OPINION

THOMAS, Circuit Judge:

The Sixth Amendment and the Jury Selection and Service Act of 1968 ("the Jury Selection Act") afford criminal defendants "the right to be tried by an impartial jury drawn from sources reflecting a fair cross section of the community." Berghuis v. Smith, 559 U.S. 314, 319, 130 S.Ct. 1382, 176 L.Ed.2d 249 (2010). Our circuit precedent required courts to evaluate challenges to the fair cross-section requirement using the "absolute disparity" test. United States v. Rodriguez-Lara, 421 F.3d 932, 943 (9th Cir.2005). On re-examining the question, we conclude that confining a fair cross-section analysis to the absolute disparity test is inappropriate. However, we affirm the conviction in this case on other grounds.

I

Salvador Hernandez-Estrada ("Hernandez") was indicted on February 18, 2010, for being a deported alien found in the United States in violation of 8 U.S.C. § 1326. Hernandez moved to dismiss the indictment, arguing that the United States District Court for the Southern District of California ("Southern District") had violated the Jury Selection Act, the equal protection component of the Due Process Clause of the Fifth Amendment, and the fair cross-section requirement of the Sixth Amendment.

Hernandez primarily assailed the Southern District for its failure to supplement its juror source list, beyond the use of voter registration rolls, with sources such as Department of Motor Vehicle records. Hernandez also argued that the Southern District violated the Jury Selection Act by (1) using outdated text in the English proficiency question on its prospective juror questionnaire to disqualify prospective jurors improperly under a superseded legal standard; (2) allowing unsupervised court clerks to disqualify prospective jurors who answered in the affirmative regarding their English proficiency but expressed doubts about their linguistic abilities elsewhere on the form; (3) failing to return juror questionnaires to prospective jurors who did not answer the form's race and ethnicity questions; and (4) failing to maintain and report jury wheel representativeness statistics (on Form AO-12 reports) unless prompted to do so by litigation.

The district court agreed with Hernandez "that there are flaws in the [Southern] District's jury selection procedures" and acknowledged that "improvements could be made." Indeed, the court recommended that the Southern District take steps to remedy flaws in its jury selection procedures.1 However, the court ultimately concluded that those flaws did not constitute constitutional violations or substantial violations of the Jury Selection Act. The court denied Hernandez's motion to dismiss, and he was convicted as charged.

A three-judge panel of our court affirmed the conviction. United States v. Hernandez-Estrada, 704 F.3d 1015, 1019 (9th Cir.2012). Chief Judge Kozinski, joined by Judge Watford, filed a concurring opinion urging us to reconsider en banc our exclusive reliance on the absolute disparity test in jury selection pool cases as enunciated in Rodriguez-Lara. Id. at 1025-26 (Kozinski, C.J., concurring). Upon the majority vote of the active, non-recused judges of the court, we agreed to rehear this case en banc. United States v. Hernandez-Estrada, 729 F.3d 1224 (9th Cir.2013).

In his appeal, Hernandez challenges only the district court's denial of his motion to dismiss. We review "independently and non-deferentially a challenge to the composition of grand and petit juries" under both the Constitution and the Jury Selection Act. United States v. Sanchez-Lopez, 879 F.2d 541, 546 (9th Cir.1989).

II

Hernandez argues that the Southern District's exclusive use of registered voter rolls as its juror source list results in underrepresentation of African American and Hispanic citizens in the jury pool and, as a result, violates the fair cross-section requirements of the Jury Selection Act and the Sixth Amendment. Because the same analysis determines whether the jury selection procedures meet the fair crosssection requirement under either the Jury Selection Act or the Sixth Amendment, we consider those two claims together. United States v. Miller, 771 F.2d 1219, 1227-28 (9th Cir.1985).

A

Under the Jury Selection Act and the Sixth Amendment, litigants in federal courts entitled to trial by jury have the right to "juries selected at random from a fair cross section of the community." 28 U.S.C. § 1861; Miller, 771 F.2d at 1227-28. Jurors must be selected from either "voter registration lists or the lists of actual voters of the political subdivisions within the district or division." Id. § 1863(b)(2). However, a district's jury selection plan must "prescribe some other source or sources of names in addition to voter lists where necessary to" meet the fair cross-section requirement, guarantee that all citizens have the opportunity to be considered for jury service, and ensure no citizen is excluded from jury service due to race, color, religion, sex, national origin, or economic status. Id. §§ 1861, 1862, 1863(b)(2).

The Supreme Court in Duren v. Missouri "established a three-part test for determining whether a jury selection process passes constitutional muster" under the fair cross-section requirement:

Miller, 771 F.2d at 1228 (quoting Duren v. Missouri, 439 U.S. 357, 364, 99 S.Ct. 664, 58 L.Ed.2d 579 (1979)). "Once the defendant has established a prima facie case, the burden shifts to the government to show that `a significant state interest be manifestly and primarily advanced by those aspects of the jury-selection process... that result in the disproportionate exclusion of a distinctive group.'" Rodriguez-Lara, 421 F.3d at 940 (quoting Duren, 439 U.S. at 367-68, 99 S.Ct. 664).

Hernandez satisfied the first Duren requirement because African Americans and Hispanics are distinctive groups in the community. United States v. Cannady, 54 F.3d 544, 547 (9th Cir.1995). The second prong "requires proof, typically statistical data, that the jury pool does not adequately represent the distinctive group in relation to the number of such persons in the community." United States v. Esquivel, 88 F.3d 722, 726 (9th Cir.1996).

Before the district court, Hernandez produced evidence based on Fisher's Exact test showing that African Americans and Hispanics were underrepresented in the Southern District jury pool. Bound by Rodriguez-Lara, however, the district court applied the absolute disparity test and found that, in 2009, the absolute disparity on the qualified jury wheel for Hispanics in the Southern District was -2.07% (i.e., Hispanics were overrepresented by 2.07%) and for African Americans was 1.71% (i.e., African Americans were underrepresented by 1.71%). Because these percentages were far below the 7.7% threshold recognized in Rodriguez-Lara, the district court dismissed Hernandez's fair cross-section claim.

In his petition for rehearing en banc, Hernandez challenges our use of the absolute disparity test, arguing that the method unfairly favors large groups, makes it impossible for small groups to successfully assert a constitutional or Jury Selection Act violation, and has been criticized or rejected by other courts. Hernandez urges us to abandon the absolute disparity test and instead to adopt another method (or methods), such as the comparative disparity or standard deviation approaches.

B

As an initial matter, the government argues that Hernandez has waived his challenge to the absolute disparity test by not specifically raising it before the three judge panel. Of course, we are not required to address an issue first raised in a petition for rehearing, and generally decline to do so. N. Mariana Islands v. Lizama, 27 F.3d 444, 448 (9th Cir.1994). However, we have the authority and discretion to decide questions first raised in a petition for rehearing en banc. See Socop-Gonzalez v. INS, 272 F.3d 1176, 1187 n. 8 (9th Cir.2001) (en banc) ("[F]ailure to raise an issue before an original appellate panel does not preclude an en banc panel's jurisdiction over the issue."). In fact, we have done so at the government's request. See Coe v. Thurman, 922 F.2d 528 (9th Cir.1990), supplemental op., 922 F.2d at 533 & n. 1 (9th Cir.1990) (per curiam) (exercising discretion in considering Teague habeas issue first raised by the government in its petition for rehearing). And we have, on occasion, raised and addressed issues of circuit-wide importance ourselves en banc. See Jeffries v. Wood, 114 F.3d 1484, 1493-99 (9th Cir.1997) (en banc) (raising and deciding the retroactive effect of a statute that became law after petitions for rehearing en banc were filed), overruled in part on other grounds by Gonzalez v. Arizona, 677 F.3d 383, 389 n. 4 (9th Cir.2012) (en banc). In addition, we have entertained issues en banc that were not preserved in the district court when, as in this case, a "`"solid wall of Circuit authority" would have rendered an objection futile.'" Costa v. Desert Palace, Inc., 299 F.3d 838, 864 (9th Cir.2002) (en banc) (quoting Knapp v. Ernst & Whinney, 90 F.3d 1431, 1438-39 (9th Cir.1996) (quoting Robinson v. Heilman, 563 F.2d 1304, 1307 (9th Cir.1977) (per curiam))).

The Supreme Court has also held that appellate courts are not obligated to treat issues raised for the first time on appeal as absolutely waived. Granberry v. Greer, 481 U.S. 129, 133-35, 107 S.Ct. 1671, 95 L.Ed.2d 119 (1987). And the Supreme Court has not deemed an issue waived when it was first raised in a petition for rehearing en banc before a circuit court. See United States v. Jimenez Recio, 537 U.S. 270, 273-77, 123 S.Ct. 819, 154 L.Ed.2d 744 (2003) (overruling a line of Ninth Circuit cases despite the fact that the government first challenged the cases only in its petition for rehearing en banc).

Therefore, contrary to the government's argument, a party does not necessarily forfeit an issue by first raising it in a petition for rehearing en banc. Rather, it is a matter directed to the exercise of our discretion. In this case, the defendant tendered statistical evidence to the district court in support of his claim that his jury panel did not reflect a fair cross-section of the community. The district court rejected the evidence because it was bound by circuit law to use a different methodology. The three judge panel lacked the authority to alter circuit law without an intervening Supreme Court or en banc decision that was clearly irreconcilable with our circuit precedent. Miller v. Gammie, 335 F.3d 889, 900 (9th Cir.2003) (en banc). Therefore, it would have been futile for the defendant to urge the three judge panel to overrule binding circuit precedent. However, Chief Judge Kozinski properly and forcefully raised the issue in his panel concurrence, and the defendant directly presented the question in his petition for rehearing en banc.

Given the significance of the questions raised by Chief Judge Kozinski in his panel concurrence and presented by the petition for rehearing en banc, and the potential impact on all districts in our circuit, we elect in this instance to exercise our discretion to address the issue en banc.

C

Courts have employed a number of analytical methods when faced with jury panel fair cross-section cases, including the absolute disparity test, the absolute impact test, the comparative disparity test, and standard deviation analysis.

The absolute disparity test, which is the test that we have employed exclusively, examines "the difference between the percentage of the distinctive group in the community and the percentage of that group in the jury pool." Rodriguez-Lara, 421 F.3d at 943. In other words, if a specific group makes up 10% of the population and 5% of the qualified jury wheel (i.e., the list of prospective jurors who have been randomly pulled from the juror source list, have been mailed juror questionnaires, have returned those questionnaires, and have been deemed qualified based on their response to those questionnaires), the absolute disparity is 5%. See id. at 950-51 app. (conducting the absolute disparity analysis by comparing the percentage of jury-eligible Hispanics in the geographic region with the percentage of Hispanics in the qualified jury wheel).

In determining the percentage of a distinctive group in the qualified jury wheel, the absolute disparity analysis excludes those jurors who did not identify their race or ethnicity on their jury questionnaire. Id. at 944 n. 11. Furthermore, in analyzing the distinctive group's representation in the district or region as a whole, a court "must rely on the statistical data that best approximates the percentage of jury-eligible [members of the distinctive group in question] in the district." United States v. Torres-Hernandez, 447 F.3d 699, 704 (9th Cir.2006). Although no bright-line rule exists as to what level of absolute disparity constitutes a constitutional or Jury Selection Act violation, we "have declined to find underrepresentation of a distinctive group where the absolute disparity was 7.7% or lower." Rodriguez-Lara, 421 F.3d at 943-44.

We initially endorsed the absolute disparity method in United States v. Potter, reasoning that a more comparative statistical analysis could "distort the actual effect[s] of [a] deviation" between a group's representation in the population at large and in the jury pool. United States v. Potter, 552 F.2d 901, 906 (9th Cir.1977). We determined that the absolute disparity method was the better and more accurate course for assessing minority representation on jury pools. Id. In later cases, we held that the absolute disparity method was the sole mode of analysis for courts in the Ninth Circuit. See, e.g., Sanchez-Lopez, 879 F.2d at 547 ("In determining the underrepresentation of a particular group in jury venires, we have consistently favored an absolute disparity analysis and have rejected a comparative disparity analysis.").

Nevertheless, although we continued to employ absolute disparity as our circuit's sole test, we have repeatedly criticized and questioned it. See, e.g., Serena v. Mock, 547 F.3d 1051, 1054 n. 2 (9th Cir.2008) (order) ("We question, however, whether the approach compelled by our case law [i.e., the absolute disparity approach] is mathematically sound."). Indeed, we have specifically highlighted the fact that if a minority group makes up less than 7.7% of the population in the jurisdiction in question, that group could never be underrepresented in the jury pool, even if none of its members wound up on the qualified jury wheel. Rodriguez-Lara, 421 F.3d at 944 n. 10 ("The necessary implication of this margin is that if a distinctive group makes up 7.7% or less of the community, then the fair cross-section requirement offers no redress even if that group is entirely shut out of the jury pool."). For example, African Americans constituted 5.2% of the population of the Southern District in 2009. Therefore, under the absolute disparity test, there could be no successful jury challenge in the Southern District for African Americans. As of the last census, the District of Montana did not have any minority group that exceeded 7.7% of its population.2 Thus, under Rodriguez-Lara, there could never be a viable fair cross-section challenge in the District of Montana. Although the Supreme Court has refused to prescribe any specific type of analysis or prohibit the use of the absolute disparity test, it too has noted that the absolute disparity test "can be misleading" when the distinctive group in question makes up only a small percentage of the population. Berghuis, 559 U.S. at 329, 130 S.Ct. 1382.

The absolute disparity test also suffers from distortion based on population size. For example, if we assume a group makes up 90% of the population, but 80% of the jury pool, there would be a 10% absolute disparity. Under those circumstances, it is doubtful that any court would consider the group underrepresented. However, if a population group constituted 10% of the population, but had no representation in a jury pool, that result might give rise to fair cross-section concerns. Yet, the absolute disparity — 10% — would be identical under both scenarios.

The absolute disparity test has been used by many courts because it is easy to administer. Sara Sun Beale, Integrating Statistical Evidence and Legal Theory to Challenge the Selection of Grand and Petit Jurors, 46 Law & Contemp. Probs. 269, 273 (1983). However, no court has been able to articulate or defend it on any sound statistical basis. And there is no statistical basis from which one could derive the 7.7% threshold that we articulated in Rodriguez-Lara. At best, the method provides a very generalized gauge of a jury pool when considering representation of groups that form a substantial portion of the community. It also has some comparative value because many courts have used it, so there is some predictive history.3

Closely related to the absolute disparity test is the absolute impact test. Under this approach, the initial calculation is the same as for the absolute disparity test. However, the resulting number is then multiplied by the number of persons on the particular panel. See, e.g., United States v. Test, 550 F.2d 577, 588 n. 11 (10th Cir.1976). So, for example, if a minority group constitutes 10% of the population and there is a jury pool of 20, one would expect 2 jurors to be from the affected population group. Applying the absolute impact test, if there was a 10% absolute disparity between the proportion of that minority group in the population and the proportion in the jury pool, one would expect the absolute impact on the 20-person jury pool to be 2 jurors. If only 1 juror from the group were represented, a court might not conclude that there was a significant difference. The advantage of the test is that it applies the disparity analysis to the actual jury pool to determine the impact. However, because it is based on the absolute disparity test, the absolute impact test bears many of the same flaws.

Recognizing the problems in the absolute disparity and absolute impact tests, some courts have employed the comparative disparity test. Comparative disparity is calculated "by taking the absolute disparity percentage and dividing it by the percentage of the distinctive group in the total population." Rodriguez-Lara, 421 F.3d at 943 n. 10. So, using our prior example, the comparative disparity of the 90% population group in an 80% jury pool would be 11%. The comparative disparity of the 10% population group with no representation in the jury pool would be 100%. Thus, the comparative disparity test illustrates, in a general way, the comparative differences in a manner that takes population size into consideration. See Hirst v. Gertzen, 676 F.2d 1252, 1258 n. 14 (9th Cir.1982) (noting that a comparative disparity method is "more informative" than the absolute disparity method when the cognizable group "represents a small percentage of the population"). However, one problem with the comparative disparity test is that it can overstate the underrepresentation of a group that has a small population percentage. Let's assume, for example, that a group constitutes .1% of the population, with no representation in the jury pool. The comparative disparity of that group would be 100%. Few would argue that the absence of a group representing just 0.1% of the population violates the fair cross-section requirement, yet comparative disparity analysis would suggest otherwise. In addition, "when the group is very large the comparative method tends to validate deviations that are unlikely to have been produced by chance despite the fact that the disparity alters the representation of the average jury substantially." Beale, supra, at 274. As with the absolute disparity test, no court has been able to articulate or defend the use of a comparative disparity test on any sound statistical basis.

Some courts have used an analysis of standard deviation, which is the "measure of the predicted fluctuations from the expected value." Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977). Standard deviation has the advantage of being firmly grounded in statistical theory, and generally applicable to both large and small population groups. However, some courts have questioned whether a pure standard deviation analysis is appropriate given that the characteristics of the general population differ from a pool of qualified jurors. See, e.g., United States v. Rioux, 97 F.3d 648, 655 (2d Cir.1996) ("It is illogical to apply a theory based on random selection when assessing the constitutionality of a qualified wheel. By definition, the qualified wheel is not the product of random selection; it entails reasoned disqualifications based on numerous factors. It is irrational to gauge the qualified wheel — an inherently non-random sample — by its potential for randomness.").4

An additional problem with exclusive reliance on standard deviation analysis is, as one commentator has noted, that "[t]he probability that the composition of a jury wheel arose by random selection from the community is not directly related to the defendant's chances of drawing a jury of a certain composition." Peter A. Detre, A Proposal for Measuring Underrepresentation in the Composition of the Jury Wheel, 103 Yale L.J.1913, 1928 (1994). "[B]y imagining larger and larger jury wheels, the probability of any degree of underrepresentation arising by chance can be made arbitrarily small." Id.

Another alternative is the disparity-of-risk test. This test measures "the likelihood that the difference between a group's representation in the jury pool and its population in the community will result in a significant risk that the jury will not fairly represent the group." Commonwealth v. Arriaga, 438 Mass. 556, 781 N.E.2d 1253, 1265 (2003). The calculation is performed by "comparing the chance that a defendant's jury (before or without voir dire) will include members of a distinct group if that group's representation in the jury pool is consistent with its population in the community with the chance that a defendant's jury will include members of the same group given the particular underrepresentation alleged." People v. Bryant, 491 Mich. 575, 822 N.W.2d 124, 143 (footnote omitted), cert. denied, ___ U.S. ___, 133 S.Ct. 664, 184 L.Ed.2d 462 (2012).

In the case at hand, the defendant tendered experts who employed Fisher's Exact test. Fisher's Exact test is used to calculate the probability that the number of individuals of a particular race-selected or gender-selected classification would be the same as the number actually selected, if the selection were independent of race or gender. It examines the difference in proportions of the subgroup in the population and the proportion appearing in the jury pool, and calculates the amount of discrepancy between the observed data and what would be expected by chance, and then fixes a probability to that result.5 It is designed to examine statistical significance in small sample sizes. Jones v. Pepsi-Cola Metro. Bottling Co., 871 F.Supp. 305, 311 (E.D.Mich.1994).

A survey of our sister circuits demonstrates the inconsistency of approaches. Some of our sister circuits still use the absolute disparity method exclusively. See, e.g., United States v. Royal, 174 F.3d 1, 10 (1st Cir.1999) ("We accordingly employ the absolute disparity test...."); Rioux, 97 F.3d at 655-56 ("Although we have admittedly waffled on this issue in the past, the law in this Circuit strongly suggests the absolute disparity/absolute numbers approach is appropriate in this case."); United States v. Pepe, 747 F.2d 632, 649 n. 18 (11th Cir.1984) ("We consider deviation from proportional representation in absolute rather than comparative terms...."). Others, however, have adopted a more flexible approach that uses multiple modes of analysis. See, e.g., United States v. Orange, 447 F.3d 792, 798 (10th Cir.2006) ("[W]e have consistently relied upon two measurements: absolute and comparative disparity."); Mosley v. Dretke, 370 F.3d 467, 479 n. 5 (5th Cir. 2004) (noting that the circuit uses absolute disparity alone when the group is a large part of the overall population but leaving "open the possibility that if the distinctive group at issue makes up less than 10% of the population, comparative disparity may be used"). The Third Circuit uses a multi-modal analysis that considers "evidence of absolute disparity, comparative disparity, and deviation from expected random selection." Ramseur v. Beyer, 983 F.2d 1215, 1231 (3d Cir.1992) (en banc).

After surveying the case law and alternative methods of analysis, and bearing in mind our own past criticism of our exclusive reliance on the absolute disparity test, we conclude that it is appropriate to abandon the absolute disparity approach. Accordingly, we overrule the requirement, as set forth in Rodriguez-Lara and its predecessor cases, that the absolute disparity test be the exclusive analytical measure employed in fair cross-section challenges.

However, we do not prescribe an alternative exclusive analysis to be applied in every case. The Supreme Court has declined to specify "the method or test courts must use to measure the representation of distinctive groups in jury pools." Berghuis, 559 U.S. at 329, 130 S.Ct. 1382. We follow its lead and also decline to confine district courts to a particular analytical method. As our discussion has illustrated, the appropriate test or tests to employ will largely depend on the particular circumstances of each case. Instead, we hold that courts may use one or more of a variety of statistical methods to respond to the evidence presented. Allowing courts and defendants to use a more robust set of analytical tools will ensure more accurate, and narrowly tailored, responses to individual Duren challenges, which we can then assess on a fully developed record specific to the circumstances presented.6

In addition, the challenging party must establish not only statistical significance, but also legal significance. The results of any statistical method must be examined in the context of the likely, actual, "real life" impact on the jury pool at issue. As we have observed in earlier cases, "we look to people not percentages." United States v. Kleifgen, 557 F.2d 1293, 1297 (9th Cir. 1977).7 In other words, if a statistical analysis shows underrepresentation, but the underrepresentation does not substantially affect the representation of the group in the actual jury pool, then the underrepresentation does not have legal significance in the fair cross-section context.

In sum, the defendant must establish a prima facie case that the jury pool does not reflect a fair cross-section of the community. We overrule our prior precedent which required courts to analyze challenges exclusively by the use of the absolute disparity test. Rather, in determining whether the defendant has satisfied the burden of establishing a prima facie case, courts must consider the evidence proffered by the defendant, including expert testimony, and employ the most appropriate method, or methods, applicable to the specific challenge in the context of the particular jury pool at issue.

D

A revision of our precedent would normally warrant remanding the case to the district court to consider the question anew. However, we need not do so here because, even assuming that Hernandez has met the second Duren requirement, he has not satisfied the third. The third Duren prong requires proof that the underrepresentation in question "`is due to systematic exclusion of the group in the juryselection process.'" Miller, 771 F.2d at 1228 (quoting Duren, 439 U.S. at 364, 99 S.Ct. 664). To be systematic, underrepresentation must be "`due to the system by which juries were selected.'" Randolph v. California, 380 F.3d 1133, 1141 (9th Cir. 2004) (quoting Duren, 439 U.S. at 367, 99 S.Ct. 664). In Duren, for example, the underrepresentation was systematic because women, but not men, could opt out of jury service by so indicating on the juror questionnaire. Id. (discussing Duren). Moreover, if they did not return the questionnaire, women, but not men, were presumed to have opted out. Id. On the contrary, in Randolph, while the appellant showed that Hispanics were underrepresented in the venire, we rejected his cursory argument that "Hispanics return questionnaires at a lower rate than the general population" and concluded that Randolph had failed to establish a prima facie case under Duren because he had "not shown any relationship between the disproportionately low percentage of Hispanics in the venire and the juror-selection system the County uses." Id.

Here, while Hernandez has introduced significant evidence regarding underrepresentation of African Americans and Hispanics in the qualified juror pool, he has failed to provide evidence that this underrepresentation is due to the system employed by the Southern District, and has therefore failed to establish a prima facie case under Duren. Although he has highlighted several procedures of the Southern District that violate the Jury Selection Act, as we discuss below, those violations are not substantial, and Hernandez has not tendered sufficient proof that the violations constitute a systemic cause of any underrepresentation in the Southern District's venire. Most importantly, like the defendant in Rodriguez-Lara, Hernandez has not provided sufficient evidence "linking sole reliance on voter registration lists for jury selection to current systematic exclusion of [distinctive groups] in the [Southern District]." Rodriguez-Lara, 421 F.3d at 945. In other words, Hernandez "has not shown that the alternative system he proposes — [supplementing the juror source list] — would increase [minority group] representation." Randolph, 380 F.3d at 1141.8

Thus, we affirm the district court's denial of Hernandez's Jury Selection Act and Sixth Amendment fair cross-section claims because he has failed to meet his burden under the third prong of Duren. Because he did not establish a prima facie case under Duren, the burden did not shift to the government to justify the infringement, and our inquiry is at an end.

III

Hernandez also alleges that underrepresentation of African Americans and Hispanics in the Southern District's venire has violated his equal protection rights under the Fifth Amendment. The Supreme Court established a framework for analyzing Fifth Amendment jury composition challenges in Castaneda v. Partida. To establish a prima facie equal protection case under Castaneda, a party must: "(1) establish that the group, of which the appellant is a member, is `one that is a recognizable, distinct class, singled out for different treatment under the laws, as written or as applied;' (2) prove the degree of underrepresentation `by comparing the proportion of the group in the total population to the proportion called to serve as grand jurors, over a significant period of time;' and (3) discriminatory intent." Esquivel, 88 F.3d at 725 (quoting Castaneda, 430 U.S. at 494, 97 S.Ct. 1272).

As with the fair cross-section cases, courts have employed differing statistical methods for assessing underrepresentation in the equal protection context. Indeed, some circuits have employed a different test for equal protection challenges than for fair cross-section challenges. Compare Alston v. Manson, 791 F.2d 255, 257-58 (2d Cir.1986) (applying statistical decision theory to equal protection jury pool challenges), with Rioux, 97 F.3d at 655-56 (using absolute disparity/absolute numbers for a fair cross-section challenge). Because the essential question of underrepresentation is the same in both equal protection and fair cross-section challenges, there is no reason to require or apply different measures. Consistent with our holding as to cross-section challenges, we decline to impose a specific form of analysis on district courts. Rather, district courts should employ the method or methods most appropriate for the specific challenge.

But statistical proof of underepresentation does not end the inquiry in equal protection cases. The challenging party must also establish discriminatory intent, which we have held is "the most crucial factor in an equal protection case." Esquivel, 88 F.3d at 727. In this case, assuming, without deciding, that Hernandez has shown underrepresentation, there is no evidence of discriminatory intent and, as a consequence, Hernandez cannot make out a prima facie case.

IV

We turn next to Hernandez's four remaining Jury Selection Act claims. The Jury Selection Act was enacted "in response to numerous complaints of racial discrimination in the selection of potential jurors." Id. at 725. The act prescribes a variety of procedures to guide districts in compiling qualified jury pools. See 28 U.S.C. §§ 1861-1869. Nevertheless, not just any violation of the Jury Selection Act is actionable. Instead, the violation must constitute a "`substantial failure to comply'" with the Jury Selection Act. United States v. Nelson, 718 F.2d 315, 318 (9th Cir.1983) (quoting 28 U.S.C. § 1867(a)). Technical violations of the Jury Selection Act are "insubstantial where they do not frustrate the Act's goals." Id. (citing United States v. Goodlow, 597 F.2d 159, 162 (9th Cir.1979)); see also United States v. Erickson, 75 F.3d 470, 477 (9th Cir. 1996). The two underlying goals of the Act are the random selection of prospective jurors "from voter lists" and exclusions of prospective jurors "on the basis of objective criteria only." Nelson, 718 F.2d at 318.

A

Hernandez argues that the Southern District violated the Jury Selection Act by using outdated text in the English proficiency question on its prospective juror questionnaire and, as a result, wrongly excluding qualified prospective jurors. Hernandez notes, and the government concedes, that the Southern District's jury questionnaire contains outdated text instead of the current and less stringent text mandated by the Jury Selection Act.9 Hernandez concludes that the Southern District violated the Jury Selection Act by wrongly excluding all prospective jurors who answered "no" to the outdated English proficiency questionnaire, some of whom might have answered the question differently if it had reflected the current wording of the Jury Selection Act.

Despite the government's concession that the questionnaire is outdated, Hernandez still must show that this violation is substantial in that it contravenes the twin policies of the Jury Selection Act. The Fifth Circuit in United States v. Bearden provides helpful guidance for determining whether the wrongful exclusion of prospective jurors constitutes a substantial violation of the Jury Selection Act.

United States v. Bearden, 659 F.2d 590, 607 (5th Cir.1981) (citation omitted).

The outdated text of Question 4 does not violate the qualitative aspect of the Jury Selection Act, because no subjective criteria seeped into the district's qualification determinations. Whether the wording was correct or not, prospective jurors who answered "no" were uniformly disqualified — an objective determination premised on each respondent's professed English-language abilities and not on subjective considerations.10

As for the quantitative aspect of the Jury Selection Act, Hernandez must show a significant number of wrongful exclusions to render the Jury Selection Act violation substantial. Here, Hernandez has failed to do so. Hernandez focuses in particular on the fact that 1,420 Hispanic citizens were disqualified "solely because of their answer to the outdated English proficiency question." Indeed, he notes that 25.2% of Hispanics disqualified for any reason were disqualified solely because of their response to the English proficiency question and that 69.7% of all those disqualified solely for answering "no" to Question 4 were Hispanics. These numbers should give the Southern District pause, but they do not constitute a substantial violation.

Even in the unlikely event that all 1,420 of those Hispanic citizens would have answered Question 4 in the affirmative had it been worded differently, and were therefore wrongfully excluded, those 1,420 only constitute 2.05% of the 69,375 who returned the jury questionnaires and 3.49% of the 40,743 on the qualified jury wheel. These percentages are similar to, if a bit more than, the 1.2% and 1.6% respectively that the Fifth Circuit found to be insubstantial in Bearden.11 659 F.2d at 607. Accordingly, the outdated text of Question 4 and the related exclusions do not constitute a substantial violation of the Jury Selection Act.

B

Hernandez also contends that the Southern District contravened the Jury Selection Act when unsupervised court clerks disqualified prospective jurors who answered in the affirmative regarding their English proficiency but expressed doubts about their English-comprehension abilities elsewhere on the form. Hernandez focuses in particular on the exclusion of twelve Hispanic prospective jurors who answered "yes" to Question 4 of the Southern District's jury questionnaire but were excluded because they expressed doubts about their linguistic abilities in the "Remarks" section of the form.

The pertinent statute, 28 U.S.C. § 1865(a), requires the jury selection process — specifically the selection of qualified prospective jurors based on responses to the jury questionnaire — to be conducted "under [the] supervision of the court." While the Southern District's local rules authorize clerks to make qualification decisions under court supervision, it mandates that "[q]uestionable requests for being excused or other status determinations must be directed to the court." S.D. Cal. Civ. R. 83.10(c)(5). Here, the Jury Selection Act and the relevant rules required either a judicial officer to make the decision as to the qualifications of these twelve Hispanic jurors or, at a minimum, closer scrutiny by judicial officers.

Nevertheless, the fact that clerks alone made these determinations does not make this Jury Selection Act violation substantial. See United States v. Evans, 526 F.2d 701, 706 (5th Cir.1976) ("While some technical errors were made, the fact that clerks, rather than a judge, made these determinations does not necessitate reversal."). Furthermore, Hernandez provides evidence of the exclusion of only a small number of prospective jurors — for example only twelve Hispanic prospective jurors — by unsupervised clerks, as compared to the 40,743 prospective jurors in the qualified jury wheel. See Bearden, 659 F.2d at 606-07 (concluding that the erroneous dismissal of 495 prospective jurors was "insignificant in relation to the large number of prospective jurors handled by the clerk's office"). Finally, the violation does not contravene the policies underlying the Jury Selection Act because it does not intrude on the random selection of jurors from voter lists at earlier stages in the jury selection process, nor does it introduce subjective criteria into the selection process. See Goodlow, 597 F.2d at 161-62 (finding no substantial violation of the Jury Selection Act where men "who take care of young children" were automatically excluded from jury service). In fact, the prospective jurors appear to have been excluded objectively and uniformly based solely on a professed difficulty comprehending the English language. Thus, we affirm the district court's denial of Hernandez's motion to dismiss with respect to the unsupervised dismissal of certain prospective jurors by court clerks.

C

Hernandez also challenges the Southern District's failure to return jury questionnaires to prospective jurors who neglected to answer the questionnaire's race and ethnicity questions ("Question 10"). Title 28 U.S.C. § 1864(a) states that in "any case in which it appears that there is an omission, ambiguity, or error in a [filled-out jury questionnaire], the clerk or jury commission shall return the form with instructions to the person to make such additions or corrections as may be necessary and to return the form to the clerk or jury commission within ten days." Nevertheless, the Southern District has not returned questionnaires on which prospective jurors have failed to complete the race or ethnicity questions, due in part to guidance from the Administrative Office that such omissions do not require returning the questionnaires. In 2009, 18.17% of respondents did not answer the race question and 35.85% did not respond to the ethnicity question.

Even assuming that the Southern District should have sent back each of these questionnaires, this violation does not constitute a substantial violation of the Jury Selection Act because it does not contravene the law's twin policy goals. Nelson, 718 F.2d at 318. First, the jurors selected from the master jury wheel to receive jury questionnaires were still randomly selected. Even if all of those who did not respond to the race or ethnicity questions were white, thereby reducing the percentage of minority distinctive groups in the qualified jury wheel, Hernandez has not sufficiently established a link between the failure to return the jury questionnaires and any underrepresentation of various distinctive groups in the 2009 qualified jury wheel. Second, because no jurors were excluded due to their failure to respond to the race and ethnicity questions, no subjective criteria were introduced into the qualification process. As a result, we affirm the district court as to the Southern District's failure to return jury questionnaires.

D

Finally, Hernandez asserts that the Southern District violated the Jury Selection Act by failing to keep up-to-date jury representativeness statistics on regular Form AO-12 reports, unless prompted by litigation. Title 28 U.S.C. § 1863(a) requires each district court to "submit a report on the jury selection process within its jurisdiction [i.e., the Form AO-12 report] to the Administrative Office of the United States Courts in such form and at such times as the Judicial Conference of the United States may specify." The form's instructions require district courts to complete a Form AO-12 report at least each time the master jury wheel is filled.

Hernandez is correct that the Southern District has failed to complete its AO-12 reports on time. Indeed, the 1999, 2001, and 2003 reports were completed in 2004, and the 2005 and 2007 reports were finished in 2008. The timing of these reports seems to coincide with jury pool litigation in the Southern District, specifically, challenges in the Martinez-Orosco and Garcia-Arellano cases. See Motion to Dismiss, United States v. Martinez-Orosco, No. 3:03-cr02601-JAH, 2004 WL 5437826 (S.D.Cal. Oct. 8, 2004), ECF No. 47; Motion to Dismiss, United States v. Garcia-Arellano, No. 3:08-cr02876-BTM (S.D.Cal. Nov. 7, 2008), ECF No. 21. Still, Hernandez had access to all the relevant AO12s he needed for his litigation, and has not demonstrated how the late filing of AO-12 reports amounts to a substantial violation of the Jury Selection Act that contravenes the goals of the law. Thus, we affirm the district court's decision to deny Hernandez's motion to dismiss as to the late filing of AO-12 reports.

V

Because Hernandez has failed to establish a prima facie case under Duren, has not established discriminatory intent in the jury selection process, and has not provided sufficient evidence of substantial violations of the Jury Selection Act, we affirm the district court's denial of Hernandez's motion to dismiss on Fifth and Sixth Amendment and Jury Selection Act grounds. However, we overrule our prior exclusive reliance on the absolute disparity test in fair cross-section and equal protection cases, and permit district courts to analyze fair cross-section and equal protection cases using the most appropriate methods applicable to the particular challenge.

AFFIRMED.

M. SMITH, Circuit Judge, with whom SILVERMAN and BEA, Circuit Judges, join, concurring in the judgment:

The "absolute disparity" test, which we have employed for nearly forty years, leaves no doubt that Hernandez-Estrada's fair cross section claims fail under Duren's second prong. See Duren v. Missouri, 439 U.S. 357, 364, 99 S.Ct. 664, 58 L.Ed.2d 579 (1979). For this reason, I agree with the majority that we should affirm the judgment of the district court. The majority, however, declines to confine its opinion to answering the questions that are necessary to the resolution of this appeal. Instead, it treats this straight-forward case as a convenient Rocinante that it can mount like a knight-errant to challenge the specter of windmill giants on the distant horizon — be they real or imagined. I decline to join the majority's glorious quest.

By overruling our circuit precedent requiring that district courts exclusively apply the "absolute disparity" test to fair cross section claims, the majority needlessly raises a host of difficult questions for which there are no clear answers, and it leaves trial courts with little guidance on how to fulfill their responsibilities in such cases. The resulting legal vacuum will likely trigger an avalanche of fair cross section claims that have almost no chance of success under Duren, but which will burden the courts for years without meaningfully improving the administration of justice.

We apply a three-part test to determine whether a jury selection process complies with the fair cross section requirement. Id. To establish a prima facie fair cross section claim, the defendant must show: (1) that the group alleged to be excluded is a "distinctive" group in the community; (2) that the representation of this group in jury pools from which juries are selected is not fair and reasonable in relation to the number of such persons in the community; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process. Id.

In assessing Duren's second prong, we require statistical data demonstrating that "the jury pool does not adequately represent the distinctive group in relation to the number of persons in the community." United States v. Esquivel, 88 F.3d 722, 726 (9th Cir.1996). Until today, we have repeatedly held that courts in this circuit must use the "absolute disparity" test to analyze this statistical data. See, e.g., United States v. Rodriguez-Lara, 421 F.3d 932, 943-44 (9th Cir.2005); United States v. Sanchez-Lopez, 879 F.2d 541, 547 (9th Cir.1989); United States v. Potter, 552 F.2d 901, 905-06 (9th Cir.1977). While the "absolute disparity" test is not flawless,1 we have explained that this specific mode of analysis is particularly useful in assessing whether the fair cross section requirement has been violated because the analysis focuses on "people and not percentages." Potter, 552 F.2d at 905. That is, the "absolute disparity" test looks at the effect of a given deviation on the actual numerical composition of grand juries, and assesses whether the absence of such a deviation would affect jury composition in a way that meaningfully affects a defendant's Sixth Amendment rights.2

Today the majority announces that it is abandoning "our exclusive reliance on the absolute disparity test." But in so doing, the majority "decline[s] to confine district courts to a particular analytical method." Instead, the majority explains that "the appropriate test or tests to employ will largely depend on the particular circumstances of each case," and it encourages courts to use "one or more of a variety of statistical methods to respond to the evidence presented." However, the majority also notes that, like the "absolute disparity" test, each of these alternative statistical methods is likewise flawed.

Hereafter, trial courts will be charged with making ad hoc determinations regarding which statistical method, or combination of statistical methods, should be used to assess individual fair cross section claims. Yet, the majority provides little more than abstractions to guide the trial courts. While the majority discusses the benefits and disadvantages of a number of statistical frameworks, it explicitly declines to advise trial courts as to when and how these frameworks should be employed. The majority even declines to illustrate how the principles announced today would apply to the facts of this case. In so doing, the majority leaves unclear what role the "absolute disparity" test now plays, when alternative statistical methods should be employed, and which combination of statistical methods are appropriate under what circumstances.

Even more troubling is that the majority's injection of these uncertainties into our jurisprudence is entirely unnecessary to the disposition of this case. The majority concludes that, regardless of any statistical disparities in the jury pool from which Hernandez-Estrada's grand jury was selected, his fair cross section claims fail under Duren's third prong, because he failed to provide evidence that any underrepresentation was systematic in nature. In reaching this conclusion, the majority seems to shift the focus of fair cross section claims from Duren's second prong to its third. But the majority provides no guidance as to how systematic underrepresentation can be demonstrated where, as here, the source of the purported underrepresentation does not appear on the face of a district's jury questionnaire. See Duren, 439 U.S. at 366-67, 99 S.Ct. 664 (holding that underrepresentation was systematic where the jury questionnaire permitted women, but not men, to opt out of jury service).

Both the district court and our three judge panel concluded that, under the "absolute disparity" test, Hernandez-Estrada's fair cross section claims fail as a matter of law. I would affirm on the same basis, and I would only consider whether a change in our fair cross section jurisprudence is warranted when the outcome of the case requires such a determination.

I respectfully concur only with the judgment.

N.R. SMITH, Circuit Judge, concurring in the judgment.

A jury pool must be "reasonably representative" of the distinctive groups in the community. Taylor v. Louisiana, 419 U.S. 522, 538, 95 S.Ct. 692, 42 L.Ed.2d 690 (1975). However, the U.S. Supreme Court has not prescribed a particular statistical test for evaluating to what degree a distinctive group's underrepresentation in a jury pool substantiates a fair cross-section claim. Berghuis v. Smith, 559 U.S. 314, 329, 130 S.Ct. 1382, 176 L.Ed.2d 249 (2010).

I would affirm the district court's decision, because Hernandez-Estrada's fair cross-section claims fail Duren's second prong1 under the tests used by any United States Circuit Court of Appeals. In the Southern District of California during the relevant period, African-Americans constituted 5.2% of the jury-eligible population and were underrepresented.2 United States v. Hernandez-Estrada, 704 F.3d 1015, 1020-21 (9th Cir.2012). The 2009 jury wheel data reflects (1) a 1.7% absolute disparity, (2) a 32.7% comparative disparity, (3) an absolute impact of 0.39 fewer African-American jurors on a 23-member grand jury, and (4) 14 standard deviations. See id. at 1018, 1021.

This court has "declined to find underrepresentation of a distinctive group where the absolute disparity was 7.7% or lower." United States v. Rodriguez-Lara, 421 F.3d 932, 943-44 (9th Cir.2005). Thus, Hernandez-Estrada's data did not evidence actionable exclusion under Ninth Circuit law.

Hernandez-Estrada's data also does not reflect a substantial exclusion under any other Circuit's test. The First, Seventh, Eighth, and Eleventh Circuits solely rely on the absolute disparity test. See United States v. Royal, 174 F.3d 1, 10-11 (1st Cir.1999); United States v. Ashley, 54 F.3d 311, 314 (7th Cir.1995); United States v. Clifford, 640 F.2d 150, 155 (8th Cir. 1981); United States v. Pepe, 747 F.2d 632, 649 n. 18 (11th Cir.1984). The 1.7% absolute disparity in this case would not be sufficient to establish a prima facie fair cross-section claim under these Circuits' thresholds. See Royal, 174 F.3d at 10-11 (upholding 2.97%); Ashley, 54 F.3d at 314 (no prima facie case of underrepresentation if disparity does not exceed 10%); Clifford, 640 F.2d at 155 (upholding 7.2%); United States v. Rodriguez, 776 F.2d 1509, 1511 (11th Cir.1985) (no prima facie case of underrepresentation if disparity does not exceed 10%).

The Second and Fifth Circuits apply absolute disparity and absolute impact. See United States v. Rioux, 97 F.3d 648, 657-58 (2d Cir.1996) (applying absolute disparity and absolute impact); Mosley v. Dretke, 370 F.3d 467, 479 n. 5 (5th Cir. 2004) (applying absolute disparity and noting comparative disparity could be used in another case); United States v. Goff, 509 F.2d 825, 826-27 (5th Cir.1975) (applying absolute impact test). Under Second and Fifth Circuit law, Hernandez-Estrada's absolute disparity figure is too low, and the absolute impact of excluding less than one grand juror would likewise be insufficient. See Rioux, 97 F.3d at 658 (upholding 2.14% absolute disparity); United States v. Biaggi, 909 F.2d 662, 678 (2d Cir.1990) (holding absolute impact of two fewer African-American jurors in a venire of 60 not actionable); United States v. Butler, 611 F.2d 1066, 1070 (5th Cir.1980) (holding absolute disparity under 10% not actionable); Goff, 509 F.2d at 826-27 (holding absolute impact of 1.4 fewer African-American jurors in the 23-person grand jury not actionable).

Hernandez-Estrada's claim would also fail the Tenth Circuit test applying absolute disparity and comparative disparity. See United States v. Shinault, 147 F.3d 1266, 1273 (10th Cir.1998) (holding insufficient a 2.56% absolute disparity and a 50.09% comparative disparity when the group at issue constituted 5.11% of the jury-eligible population). The 1.7% absolute disparity and 32.7% comparative disparity for a small minority population (5.2%) here would evidence too insignificant an underrepresentation in the jury pool under Tenth Circuit law.

Similarly, the Third Circuit's test, applying absolute disparity, comparative disparity, and standard deviation, would defeat Hernandez-Estrada's claim (registering 14 standard deviations). See Ramseur v. Beyer, 983 F.2d 1215, 1230, 1232-33 (3d Cir.1992) (en banc) (upholding 14.1% absolute disparity, 40.1% comparative disparity when distinctive group made up 35.9% of jury-eligible population, 28.9 standard deviations).

Finally,3 Hernandez-Estrada's statistical evidence would not be actionable under the Fourth Circuit's test. The Fourth Circuit conflates the second and third Duren prongs and holds that "use of current voter registration lists as the source for a jury pool from which random selection of jurors is made presumptively provides a fair cross-section." United States v. Lewis, 10 F.3d 1086, 1090 (4th Cir.1993). To overcome the presumption, there must be a showing of "affirmative discrimination in [voter] registration." Id. Here, Hernandez-Estrada's claim would fail, because there is no evidence of such affirmative discrimination.

While Hernandez-Estrada's claims do not meet Duren's second prong, the majority is correct that exclusive use of the absolute disparity test seems inappropriate. United States v. Rodriguez-Lara, 421 F.3d 932 (9th Cir.2005) and its predecessors required us to accept up to a 7.7% absolute disparity based on a distinctive group's representation in a district's general populace and the group's presence in the district's jury pool. Id. at 943-44. This threshold necessarily doomed claims challenging the underrepresentation of minority populations comprising less than 7.7% of the general population. Id. Consequently, Rodriguez-Lara tended to deny the historically disenfranchised the "opportunity to be considered for service on grand and petit juries," an interest the Jury Selection and Service Act endeavors to protect. 28 U.S.C. § 1861.

Those facts should cause us to question Rodriguez-Lara, and overrule it in the appropriate case. However, we should do so where a workable standard could be developed, based on data and statistics in that case. Here, the majority relies on the third Duren prong to affirm Hernandez-Estrada's conviction and avoids applying any new standard to replace the rule expressed in Rodriguez-Lara. Had some statistical analysis under Duren's second prong been necessary to the outcome of Hernandez-Estrada's case (because he had presented statistics tending to show actionable underrepresentation), the majority could have demonstrated a reasoned application of the appropriate statistical tests. Such analysis could have served as a framework for district courts to apply to future fair cross-section claims.

We owe the district courts more direction than a survey of statistical measures to solve this problem. While the discussion of available tests may aid the district courts in choosing a fitting measure for a given fair cross-section challenge, the majority still provides no standard to evaluate minority exclusion. With only discussion, the district courts are left with at least these questions: In what circumstances would the district court consider statistics from a particular test? Should it apply more than one test? If so, which ones? If it were to evaluate multiple tests, which would be controlling? What outcomes under any test or tests would constitute a legally intolerable exclusion?

Formerly, Rodriguez-Lara compelled us to apply an overly rigid rule, which, while providing certainty, also tended to discriminate against some minority groups. Now at the other end of the spectrum, the majority establishes a laissez faire approach likely to precipitate entirely uncertain — and likely conflicting — outcomes.

Consequently, I respectfully concur only in the judgment.