concurring:
I concur with our panel’s result and reasoning as far as they go, but I would also have addressed the trial court’s analysis of the first two Thornburg factors: the size and geographical compactness of the minority groups, and the political cohesiveness between these two racial groups. In light of our court’s recent decision that Section 2 of the Voting Rights Act applies to judicial elections, Chisom v. Edwards, 839 F.2d 1056 (5th Cir.1988), together with the advent of another Census-related round of legislative redistricting, we would be wise to resolve issues that are likely to recur. Additionally, our panel ought to have clarified an apparent misperception among courts as to the appropriate evaluation of statistical evidence in vote dilution cases. The district court’s thorough analysis of the case furnishes a well-documented steppingstone to these ends.
A. Size and Geographical Compactness.
The appellants’ first hurdle in the wake of Thornburg is to show that they are sufficiently numerous and geographically compact to form a majority in a single member district or districts. 478 U.S. at 50, 106 S.Ct. at 2766. In appellants’ six/one single-member plan, neither blacks nor Mexican-Americans would command a majority of the voting age population in any district. Consequently, in order to obtain legal relief, appellants propose three refinements to this prong of Thornburg: that total population figures rather than those of voting age minority citizens may be used to fulfill this test; that the court may order the council expanded from six to eight members, thus reducing the threshold population requirement in each district; and that blacks and Mexican-Americans may be aggregated as a politically cohesive minority. The district court ruled with appellants on only the second of these three refinements.
The appellants’ propositions are ill-founded. First, the raison d’etre of Thornburg and of amended § 2 is to facilitate participation by minorities in our political processes, by preventing dilution of their votes. Only voting age persons can vote. It would be a Pyrrhic victory for a court to create a single-member district in which a minority population dominant in absolute, but not in voting age numbers, continued to be defeated at the polls. Thornburg implicitly recognized this fact:
Unless minority voters possess the potential to elect representatives in the absence of the challenged structure or practice, they cannot claim to have been injured by that practice.
478 U.S. at 50-51 n. 17, 106 S.Ct. at 2766-67 n. 17 (emphasis added).
Courts which have addressed this issue have concluded that Thornburg’s first prong refers to a majority voting age population in a proposed single-member district. McNeil v. Springfield Park District, 851 F.2d 937, 944-45 (7th Cir.1988); Ketchum v. Byrne, 740 F.2d 1398, 1412-13 (7th Cir.1984); Romero v. City of Pomona, 665 F.Supp. 853, 854 (C.D.Cal.1987); Martin v. Allain, 658 F.Supp. 1183, 1204 (S.D.Miss.1987); Latino Political Action Committee v. City of Boston, 609 F.Supp. 739 (D.C. Mass.1985), aff'd, 784 F.2d 409 (1st Cir.1986); Potter v. Washington County, 653 F.Supp. 121, 129 (N.D.Fla.1986); Gingles v. Edmisten, 590 F.Supp. 345, 381 n. 3 (E.D.N.C.1984), aff'd in part and rev’d in part, sub nom. Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986). See also, Blacksher and Menefee, From Reynolds v. Sims to City of Mobile v. Bolden, 34 Hastings L.J. 1, 55-56 (1982). Our court’s previous cases have not addressed this issue,1 but in each of them the newly-created single-member districts contained a minority population well in excess of 50 percent, raising the inference that voting age population was also comfortably over 50 percent. See, Campos v. City of Baytown, 840 F.2d 1240 (5th Cir.1988); League of United Latin American Citizens v. Midland Indep. Sch. Dist., 812 F.2d 1494, vacated en banc 829 F.2d 546 (5th Cir.1987).
*543The appellants’ advocacy of an eight-member council as a means of overcoming the first prong of Thornburg is likewise deficient. The district court assumed ar-guendo that it might order an expansion of the city council to accommodate single-member districts. This reasoning puts the cart before the horse, by authorizing a remedy for voter dilution before a violation of Section 2 has been found. Actionable vote dilution must be measured against the number of positions in the existing governmental body rather than some hypothetical model based upon whatever size is necessary to accomplish proportional representation. Adding council member districts “would create a voting rights violation where none presently exists by enabling appellants to meet the necessary precondition of their Section 2 claim.” McNeil v. Springfield Park District, supra at 946. The district court should therefore have considered only whether a six-member single-district council would afford appellants a greater potential for electing candidates of their choice.
If appellants are required to utilize the six-one single-member district plan and voting age majorities to satisfy Thornburg’s first prong, they must establish that blacks and Mexican-Americans are a politically cohesive minority.2 It is appropriate to consider this argument in the larger context of Thornburg’s, second prong.
B. The Political Cohesiveness of the Minority Groups.
It is uncontested that blacks and Mexican-Americans, as individual groups, are politically cohesive within the understanding of Thornburg. The parties dispute vigorously, however, whether blacks and Mexican-Americans may be aggregated into one politically cohesive minority. If this is not possible, there is an insufficient Mexican-American population to obtain § 2 relief under Thornburg's requirements for size and geographical compactness.3 This court has previously held (although I participated in the dissent from the denial of rehearing en banc), that minorities may be aggregated for purposes of establishing § 2 voter dilution claims if, in addition to otherwise demonstrating a violation of § 2, they show that they are politically cohesive. Campos v. City of Baytown, 840 F.2d 1240; see also, Campos v. City of Baytown, 849 F.2d 943 (5th Cir.1988) (dissent from denial of rehearing en banc). The issue before us is whether blacks and Mexican-Americans in Austin, as a single group, have proven themselves politically cohesive.
The principal evidence underlying the district court’s conclusion is a chart, prepared by the City from appellants’ expert’s figures, depicting the estimated votes of minority candidates in 19 city council races between 1975 and 1983.4 Appellants contend that this chart demonstrates consistent support by blacks and Mexican-Americans for the same minority candidates. At the very least, however, the district court was not clearly erroneous in reading the chart differently and finding that in eight of the 19 races, whites voted with both minorities for minority candidates; in two races a minority candidate failed to receive a plurality from either minority group; and *544in the remaining nine races, blacks and Mexican-Americans voted for the same candidate only five times. Appellants misstate the proof necessary to support their position of mutual cohesiveness by considering those races in which both minority groups voted the same way as white voters. Even as such evidence tends to show black-Hispanic political solidarity, it simultaneously refutes any notion that the white vote was racially polarized.5 Although there was testimonial evidence of similar political goals espoused by blacks and Mexican-Americans in Austin, the fact remains that the appellants’ statistical analysis demonstrated a more complex pattern of voting by race and ethnicity than appellants would portray. Thus, while black voters were extremely cohesive and Mexican-American voters were somewhat cohesive among themselves in races where a minority candidate ran, they did not usually combine to support candidates who were usually disfavored by Anglo voters. Thornburg, 478 U.S. at 56, 106 S.Ct. at 2769-70.6
C. The Significance of the Statistical Evidence Presented.
In part IIA of our opinion we said, “Crucial to the validity of regression analysis are the values for “r” and “r2”, which measure the strength of the correlation and linear relationship of the variables being examined, in this case the race of the voter and the candidate he supports. In this case, Dr. Miller calculated “r” values mainly between 0.5 and 0.7 for the 43 races the plaintiffs claim are polarized, and “r” values above 0.8 in only 6 cases.”
By contrast, in Gingles v. Edmisten, 590 F.Supp. 345 (E.D.N.C.1984), aff'd in part and rev’d in part, sub nom., Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986), Dr. Grofman’s bivariate ecological regression yielded “r” values ranging from 0.7 to 0.98; most exceeded 0.9. 590 F.Supp. at 368 n. 30. The expert’s regression analysis relied on in Campos yielded “r” values generally above 0.68, and three out of five “r” values exceeded 0.84. To date courts have based vote polarization conclusions on data yielding “r” values of 0.8 or higher for the majority of elections examined. See, e.g., Campos, 840 F.2d at 1246; Solomon v. Liberty County, Fla., 865 F.2d 1566 (11th Cir.1988); Jackson v. Edgefield County, 650 F.Supp. 1176, 1197 (D.S.C.1986).
Whether a given “r” value should be regarded as statistically significant must be determined on a case by case basis since the value signifying statistical significance is dependent upon sample size (e.g., the number of precincts studied in each election). See generally D. Barnes & J. Conley, Statistical Evidence in Litigation (1986). A review of the existing case law beginning with Major v. Treen, 574 F.Supp. 325 (E.D.La.1983), suggests that courts have often failed to appreciate this important fact. On several occasions courts have made the seemingly unqualified assertion that “r” values at or above 0.5 are statistically significant. See Major v. Treen, 574 F.Supp. at 338; Gingles v. Edmisten, 590 F.Supp. at 368 (“In experience, correlations above an absolute value of .5 are relatively rare and correlations above .9 extremely rare.”). Cf. Solomon v. Liberty County, Fla., 865 F.2d at 1575 (“r” values become statistically significant at 0.3).7 Statistical theory simply precludes such universal conclusions.
*545In contrast, a careful reading of the Campos opinion indicates that the district court was presented with, and took note of, expert testimony as to the level at which the “r” value became statistically significant for the regression analysis of the election yielding the lowest correlation coefficient. Our court was careful to note that, “[f]or the Campos race, the court found that the “r” value of .52, slope of .33 and significance of .0456 were the lowest values introduced but, as testified by [the plaintiffs’ expert] Brishetto, they were still statistically significant.” Campos, 840 F.2d at 1247. We ought to encourage district courts and litigants alike to pay close attention to the signifcance of the “r” values generated by regression analysis. Statistics are a mischievous tool, especially in court, if they are not prepared and offered with a convincing explanation of their mathematical characteristics and limitations. The absence here of customary levels of statistical reliability was rightly acknowledged by the district court.
CONCLUSION
Previous cases and the above discussion establish three propositions regarding the first two Thornburg prongs that should be explicitly recognized by our circuit. First, voting age majority in a proposed single-member district, rather than population majority, should determine whether a minority group is sufficiently numerous. Second, the Thornburg analysis should be conducted according to the existing number of districts in a political subdivision, not according to a larger number tailored to accommodate a single-member district racial majority. Third, although we have now held that two racial minorities may prove that they are jointly politically cohesive under Thornburg, this factual determination in one or two cases does not suggest that in every case blacks and Mexican-Americans will satisfy their burden of proof. Finally, courts should insist not only on the provision of “r” values generated by the regression analyses, but also on evidence as to the level at which those “r” values become significant. Courts should continue to investigate these issues carefully, as the district court did here.
. But see, Houston v. Haley, 859 F.2d 341 (5th Cir.1988) (Brown, J., dissenting) (arguing that voting age must be the determinative factor), vacated, 869 F.2d 807 (5th Cir.1989).
. Thornburg notes that "... if, although geographically compact, the minority group is so small in relation to the surrounding white population that it could not constitute a majority in a single-member district, these minority voters cannot maintain that they would have been able to elect representatives of their choice in the absence of the multi-member electoral structure.” 478 U.S. at 50 n. 17, 106 S.Ct. at 2766 n. 17.
. The district court found that Dr. Miller's analysis yielded highly questionable results. But even if these results are entitled to credence, the trial court found that they do not support appellants' arguments.
. Cf. Thornburg, 478 U.S. at 56, 106 S.Ct. at 2769-70 (the same evidence of racial polarization will be probative both to establish the political cohesiveness of the minority group and to show white racial polarization).
. In three of the five races in which blacks and Mexican-Americans supported the same minority candidate in opposition to the majority of Anglos, those candidates actually won election because they received a sizeable percentage of the Anglo vote — in no instance less than forty-seven percent (47%). This reinforces the inference that Austin’s voting patterns are not racially correlated in a politically meaningful sense and that blacks and Mexican-Americans have no monopoly on supporting minority candidates.
.The comment in Major v. Treen may have been based on testimony from Dr. Henderson. If so, this statement — indicating a threshold significance for "r" — is obviously confined to the specific evidence presented in that case.