
    Betty DUKES; Patricia Surgeson; Cleo Page; Deborah Gunter; Karen Williamson; Christine Kwapnoski; Edith Arana, Plaintiffs-Appellees, v. WAL-MART, INC., Defendant-Appellant. Betty Dukes; Patricia Surgeson; Cleo Page; Deborah Gunter; Karen Williamson; Christine Kwapnoski; Edith Arana, Plaintiffs-Appellants, v. Wal-Mart, Inc., Defendant-Appellee.
    Nos. 04-16688, 04-16720.
    United States Court of Appeals, Ninth Circuit.
    Argued and Submitted Aug. 8, 2005.
    Filed Feb. 6, 2007.
    
      See also 222 F.R.D. 189.
    
      Theodore J. Boutrous, Jr., (argued & briefed) Gibson, Dunn & Crutcher, Los Angeles, CA, for the defendant-appellant-cross-appellee.
    Brad Seligman (argued), The Impact Fund, Berkeley, California, and Elizabeth A. Lawrence, Steve Stemerman, Davis, Cowell & Bowe, LLP, San Francisco, CA. Christine E. Webber, Joseph M. Sellers, Julie Goldsmith Reiser, Cohen, Milstein, Hausfeld & Toll, PLLC, Washington, D.C., Irma D. Herrera, Debra A. Smith, Equal Rights Advocates, San Francisco, CA, Stephen Tinkler, Charles Firth, Tinkler & Firth, Santa Fe, NM, Debra Gardner, Public Justice Center, Baltimore, MD, Merit Bennett, Talia V. Kosh, Bennett & Kosh, Santa Fe, NM and Jocelyn D. Lar-kin, The Impact Fund (briefed), for the plaintiffs-appellees-cross-appellants.
    Terri L. Ross, McDermott Will & Emery LLP, New York, NY, for the amicus curiae.
    Marissa M. Tirona, National Employment Lawyers Association, Sari Francisco, CA, for the amici curiae.
    Ann Elizabeth Reesman, McGuiness Norris & Williams, LLP, Washington, DC, for the amicus curiae.
    Michael Foreman, Lawyers’ Committee for Civil Rights Under Law, Washington, DC, for the amici curiae.
    Daniel B. Kohrman, AARP Foundation Litigation, Washington, DC, for the .amici curiae.
    
      Jeffrey A. Berman, Sidley Austin Brown & Wood, Los Angeles, CA, and Bill Lann Lee, Lieff, Cabraser, Heimann & Bernstein, LLP, San Francisco, CA, for the amici curiae.
    Richard A. Samp, Washington Legal Foundation, Washington, DC, for the ami-cus curiae.
    Evelyn L. Becker, O’Melveny & Meyers LLP, Washginton, DC, for the amicus curiae.
    Before HARRY PREGERSON, ANDREW J. KLEINFELD, and MICHAEL DALY HAWKINS, Circuit Judges.
   PREGERSON, Circuit Judge.

Plaintiffs filed a class action suit against Wal-Mart alleging sexual discrimination under Title VII of the 1964 Civil Rights Act. The district court certified the class with minor modifications to Plaintiffs’ proposed class. We have jurisdiction under 28 U.S.C. § 1292(e). For the reasons set forth below, we affirm the district court, concluding that it did not abuse its discretion when it certified the class.

BACKGROUND

Plaintiffs’ Third Amended Complaint, brought on behalf of six named plaintiffs and all others similarly situated, asserts claims against Wal-Mart for sex discrimination under Title VII of the 1964 Civil Rights Act. Plaintiffs alleged that women employed in Wal-Mart stores: (1) are paid less than men in comparable positions, despite having higher performance ratings and greater seniority, and (2) receive fewer — and wait longer for — promotions to in-store management positions than men. Plaintiffs contend that Wal-Mart’s strong, centralized structure fosters or facilitates gender stereotyping and discrimination, that the policies and practices underlying this discriminatory treatment are consistent throughout Wal-Mart stores, and that this discrimination is common to all women who work or have worked in Wal-Mart stores.

Plaintiffs seek class-wide injunctive and declaratory relief, lost pay, and punitive damages. They do not seek any compensatory damages on behalf of the class, which is estimated to include more than 1.5 million women. The class encompasses women employed in a range of Wal-Mart positions — from part-time, entry-level, hourly employees to salaried managers.

On April 28, 2003, Plaintiffs filed a motion to certify a nationwide class of women who have been subjected to Wal-Mart’s allegedly discriminatory pay and promotions policies. Plaintiffs proposed that the district court certify the following class pursuant to Federal Rule of Civil Procedure 23:

All women employed at any Wal-Mart domestic retail store at any time since December 26, 1998, who have been or may be subjected to Wal-Mart’s challenged pay and management track promotions policies and practices.

Dukes v. Wal-Mart Stores, Inc. (“Dukes I”), 222 F.R.D. 137, 141-42 (N.D.Cal.2004). On September 23, 2004, after the parties had conducted extensive discovery and filed copious briefs, the district court heard oral argument. At the hearing, Wal-Mart emphasized the “historic” nature of Plaintiffs’ motion, inasmuch as it concerns a class of approximately 1.5 million women who work or worked in one or more of Wal-Mart’s 3,400 stores in 41 regions at any time since 1998. The court acknowledged Wal-Mart’s concerns but noted that, while the class size was large, the issues were not unusual. Before ruling on the class certification motion, the district court clearly stated that its decision would be limited to procedural questions because an adjudication of the merits was not appropriate at that early stage.

I. District Court Proceedings

On June 21, 2004, the district court issued an eighty-four-page order granting in part and denying in part Plaintiffs’ motion for class certification. See Dukes I, 222 F.R.D. at 187-88. With respect to Plaintiffs’ claims for equal pay, the district court granted Plaintiffs’ motion as to issues of alleged discrimination and all forms of requested relief. With respect to Plaintiffs’ promotion claim, the court’s finding was mixed. The court certified the proposed class as it related to issues of alleged discrimination (including liability for punitive damages) as well as injunctive and declaratory relief. However, the court denied Plaintiffs’ request for certification with respect to backpay because data relating to challenged promotions were not available for all class members. Both parties appealed.

II. The Appeal

Pursuant to Federal Rule of Civil Procedure 23(f), Wal-Mart appealed, contending that the district court erred by: (1) concluding that the class met Rule 23(a)’s commonality and typicality requirements; (2) eliminating Wal-Mart’s ability to respond to individual Plaintiffs claims; and (3) failing to recognize that Plaintiffs’ claims for monetary relief predominated over their claims for injunctive or declaratory relief. Plaintiffs cross-appealed, asserting that the district court erroneously limited the backpay relief for many of Plaintiffs’ promotion claims.

DISCUSSION

I. Standard And Scope Of Review

We review a district court’s decision regarding class certification for abuse of discretion. See Staton v. Boeing Co., 327 F.3d 938, 953 (9th Cir.2003). The district court’s decision to certify this class is subject to “very limited” review and will be reversed “only upon a strong showing that the district court’s decision was a clear abuse of discretion.” Armstrong v. Davis, 275 F.3d 849, 867 (9th Cir.2001) (citation omitted); see also Gonzales v. Free Speech Coalition, 408 F.3d 613, 618 (9th Cir.2005) (“Abuse of discretion is ‘a highly deferential standard,’ under which the appellate court cannot substitute its ‘view of what constitutes substantial justification for that of the district court’; rather, the review ‘is limited to assuring that the district court’s determination has a basis in reason.’ ” (citation omitted)); Blyden v. Mancusi, 186 F.3d 252, 269 (2d Cir.1999) (“A district court’s decision to certify a class is reviewed for abuse of discretion, and’[a] reviewing court must exercise even greater deference when the district court has certified a class than when it has declined to do so.’ ” (citation omitted)); Doninger v. Pac. Nw. Bell, Inc., 564 F.2d 1304, 1309 (9th Cir.1977) (“[J]udgment of the trial court should be given the greatest respect and the broadest discretion” (citation omitted)). A court abuses its discretion if it applies an impermissible legal criterion. See Molski v. Gleich, 318 F.3d 937, 946 (9th Cir.2003). Moreover, the district court’s factual findings as to the applicability of Rule 23 criteria are entitled to the traditional deference given to such a determination. Local Joint Executive Trust Fund v. Las Vegas Sands, 244 F.3d 1152, 1161 (9th Cir.2001) (citation omitted).

Rule 23 provides district courts with broad discretion to determine whether a class should be certified, and to revisit that certification throughout the legal proceedings before the court. See Armstrong v. Davis, 275 F.3d 849, 872 n. 28 (9th Cir.2001). If later evidence disproves Plaintiffs’ contentions that common issues predominate, the district court can at that stage modify or decertify the class, see Gen. Tel. Co. of Sw. v. Falcon, 457 U.S. 147, 160, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982) (“Even after a certification order is entered, the judge remains free to modify it in light of subsequent developments in the litigation.”), or use a variety of management devices, see In re Visa Check/MasterMoney Antitrust Litig., 280 F.3d 124, 141 (2d Cir.2001); 1 Newberg on Class Actions § 4.26 at 4-91 to 4-97.

Our review is limited to whether the district court correctly selected and applied Rule 23’s criteria. See Bogus v. Am. Speech & Hearing Ass’n., 582 F.2d 277, 289 (3d Cir.1978); Waste Mgmt. Holdings, Inc. v. Mowbray, 208 F.3d 288, 295 (1st Cir.2000) (“An abuse occurs when a court, in making a discretionary ruling, relies upon an improper factor, omits consideration of a factor entitled to substantial weight, or mulls the correct mix of factors but makes a clear error of judgment in assaying them.”) Thus, if Plaintiffs demonstrate that they meet Rule 23’s requirements, they should be allowed to pursue their action as a class. See Smilow v. Sw. Bell Mobile Sys., Inc., 323 F.3d 32, 40 (1st Cir.2003) (“There is even less reason to decertify a class where the possible existence of individual damages issues is a matter of conjecture.”).

II. Class Certifioation And Rule 23

A district court may certify a class only if: “(1) the class is so numerous that join-der of all members is impracticable; (2) there are questions of law and fact common to the class; (3) the claims or defenses of the representative parties are typical of the claims or defenses of the class; and (4) the representative parties will fairly and adequately protect the interests of the class.” Fed.R.Civ.P. 23(a).

The district court must also find that at least one of the following three conditions are satisfied: (1) the prosecution of separate actions would create a risk of: (a) inconsistent or varying adjudications or (b) individual adjudications dispositive of the interests of other members not a party to those adjudications; (2) the party opposing the class has acted or refused to act on grounds generally applicable to the class; or (3) the questions of law or fact common to the members of the class predominate over any questions affecting only individual members, and a class action is superior to other available methods for the fair and efficient adjudication of the controversy. See Fed.R.Civ.P. 23(b).

The party seeking certification bears the burden of showing that each of the four requirements of Rule 23(a) and at least one requirement of Rule 23(b) have been met. See Zinser v. Accufix Research Inst., Inc., 253 F.3d 1180, 1186, amended, 273 F.3d 1266 (9th Cir.2001).

A. Rule 23(a)

The class in this case is broad and diverse. It encompasses approximately 1.5 million employees, both salaried and hourly, with a range of positions, who are or were employed at one or more of Wal-Mart’s 3,400 stores across the country. Plaintiffs contend, and the district court found, that the large class is united by a complex of company-wide discriminatory practices against women.

1. Numerosity

Rule 23(a)(1) requires that the class be “so numerous that joinder of all members is impracticable.” Fed.R.Civ.P. 23(a)(1). Wal-Mart does not contest that numerosity is satisfied here, given that both parties estimate that the proposed class includes approximately 1.5 million women.

2. Commonality

Rule 23(a)(2) requires that “there are questions of law or fact common to the class.” Fed.R.Civ.P. 23(a)(2). Commonality focuses on the relationship of common facts and legal issues among class members. See, e.g., 1 Herbert B. New-berg & Alba Conte, Newberg on Class Actions § 3:10 at 271 (4th ed.2002). We noted in Hanlon v. Chrysler Corp., 150 F.3d 1011 (9th Cir.1998):

Rule 23(a)(2) has been construed permissively. All questions of fact and law need not be common to satisfy the rule. The existence of shared legal issues with divergent factual predicates is sufficient, as is a common core of salient facts coupled with disparate legal remedies within the class.

Id. at 1019.

The commonality test is qualitative rather than quantitative—one significant issue common to the class may be sufficient to warrant certification. See e.g., Savino v. Computer Credit, Inc., 173 F.R.D. 346, 352 (E.D.N.Y.1997), aff'd, 164 F.3d 81 (2d Cir.1998); see also 1 Newberg on Class Actions § 3:10 at 272-74. As the district court properly noted, “plaintiffs may demonstrate commonality by showing that class members have shared legal issues by divergent facts or that they share a common core of facts but base their claims for relief on different legal theories.” Dukes I, 222 F.R.D. at 145 (citing Hanlon, 150 F.3d at 1019).

The district court found that Plaintiffs had provided evidence sufficient to support their contention that significant factual and legal questions are common to all class members. After analyzing Plaintiffs’ evidence, the district court stated:

Plaintiffs have exceeded the permissive and minimal burden of establishing commonality by providing: (1) significant evidence of company-wide corporate practices and policies, which include (a) excessive subjectivity in personnel decisions, (b) gender stereotyping, and (c) maintenance of a strong corporate culture; (2) statistical evidence of gender disparities caused by discrimination; and (3) anecdotal evidence of gender bias. Together, this evidence raises an inference that Wal-Mart engages in discriminatory practices in compensation and promotion that affect all plaintiffs in a common manner.

Dukes I, 222 F.R.D. at 166. The court noted that Wal-Mart raised a number of challenges to Plaintiffs’ evidence of commonality but held that such objections related to the weight of the evidence, rather than its validity, and thus should be addressed by a jury at the merits phase. See id. Wal-Mart renews a number of those challenges. We address each challenge below.

a. “Significant Proof’ of a Corporate Policy of Discrimination

Plaintiffs presented four categories of evidence: (1) facts supporting the existence of company-wide policies and practices; (2) expert opinions supporting the existence of company-wide policies and practices; (3) expert statistical evidence of class-wide gender disparities attributable to discrimination; and (4) anecdotal evidence from class members around the country of discriminatory attitudes held or tolerated by management. See Dukes I, 222 F.R.D. at 145. Wal-Mart contends that this evidence is not sufficient to raise an inference of discrimination.

(1) Factual Evidence

Plaintiffs presented evidence of: (1) uniform personnel and management structure across stores; (2) Wal-Mart headquarter’s extensive oversight of store operations, company-wide policies governing pay and promotion decisions, and a strong, centralized corporate culture; (3) consistent gender-related disparities in every domestic region of the company; and (4) gender stereotyping. ■ Such evidence supports Plaintiffs’ contention that Wal-Mart operates a highly centralized company that promotes policies common to all stores and maintains a single system of oversight. Wal-Mart does not challenge this evidence.

(2) Expert Opinion

Plaintiffs presented evidence from Dr. William Bielby, a sociologist, to interpret and explain the facts that suggest that Wal-Mart has and promotes a strong corporate culture — a culture that may include gender stereotyping. Dr. Bielby based his opinion on, among other things, Wal-Mart managers’ deposition testimony; organizational Charts; correspondence, memos, reports, and presentations relating to personnel policy and practice, diversity, and equal employment opportunity issues; documents describing the culture and history of the company; and a large body of social science research on organizational policy and practice and on workplace bias.

Dr. Bielby testified that by employing a “social framework analysis,” he examined the distinctive features of Wal-Mart’s policies and practices and evaluated them “against what social science shows to be factors that create and sustain bias and those that minimize bias.” In Dr. Bielby’s opinion, “social science research demonstrates that gender stereotypes are especially likely to influence personnel decisions when they are based on subjective factors, because substantial decision-maker discretion tends to allow people to ‘seek out and retain stereotyping-confirming information and ignore or minimize information that defies stereotypes.’ ” Dukes I, 222 F.R.D. at 154. Dr. Bielby concluded: (1) that Wal-Mart’s centralized coordination, reinforced by a strong organizational culture, sustains uniformity in personnel policy and practice; (2) that there are significant deficiencies in Wal-Mart’s equal employment policies and practices; and (3) that Wal-Mart’s personnel policies and practices make pay and promotion decisions vulnerable to gender bias. See id.

Wal-Mart challenges Dr. Bielby’s third conclusion as vague and imprecise because he concluded that Wal-Mart is “vulnerable” to bias or gender stereotyping but failed to identify a specific discriminatory policy at Wal-Mart. Specifically, Wal-Mart contends that Dr. Bielby’s testimony does not meet the standards for expert testimony set forth in Federal Rule of Evidence 702 and Daubert v. Merrell Dow Pharm., Inc. (“Daubert I ”), 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), which held that a trial court must act as a “gatekeeper” in determining whether to admit or exclude evidence.

Wal-Mart made an identical argument to the district court, and the district court rejected it. See Dukes v. Wal-Mart (“Dukes II”), 222 F.R.D. 189 (N.D.Cal.2004). In a published order, the district court denied Wal-Mart’s motion to strike Dr. Bielby’s testimony, recognizing that an expert’s testimony need not be exact or quantifiable. See id. at 192; see also Dukes I, 222 F.R.D. at 154. In fact, it is well-recognized that “[e]xperts ordinarily deal in probabilities, in ‘coulds’ and ‘mights.’ ” United States v. Rahm, 993 F.2d 1405, 1412 (9th Cir.1993).

The district court noted that Wal-Mart’s challenges—specifically its challenge that Dr. Bielby failed to identify specific stereotyping policies or incidents— “are of the type that go to the weight, rather than the admissibility, of the evidence.” Dukes I, 222 F.R.D. at 191-92. The district court was on very solid ground here as it has long been recognized that arguments evaluating the weight of evidence or the merits of a case are improper at the class certification stage. See Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 177, 94 S.Ct. 2140, 40 L.Ed.2d 732 (1974) (“We find nothing in either the language or history of Rule 23 that gives a court any authority to conduct a preliminary inquiry into the merits of a suit in order to determine whether it may be maintained as a class action.”); Selzer v. Bd. of Educ. of City of New York, 112 F.R.D. 176, 178 (S.D.N.Y.1986) (“A motion for class certification is not the occasion for a mini-hearing on the merits.”).

In addition, courts need not apply the full Daubert “gate-keeper” standard at the class certification stage. Rather, “a lower Daubert standard should be employed at this [class certification] stage of the proceedings.” Thomas & Thomas Rodmakers, Inc. v. Neurport Adhesives & Composites, Inc., 209 F.R.D. 159, 162 (C.D.Cal.2002); see also In re Visa Check/MasterMoney Antitrust Litig., 280 F.3d at 132 n. 4 (“A Daubert motion is typically not made until later stages in litigation ... and a district court should not postpone consideration of a motion for class certification for the sake of waiting until a Daubert examination is appropriate”). Wal-Mart cites no authority for its argument that the district court should have applied Daubert at the class certification stage.

Further, Wal-Mart does not challenge Dr. Bielby’s methodology, acknowledging what courts have long accepted— namely, that social science statistics may add probative value to plaintiffs’ class action claims. See Price Waterhouse v. Hopkins, 490 U.S. 228, 235-36, 255, 109 S.Ct. 1775, 104 L.Ed.2d 268 (1989) (considering similar evidence offered by an expert social psychologist); Fed.R.Evid. 702 (recognizing that “scientific, technical, or other specialized knowledge” may assist the trier of fact). Instead, Wal-Mart challenges the validity of Dr. Bielby’s findings because he was unable to quantify with certainty the level of alleged discrimination at Wal-Mart. However, case law clarifies that certainty is not required for an expert’s findings to have probative value. See Price Waterhouse, 490 U.S. at 235-36, 109 S.Ct. 1775 (allowing social psychologist’s testimony that the defendant was “likely influenced by sex stereotyping,” even though the expert “admitted that she could not say with certainty whether any particular comment was the result of stereotyping”); Daubert v. Merrell Dow Pharm., Inc. (“Daubert II”), 43 F.3d 1311, 1316 (9th Cir.1995) (noting that scientific knowledge “does not mean absolute certainty” and that expert testimony should be admitted when “the proffered testimony is based on scientifically valid principles” (internal quotations omitted)). Accordingly, the district court was not required to apply Daubert at the class certification stage. Even if Daubert did apply at the certification stage, however, Dr. Bielby’s testimony would satisfy the Daubert test because Dr. Bielby employed a well-accepted methodology to reach his opinions and because his testimony has a “rehable basis in the knowledge and experience of [the relevant] discipline.” Daubert I, 509 U.S. at 592, 113 S.Ct. 2786.

(3) Statistical Evidence

It is well-established that commonality may be established by raising an inference of class-wide discrimination through the use of statistical analysis. See Caridad v. Metro-North Commuter R.R., 191 F.3d 283, 292 (2d Cir.1999); see also Stastny v. S. Bell Tel. & Tel. Co., 628 F.2d 267, 278 (4th Cir.1980) (recognizing that statistical data showing comparable disparities experienced by protected employees may raise an inference of a policy or practice of discrimination).

Dr. Richard Drogin, Plaintiffs’ statistician, analyzed data at a regional level. He ran separate regression analyses for each of the forty-one regions containing Wal-Mart stores. He concluded that “there are statistically significant disparities between men and women at Wal-Mart in terms of compensation and promotions, that these disparities are wide-spread across regions, and that they can be explained only by gender discrimination.” Dukes I, 222 F.R.D. at 154. Dr. Marc Bendick, Plaintiffs’ labor economics expert, conducted a “bench-marking” study comparing Wal-Mart with twenty of its competitors and concluded that Wal-Mart promotes a smaller percentage of women than its competitors. See id.

Wal-Mart challenges Dr. Drogin’s findings and faults his decision to conduct his research on the regional level, rather than analyze the data store-by-store. However, the proper test of whether workforce statistics should be viewed at the macro (regional) or micro (store or sub-store) level depends largely on the similarity of the employment practices and the interchange of employees at the various facilities. See Kirkland v. New York State Dept. of Corr. Servs., 520 F.2d 420, 425 (2d Cir.1975) (recognizing that the focus of analysis depends on nature of defendant’s employment practices); 2 Barbara Linde-mann & Paul Grossman, Employment Discrimination Law 1598, 1723 (3d ed.1996).

Here, Dr. Drogin explained that a store-by-store analysis would not capture: (1) the effect of district, regional, and eompa-ny-wide control over Wal-Mart’s uniform compensation policies and procedures; (2) the dissemination of Wal-Mart’s uniform compensation policies and procedures resulting from the frequent movement of store managers; or (8) Wal-Mart’s strong corporate culture. Such evidence supports Plaintiffs’ claim that the discrimination was closely related to Wal-Mart’s corporate structure and policies. Because Dr. Drogin provided a reasonable explanation for conducting his research at the regional level, the district court did not abuse its discretion when it credited Dr. Drogin’s analysis.

Wal-Mart also contends that the district court erred by not finding Wal-Mart’s statistical evidence more probative than Plaintiffs’ evidence because, according to Wal-Mart, its analysis was conducted store-by-store. However, contrary to Wal-Mart’s characterization of its analysis, its research was not conducted at the individual store level. Dr. Joan Ha-worth, Wal-Mart’s expert, did not conduct a store-by-store analysis; instead she reviewed data at the sub-store level by comparing departments to analyze the pay differential between male and female hourly employees. Further, our job on this appeal is to resolve whether the “evidence is sufficient to demonstrate common questions of fact warranting certification of the proposed class, not whether the evidence ultimately will be persuasive ” to the trier of fact. In re Visa Check/MasterMoney Antitrust Litig., 280 F.3d at 135 (emphasis added). Thus, it was appropriate for the court to avoid resolving “the battle of the experts” at this stage of the proceedings. See Caridad, 191 F.3d at 292-93 (noting that a district court may not weigh conflicting expert evidence or engage in “statistical dueling” of experts).

Finally, it is important to note that much of Dr. Haworth’s evidence, which Wal-Mart argues was “unrebutted” by Wal-Mart, was in fact stricken by the district court for failing to satisfy the standards of Federal Rules of Evidence 702 and 703. See Dukes II, 222 F.R.D. at 196. The district court specifically stated that Dr. Haworth’s stricken testimony could not be used to undermine or contradict Dr. Dro-gin’s analysis, see Dukes I, 222 F.R.D. at 157 (“As discussed in this Court’s Order re Motions to Strike, however, [Dr. Ha-worth’s] survey is stricken from the record. Accordingly, [Wal-Mart’s] reliance on this survey to challenge Dr. Drogin’s statistical methods is misplaced.”), and, as noted above, Wal-Mart does not appeal this ruling. Thus, while Dr. Haworth’s testimony may be relevant to an analysis of the merits of Plaintiffs’ claims, it does not rebut Dr. Drogin’s evidence and does not support Wal-Mart’s contention that its statistical evidence is more probative than Plaintiffs’ at the certification stage.

Because the district court reasonably concluded that Dr. Drogin’s regional analysis was probative and based on well-established scientific principles, and because Wal-Mart provided little or no proper legal or factual challenge to it, the district court did not abuse its discretion when it relied on Dr. Drogin’s use and interpretation of statistical data as a valid component of its commonality analysis.

(4) Anecdotal Evidence

Circumstantial and anecdotal evidence of discrimination is commonly used in Title VII “pattern and practice” cases to bolster statistical proof by bringing “the cold numbers convincingly to life.” Int’l Bhd. of Teamsters v. United States, 431 U.S. 324, 339, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977); Rudebusch v. Hughes, 313 F.3d 506, 517 (9th Cir.2002). Wal-Mart contends that the district court erred by concluding that the anecdotal evidence, presented by Plaintiffs in the form of 120 declarations, supported a finding of commonality. Wal-Mart maintains that the declarations depict a handful of “widely divergent” events that cannot be deemed probative or representative of discrimination in pay or management-track promotions.

In their declarations, the potential class members testified to being paid less than similarly situated men, being denied or delayed in receiving promotions in a disproportionate manner when compared with similarly situated men, working in an atmosphere with a strong corporate culture of discrimination, and being subjected to various individual sexist acts. The district court credited this evidence.

Wal-Mart contends that the district court erred because the 120 declarations cannot sufficiently represent a class of 1.5 million. However, we find no authority requiring or even suggesting that a plaintiff class submit a statistically significant number of declarations for such evidence to have any value.

Further, the district court did not state that this anecdotal evidence provided sufficient proof to establish commonality by itself, but rather noted that such evidence provides support for Plaintiffs’ contention that commonality is present. See Dukes I, 222 F.R.D. at 166 (“This anecdotal evidence, in combination with the other evidence previously discussed, further supports an inference that [Wal-Mart’s] policies and procedures have the effect of discriminating against Plaintiffs in a common manner.”). Because the declarations raise an inference of common discriminatory experiences and are consistent with Plaintiffs’ statistical evidence, the district court did not abuse its discretion when it credited Plaintiffs’ anecdotal evidence.

b. Subjective Decision-Making

As discussed above, the district court found substantial evidence suggesting common pay and promotion policies among Wal-Mart’s many stores. See Dukes I, 222 F.R.D. at 149. The court also reasoned that Wal-Mart’s decision to permit its managers to utilize subjectivity in interpreting those policies offers additional support for a commonality finding. See id. Relying on Sperling v. Hoffmann-La Roche, Inc., 924 F.Supp. 1346 (D.N.J.1996), Wal-Mart challenges the latter conclusion, contending that managers’ discretionary authority does not support a finding of commonality because “[decentralized, discretionary decision-making is not inherently discriminatory.”

It is well-established that subjective decision-making is a “ready mechanism for discrimination” and that courts should scrutinize it carefully. Sengitpta v. Morrison-Knudsen Co., 804 F.2d 1072, 1075 (9th Cir.1986). Wal-Mart is correct that discretionary decision-making by itself is insufficient to meet Plaintiffs’ burden of proof. The district court recognized this, noting that managerial discretion is but one of several factors that supported a finding of commonality. See Dukes I, 222 F.R.D. at 148-50 (“And while the presence of excessive subjectivity, alone, does not necessarily create a common question of fact, where, as here, such subjectivity is part of a consistent corporate policy and supported by other evidence giving rise to an inference of discrimination, courts have not hesitated to find that commonality is satisfied.”); see also Shipes v. Trinity Indus., 987 F.2d 311, 316 (5th Cir.1993) (“Allegations of similar discriminatory employment practices, such as the use of entirely subjective personnel processes that operate to discriminate, satisfy the commonality and typicality requirements of Rule 23(a).” (citation omitted)).

Plaintiffs produced substantial evidence of Wal-Mart’s centralized company culture and policies, see Dukes I, 222 F.R.D. at 151-54, which provides a nexus between the subjective decision-making and the considerable statistical evidence demonstrating a pattern of discriminatory pay and promotions for female employees, see id. at 154-65; see also Reid v. Lockheed Martin Aeronautics Co., 205 F.R.D. 655, 670-72 (N.D.Ga.2001) (recognizing that subjective decision-making may give rise to an inference of discrimination where there is evidence to provide a nexus between the subjective decision-making and discrimination). Therefore, for the reasons stated above, we find that the district court did not abuse its discretion when it held that Wal-Mart’s subjective decision-making policy raises an inference of discrimination, and provides support for Plaintiffs’ contention that commonality exists among possible class members.

c. Conclusion

Plaintiffs’ expert opinions, factual evidence, statistical evidence, and anecdotal evidence present significant proof of a corporate policy of discrimination and support Plaintiffs’ contention that female employees nationwide were subjected to a common pattern and practice of discrimination. Evidence of Wal-Mart’s subjective decision-making policy raises an inference of discrimination and provides further evidence of a common practice. Accordingly, we conclude that the district court did not abuse its discretion in holding that Plaintiffs satisfied the commonality factor.

3. Typicality

As an initial matter, Plaintiffs contend that Wal-Mart has waived a challenge to the district court’s typicality finding by failing to offer specific objections to the district court’s typicality finding. However, because Wal-Mart refers, somewhat obliquely, to the typicality factor in its opening brief and because typicality and commonality are similar and tend to merge, see Gen. Tel. Co. of Sw., 457 U.S. at 157 n. 13, 102 S.Ct. 2364, we conclude that Wal-Mart did not waive its opportunity to challenge the district court’s findings with regard to typicality. Thus, although Wal-Mart did not raise a specific challenge, it nevertheless raised a general objection to the district court’s conclusion that Plaintiffs’ evidence satisfies the typicality requirement.

a. Plaintiffs’ Claims Are Sufficiently Typical

Rule 23(a)(3) requires that “the claims or defenses of the representative parties are typical of the claims or defenses of the class.” Fed.R.Civ.P. 23(a)(3). We stated in Hanlon that “[u]nder the rule’s permissive standards, representative claims are ‘typical’ if they are reasonably coextensive with those of absent class members; they need not be substantially identical.” 150 F.3d at 1020. Some degree of individuality is to be expected in all cases, but that specificity does not necessarily defeat typicality. See Staton, 327 F.3d at 957.

We must consider whether the named plaintiffs allegedly suffered injury from a specific discriminatory practice by the employer in the same manner that the members of the proposed class did, and whether the named plaintiffs and the remaining class members suffered a similar injury from a general policy of employment discrimination. See id. Thus, even though individual employees in different stores with different managers may have received different levels of pay and were denied promotion or promoted at different rates, because the discrimination they allegedly suffered occurred through an alleged common practice&emdash;e.g., excessively subjective decision-making in a corporate culture of uniformity and gender stereotyping&emdash;their claims may be sufficiently typical to satisfy Rule 23(a)(3).

b. Plaintiffs’ Representatives Are Sufficiently Typical of the Class

“The test of typicality is whether other members have the same or similar injury, whether the action is based on conduct which is not unique to the named plaintiffs, and whether other class members have been injured by the same conduct.” Hanon v. Dataproducts Corp., 976 F.2d 497, 508 (9th Cir.1992) (internal quotation omitted); 1 Newberg on Class Actions § 3:13 at 327. There is no dispute that the class representatives are reasonably co-extensive with the hourly class members, because almost all of the class representatives hold hourly positions. Instead, Wal-Mart contends that the class representatives are not typical of all female in-store managers because only one of six class representative holds a salaried management position, and she holds a lower level position.

However, the lack of a class representative for each management category does not undermine Plaintiffs’ certification goal because all female employees faced the same discrimination. See Hartman v. Duffey, 19 F.3d 1459, 1471 (D.C.Cir.1994) (recognizing that an employee can challenge discrimination in “different job categories where the primary practices used to discriminate in the different categories are themselves similar. While it may be prudent to have the class divided into subclasses represented by a named plaintiff from each of the differing job categories, it would not be necessary to the validity of the class certification to do so.”); Paxton v. Union Nat’l Bank, 688 F.2d 552, 562 (8th Cir.1982) (holding that “[t]ypieality is not defeated because of the varied promotional opportunities at issue, or the differing qualifications of plaintiffs and class members”).

In addition, because the range of managers in the proposed class is limited to those working in Wal-Mart’s stores, it is not a very broad class, and a named plaintiff occupying a lower-level, salaried, in-store management position is sufficient to satisfy the “permissive” typicality requirement. Staton, 327 F.3d at 957 (recognizing that “[u]nder the rule’s permissive standards,” plaintiffs are not required to offer a class representative for each type of discrimination claim alleged (quoting Hanlon, 150 F.3d at 1020)).

Because Plaintiffs’ claims and Plaintiffs’ representatives are sufficiently typical of the class, the district court acted within its discretion when it found that Plaintiffs satisfied the typicality factor.

4. Adequate Representation

Rule 23(a)(4) permits certification of a class action only if “the representative parties will fairly and adequately protect the interests of the class.” Fed.R.Civ.P. 23(a)(4). This factor requires: (1) that the proposed representative Plaintiffs do not have conflicts of interest with the proposed class, and (2) that Plaintiffs are represented by qualified and competent counsel. See Hanlon, 150 F.3d at 1020; see also Molski, 318 F.3d at 955.

Before the district court, Wal-Mart argued that Plaintiffs cannot satisfy this factor because of a conflict of interest between female in-store managers who are both plaintiff class members and decision-making agents of Wal-Mart. Relying on Staton, the district court recognized that courts need not deny certification of an employment class simply because the class includes both supervisory and non-supervisory employees. See Dukes I, 222 F.R.D. at 168; see also Staton, 327 F.3d at 958-59. We agree. Finally, because Wal-Mart does not challenge the district court’s finding that Plaintiffs’ class representatives and counsel are adequate, we need not analyze this factor.

5. Conclusion

Significant evidence and substantial legal authority support the district court’s conclusion that Plaintiffs satisfied the nu-merosity, commonality, typicality, and adequacy requirements. Accordingly, we conclude that the district court did not abuse its discretion when it found that Plaintiffs offered evidence sufficient to satisfy Rule 23(a).

B. Rule 23(b)

As mentioned earlier, Plaintiffs moved to certify the class under Rule 23(b)(2), which requires that plaintiffs show that “the party opposing the class has acted or refused to act on grounds generally applicable to the class, thereby making appropriate final injunctive relief ... with respect to the class as a whole.” Fed.R.Civ.P. 23(b)(2). The district court agreed with Plaintiffs. See Dukes I, 222 F.R.D. at 170 (“Resolution of this issue is governed by Molski v. Gleich, 318 F.3d 937 (9th Cir.2003), which holds that (b)(2) class actions can include claims for monetary damages so long as such damages are not the ‘predominant’ relief sought, but instead are ‘secondary to the primary claim for injunctive or declaratory relief.’ ”). Wal-Mart contends that the district court merely “paid lip service” to Rule 23(b)(2) and erred in certifying the class under Rule 23(b)(2) because claims for monetary relief predominate over claims for injunctive and declaratory relief.

Rule 23(b)(2) is not appropriate for all classes and “does not extend to cases in which the appropriate final relief relates exclusively or predominantly to money damages.’’ Fed.R.Civ.P. 23(b)(2), Adv. Comm. Notes to 1966 amend., 39 F.R.D. 69, 102; see also Zinser, 253 F.3d at 1195 (“Class certification under Rule 23(b)(2) is appropriate only where the primary relief sought is declaratory or injunc-tive.”). In Molski we refused to adopt a bright-line rule distinguishing between incidental and non-incidental damages for the purposes of determining predominance because such a rule “would nullify the discretion vested in the district courts through Rule 23.” Molski, 318 F.3d at 950. Nor have we recognized a distinction between incidental and non-incidental damages in determining predominance for the purposes of Rule 23(b)(2) certification. See id. Instead, we examine the specific facts and circumstances of each case, focusing predominantly on the plaintiffs’ intent in bringing the suit. See id.; Kanter v. Warner-Lambert Co., 265 F.3d 853, 860 (9th Cir.2001); Linney v. Cellular Alaska P’ship, 151 F.3d 1234, 1240 n. 3 (9th Cir.1998).

1. Wal-Mart’s “Unrebutted” Evidence Does Not Undermine Plaintiffs’ Claim That Injunctive and Declaratory Relief Predominate

Wal-Mart first asserts that the district court “failed to even evaluate” Rule 23(b)’s requirement that the challenged conduct be generally applicable to the class. Wal-Mart maintains that its “unrebutted” statistics demonstrate that there is no evidence of pervasive discrimination that would justify injunctive relief and that, therefore, the “challenged conduct” does not affect all members. However, Wal-Mart’s contention is not persuasive. As explained above, Wal-Mart’s evidence was rebutted by Plaintiffs to the extent that Plaintiffs’ evidence and theories remain viable at this pre-merits analysis stage. Further, the issue before us is whether Plaintiffs’ primary goal in bringing this action is to obtain injunctive relief; not whether Plaintiffs will ultimately prevail. See Molski, 318 F.3d at 950. Consequently, Wal-Mart cannot derive support from this argument.

2. Employment Status of Certain Plaintiffs Does Not Obviate Claim That Injunctive and Declaratory Relief Predominate

Wal-Mart next argues that in-junctive relief claims cannot predominate—as Rule 23(b)(2) requires—because many of the class members are no longer employed,by Wal-Mart. However, there is little support for this contention. The Advisory Committee Notes to Rule 23(b)(2) state that the subsection “is intended to reach situations where a party has taken action or refused to take action with respect to a class, and final relief of an injunctive ... or ... declaratory nature, settling the legality of the behavior with respect to the class as a whole, is appropriate.” 39 F.R.D. at 102. The Advisory Committee illustrates this principle with cases, such as civil-rights actions, where a single set of actions or inactions harm an entire class of plaintiffs. Id. In cases such as these, stopping the illegal behavior is vital to the interests of the class as a whole.

Here, not only do the plaintiffs, current and former employees alike, state their common intention as ending Wal-Mart’s allegedly discriminatory practices, but logic also supports their declared intent. It is reasonable that plaintiffs who feel that their rights have been violated by an employer’s behavior would want that behavior, and the injustice it perpetuates, to end. In cases involving discrimination, it is especially likely that even those plaintiffs safe from immediate harm will be concerned about protecting those class members that are suffering as they once did. Perhaps that is why no case discusses the employment status of the plaintiffs as a factor in granting or denying class-certification under Rule 23(b)(2) even when former employees are explicitly mentioned as part of the class. See, e.g., Robinson v. Metro-North Commuter R.R. Co., 267 F.3d 147 (2d Cir.2001) (failing to discuss the presence of former employees in the class as a consideration in Rule 23(b)(2) analysis).

That some of the class members are former employees does not alter the primary intent of the plaintiffs as a whole and, therefore, does not subordinate Plaintiffs’ injunctive relief claims.

3. The Size of Plaintiffs’ Damages Request Does Not Undermine Plaintiffs’ Claim That Injunctive and Declaratory Relief Predominate

Wal-Mart contends that monetary claims necessarily predominate because this case involves claims that may amount to billions of dollars. However, such a large amount is principally a function of Wal-Mart’s size, and the predominance test turns on the primary goal of the litigation — not the theoretical or possible size of the damage award. As the district court stated,

[Fjocusing on the potential size of a punitive damage award would have the perverse effect of making it more difficult to certify a class the more egregious the defendant’s conduct or the larger the defendant. Such a result hardly squares with the remedial purposes of Title VII.

Dukes I, 222 F.R.D. at 171. Because Wal-Mart has not shown that the size of the damages request undermines Plaintiffs’ claim that injunctive and declaratory relief predominate, we find that Wal-Mart’s argument fails.

4. A Request for Punitive Damages Does Not Undermine Plaintiffs’ Claim That Injunctive and Declaratory Relief Predominate

While Plaintiffs do not ask for compensatory damages in this case, they do seek punitive damages to punish Wal-Mart for its allegedly “reckless disregard of the rights of its women employees to equal employment opportunity, and to deter similar misconduct by Wal-Mart and other large retailers in the future.” Dukes I, 222 F.R.D. at 170. Wal-Mart contends that Plaintiffs’ request for punitive damages is ‘‘wholly inconsistent” with Rule 23(b)(2) certification. This view, however, has not been adopted by this circuit. Rather, Molski states that courts should look to the plaintiffs’ intent in bringing the action. See Molski, 318 F.3d at 950 (“In order to determine predominance, we have focused on the language of- Rule 23(b)(2) and the intent of the plaintiffs in bringing the suit.”). As mentioned above, Plaintiffs stated that their primary intention in bringing this case was to obtain injunctive and declaratory relief — not money damages — and Wal-Mart has failed to effectively rebut Plaintiffs’ statements or cast doubt on their reliability. Therefore, we find that the district court acted within its discretion when it concluded that Plaintiffs’ claims for punitive damages do not predominate over claims for injunctive and declaratory relief. See Molski, 318 F.3d at 947-50; Robinson, 267 F.3d at 164 (recognizing that a district court may certify class under (b)(2) if it finds in its discretion that the positive weight or value of the injunctive relief sought is predominant even though punitive damages are claimed).

In addition, the district court’s order contains a provision to allow Plaintiffs to opt-out of claims for punitive damages. See Dukes I, 222 F.R.D. at 173 (“Accordingly, notice and an opportunity to opt-out shall be provided to the plaintiff class with respect to Plaintiffs’ claim for punitive damages.”). Although there is no absolute right of opt-out in a rule 23(b)(2) class, “even where monetary relief is sought and made available,” other courts have recognized that district courts should consider the possibility of opt-out rights. In re Monumental Life Ins. Co., 365 F.3d 408, 417 (5th Cir.2004); Jefferson v. Ingersoll Int’l, Inc., 195 F.3d 894, 898 (7th Cir.1999); see also Ticor Title Ins. Co. v. Brown, 511 U.S. 117, 121, 114 S.Ct. 1359, 128 L.Ed.2d 33 (1994) (suggesting that provisions allowing plaintiffs to opt-out of damages claims may be appropriate where plaintiffs move to certify a class bringing a claim for punitive damages). We note that a district court’s discretion to include an opt-out provision is well-established. See, e.g., In re Monumental Life Ins. Co., 365 F.3d at 417 (noting that district courts have discretion to order notice and opt-out rights when certifying a Rule 23(b)(2) class); Robinson, 267 F.3d at 165-67 (recognizing that notice and opt-out can be afforded (b)(2) class members with respect to non-incidental damage claims); Jefferson, 195 F.3d at 898-99.

5. A Request for Backpay Does Not Undermine Plaintiffs’ Claim That Injunctive and Declaratory Relief Predominate

Lastly, Wal-Mart asserts that Plaintiffs’ request for backpay weighs against certification because it proves that claims for monetary relief predominate. The district court reasoned that backpay “is recoverable as an equitable, make-whole remedy in employment class actions notwithstanding its monetary nature.” Dukes I, 222 F.R.D. at 170. Wal-Mart contends that the district court erroneously deemed backpay “equitable” and erred by failing to recognize that backpay, whether “equitable” or not, is a form of monetary relief.

As the district court noted, it is well-established that backpay is an equitable, make-whole remedy under Title VII that is fully consistent with Rule 23(b)(2), notwithstanding its monetary nature. See Dukes I, 222 F.R.D. at 170; see also Gotthardt v. Nat’l R.R. Passenger Corp., 191 F.3d 1148, 1152-55 (9th Cir.1999) (recognizing that backpay is equitable relief); Allison v. Citgo Petroleum Corp., 151 F.3d 402, 415 (5th Cir.1998) (“Back pay, of course, had long been recognized as an equitable remedy under Title VII.”); Eubanks v. Billington, 110 F.3d 87, 92 (D.C.Cir.1997) (“[I]t is not uncommon in employment discrimination [ (b)(2)] cases for the class also to seek monetary relief in the form of backpay or front pay.”).

Wal-Mart concedes that Rule 23(b)(2) may be appropriate in some cases where plaintiffs seek backpay, but maintains that Plaintiffs’ backpay claims cut against them in this case. In Eubanks, the D.C. Circuit recognized that “back pay is characterized as a form of ‘equitable relief in Title VII cases,” but that this “does not undercut the fact that variations in individual class members’ monetary claims may lead to divergences of interest that make unitary representation of a class problematic in the damages phase.” 110 F.3d at 95 (internal citations omitted). Eubanks envisioned that an opt-out option provision in the final certification decree might eliminate this concern. See id. (reiterating that requests for backpay are not inconsistent with Rule 23(b)(2), but that where conflicts of interests over backpay arise, a court can require additional measures, like an opt-out right, to maintain the class). Here, however, the district court did not make such a provision for Plaintiffs to opt-out of the claim for backpay damages.

Thus Plaintiffs request for backpay, despite its equitable nature, may weigh against a finding that injunctive or declaratory relief predominates.

Case law supports the district court’s conclusion that Plaintiffs’ requests for in-junctive and declaratory relief pre-domi-nate over their request for monetary relief. Plaintiffs have stated that it was their intent to obtain injunctive and declaratory relief by bringing this suit, see Molski, 318 F.3d at 950, and Wal-Mart has failed to effectively rebut Plaintiffs’ contention. The district court’s interpretation of Plaintiffs’ backpay request may have been erroneous, but that finding does not require reversal because the district court did not rely on improper factors, omit consideration of important factors, or clearly err in assaying factors. See Waste Mgmt. Holdings, Inc., 208 F.3d at 295. Accordingly, the district court did not abuse its discretion when it found that Plaintiffs offered evidence sufficient to satisfy Rule 23(b)(2)’s requirement that claims for declaratory or injunctive relief predominate.

III. The District Court Did Not Deprive Wal-Mart Of Defenses Or Alter Substantive Law

This case involves the largest certified class in history. The district court was cognizant of this fact when it concluded that the class size, although large, was not unmanageable. In analyzing the manageability of the class at all stages of the case, the district court reasoned that if, at the merits stage, Wal-Mart was found liable of discrimination, the court could employ a formula to determine the amount of back-pay and punitive damages owed to- the class members. Wal-Mart contends that, by reaching this conclusion, the district court “decided to strip Wal-Mart of its right to defend itself.”

Raising objections more appropriate for the merits stage, Wal-Mart maintains that it has the right to an individualized hearing for each class member’s claim so that it may present a defense relevant to the facts raised but that such a right cannot be exercised in a class action because of the enormous class size. Wal-Mart further contends that, by eliminating Wal-Mart’s ability to present a defense to each individual’s claims, the district court altered substantive law. For the reasons stated below, we find that the district court neither deprived Wal-Mart of substantive defenses nor altered substantive law when it certified the class.

A. Teamsters Does Not Require Individualized Hearings

Title VII recognizes that it is an “unlawful employment practice” for an employer “to discriminate against any individual ... because of such an individual’s race, color, religion, sex or national origin.” 42 U.S.C. § 2000e-2(a)(l). An employee who has suffered discrimination may obtain a declaration to that effect as well as an injunction against further discrimination. See id. § 2000e-5(g). That employee may also seek monetary relief, including compensatory damages and backpay, unless the employer is able to demonstrate that it “would have taken the same action in the absence of the impermissible motivating factor.” Id. § 2000e-5(g)(2)(B). Further, an employee may seek punitive damages if he or she can show that the employer acted “with malice or with reckless indifference to the federally protected rights of an aggrieved individual.” Id. § 1981a(b)(l).

A class action challenging a “pattern or practice” of discrimination typically proceeds in two stages. First, at the merits stage, the plaintiffs must prove that “discrimination was the company’s standard operating procedure.” Int’l Bhd. of Teamsters, 431 U.S. at 336, 97 S.Ct. 1843. If the plaintiffs carry their burden at this stage, all class members are entitled to a rebuttable presumption that they are entitled to relief. See id. at 361, 97 S.Ct. 1843. Second, at the remedy stage, the district court “must usually conduct additional proceedings ... to determine the scope of individual relief.” Id. (emphasis added).

Contrary to Wal-Mart’s assertion, Teamsters does not require that a district court utilize individualized hearings at the second stage. Rather, Teamsters notes that “additional proceedings” are usually employed, but that the district court has the discretion to be flexible and to “fashion such relief as the particular circumstances of a case may require to effect restitution.” Id. at 364, 97 S.Ct. 1843 (quoting Franks v. Bowman Transp. Co., 424 U.S. 747, 764, 96 S.Ct. 1251, 47 L.Ed.2d 444 (1976)); see also Carnegie v. Household Int’l, Inc., 376 F.3d 656, 661 (7th Cir.2004) (“Rule 23 allows district courts to devise imaginative solutions to problems created by the presence in a class action litigation of individual damages issues.”).

Thus, Teamsters does not require that the district court afford Wal-Mart the opportunity to present individualized defenses. See McKenzie v. Sawyer, 684 F.2d 62, 76 (D.C.Cir.1982) (recognizing that Teamsters “does not mandate individualized hearings in every case,” but instead requires only “some demonstration that the individual class members receiving compensation were likely victims of illegal discrimination”).

B. Title VII Does Not Require Individualized Hearings

In Pettway v. American Cast Iron Pipe Co. (“Pettway I”), 494 F.2d 211, 260 (5th Cir.1974), the Fifth Circuit reasoned that individualized hearings may be inappropriate where the employer’s conduct would reduce efforts to reconstruct individually what would have happened in the absence of discrimination to a “quagmire of hypothetical judgments.” We have already stated our agreement with this proposition, see Domingo, 727 F.2d at 1444, as have many other circuits, Pitre v. W. Elec. Co., 843 F.2d 1262, 1274 (10th Cir.1988); Pettway II, 681 F.2d at 1266; Segar v. Smith, 738 F.2d 1249, 1289-91 (D.C.Cir.1984); Hameed v. Int’l Ass’n of Bridge, Structural & Ornamental Iron Workers, 637 F.2d 506, 520 (8th Cir.1980); Stewart v. Gen. Motors Corp., 542 F.2d 445, 452-53 (7th Cir.1976). Thus, the district court did not abuse its discretion when it found that Title VII does not require a district court to employ individualized hearings in this ease.

C. Statistical Methods May Be Applied to Determine Relief

The district court found that statistical formulas can incorporate detailed information from employee databases about each individual to calculate whether, and in what amount, a specific individual has been underpaid or been denied a promotion. See Dukes I, 222 F.R.D. at 184-85. Wal-Mart contends that the district court lacked authority to determine that a statistical formula could be used to determine the total amount of backpay and punitive damages owed to Plaintiffs in the event that Wal-Mart is found liable for discriminating against Plaintiffs. Wal-Mart is understandably concerned that every class member could be given the same award or that non-victims could receive awards.

However, this concern is irrelevant to this interlocutory appeal. Numerous cases recognize the validity and potential advantage of statistical evidence and formulas. McDonnell Douglas v. Green, 411 U.S. 792, 805, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973) (suggesting that statistics as to an employer’s employment policy and practice “may be helpful” in establishing that a particular employment decision was in conformance with a general pattern of discrimination); Obrey v. Johnson, 400 F.3d 691, 694-95 (9th Cir.2005) (“In a case in which the plaintiff has alleged that his employer has engaged in a ‘pattern or practice’ of discrimination, ‘[statistical data is relevant because it can be used to establish a general discriminatory pattern in an employer’s hiring or promotion practices. Such a discriminatory pattern is probative of motive and can therefore create an inference of discriminatory intent with respect to the individual employment decision at issue.’ ”) (quoting Diaz v. Am. Tel. & Tel, 752 F.2d 1356, 1363 (9th Cir.1985)); see also Ratanasen v. California, 11 F.3d 1467, 1470-71 (9th Cir.1993); Coral Constr. Co. v. King County, 941 F.2d 910, 918 (9th Cir.1991) (“[F]or purposes of Title VII, ‘[w]here gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination.’ ”) (quoting Hazelwood Sch. Dist. v. United States, 433 U.S. 299, 307-08, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977)).

In fact, statistical methods can be more accurate than other methods for determining class member remedies. See Int’l Bhd. of Teamsters, Local 734 Health & Welfare Trust Fund v. Philip Morris, Inc., 196 F.3d 818, 823 (7th Cir.1999) (“Statistical methods could provide a decent answer—likely a more accurate answer than is possible when addressing the equivalent causation question in a single person’s suit.”). Finally, the allocation of relief need not be perfect; when computing a backpay award, “unrealistic exactitude is not required and all doubts should be resolved against the discriminating employer.” Shipes, 987 F.2d at 317; see also Domingo, 727 F.2d at 1445.

Thus, the district court did not abuse its discretion when it found that statistical methods may be applied to determine relief in this case.

D. Civil Rights Act of 1991

Wal-Mart contends that the Civil Rights Act of 1991, Pub.L. No. 108-198, 105 Stat. 1071 (1991) (“1991 Act”) (codified at 42 U.S.C. § 2000e), precludes use of the class action format in this case because Wal-Mart is entitled to present a “same decision” defense, which allows relief only to those individuals who can prove injury.

As mentioned above, Title VII makes it an “unlawful employment practice for an employer ... to discriminate against any individual ... because of such individual’s ... sex.” 42 U.S.C. § 2000e-2(a)(1). Courts often view the causation issues in employment discrimination cases in two categories. In “single-motive” cases, causation is seen as a single issue where the true basis for the adverse employment action is either legal or illegal. See Costa v. Desert Palace, Inc. (“Costa I”), 299 F.3d 838, 856 (9th Cir.2002), aff'd, Costa II, 539 U.S. 90, 123 S.Ct. 2148, 156 L.Ed.2d 84. In other words, in “single-motive” gender discrimination cases, plaintiffs succeed if they can demonstrate that an adverse employment action was taken “because of’ the plaintiffs’ sex. 42 U.S.C. § 2000e-2(a).

The 1991 Act recognized a second category for proving intentional discrimination: plaintiffs may attempt to establish liability for a “mixed motive” violation. 42 U.S.C. § 2000e-2(m). In “mixed-motive” cases, plaintiffs may attempt to prove that impermissible discrimination was a “motivating” factor for the employer’s challenged action. Costa I, 299 F.3d at 856. If plaintiffs choose to prove their case under this theory, the employer must prove that it would have made the same decision in the absence of the impermissible factor (“same decision defense”). See 42 U.S.C. § 2000e-5(g)(2)(B). If the employer does, the plaintiffs may still prevail but with limited remedies. Thus, under the 1991 Act, if the plaintiffs pursue their case under a “mixed motive” theory, a defendant may present a “same decision defense.”

Plaintiffs have the choice to proceed under a “single motive” theory or a “mixed motive” theory; Wal-Mart cannot force Plaintiffs to proceed under a “mixed motive” theory simply because it wishes to present a “same decision defense.” Bogle v. McClure, 332 F.3d 1347, 1357 (11th Cir.2003). In this case, Plaintiffs have elected to prove the “single motive” theory. This means that Wal-Mart is not entitled to present a “same decision defense” because such a defense at the remedy stage applies only where the conduct was the result of “mixed motives.” 42 U.S.C. § 2000e-5(g)(2)(B). Accordingly, the Civil Rights Act of 1991 does not preclude use of the class action format in this case.

E. Class Actions Involving Punitive Damages Do Not Necessarily Require Individualized Hearings

Wal-Mart contends that 42 U.S.C. § 1981a(b)(l), which permits punitive damages for “malice [or] reckless indifference to the federally protected rights of an aggrieved individual,” requires individualized remedy proceedings. Section 1981a(b)(l) states that a plaintiff may recover punitive damages if he or she “demonstrates that the respondent engaged in a discriminatory practice or discriminatory practices with malice or with reckless indifference to the federally protected rights of an aggrieved individual.” Wal-Mart contends that use of the singular “aggrieved individual” means that claims must be pursued and defended individually.

However, “aggrieved person” or “person aggrieved” is used throughout the statute to refer to more than one person. See 42 U.S.C. § 2000e-5(b), (c), (f)(1), (g)(1). Further, statutory reference to an “individual” has never before been read to preclude class format. See Califano v. Yamasaki 442 U.S. 682, 698-99, 99 S.Ct. 2545, 61 L.Ed.2d 176 (1979) (holding that language in the Social Security Act authorizing suit by “individual” did not preclude class relief). Thus, § 1981a(b)(l) does not require individualized remedy proceedings nor does it preclude use of the class action format in this case.

F. Due Process Does Not Require Individualized Hearings

Wal-Mart maintains that its due process rights will be violated if the district court is allowed to apply a statistical formula at the remedy stage. In essence, Wal-Mart contends that an ordinary defendant is entitled to hearings so that he or she may have the opportunity to review and rebut individualized claims but that, because of Wal-Mart’s size and the size of the class, it is deprived of opportunities afforded other defendants. Wal-Mart contends that individualized hearings, and not the analysis of aggregated data, are necessary to preserve its due process rights. We disagree.

“[The] aggregate computation of class monetary relief is lawful and proper. Challenges that such aggregate proof affects substantive law and otherwise violates the defendant’s due process or jury trial rights to contest each member’s claim individually, will not withstand analysis.” 3 Newberg on Class Actions § 10.05 at 483. Rather, “[f]ar from being vulnerable to constitutional or statutory authorization challenges, aggregate proof of the defendant’s monetary liability promotes the deterrence objectives of the substantive laws underlying the class actions and promotes the economy and judicial access for small claims objectives of Rule 23.” Id. at 487.

Relying on State Farm Automobile Insurance Co. v. Campbell, 538 U.S. 408, 123 S.Ct. 1513, 155 L.Ed.2d 585 (2003), Wal-Mart argues that a punitive damages award in the absence of individualized hearings would violate its due process rights because it might punish legal conduct and award damages to non-victims. However, State Farm is readily distinguishable from this case. State Farm involved an action brought on behalf of one individual under state law. See id. Moreover, as Plaintiffs note, there is no danger in this case that Wal-Mart will be punished for conduct that is legal where it occurred, because “Title VII is a federal law which applies to every Wal-Mart store in the United States.”

Further, in its order, the district court imposed several due process protections to prevent unjust enrichment by non-injured plaintiffs. First, the order specifies that any punitive damages award will be “based solely on evidence of conduct that was directed toward the class.” Dukes I, 222 F.R.D. at 172. This ensures that the punitive damage award will be calibrated to the specific harm suffered by the plaintiff class. In addition, the order states that recovery of punitive damages will be limited “to those class members who actually recover an award of lost pay, and thus can demonstrate that they were in fact personally harmed by the defendant’s conduct.” Id. Finally, the order requires that allocations of punitive damages to individual class members must be “in reasonable proportion to individual lost pay awards.” Id. Thus, in the event that Wal-Mart faces a punitive damages award, the district court took — and presumably will continue to take — sufficient steps to ensure that any award will comply with due process.

Caselaw supports the district court’s findings that substantive law does not mandate individualized hearings and that Wal-Mart’s Constitutional rights will not be violated if statistical formulas are employed to fashion the appropriate remedy. Therefore, we reject Wal-Mart’s contention that “the district court’s repeated disregard for governing substantive law compels reversal,” and find that the district court did not abuse its discretion when it found that the class size does not deprive Wal-Mart of its opportunity to present a defense.

IV. The District Court Did Not Abuse Its Discretion When It Limited The Backpay For Promotions Remedy To Plaintiffs With Objective Data

Plaintiffs cross-appealed the district court’s order, contending that it erred in limiting a promotion backpay remedy “to that subset of the class for whom objective applicant data exists.” Dukes I, 222 F.R.D. at 183. As the district court explained, ‘"While proof of a pattern of discrimination establishes a presumption in favor of class members, it does not in and of itself entitle each class member to back (or front) pay.” Id. at 175 (citing Pettway I, 494 F.2d at 259).

A class is defined not only by the members it comprises, but also by the particular kinds of relief to which those members are entitled. The district court determined that Plaintiffs could not seek promotional back pay as a class, but only as individual claimants. In fact, only those class members who can make a showing that they were either actually harmed by the discriminatory policy or were at least “a potential victim of the proved discrimination” are eligible to recover an award of lost pay. Int’l Bhd. of Teamsters, 431 U.S. at 362, 97 S.Ct. 1843; Robinson, 267 F.3d at 159. Plaintiffs must prove that they were both qualified and interested in obtaining the promotion. See Domingo, 727 F.2d at 1445 (recognizing that to be eligible for backpay, plaintiffs must prove that they applied for a promotion or would have applied if not for the employer’s discriminatory practices).

Wal-Mart’s corporate records may provide substantial objective information about class members’ qualifications for promotions, but there is no suggestion that such records demonstrate or quantify Plaintiffs’ interest. See Dukes I, 222 F.R.D. at 180. Thus, the district court reasoned, individual hearings would be necessary to determine which class members had an interest in, promotions. See id.

Conceding that individualized hearings would be unmanageable, Plaintiffs suggest that this court overlook the district court’s interest requirement. However, there is no support for this proposition. Rather, courts have recognized that a class member may be qualified for a promotion but not interested in taking advantage of that opportunity. See, e.g., Int’l Bhd. of Teamsters, 431 U.S. at 369, 97 S.Ct. 1843 (noting that “the desirability of [a promotion] is not so self-evident as to warrant a conclusion that all employees would prefer [the promotion] if given a free choice”); McKenzie, 684 F.2d at 76 (“The benefits illegally denied to the plaintiffs as a class were opportunities neither automatically sought nor automatically bestowed.... [It is not] reasonable to assume that all journeymen would wish to assume supervisory responsibilities”). Although Plaintiffs are correct that neither Teamsters nor McKenzie definitively requires individualized proof of interest at the remedy stage, Plaintiffs fail to present any case where a court states that individualized proof of interest is irrelevant.

We recognize that awarding backpay relief only to those plaintiffs who can demonstrate an interest in a promotion may deny relief to those class members exposed to the greatest opportunities for discrimination in promotions, Albemarle Paper Co. v. Moody, 422 U.S. 405, 421, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975), and in turn fail to provide the class with “the most complete relief possible,” id. However, in light of relevant case law, the district court acted reasonably when it concluded that class members must be able to prove with objective data an interest in a promotion in order to be eligible to collect certain damages. See Smilow, 323 F.3d at 40 (“Common issues predominate where individual factual determinations can be accomplished using computer records, clerical assistance, and objective criteria — thus rendering unnecessary an evidentiary hearing on each claim.”)- Therefore, we find that the district court did not abuse its discretion when it concluded that back-pay for promotions may be limited to those plaintiffs for whom actual proof of qualification and interest exists.

CONCLUSION

For the reasons set forth above, we hold that the district court acted within its broad discretion in concluding that it would be better to handle this case as a class action instead of clogging the federal courts with innumerable individual suits litigating the same issues repeatedly. The district court did not abuse its discretion in finding that Plaintiffs have met the pleading requirements of Rule 23. Wal-Mart failed to point to any specific management problems that would render a class action impracticable in this case, and the district court has the discretion to modify or de-certify the class should it become unmanageable. Although the size of this class action is large, mere size does not render a case unmanageable. We deny Plaintiffs cross-appeal, because the district court did not abuse its discretion when it found that backpay for promotions may be limited to those Plaintiffs for whom proof of qualification and interest exists. Finally, we must reiterate that our findings relate only to class action procedural questions; we neither analyze nor reach the merits of Plaintiffs’ allegations of gender discrimination.

AFFIRMED.

KLEINFELD, Circuit Judge,

dissenting:

I respectfully dissent. Class action certification violates the Rule 23 class action certification criteria and deprives Wal-Mart of due process of law.

Class actions need special justification because they are “an exception to the usual rule that litigation is conducted by and on behalf of the individual named parties only.” They are designed largely to solve an attorneys’ fees problem. “The policy at the very core of the class action mechanism is to overcome the problem that small recoveries do not provide the incentive for any individual to bring a solo action prosecuting his or her rights. A class action solves this problem by aggregating the relatively paltry potential recoveries into something worth someone’s (usually an attorney’s) labor.” That need does not pertain here, because the substantial value of sex discrimination claims, the availability of lawyers on contingent fee, and statutory attorney’s fees awards “eliminate financial barriers that might make individual lawsuits unlikely or infeasible.”

While a class action can have the virtue of assuring equal justice to all class members, it can also have the vice of binding them to something less than justice. This case poses a considerable risk of enriching undeserving class members and counsel, but depriving thousands of women actually injured by sex discrimination of their just due. Under Rule 23, the judgment “shall include” all class members, “whether or not favorable to the class.” That means that if the class loses, all the women presently or formerly employed by Wal-Mart lose.

A lawyer representing a class is in practical effect a lawyer without a client who can make the lawyer serve the client’s interest. A settlement serving the lawyer’s interests may disserve the interests of the class. These lawyers without clients must obtain judicial approval of a settlement, but often that works poorly, because a class action settlement is “a bargain proffered for its approval without benefit of adversarial investigation.” The class action device also threatens unfairness to the defendant. A lawsuit, like surgery, cannot be risk-free. Defendants are ordinarily wise to settle for an amount equal to the risk of losing multiplied by the potential loss. When the potential loss is stratospheric, a rational defendant will settle even the most unjust claim.

Class actions have four “threshold requirements”: (1) numerosity; (2) commonality; (3) typicality; and (4) adequacy of representation. While Rule 23 does not authorize courts considering class certification to evaluate the merits of a plaintiffs underlying claim, it does require “rigorous analysis” to ensure “actual, not presumed, conformance” with the criteria for class certification. As the Supreme Court recognized in Falcon, “the class determination generally involves considerations that are enmeshed in the factual and legal issues comprising the plaintiffs cause of action.” Accordingly, as the Second Circuit recently held in In re IPO, a district judge considering class certification must make a “definitive assessment of Rule 23 requirements, notwithstanding their overlap with merits issues” and “must receive enough evidence, by affidavits, documents or testimony, to be satisfied that each Rule 23 requirement has been met.” The relevance of a commonality depends on the proposition at issue. “All men are mortal” answers the question whether Socrates is mortal, but not who won the World Series. This class has numerosity to spare — 1.5 million women — but none of the other three requirements.

This class lacks “commonality” because there are no “questions of law or fact common to the class.” The only common question Plaintiffs identify with any precision is whether Wal-Mart’s promotion criteria are “excessively subjective.” That is not a commonality with any clear relationship to sex discrimination in pay, promotions, or terminations. Plaintiffs’ sociologist claims subjectivity makes the criteria “vulnerable” to sex discrimination. But the Supreme Court has already held that “leaving promotion decisions to the unchecked discretion of lower level supervisors should itself raise no inference of discriminatory conduct” because it is “self-evident” that standardized testing cannot sort out who ought to be a manager. “Vulnerability” to sex discrimination is not sex discrimination.

Plaintiffs’ only evidence of sex discrimination is that around 2/3 of Wal-Mart employees are female, but only about 1/3 of its managers are female. But as the Supreme Court recognized in Watson, “It is entirely unrealistic to assume that unlawful discrimination is the sole cause of people failing to gravitate to jobs and employers in accord with the laws of chance.” Not everybody wants to be a Wal-Mart manager. Those women who want to be managers may find better opportunities elsewhere. Plaintiffs’ statistics do not purport to compare women who want to be managers at Wal-Mart with men who want to be managers at Wal-Mart, just female and male employees, whether they want management jobs or not.

This class lacks “typicality” because “the claims or defenses of the representative parties” are not “typical of the claims or defenses of the class.” Plaintiffs must show “the existence of a class of persons who have suffered the same injury” as themselves. There are seven named plaintiffs, from different stores. Here they are, with the gist of the claims they make in the complaint:

Betty Dukes African American female promoted to manager, then demoted in retaliation for discrimination complaints. Did not apply for several slots filled by African American females, African American males, Hispanic female, Filipino male, and Caucasian male because she was discouraged by discrimination against women.
Patricia Surgeson Sexually harassed, replaced by a male who got a better title and more money, denied management opportunities, quit.
Cleo Page Quickly promoted to manager, but denied a department manager position after being told it’s “a man’s world.” A “Caucasian female” got the department manager position. Page later got a different department manager position. But a “Caucasian male,” a “Latina,” and a “Caucasian female” got other management positions she sought and she got paid less than a “Caucasian male” with less seniority-
Chris Kwapnoski Sought management positions given to less qualified men. Manager made sexist remarks.
Deborah Gunter Sought management positions given to less experienced males. Males she trained were promoted instead of her. Never got a management position. Fired after complaining about discrimination and a reduction in her hours.
Karen Williamson Sought management position but never promoted, even though “qualified.” Males got promotions that were not posted.
Edith Arana African-American woman. Sought management position but never promoted. Store manager told her he “did not want women.” Fired after “falsely accused of ‘stealing time’ ” in retaliation for her discrimination complaints.

“Typicality” exists only if these claims or defenses are “typical of the claims or defenses of the class.” They are not. Some plaintiffs work at Wal-Mart, some do not. Some were promoted to management, some were not. Some claim sex discrimination, some claim mixed motive race and sex discrimination, some appear to claim race discrimination, some claim retaliation, and some appear to claim unfairness but not discrimination. Some plead a prima facie case, some do not. Some are vulnerable to defenses like misconduct, some are not. They worked at different stores and complain of different actions taken by different managers. Whatever the “vulnerability” to sex discrimination of the “corporate culture” of this national corporation with no centralized system for promotion, the various Plaintiffs’ claims and Wal-Mart’s defenses against them do not resemble one another.

Whether these seven named plaintiffs “will fairly and adequately protect the interests of the class,” gets no serious attention, no doubt because everyone assumes that the lawyers will manage the case without much interference from their supposed clients. But if the named plaintiffs were really zealously represented, as they are entitled to be, their interests would diverge and require separate counsel. Women who still work at Wal-Mart have an interest in the terms of an injunction. But an injunction or declaratory judgment cannot benefit women who have quit or been fired and do not want to return. Those who are managers have interests different from those who have not been promoted. Those who face defenses, such as whether they were fired for stealing time, may have a greater interest in a compromise settlement than those whose records are unblemished. None of these plaintiffs adequately represent women at Wal-Mart who have been repeatedly promoted and are company favorites at high levels. Those women have an interest in broad management discretion in order to maximize company success and avoid burdening high performing women with the stigma of being dangerous to the company.

This class was certified under Rule 23(b)(2), which requires that declaratory and injunctive relief “predominate.” But these forms of relief cannot even benefit class members who no longer work for Wal-Mart and have no intention of returning, let alone “predominate.” Those class members lack standing to sue for declaratory and injunctive relief. They are like the summer temporary employee who sued after leaving her state job in Arizonans for Official English v. Arizona.

Although we accorded her standing, the same mistake we make here,- the Supreme Court unanimously disagreed.

The majority argues that former employees have standing to seek injunctive relief because “it is reasonable that plaintiffs who feel that their rights have been violated by an employers behavior would want that behavior, and the injustice it perpetuates, to end.” No doubt. And no doubt many people, some of whom have never set foot in a Wal-Mart, as an employee or even a customer, also feel that unjust behavior ought to end. But “the psychological consequence presumably produced by observation of conduct with which one disagrees ... is not an injury sufficient to confer standing under Art. III.”

It is hard to say that injunctive and declaratory relief “pre-dominate” even for those still employed who might benefit from an injunction, when they seek billions of dollars in punitive damages. Maybe that kind of money is “incidental” to those not paying it or getting it, but to most people billions of dollars would indeed “predominate.” What non-management employee would care much about how the district court told Wal-Mart to run its personnel system after getting enough cash to quit?

The punitive damages claim poses a constitutional barrier to class certification. The district court devised a scheme under which an “expert or special master” using an unspecified formula will allocate back and front pay to the class members. Plaintiffs waive other consequential compensatory damages. But before the “expert or special master” allocates pay, the jury will decide upon a lump sum amount of punitive damages. The special master will then decide on a formula to divide up all the money. There will never be an adjudication, by the jury or the special master, of whether any individual woman was injured by sex discrimination.

The scheme the majority approves cannot satisfy due process, because (1) there will never be an adjudication of compensatory damages, and (2) the allocation of back and front pay will follow the jury determination of punitive damages. As the Supreme Court held in State Farm, “few awards exceeding a single-digit ratio between punitive and compensatory damages, to a significant degree, will satisfy due process.” “Thus, punitive damages must be determined after proof of liability to individual plaintiffs at the second stage of a pattern or practice case, not upon the mere finding of general liability to the class at the first stage.”

The Civil Rights Act of 1991, and the Due Process Clause, require more individual justice than Wal-Mart will receive. “[I]n a multi-plaintiff, multi-defendant action, an approach that compares each plaintiffs individual compensatory damages with the punitive damages awards against each defendant more accurately reflects the true relationship between the harm for which a particular defendant is responsible, and the punitive damages assessed against that defendant.” The Civil Rights Act expressly prohibits orders requiring the reinstatement, promotion, or payment of back pay to anyone injured “for any reason other than discrimination.” The district court’s class certification scheme requires what the Civil Rights Act prohibits, the district court having decided “that this ‘rough justice’ is better than the alternative of no remedy at all for any class member.”

The district court calls this class certification “historic,” a euphemism for “unprecedented.” In the law, the absence of precedent is no recommendation. This class certification violates the requirements of Rule 23. It threatens the rights of women injured by sex discrimination. And it threatens Wal-Mart’s rights. The district court’s formula approach to dividing up punitive damages and back pay means that women injured by sex discrimination will have to share any recovery with women who were not. Women who were fired or not promoted for good reasons will take money from Wal-Mart they do not deserve, and get reinstated or promoted as well. This is “rough justice” indeed. “Rough,” anyway. Since when were the district courts converted into administrative agencies and empowered to ignore individual justice? 
      
      . For a description of the "social framework analysis,” see John Monahan and Larry Walker, Social Science in the Law: Cases and Materials (4th ed.1998).
     
      
      . Wal-Mart first challenged Dr. Bielby’s analysis in a motion to strike his declaration. Although the district court’s order denying Wal-Mart's motion is not specifically before us, its reasoning and conclusions have a bearing on Wal-Mart’s challenge to its commonality finding.
     
      
      . Each region contains approximately 80 to 85 stores.
     
      
      . Regression analyses, in general terms, provide estimates of the effect of independent variables on a single dependent variable. See Hemmings v. Tidyman's, Inc., 285 F.3d 1174, 1183-84 & n. 9 (9th Cir.2002). The purpose of this methodology is to estimate the extent to which a particular independent variable (in this case, gender) has influenced the dependent variables of compensation and promotion. See id.; see also Rudebusch v. Hughes, 313 F.3d 506, 511-12 (9th Cir.2002). As long as the analyses include enough relevant non-discriminatory independent variables (e.g., education, experience, performance, etc.), the results will indicate whether any salary disparities are attributable to gender (thereby raising an inference of discrimination) or whether the disparities are attributable to other factors (and thereby refuting such an inference). See Hemmings, 285 F.3d at 1183-84 & n. 9; see also EEOC v. Gen. Tel. Co. of Nw., Inc., 885 F.2d 575, 577 n. 3 (9th Cir.1989) (“A regression analysis is a common statistical tool ... designed to isolate the influence of one particular factor' — [e.g.,] sex — on a dependent variable- — [e.g.,] salary.” (citation omitted)).
     
      
      .Specifically, Dr. Bendick compared, or "benchmarked,” Wal-Mart against twenty other similar general merchandise retailers by comparing workforce data provided by the companies to the Equal Employment Opportunity Commission ("EEOC”). Dukes I, 222 F.R.D. at 164. Dr. Bendick analyzed the data to determine the extent to which women in the relevant market sought promotion, so that an inference could be made that roughly the same percentage of women would have sought promotion at Wal-Mart if given the opportunity. See id. As Dr. Bendick ex- ' plained, "The logic in benchmarking is that, if retail chains comparable to Wal-Mart are successfully employing women at some rate, then women are presumably available, interested, and qualified to hold comparable positions at Wal-Mart at a similar rate.” See id.
      
     
      
      . This means that Dr. Haworth ran separate regression analyses for: (1) each of the specialty departments in the store, (2) each grocery department in the store, and (3) the store’s remaining departments. She did not run regression analyses to examine pay differential between male and female salaried employees.
     
      
      . Wal-Mart maintains that the district court erred by not requiring Dr. Drogin to perform a “Chow test” to determine whether data could be properly aggregated. The Chow test (named after the statistician who created it) can be used to analyze whether two or more sets of data may be aggregated into a single sample in a statistical model. Dukes I, 222 F.R.D. at 157. However, there is no legal support for the contention that a Chow test must — or even should — be applied at the class certification stage. Further, we have not found a single case suggesting that commonality would be undermined if Plaintiffs’ evidence failed this test.
     
      
      .In addition to her sub-store analysis, Dr. Haworth conducted a survey of store managers. After reviewing the survey and its methodology, the district court concluded that the store manager survey was biased both "on its . face” and in the way that it was conducted. See Dukes II, 222 F.R.D. at 196-97 (noting that the survey's results "are not the 'product of reliable principles and methods,’ and therefore are not the type of evidence that would be ’reasonably relied upon by experts’ ” (quoting Fed.R.Evid. 702, 703)). Dr. Haworth’s disaggregated analysis created pools too small to yield any meaningful results. Wal-Mart has not appealed this issue. Accordingly, this evidence is not properly before us. See Kohler v. Inter-Tel Tech., 244 F.3d 1167, 1179 n. 8 (9th Cir.2001) (recognizing that appellant waived a claim by failing to raise it in her briefs).
     
      
      . Plaintiffs submitted declarations from each of the class representatives, as well as 114 declarations from putative class members around the country. See Dukes I, 222 F.R.D. at 165.
     
      
      . Although the "commonality and typicality requirements of Rule 23(a) tend to merge,” Gen. Tel. Co. of Sw., 457 U.S. at 157 n. 13, 102 S.Ct. 2364, each factor serves a discrete purpose. Commonality examines the relationship of facts and legal issues common to class members, while typicality focuses on the relationship of facts and issues between the class and its representatives. See 1 Newberg on Class Actions, §3:13 at 317.
     
      
      . The purported class need only satisfy one of Rule 23(b)'s prongs to be sustainable. See Zinser, 253 F.3d at 1186.
     
      
      . Plaintiffs submitted declarations supporting their contention that their requests for injunctive and declaratory relief predominate. Betty Dukes, for example, stated that her "primary goal [in this litigation] is to ensure that the employment practices at Wal-Mart which hinder the progress of women wishing to enter management be changed to ensure fair and equitable treatment of female employees, and to ensure women receive equal pay.” Edith Arana similarly noted that her "main concern is to end all those employment practices at Wal-Mart that have prevented women from obtaining management positions and to ensure equal pay for comparable work and equal access to the training and mentoring necessary to advance in the Company.” Wal-Mart counters that Plaintiffs "contend that injunctive relief predominates because the self-serving declarations of a few representatives say it does” but that money damages is their primary goal. However, Wal-Mart fails to offer any evidence to cast doubt on Plaintiffs' motivations. Accordingly, the district court reasonably relied on the statements in Plaintiffs' declarations.
     
      
      . Wal-Mart cites to two cases, Williams v. Owens-Illinois, Inc., 665 F.2d 918, 928-29 (9th Cir.1982), and Zinser, 253 F.3d at 1195, for the proposition that this circuit will not certify a class action that involves punitive damages. However, Williams and Zinser do not support Wal-Mart's contention. Rather, this court merely held that it was not an abuse of discretion to deny class certification based on the specific facts presented in those cases. See Williams, 665 F.2d at 929 (holding that damages requests were not incidental to the request for injunctive relief where requested compensatory damages were not clearly compatible with class injunctive relief); Zinser, 253 F.3d at 1195 (finding that a request for medical monitoring claims against manufacturer of pacemaker cannot be categorized as primarily equitable or injunctive per se because many state courts have recognized that medical monitoring relief is appropriate only as an element of damages after independent proof of liability).
     
      
      . Wal-Mart cites to Great-West Life & Annuity Insurance Co. v. Knudson, 534 U.S. 204, 122 S.Ct. 708, 151 L.Ed.2d 635 (2002), arguing that the district court erred in failing to recognize that backpay is not a form of equitable relief. However, Great-West Life does not support Wal-Mart’s contention. In fact, Great-West Life states that backpay under Title VII is an "integral part of the equitable remedy.” Id. at 218 n. 4, 122 S.Ct. 708.
     
      
      . Wal-Mart cites a law review article for the proposition that Pettway I authorizes use of a formula to determine backpay but requires individual hearings to determine whether class member's were entitled to relief. See Douglas L. Parker, Escape from the Quagmire: A Reconsideration of the Role of Teamsters Hearings in Title VII Litigation, 10 Indus. Rel. L.J. 171, 177 (1988). On the contrary, Pettway I vacated the district court's order that required individual hearings, rejected the employer’s due process argument, and remanded with specific instructions that the lower court consider a class-wide award, making no reference to individual hearings. See Pettway v. Am. Cast Iron Pipe Co. (“Pettway II”), 681 F.2d 1259, 1266 (11th Cir.1982).
     
      
      . Wal-Mart cites to several cases to support its contention that statistical formulas may be appropriate where there are hundreds of class members—rather than tens or hundreds of thousands. See Shipes, 987 F.2d at 315; Catlett v. Mo. Highway & Transp. Comm’n, 828 F.2d 1260, 1268 (8th Cir.1987); Domingo, 727 F.2d at 1435; Hameed, 637 F.2d at 520; Stewart, 542 F.2d at 450; EEOC v. O & G Spring & Wire Forms Specialty Co., 38 F.3d 872, 874 (7th Cir.1994). However, none of these cases require the application of a statistical formula to be limited to small class actions.
     
      
      . Wal-Mart also contends that the 1991 Act mandates that a district court hold individualized hearings where a defendant pursues a "mixed motive” defense. However, Wal-Mart offers no support for this theory. Nor does caselaw or legislative history suggest that individualized hearings are required where plaintiffs pursue a "mixed motive” theory. Regardless, this issue is irrelevant to the case at hand because, as discussed above, Plaintiffs are proceeding under the "single motive” theory.
     
      
      . Wal-Mart’s assertions that the use of statistical formulas deprives it of any defense is also without merit. For example, at the first post-class certification stage — the liability stage — Wal-Mart can: (1) present evidence that it did not engage in discrimination and (2) challenge Plaintiff's statistical model for liability. Wal-Mart is free to argue that business necessity justified its use of subjective pay and promotions criteria and/or contest the factors and criteria considered in determining whether there is a pattern and practice of discrimination. Further, at the remedial stage, Wal-Mart can argue and present evidence pertaining to the appropriate model for relief.
     
      
      . The district court speculated that a Special Master might assist the court by developing and employing a formula to compute damages at the remedy stage. See Dukes I, 222 F.R.D. at 176, 178. Wal-Mart contends that its Seventh Amendment rights to a jury trial will be violated if the district court assigns this task to a Special Master. However, neither Plaintiffs nor the district court has suggested that a Special Master would be substituted for the jury as the fact-finder. Further, as Plaintiffs note, any formula, whether prepared by a Special Master or the parties' experts, can be subjected to a jury's review. See, e.g., Hilao v. Estate of Marcos, 103 F.3d 767, 786 (9th Cir.1996).
     
      
      . Califano v. Yamasaki, 442 U.S. 682, 700-701, 99 S.Ct. 2545, 61 L.Ed.2d 176 (1979).
     
      
      . Amchem Prods, v. Windsor, 521 U.S. 591, 617, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997) (quoting Mace v. Van Ru Credit Corp., 109 F.3d 338, 344 (1997)).
     
      
      . 42 U.S.C. § 2000e-5(k).
     
      
      . Allison v. Citgo Petroleum Corp., 151 F.3d 402, 420 (5th Cir.1998).
     
      
      . Fed.R.Civ.P. 23(c)(3).
     
      
      . Amchem Products, Inc. v. Windsor, 521 U.S. 591, 621, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997) (affirming denial of class certification for purpose of asbestos claims settlement).
     
      
      . Amchem Products, Inc. v. Windsor, 521 U.S. 591, 613, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997); Staton v. Boeing Co., 327 F.3d 938, 953 (9th Cir.2003).
     
      
      . Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 178, 94 S.Ct. 2140, 40 L.Ed.2d 732 (1974).
     
      
      . General Telephone Co. of the Southwest v. Falcon, 457 U.S. 147, 160-61, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982).
     
      
      . General Telephone Co. of the Southwest v. Falcon, 457 U.S. 147, 160, 102 S.Ct 2364, 72 L.Ed.2d 740 (1982) (internal quotation marks omitted).
     
      
      . Miles v. Merrill Lynch & Co. (In re Initial Pub. Offering Sec. Litig.), 471 F.3d 24, 51-52 (2d Cir.2006).
     
      
      . Fed.R.Civ.P. 23(a)(2).
     
      
      . Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 990, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988).
     
      
      . Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 999, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988).
     
      
      . Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 992, 108 S.Ct. 2777, 101 L.Ed.2d 827 (1988).
     
      
      . Fed.R.Civ.P. 23(a)(3). Amchem Products, Inc. v. Windsor, 521 U.S. 591, 613, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997).
     
      
      . Gen. Tel. Co. of the Southwest v. Falcon, 457 U.S. 147, 157, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982).
     
      
      . I do not know why the district court and the majority say there are six.
     
      
      . Fed.R.Civ.P. 23(a)(3). Amchem Products, Inc. v. Windsor, 521 U.S. 591, 613, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997).
     
      
      . Fed.R.Civ.P. 23(b)(4).
     
      
      . Arizonans for Official English v. Ariz., 520 U.S. 43, 67, 117 S.Ct. 1055, 137 L.Ed.2d 170 (1997).
     
      
      . Yniguez v. Arizona, 939 F.2d 727, 734 (9th Cir.1991).
     
      
      . Maj. at 1235.
     
      
      . Valley Forge Christian College v. Americans United for Separation of Church & State, 454 U.S. 464, 485, 102 S.Ct. 752, 70 L.Ed.2d 700 (1982).
     
      
      . Dukes v. Wal-Mart Stores, Inc., 222 F.R.D. 137, 180 (D.Cal.2004).
     
      
      . State Farm Mut. Auto. Ins. Co. v. Campbell, 538 U.S. 408, 425, 123 S.Ct. 1513, 155 L.Ed.2d 585 (2003). See also Bains LLC v. Arco Prods. Co., 405 F.3d 764, 777 (9th Cir.2005) and Zhang v. Am. Gem Seafoods, Inc., 339 F.3d 1020, 1044 (9th Cir.2003) (holding 7 to 1 ratio constitutional in discrimination case).
     
      
      . Allison v. Citgo Petroleum Corp., 151 F.3d 402, 417-18 (5th Cir.1998) (internal citation omitted).
     
      
      . Planned Parenthood of the Columbia/Willamette, Inc. v. Am. Coalition of Life Activists, 422 F.3d 949, 961 (9th Cir.2005).
     
      
      . 42 U.S.C. § 2000e-5(g)(2)(A).
     
      
      . Dukes v. Wal-Mart Stores, Inc., 222 F.R.D. 137, 177 (D.Cal.2004).
     
      
      . Dukes v. Wal-Mart Stores, Inc., 222 F.R.D. 137, 142 (D.Cal.2004).
     