularly Chairman John B. Greenholtz, and then to obtain comments from expert witnesses on the Board members’ testimony. We provide a brief summary.

The Board members uniformly denied that racial or ethnic identity played any role in the decisionmaking process and steadfastly maintained that all inmates were evaluated by the same criteria. Plaintiffs’ experts largely agreed. They testified that native American and Mexican-American inmates should be evaluated by criteria which take into account the unique characteristics of those inmates’ cultures. They also testified that certain portions of the Board members’ testimony manifested racial or ethnic bias.

Chairman Greenholtz acknowledged that, in addition to the absence of native Americans and Mexican-Americans on the Board, there were no native American or Mexican-American caseworkers, no native American district parole officers, and either one or no Mexican-American district parole officers. Greenholtz and other Board members were examined at length concerning their view of a favorable or unfavorable parole situation; this testimony was in large part correlated to the statutory criteria which circumscribe the Board’s decisionmaking. Based on this testimony a factfinder probably could conclude that Board members are unfamiliar with some racial or ethnic practices or traits which possibly could have a bearing on the decision to parole and that some of the examples chosen by Board members to illustrate a favorable parole situation are primarily attuned to values of the dominant culture.

Plaintiffs’ experts expressed a view that Board members render racially and ethnically biased decisions because of the “ethnocentric” manner in which they perceive and apply the statutory criteria. According to these witnesses, Board members judge all inmates in light of a “stereotypical white Anglo-Saxon person or life style” and fail to understand native American and Mexican-American mores and values in virtually every area of importance. The problem is in part attributable to and is exacerbated by the fact that native Americans and Mexican-Americans have little or no input into the decisionmaking.

3. Plaintiffs examined defense witness Richard Anderson concerning the Board’s failure to grant discretionary parole to several members of the subclass. Anderson is a hearing officer who conducts preliminary hearings for parole violators. See Neb.Rev. Stat. § 83-1,119 (Reissue 1976). The testimony was elicited in connection with defendants’ Exhibit 20 during the surrebuttal portion of the defendants’ ease.

Exhibit 20 indicated that native American inmate John Grant had received a flat three-year sentence on August 4, 1970, following conviction on a charge of burglary; he was not paroled until his mandatory parole date of September 4, 1972. Plaintiffs elicited testimony that a progress report on this inmate stated he had “a better than average chance of staying out” and that he “is a quiet, easy going individual, can be a good worker when he is motivated.” The evidence discloses almost nothing else. The progress report was not offered in evidence, and the trial testimony does not enlighten us as to even its date.

Exhibit 20 indicated that native American inmate William Twiss had received a one-to-four-year sentence on February 26, 1973, following conviction on a charge of uttering a forged instrument; he was first eligible for discretionary parole on October 10, 1973, and was in fact discretionarily paroled on February 21,1974. A progress report dated July 18, 1973, stated: “Twiss has maintained a good institutional record so far” and “Early parole is recommended, incarceration does not provide as much correction as close-up supervision for this man.” Again, we are informed of little else.

Exhibit 20 indicated that Mexican-American inmate Manuel Flores had received a flat two-year sentence on December 13, 1971, following conviction on a charge of carrying a concealed weapon; he was not paroled until his mandatory parole date of May 23, 1973. A progress report, date not in evidence, revealed a good institutional record and stated: “A first offender, and he should be given consideration for parole.” In this case, too, the record is of little assistance in gleaning additional details.

With respect to several other subclass members, Anderson stated he didn’t know why they had been denied discretionary parole.

4. On surrebuttal Board Chairman Greenholtz was recalled to testify on behalf of defendants. During cross-examination, solely for purposes of impeaching the witness, plaintiffs introduced three exhibits (21, 22 and 24) and questioned the witness with respect thereto. These exhibits, all transcripts of Board proceedings, contain what plaintiffs contend are racial slurs and epithets by Board members against native Americans.

The comments by Board members contained in these exhibits which plaintiffs contend manifest racial bias are: (1) one native American was asked by a Board member whether his tribe was among the “bad Sioux” or “fighting Sioux”; (2) a second native American was asked whether his tribe was “friendly”; (3) following his dismissal from the hearing, the second native American was referred to as a “friendly Indian that’s a parasite on society” and as a “Chippewa off the old block”; and (4) during a discussion of alcohol use by native Americans, one Board member commented: “They are professionally immune to snake bite.” The exhibits indicate that a number of these comments were followed by laughter.

Our attention is also drawn to two portions of testimony from plaintiffs’ case-in-chief concerning the use of alcohol by native Americans. Chairman Greenholtz acknowledged having previously made the following statement with reference to a particular inmate:

Indians are children of nature, really. They have a certain culture engrained in their psychological makeup. Most of them, I mean the Reservation type like he and he learns and he knows he’s done time before. . . . And drinking is a status symbol with those kind of guys.

Part-time Board member Marshall Tate similarly acknowledged having asked an inmate why “normally they don’t think drinking is a problem on the Reservation, even though 99 per cent of the people drink.” His trial testimony proceeded as follows:

Q. And do you have any studies or authorities to back that?
A. I believe I got those figures . . . from Mr. Wayne Tyndall, who is Secretary of the Omaha tribe.
Q. Does that strike you as somewhat outrageous?
A. I felt it was outrageous, that is the reason I asked the question.

Plaintiffs contend that these comments manifest racial bias.

H.

However difficult of application, the controlling legal principles in this case are relatively clear. The central purpose of the fourteenth amendment’s equal protection clause is of course the prevention of official conduct discriminating on the basis of race. Washington v. Davis, 426 U.S. 229, 239, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976). Yet the Supreme Court has made abundantly clear that official conduct is not always discriminatory merely because it adversely affects a greater proportion of one race than another:

Disproportionate impact is not irrelevant, but it is not the sole touchstone of an invidious racial discrimination forbidden by the Constitution. Standing alone, it does not trigger the rule that racial classifications are to be subjected to the strictest scrutiny and are justifiable only by the weightiest of considerations.

Id. at 242, 96 S.Ct. at 2049 (citation omitted). It is incumbent upon plaintiffs to establish that a racially disproportionate impact, if there is one, was occasioned by a racially motivated purpose. Arlington Heights v. Metropolitan Housing Corp., 429 U.S. 252, 265, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977); Washington v. Davis, supra 426 U.S. at 239, 96 S.Ct. 2040.

This is not to say that evidence of' disproportionate impact, or statistical evidence in particular, is unimportant. Necessarily, an invidious discriminatory purpose may often be inferred from the totality of the relevant facts, including the fact, if it is true, that the challenged conduct bears more heavily upon one race than another. Washington v. Davis, supra at 242, 96 S.Ct. 2040. The determination ultimately required demands a sensitive inquiry into such circumstantial and direct evidence of intent as may be available, including the impact of the challenged action, its historical background and its legislative or administrative history. Arlington Heights v. Metropolitan Housing Corp., supra 429 U.S. at 266-68, 97 S.Ct. 555. Moreover, because legislative and administrative bodies operating under broad mandates rarely make decisions motivated by a single concern, it is not necessary that plaintiffs prove the challenged conduct rested solely on racially motivated purposes. Id. 429 U.S. at 265, 97 S.Ct. 555.

The Supreme Court has made it “unmistakably clear that ‘[statistical analyses have served and will continue to serve an important role’ in cases in which the existence of discrimination is a disputed issue.” International Brotherhood of Teamsters v. United States, 431 U.S. 324, 339, 97 S.Ct. 1843, 1856 (1977). “Statistics showing racial or ethnic imbalance are probative . . [because and] only because such imbalance is often a telltale sign of purposeful discrimination.” Id. n.20, 97 S.Ct. at 1856, see Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977). Indeed, the statistical disparity shown may occasionally be so “gross” or “stark” or “dramatic” that it alone will constitute prima facie proof of purposeful discrimination. Hazelwood School Dist. v. United States, 433 U.S. 299, 305, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977); Arlington Heights v. Metropolitan Housing Corp., supra 429 U.S. at 266, 97 S.Ct. 555; Washington v. Davis, supra 426 U.S. at 254, 96 S.Ct. 2040 (Stevens, J., concurring); Williams v. Anderson, 562 F.2d 1081, 1087 (8th Cir. 1977) (Nos. 76-1172 & -1108). We are only cautioned that such extreme disparities are rare, Arlington Heights v. Metropolitan Housing Corp., supra 429 U.S. at 266, 97 S.Ct. 555, that statistical evidence, like any other kind of evidence, may be rebutted, International Brotherhood of Teamsters v. United States, supra 431 U.S. at 338, 97 S.Ct. 1843, and that the probative worth of statistical evidence depends on all of the surrounding facts and circumstances, id.

III.

We examine plaintiffs’ statistical evidence first. According to Exhibit 18, whites, blacks, native Americans and Mexican-Americans were discretionarily paroled in 1972 and 1973 at the respective percentage rates of 60.7, 63.0, 40.7 and 27.8. The district court, following its own reanalysis of the figures contained in the exhibit, was unconvinced that the statistics demonstrated any significant disparities in the treatment of the several racial and ethnic groups. It reasoned:

[Caucasian inmates comprise 65.4 per cent of the population eligible for a discretionary parole; Caucasians received 66.9 per cent of the discretionary paroles awarded. Black inmates comprise 26.1 per cent of the population eligible for a discretionary parole; blacks received 27.7 per cent of the discretionary paroles awarded. Indian inmates comprised 6.5 per cent of the population eligible for a discretionary parole; Indians received 4.5 per cent of the discretionary paroles awarded. Mexican-American inmates comprise 2 per cent of the population eligible for a discretionary parole; Mexican-Americans received .9 per cent of the discretionary paroles awarded. These figures show statistical disparities of two per cent or less which the Court considers to be insignificant.

436 F.Supp. at 441-42.

Before discussing our view of the significance or insignificance of the statistical disparities shown, we point out that plaintiffs’ statistics are assailed on other grounds as well. Contrary to assertions in plaintiffs’ brief, the district court did not find plaintiffs’ method of study reliable and their results accurate, although there was expert testimony to this effect and the court did find defendants had produced no substantial evidence to rebut it. 436 F.Supp. at 440. The court expressed concern that the size of the Mexican-American group (18) on which the study was based might be too small to yield a reliable result, 436 F.Supp. at 442 n.4, a concern which we share but need not expressly resolve. The court also expressed concern that racial and ethnic identity was the only variable controlled by the study, while a number of obviously important factors were left uncontrolled. 436 F.Supp. at 440. Defendants additionally urge that the 1972-1973 time period chosen by plaintiffs is too “stale” to support an inference that Board practices are now, or were at the time of trial, discriminatory. In short plaintiffs’ statistics provide much grist for argument, most of it not resolved by the district court and most of it ill-suited to resolution for the first time on appeal. Accordingly, we bypass this entire phase of the controversy and assume without deciding that plaintiffs’ statistics accurately and reliably reflect what they purport to reflect.

So assuming, then, we consider whether the statistical disparities shown are sufficiently significant substantially to assist plaintiffs in establishing a prima facie case of racial and ethnic discrimination. We are mindful of the Supreme Court’s recent admonition that the primary responsibility for evaluating statistical evidence rests with the trial court. Hazelwood School Dist. v. United States, supra 433 U.S. at 312, 97 S.Ct. 2736.

The district court’s conclusion that the disparities are insignificant rests on its comparison of the percentage of eligible inmates who were native American and Mexican-American with the percentage of discretionary paroles awarded which were awarded to native Americans and Mexican-Americans. Plaintiffs contend that this method of analysis is deceptive and the conclusion reached by the district court illusory. Plaintiffs further contend the disparities shown are indeed significant.

First, we find nothing inherently deceptive in the district court’s method of analysis. A similar approach has proved useful in a variety of contexts. For example, in Castaneda v. Partida, supra, the Supreme Court assessed a claim of discrimination in the selection of grand jurors by comparing the percentage of a county’s population which was Mexican-American with the percentage of grand jurors selected to serve in the county who were Mexican-American. And in Hazelwood School District v. United States, supra, the Supreme Court, in assessing a claim of discriminatory employment practices, indicated the relevance .of comparing the percentage of the relevant labor market which was black with the percentage of persons employed who were black. The district court’s analysis in this case was not fundamentally different.

Second, we nonetheless agree with plaintiffs that the district court’s conclusion does not follow from that court’s analysis. Specifically, we do not think “disparities of two per cent or less” are always insignificant. Although the method of analysis employed by the district court is indeed often useful, it is not invariably a sure guide to a correct result. Like all statistical evidence, the district court’s figures must be considered in light of all the surrounding facts and circumstances. International Brotherhood of Teamsters v. United States, supra 431 U.S. at 339, 97 S.Ct. 1843. Necessarily, as a minority group’s comparative size in a relevant population (in this case those eligible for discretionary parole) diminishes, increasingly smaller differences between the two percentage figures become significant. This is so because the use of such percentages considers the disparate impact upon a minority group as a function of the minority group’s comparative size in the larger population. It follows that the disparate impact is diluted in cases, like this one, where the group is comparatively small. Cf. Green v. Missouri P. R.R., 523 F.2d 1290, 1295 (8th Cir. 1975).

Third and finally, although we decline to agree with the district court that the disparities here shown are entirely without significance, we conclude that they are not sufficiently significant substantially to assist plaintiffs in establishing a prima facie case of racial and ethnic discrimination. To be sure, Exhibit 18 reveals some disparity. Eligible whites and blacks, over a two-year period, were discretionarily paroled at the respective rates of 60.7 and 63.0 per cent, while eligible native Americans and Mexican-Americans, over the same period, were discretionarily paroled at the respective rates of 40.7 and 27.8 per cent. This of course means that whites and blacks were discretionarily paroled at rates roughly one- and-one-half times that for native Americans and more than twice that for Mexican-Americans. These figures, like the district court’s, are unquestionably relevant ones. See, e. g., Green v. Missouri P. R.R., supra at 1293-95.

Although these percentages are on first glance somewhat disturbing, we think the bare numbers in Exhibit 18 tell the most revealing story. The 40.7 per cent figure relative to native Americans represents but 24 individuals, and the 27.8 per cent figure relative to Mexican-Americans represents but 5. If the 535 discretionary paroles awarded to all inmates had been distributed proportionately among all racial and ethnic groups, native Americans would have received only 35 (6.5 per cent of 535) and Mexican-Americans only 11 (2.0 per cent of 535) discretionary paroles. Thus, for native Americans the difference between "expected” (35) and observed (24) number of discretionary paroles received was only 11, and for Mexican-Americans the difference between “expected” (11) and observed (5) number of discretionary paroles received was only 6. In each instance the difference represents less than two standard deviations. Even with substantially larger populations, the Supreme Court has recently been unwilling to conclude that racial or ethnic identity plays a substantial role in challenged conduct unless observed and expected numbers differ by more than “two or three standard deviations.” Hazelwood School Dist. v. United States, supra 433 U.S. at 309, 97 S.Ct. 2736 n.14; Castaneda v. Partida, supra 430 U.S. at 496-97 n.17, 97 S.Ct. 1272.

The specific analysis in Hazelwood School Dist. v. United States is instructive. The Supreme Court there considered a claim that the school district had engaged in a pattern or practice of employment discrimination against blacks, allegedly in violation of Title VIL A majority of this court, in part because the percentage of black teachers employed by the district was very low in comparison with the percentage of black teachers available in the St. Louis County and City area, had previously concluded the Government had established an unrebutted prima facie pattern or practice case. 534 F.2d 805 (8th Cir. 1976). The Supreme Court vacated our judgment. Since Title VII was not applicable to the district until 1972, the Court explained, the district could have rebutted the Government’s prima fa-cie case by showing racially neutral hiring practices after 1972. 433 U.S. at 309, 97 S.Ct. 2736. Statistical data of record revealed that 3.7 per cent (15 of 405) of the teachers hired in the 1972-73 and 1973-74 school years were black. This figure, the Court noted, should be compared with the percentage of blacks in the relevant labor market. Id. The Court did not make the comparison, however, because the relevant labor market area was disputed, the Government contending it included both St. Louis County and St. Louis City (15.4 per cent black) and the district contending it included St. Louis County but not St. Louis City (5.7 per cent black). The Court did comment, however:

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.

Id. (emphasis supplied).

The emphasized portions of the above quote are highly pertinent to our analysis because the statistics there referred to are qualitatively and quantitatively comparable to the statistics here. Specifically, the 5.7 per cent/3.7 per cent disparity is comparable to the 6.5 per cent/4.5 per cent (native American) and the 2.0 per cent/.9 per cent (Mexican-American) disparities noted by the district court below. In addition, the 15 and 23 observed and expected numbers are not far afield from the 24 and 35 “(native American) and the 5 and 11 (Mexican-American) observed and expected numbers here; in each case the variance is slightly less than two standard deviations.

Plaintiffs place considerable reliance on our decision in Green v. Missouri Pacific Railroad, 523 F.2d 1290 (8th Cir. 1975). In that case, applying the rule of Griggs v. Duke Power Co., 401 U.S. 424, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971), that employment practices having a racially disproportionate impact are prima facie discriminatory under Title VII, we accepted a statistical analysis purporting to demonstrate that a rigid policy of refusing to hire persons previously convicted of a crime (other than a minor traffic offense) disqualified a substantially higher rate of black applicants than white applicants. Plainly, however, the statistical showing made there was stronger than the one made here. From a total job applicant pool of 8488, the challenged policy had disqualified 292 individuals, 174 black and 118 white. Since the applicant pool was 39 per cent black and 61 per cent white, an expected random distribution of the 292 disqualifications would have been 114 black and 178 white. Observed and expected values in Green thus differed by 60, more than seven standard deviations.

The above analysis leads us to the conclusion that the statistical showing in this case is not quite sufficient to permit a confident determination that the disparities shown are related to racial and ethnic factors and is therefore not quite sufficient substantially to assist plaintiffs in establishing a prima facie case of racial and ethnic discrimination. Although the Supreme Court has not in terms established a two standard deviation “floor” for statistical significance, Castaneda and Hazelwood certainly imply that a confident showing of statistical significance begins to arise at that level.

We recognize, of course, that the statistical disparities in this case approach the level seemingly deemed significant in Castaneda and Hazelwood. For that reason we decline to go the distance with the district court and hold the disparities utterly without significance. If the remainder of plaintiffs’ evidence came close to establishing a prima facie case, we might agree that their statistics would tip the balance. Insofar as plaintiffs rely on their statistics as a primary component of their prima facie case, however, we are in disagreement.

IY.

Our conclusion that the statistical disparities shown are not sufficiently significant substantially to support an inference of purposeful discrimination does not end the judicial inquiry. Under Washington v. Davis, supra, the inference can arise from any probative evidentiary sources, including but not limited to statistics. Of course, as the significance of the statistical disparities lessens, the quality and quantity of nonstatistical evidence required to raise the inference become correspondingly greater. We accordingly turn to a consideration of plaintiffs’ nonstatistical evidence.

Plaintiffs elicited considerable testimony from Board members and from their own experts to the effect that Board members are ignorant of and insensitive to native American and Mexican-American values and practices. Based on this testimony, plaintiffs maintain that uniform application of the statutory criteria to members of all racial and ethnic groups results in comparatively adverse treatment for minority individuals whose cultural traits and background differ from those of the dominant society. Plaintiffs broadly contend that native American and Mexican-American inmates constitutionally must be evaluated “in a manner which takes into consideration the racial and cultural differences between what is expected from a Caucasian, an Indian, or a Mexican-American.”

Plaintiffs, in so arguing, attach far more constitutional significance to the evidence than we possibly could. Even if the testimony does show that Board members fail to consider cultural factors and that such failure results in some comparatively adverse treatment to plaintiffs, and we will assume that it does, to hold that this alone is a denial of equal protection would be to ignore the controlling principle carefully set out by the Supreme Court in Washington v. Davis and Arlington Heights v. Metropolitan Housing Corporation, both supra, that discriminatory purpose is essential to an equal protection claim. This we are obviously not free to do. The evidence is relevant only to the extent it might evince such discriminatory purpose.

The district court discounted testimony elicited from Board members as entitled to “little or no weight in determining whether the defendants have discriminated” and dismissed the testimony of plaintiffs’ experts as frivolous. 436 F.Supp. at 439 & 438. It thus implicitly found that defendants’ unfamiliarity with native American and Mexican-American cultures was not indicative of discriminatory purpose. We agree.

We need not decide whether proof of a defendant’s unfamiliarity with or insensitivity to the particular cultural traits of a minority group could ever be of probative assistance in establishing discriminatory purpose. Assuming it could, we are simply unconvinced on this record. In the first place, plaintiffs’ assertions that all inmates are evaluated in light of and are expected to conform to stereotyped “anglo” norms and values are all but conclusively negated by the fact that black inmates have been discretionarily paroled at a rate slightly higher than that for white inmates. While it is true that one Board member is black, it is equally true that his one vote could not prevent the white Board majority from invidiously discriminating against blacks if it were predisposed to do so.

Plaintiffs’ experts isolated a number of problems which native Americans and to a lesser extent Mexican-Americans commonly encounter when considered for parole. It was noted that native Americans “have somewhat of a higher rate of problem with alcohol” than others and that, due to the native American culture’s conception of individual property, stealing “was considered to be good in some instances.” It was also noted that native American and Mexican-American cultures do not share the “aggressive” or “competitive” attitudes and habits toward work often held by members of the dominant culture. Although sound penology would arguably dictate some sensitivity to these problems, that is not of itself a matter of constitutional concern. Factors such as these could well provide a noninvidious explanation for such variance in treatment as may exist. There is accordingly no necessary or even likely inference of discriminatory purpose, and the district court was not compelled to find one.

Plaintiffs questioned hearing officer Richard Anderson concerning two native American inmates and one Mexican-American inmate who were denied discretionary parole in 1972 and 1973 despite favorable comments in progress reports. In each case the testimony reveals only the sketchiest of details. In one of these cases the inmate was in fact discretionarily paroled on February 21, 1974, after first becoming eligible for discretionary parole on October 10, 1973. It is questionable whether the few facts of record are sufficient to raise a prima facie inference of purposeful discrimination in these individual cases. Cf. United States v. Hazelwood School Dist., 534 F.2d 805, 814-18 (8th Cir. 1976), vacated on other grounds, supra. In any event two or three individual cases are insufficient to provide more than minimal support to an inference of classwide purposeful discrimination. Cf. id. (sixteen individual cases); International Brotherhood of Teamsters v. United States, supra (more than forty individual cases). The additional fact that hearing officer Anderson did not know in 1976 why the Board failed to grant discretionary parole to certain other individuals in 1972 and 1973 is without relevance.

Finally, we consider alleged racial slurs made by defendant Board members. The district court found these statements “subject to varying interpretations” and afforded them “little or no weight.” 436 F.Supp. at 439. Viewing these alleged slurs in context, we agree. We additionally note that most of these comments were not produced as evidence until the surrebuttal portion of the defendant’s case and were offered by plaintiffs for the purpose of impeaching witness Greenholtz. Defendants objected to their receipt in evidence on grounds of timeliness. Under these circumstances, the comments are not available as substantive evidence to support an inference of purposeful discrimination. See Fed. R.Evid. 105.

V.

Our discussion has embraced those portions of plaintiffs’ evidence which we find to be of the most arguable relevance in establishing purposeful discrimination. Further elucidation of the evidence and of our reasons for rejecting it would unduly prolong this opinion and serve no useful purpose. Although we cannot fully subscribe to the views expressed by the district court, particularly with reference to plaintiffs’ statistics, a careful review of plaintiffs’ entire case convinces us that the district court correctly found no substantial support for an inference of discriminatory purpose. We accordingly agree with the district court that plaintiffs failed to establish a prima facie equal protection case.

The judgment appealed from, insofar as it concerns the subclass of plaintiffs alleging denial of discretionary parole on grounds of racial and ethnic discrimination, is affirmed. 
      
      . At oral argument counsel for the subclass expressly disavowed any claim to damages. The subclass has not fully briefed or argued what form of injunctive relief might be appropriate, assuming injunctive relief is in order, but has suggested instead that that question should be initially addressed by the district court.
     
      
      . The original complaint was filed on behalf of a larger class of inmates and asserted a number of distinct constitutional claims. The district court divided the class into three subclasses as follows: (1) those allegedly denied discretionary parole on racial or ethnic grounds; (2) those allegedly denied discretionary parole because they had actions pending in court at the time of consideration for parole; and (3) those allegedly denied discretionary parole without procedural due process. The district court subsequently consolidated the claims of the first two subclasses for trial. In a memorandum opinion reported at 436 F.Supp. 432 (D.Neb. 1976) (Civ. 72-L-335), the court denied relief to both of these subclasses and directed the entry of final judgment on their respective claims in accordance with Rule 54(b). Both subclasses filed timely appeals from that judgment. We here consider the claim of the first subclass. The claim of the second subclass is pending decision in this court in Nos. 77-1284 (direct appeal) and 77-1098 (cross-appeal), submitted September 16, 1977. The claim of the third subclass has not yet, so far as we are aware, been finally adjudicated in the district court.
     
      
      . “Minimum term” is defined as “the minimum sentence provided by law or the minimum sentence imposed by a court, whichever is longer.” Neb.Rev.Stat. § 83-170(5) (Reissue 1976).
     
      
      . The only statistical evidence presented during plaintiffs’ case-in-chief was contained in their Exhibit 9, which purported to show that a disproportionately low percentage of the native American and Mexican-American inmates released on parole were released on discretionary, as opposed to mandatory, parole. On appeal plaintiffs place no reliance on Exhibit 9.
     
      
      . Exhibit 18 originally showed 61 (rather than 59) native Americans and 17 (rather than 18) Mexican-Americans eligible for discretionary parole. The district court, after correcting two errors it found in plaintiffs’ study, 436 F.Supp. at 440, calculated the relevant percentage figures shown in the above table. These percentages quickly reveal the district court’s finding, in light of the corrections, that 59 native Americans and 18 Mexican-Americans were eligible for discretionary parole. Since neither party challenges the corrections, we accept this finding. For the sake of clarity, we point out that the one native American inmate who the district court found had actually been released on parole was so released in 1971; this explains why the district court excluded him from the group of native Americans eligible for discretionary parole in 1972 and 1973.
     
      
      . Two other witnesses generally corroborated this line of testimony at a post-trial hearing on motion for new trial. Defendants objected to this latter testimony on grounds that plaintiffs were attempting to reopen the case. The district court took the objection under advisement and conditionally allowed the testimony. Subsequently the court denied the motion for new trial without substantial comment. At least in the absence of an affirmative exercise of discretion by the trial court allowing the testimony, we think defendants’ objection was well made. The matter is of little consequence, however, since, as found by the district court, the defendants (with minor exceptions) produced no evidence to show that plaintiffs’ methods were unreliable or that the alleged disparity could have resulted by accident or chance. 436 F.Supp. at 440.
     
      
      . Plaintiffs called experts in the fields of anthropology, sociology, penology and education. By stipulation, the testimony of two of these witnesses was presented in deposition form.
     
      
      . While somewhat equivocal in answer to questions about whether native American and Mexican-American inmates face communication problems in the parole process, Greenholtz agreed that such communication would be facilitated through the hiring of native American and Mexican-American personnel. He further testified, however, that the Board had no hiring authority. When asked if he had recommended to appropriate officials the employment of native American and Mexican-American caseworkers, he replied he had not.
     
      
      . Religion is a good example. Although Green-holtz acknowledged that an inmate’s religion plays a role in the Board’s decisionmaking, he stated he was unfamiliar with native American religious practices.
     
      
      . In assessing whether an inmate has constructive community ties, for instance, Green-holtz considers whether the inmate has “some professional friends” such as “the Sheriff, the City Police . . ., the minister in his community.”
     
      
      . “Ethnocentrism” was defined as “bias in favor of making value judgment on the basis of the observer’s own culture.”
     
      
      . As already noted plaintiffs’ statistical analysis was not presented until the rebuttal portion of their case. Defendants were accordingly afforded surrebuttal time in which to attempt to rebut the statistics. Surrebuttal (which consumes some four hundred of a total of nine hundred pages of trial transcript) was confined almost exclusively to a presentation of and interrogation with respect to defendants’ Exhibit 20. This exhibit contained summaries of allegedly pertinent data on each of the forty-nine subclass members who, according to plaintiffs’ Exhibit 18, were eligible for but were denied discretionary parole in 1972 and 1973. Largely on grounds of relevance, major portions of this exhibit were stricken by the district court. On final analysis the district court accorded the exhibit no weight (except with respect to the matters noted supra at note 5) “because it did not provide an adequate basis on which to compare the treatment of races and because it was based upon factual assumptions which the defendants were unable to support.” 436 F.Supp. at 440. In innumerable particulars, the parties are at odds over the court’s determination in this respect. For reasons which appear infra, we ultimately find no occasion to consider what, if any, probative force the district court should have attached to any or all of Exhibit 20.
     
      
      . Because Twiss was eligible for discretionary parole during 1973 and did not receive discretionary parole in 1973, he was treated in plaintiffs’ Exhibit 18 as having been eligible for, but not having received, discretionary parole. Defendants object to the placement of Twiss, and others similarly situated, in this statistical cate- , gory.
     
      
      . Defendants persistently objected that this evidence was being offered much too late in the trial.
     
      
      . The exhibit reveals that the inmate had five convictions prior to the one for which he was then under sentence.
     
      
      . The constitutional rule accordingly differs from the rule in those cases governed by Title VII of the Civil Rights Act of 1964 in which disproportionate impact is alleged. International Brotherhood of Teamsters v. United States, 431 U.S. 324, 335 n.15, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977); Washington v. Davis, supra 426 U.S. at 238-39, 96 S.Ct. 2040; Williams v. Anderson, 562 F.2d 1081, 1087 (8th Cir. 1977) (Nos. 76-1172 & -1108).
     
      
      . Proof that the challenged conduct was motivated in part by a racially discriminatory purpose shifts to the defendants the burden of establishing that the same decision would have resulted even had the impermissible purpose not been considered. Arlington Heights v. Metropolitan Housing Corp., supra 429 U.S. at 270-71 n.21, 97 S.Ct. 555.
     
      
      . The point is aptly illustrated by the Mexican-American subclass members in this case, who comprise only 2.0 per cent of the relevant population. Even if no Mexican-Americans had been discretionarily paroled, the statistical disparity would have been only 2.0 per cent and therefore, under the district court’s reasoning, insignificant.
      We additionally point out that our comments in this regard bear no necessary relation to the problem of small population size. We may suppose that plaintiffs’ study spanned twenty rather than two years and that all nonpercen-táge figures in Exhibit 18 were precisely ten times larger. If that were so, the population sizes would clearly be large enough, but the pertinent percentage figures, and therefore the district court’s analysis, would remain unaltered. Moreover, if 5350 of 9020 eligible inmates, but among them only 240 of 590 native Americans and 50 of 180 Mexican-Americans, had received discretionary paroles, standard deviation calculations of the type explained in Castaneda v. Partida, supra 430 U.S. at 496-97 n.17, 97 S.Ct. 1272, would quickly reveal the considerable unlikelihood that racial and ethnic identity played no role in the receipt of a discretionary parole.
     
      
      . In computing a standard deviation, we use the method described in Castaneda v. Partida, supra at 496-97 n.17, 97 S.Ct. 1272. For native Americans one standard deviation equals the square root of the product of the total number of individuals who received discretionary paroles (535) times the probability of randomly selecting a native American from the eligible inmate population (.065) times the probability of randomly selecting someone other than a native American from the same population (.935). This computes to approximately 5.7. A similar computation for Mexican-Americans yields approximately 3.2.
     
      
       Indeed, under the statistical methodology explained in Castaneda v. Partida, [430 U.S. at 496-97 n.17, 97 S.Ct. 1272,] involving the calculation of the standard deviation as a measure of predicted fluctuations, the difference between using 15.4% and 5.7% as the area-wide figure would be significant. If the 15.4% figure is taken as the basis for comparison . 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. . If, however, the 5.7% areawide figure is used . . . the expected value of 23 would be less than two standard deviations from the observed total of 15.
      
     
      
      . Petition for rehearing en banc was denied on a closely divided vote. 523 F.2d at 1299-1300.
     
      
      . The statistical showing in Murrah v. Arkansas, 532 F.2d 105 (8th Cir. 1976), a jury discrimination case also cited by plaintiffs, was similarly much stronger than that here. In a county 19.7 per cent black, jury commissioners had selected 800 names to be placed in a jury wheel, no more than 58 of them black. Had 19.7 per cent of the 800 been black, the number of blacks placed in the jury wheel would have been 158. Observed and expected values thus differed by 100, nearly nine standard deviations.
     
      
      . Even so, the district court may ultimately prove to be correct. The Supreme court majority in Hazelwood went so far as to say that a disparity comparable to those here “may be sufficiently small to weaken” the plaintiffs’ other proof, 433 U.S. at 311, 97 S.Ct. at 2743 presumably because classwide purposeful discrimination would ordinarily result in a greater disparity. The use of the word “may”, however, and the fact that Mr. Justice Brennan, concurring, 433 U.S. at 313, 97 S.Ct. 2736, and Mr. Justice Stevens, dissenting, 433 U.S. at 317, 97 S.Ct. 2736, appear to regard the Ha-zelwood figures in a somewhat different light, perhaps suggest that the Supreme Court has not yet reached a definitive resolution. We accordingly go only as far as the facts of this case require and hold that the statistical disparities here are not of substantial assistance to plaintiffs.
     
      
      . It is a foregone conclusion that plaintiffs’ statistics do not exhibit the sort of “gross” or “stark” or “dramatic” disparities which in rare cases can alone establish a prima facie case. This case is a far cry from Castaneda, where over an eleven-year period Mexican-Americans constituted 79 per cent of a county’s population but only 39 per cent of its grand jurors; the difference between observed and expected number of Mexican-American grand jurors equaled approximately twenty-nine standard deviations. 430 U.S. at 497 n. 17.
      Plaintiffs also suggest that defendants’ decision-making on parole matters, like the method of grand juror selection in Castaneda, is “highly subjective” and “susceptible to abuse as applied.” See 430 U.S. at 497. Even if we assume that the analogy is an apt one, it would only be useful where the disparities themselves were substantial.
     
      
      . Wholly apart from their equal protection challenge, plaintiffs contend that the Board’s alleged failure to consider unique cultural traits results in arbitrary and capricious decision-making in violation of the fourteenth amendment’s due process clause. The district court characterized this argument as frivolous. 436 F.Supp. at 438. We agree with the district court.
     
      
      . It appears that the district court implicitly so found. The court stated: “It is true that a man who is knowledgeable about an inmate’s culture and the social environment from which he came might make a more informed evaluation of his suitability for parole than an individual without such information.” 436 F.Supp. at 438.
     
      
      . Many of the cases relied upon by plaintiffs were decided prior to Washington v. Davis. The Washington v. Davis Court recognized that prior cases in the lower federal courts “impressively demonstrate that there is another side to the issue”, but the Court went on to state “to the extent that those cases rested on or expressed the view that proof of discriminatory racial purpose is unnecessary in making out an equal protection violation, we are in disagreement.” 426 U.S. at 245, 96 S.Ct. at 2050. Among the cases expressly disapproved by the Court is Norwalk CORE v. Norwalk Redevelopment Agency, 395 F.2d 920 (2d Cir. 1968), twice cited by plaintiffs. See 426 U.S. at 245 n. 12, 96 S.Ct. 2040.
     
      
      . Consequently, we need not decide whether defendants established a case in rebuttal. In particular, we need not resolve the numerous disputes over defendants’ Exhibit 20.
     