EDITH H. JONES, Circuit Judge:
This case, on review pursuant to Fed. Rule Civ. PROC. 23(f), implicates the standards and procedures used by district courts when considering certification of securities class actions dependent on the “fraud on the market” theory. See Basic, Inc. v. Levinson, 485 U.S. 224, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988). Like our brethren in the Third, Fourth, Seventh and Ninth Circuits, we hold that a careful certification inquiry is required and findings must be made based on adequate admissible evidence to justify class certification. Because the district court erroneously applied too lax a standard of proof to the plaintiffs’ fraud-on-the-market allegations, we must vacate the class certification and remand.
BACKGROUND
Amedisys provides home health care, nursing, home infusion therapy, and ambulatory surgery services. The company’s stock is traded on the NASDAQ Over The Counter Bulletin Board (“OTCBB”). Approximately ninety percent of Amedisys’s revenue comes from Medicare. This case stems from the conduct of Amedisys and its directors in reporting profits based on new Medicare procedures.
Beginning October 1, 2000, Medicare implemented the Prospective Payment System (“PPS”), which altered the way Medicare compensated home health care companies. Under PPS, Medicare paid health care companies like Amedisys a portion of their fees in advance, based on forward-looking estimates of the cost of services. After the company provided the service, the remainder of the fee was paid; alternatively, if the initial payment proved too high, the company had to reimburse Medicare the difference. To comply with the new PPS procedures, Amedisys purchased and implemented new computer software.
Plaintiffs allege that Amedisys willfully manipulated the PPS program to inflate the estimated costs for certain health services; that it thereby artificially fueled company earnings; and, ultimately, that Amedisys’s actions wrongfully enhanced its stock price. On June 13, 2001, Amedi-sys issued a curative statement, conceding that it had overstated revenues, but maintaining that the overstatements were inadvertently caused by the new software used with the PPS program. The stock price fell.
On August 21, 2001, Frances Unger filed suit against Amedisys, alleging violations [320]*320of Sections 10(b) and 20(a) of the Securities Exchange Act of 1934 and Rule 10b-5 promulgated thereunder. As is often the case, plaintiffs’ lawyers solicited potential class members over the Internet and through newspaper advertisements. Several other suits were consolidated with Un-ger’s ahd five individuals were chosen as lead plaintiffs. Class certification was requested for “all persons and entities who purchased the common stock of Amedisys, Inc. between November 15, 2000 through [sic] June 13, 2001.” Discovery occurred to ascertain the qualifications of the proposed class representatives. At a hearing, the district court evaluated this evidence and the plaintiffs’ sketchy evidence in support of the fraud-on-the-market basis for their presumed reliance on Amedisys’s misrepresentations. The district court certified the- class under Rule 23(b)(3).
The Amedisys defendants timely sought, and this court granted, an interlocutory appeal raising two issues embodied in the class certification: the adequacy of the lead plaintiffs’ qualifications and the sufficiency of plaintiffs’ evidence to support the fraud on the market presumption.
DISCUSSION
The class certification determination rests within the sound discretion of the'trial court. Gulf Oil Co. v. Bernard, 452 U.S. 89, 100, 101 S.Ct. 2193, 2200, 68 L.Ed.2d 693 (1981). That discretion, however, must be exercised within the constraints of Rule 23. Id. A district court that premises its legal analysis on an erroneous understanding of the governing law has abused its discretion. U.S. v. Insaulgarat, 378 F.3d 456, 464 (5th Cir.2004); U.S. v. Mann, 161 F.3d 840, 860 (5th Cir.1998).
Rule 23 requires the claims of a proposed class to meet several requirements before the class can be certified. The party seeking certification bears the burden of establishing that all requirements of Rule 23 have been satisfied. Berger v. Compaq Computer Corp., 257 F.3d 475, 479-80 (5th Cir.2001). First, the district court must find what has been termed numerosity, commonality, typicality, and representativeness.1 For class actions seeking money damages, like this one, the district court must make additional findings of predominance and superiority. Rule 23(b)(3). The predominance element requires a finding that common issues of law or fact “predominate over any questions affecting only individual members.” Id. This requirement, although reminiscent of the commonality requirement of Rule 23(a), is “far more demanding” because it “tests whether proposed classes are sufficiently cohesive to warrant adjudication by representation.” Amchem Prods., Inc. v. Windsor, 521 U.S. 591, 623-24, 117 S.Ct. 2231, 2249-50, 138 L.Ed.2d 689 (1997). Finally, a class action must afford the superior means to achieve “fair and efficient adjudication of the controversy.” Rule 23(b)(3).
Recognizing the important due process concerns of both plaintiffs and defendants inherent in the certification decision, the Supreme Court requires district courts to conduct a rigorous analysis of Rule 23 prerequisites. Gen’l Tel. Co. v. [321]*321Falcon, 457 U.S. 147, 161, 102 S.Ct. 2364, 2372, 72 L.Ed.2d 740 (1982). District courts are required to take a “close look” at the parties’ claims and evidence in making its Rule 23 decision. Amchem, 521 U.S. at 615, 117 S.Ct. at 2246. Class certification hearings should not be mini-trials on the merits of the class or individual claims. Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 177-78, 94 S.Ct. 2140, 2152-53, 40 L.Ed.2d 732 (1974). At the same time, however, “[g]oing beyond the pleadings is necessary, as a court must understand the claims, defenses, relevant facts, and applicable substantive law in order to make a meaningful determination of the certification issues.” Castano v. Am. Tobacco Co., 84 F.3d 734, 744 (5th Cir.1996). To assist the court in this process it may sanction controlled discovery at the certification stage. See Fed.R.Civ.P. 23 Advisory Committee’s Note to 2003 amendments. The plain text of Rule 23 requires the court to “find,” not merely assume, the facts favoring class certification. Rule 23(b)(3).
Appellants first challenge the qualifications of the class representatives under Rule 23(a)(4).
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EDITH H. JONES, Circuit Judge:
This case, on review pursuant to Fed. Rule Civ. PROC. 23(f), implicates the standards and procedures used by district courts when considering certification of securities class actions dependent on the “fraud on the market” theory. See Basic, Inc. v. Levinson, 485 U.S. 224, 108 S.Ct. 978, 99 L.Ed.2d 194 (1988). Like our brethren in the Third, Fourth, Seventh and Ninth Circuits, we hold that a careful certification inquiry is required and findings must be made based on adequate admissible evidence to justify class certification. Because the district court erroneously applied too lax a standard of proof to the plaintiffs’ fraud-on-the-market allegations, we must vacate the class certification and remand.
BACKGROUND
Amedisys provides home health care, nursing, home infusion therapy, and ambulatory surgery services. The company’s stock is traded on the NASDAQ Over The Counter Bulletin Board (“OTCBB”). Approximately ninety percent of Amedisys’s revenue comes from Medicare. This case stems from the conduct of Amedisys and its directors in reporting profits based on new Medicare procedures.
Beginning October 1, 2000, Medicare implemented the Prospective Payment System (“PPS”), which altered the way Medicare compensated home health care companies. Under PPS, Medicare paid health care companies like Amedisys a portion of their fees in advance, based on forward-looking estimates of the cost of services. After the company provided the service, the remainder of the fee was paid; alternatively, if the initial payment proved too high, the company had to reimburse Medicare the difference. To comply with the new PPS procedures, Amedisys purchased and implemented new computer software.
Plaintiffs allege that Amedisys willfully manipulated the PPS program to inflate the estimated costs for certain health services; that it thereby artificially fueled company earnings; and, ultimately, that Amedisys’s actions wrongfully enhanced its stock price. On June 13, 2001, Amedi-sys issued a curative statement, conceding that it had overstated revenues, but maintaining that the overstatements were inadvertently caused by the new software used with the PPS program. The stock price fell.
On August 21, 2001, Frances Unger filed suit against Amedisys, alleging violations [320]*320of Sections 10(b) and 20(a) of the Securities Exchange Act of 1934 and Rule 10b-5 promulgated thereunder. As is often the case, plaintiffs’ lawyers solicited potential class members over the Internet and through newspaper advertisements. Several other suits were consolidated with Un-ger’s ahd five individuals were chosen as lead plaintiffs. Class certification was requested for “all persons and entities who purchased the common stock of Amedisys, Inc. between November 15, 2000 through [sic] June 13, 2001.” Discovery occurred to ascertain the qualifications of the proposed class representatives. At a hearing, the district court evaluated this evidence and the plaintiffs’ sketchy evidence in support of the fraud-on-the-market basis for their presumed reliance on Amedisys’s misrepresentations. The district court certified the- class under Rule 23(b)(3).
The Amedisys defendants timely sought, and this court granted, an interlocutory appeal raising two issues embodied in the class certification: the adequacy of the lead plaintiffs’ qualifications and the sufficiency of plaintiffs’ evidence to support the fraud on the market presumption.
DISCUSSION
The class certification determination rests within the sound discretion of the'trial court. Gulf Oil Co. v. Bernard, 452 U.S. 89, 100, 101 S.Ct. 2193, 2200, 68 L.Ed.2d 693 (1981). That discretion, however, must be exercised within the constraints of Rule 23. Id. A district court that premises its legal analysis on an erroneous understanding of the governing law has abused its discretion. U.S. v. Insaulgarat, 378 F.3d 456, 464 (5th Cir.2004); U.S. v. Mann, 161 F.3d 840, 860 (5th Cir.1998).
Rule 23 requires the claims of a proposed class to meet several requirements before the class can be certified. The party seeking certification bears the burden of establishing that all requirements of Rule 23 have been satisfied. Berger v. Compaq Computer Corp., 257 F.3d 475, 479-80 (5th Cir.2001). First, the district court must find what has been termed numerosity, commonality, typicality, and representativeness.1 For class actions seeking money damages, like this one, the district court must make additional findings of predominance and superiority. Rule 23(b)(3). The predominance element requires a finding that common issues of law or fact “predominate over any questions affecting only individual members.” Id. This requirement, although reminiscent of the commonality requirement of Rule 23(a), is “far more demanding” because it “tests whether proposed classes are sufficiently cohesive to warrant adjudication by representation.” Amchem Prods., Inc. v. Windsor, 521 U.S. 591, 623-24, 117 S.Ct. 2231, 2249-50, 138 L.Ed.2d 689 (1997). Finally, a class action must afford the superior means to achieve “fair and efficient adjudication of the controversy.” Rule 23(b)(3).
Recognizing the important due process concerns of both plaintiffs and defendants inherent in the certification decision, the Supreme Court requires district courts to conduct a rigorous analysis of Rule 23 prerequisites. Gen’l Tel. Co. v. [321]*321Falcon, 457 U.S. 147, 161, 102 S.Ct. 2364, 2372, 72 L.Ed.2d 740 (1982). District courts are required to take a “close look” at the parties’ claims and evidence in making its Rule 23 decision. Amchem, 521 U.S. at 615, 117 S.Ct. at 2246. Class certification hearings should not be mini-trials on the merits of the class or individual claims. Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 177-78, 94 S.Ct. 2140, 2152-53, 40 L.Ed.2d 732 (1974). At the same time, however, “[g]oing beyond the pleadings is necessary, as a court must understand the claims, defenses, relevant facts, and applicable substantive law in order to make a meaningful determination of the certification issues.” Castano v. Am. Tobacco Co., 84 F.3d 734, 744 (5th Cir.1996). To assist the court in this process it may sanction controlled discovery at the certification stage. See Fed.R.Civ.P. 23 Advisory Committee’s Note to 2003 amendments. The plain text of Rule 23 requires the court to “find,” not merely assume, the facts favoring class certification. Rule 23(b)(3).
Appellants first challenge the qualifications of the class representatives under Rule 23(a)(4). To meet Rule 23 requirements, the court must find that class representatives, their counsel, and the relationship between the two are adequate to protect the interests of absent class members. Stirman v. Exxon Corp., 280 F.3d 554, 562 (5th Cir.2002). Class representatives must satisfy the court that they, and not counsel, are directing the litigation. To do this, class representatives must show themselves sufficiently informed about the litigation to manage the litigation effort. Berger, 257 F.3d at 479.
Nothing in the record indicates that the district court abused its discretion with regard to the Rule 23(a)(4) requirement. The district court fully evaluated the evidence, which included depositions and testimony of the class representatives. The court was neither clearly erroneous in its factfindings nor in error legally. To address this argument further would pointlessly require us to recount the case-specific evidence.
The crux of this appeal lies in the legal basis for and sufficiency of evidence supporting the district court’s finding of predominance under Rule 23(b)(3). The district court here expressed skepticism that Castaño, which discussed fraud and other claims raised by a putative nationwide class of tobacco smokers, should govern securities fraud class actions. Its skepticism was unfounded. Castaño is not logically so limited, and its reasoning has been approved in the securities fraud context by other circuit courts as well as by district courts in this circuit. Gariety v. Grant Thornton LLP, 368 F.3d 356, 362-64 (4th Cir.2004); Newton v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 259 F.3d 154, 168 (3d Cir.2001); see also Johnston v. HBO Film Management., Inc., 265 F.3d 178, 186-88 (3d Cir.2001); Szabo v. Bridgeport Mach., Inc., 249 F.3d 672, 676-77 (7th Cir.2001); Lehocky v. Tidel Techs., Inc., 220 F.R.D. 491, 504 (S.D.Tex.2004); Krogman v. Sterritt, 202 F.R.D. 467, 473 (N.D.Tex.2001); Griffin v. G K Intelligent Sys., Inc., 196 F.R.D. 298, 303-04 (S.D.Tex.2000).
One of the lessons emphasized by Castaño and related cases is that a district court must perform sufficient analysis to determine that class members’ fraud claims are not predicated on proving individual reliance. If the circumstances surrounding each plaintiffs alleged reliance on fraudulent representations differ, then reliance is an issue that will have to be proven by each plaintiff, and the proposed class fails Rule 23(b)(3)’s predominance requirement. Castano, 84 F.3d at 745; see also Simon v. Merrill Lynch, Pierce, Fen[322]*322ner & Smith, Inc., 482 F.2d 880, 882 (5th Cir.1973).
Only by invoking the fraud on the market theory can these plaintiffs establish a classwide rebuttable presumption of reliance on Amedisys’s alleged misrepresentations.2 In Basic, Inc., the Supreme Court held that reliance may be presumed, enabling 10b-5 class actions to proceed, “when a fraudulent misrepresentation or omission impairs the value of a security traded in an efficient market.”3 As the Court explained,
The fraud on the market theory is based on the hypothesis that, in an open and developed securities market, the price of a company’s stock is determined by the available material information regarding the company and its business .... Misleading statements will therefore defraud purchasers of stock even if the purchasers do not directly rely on the misstatements .... The causal connection between the defendants’ fraud and the plaintiffs’ purchase of stock in such a case is no less significant than in a case of direct reliance on misrepresentations.
Basic, Inc., 485 U.S. at 241-42, 108 S.Ct. at 989 (internal citations omitted) (emphasis added).
To support this rebuttable presumption, a securities plaintiff must prove, inter alia, that the security at issue is traded in an “efficient market.” Id. at 248-49, 108 S.Ct. at 992-93. In many cases, where heavily-traded or well known stocks are the target of suits, market efficiency will not even be an issue. But where, as here, the suit involves small-cap stocks traded in less-organized markets, a demonstration of an efficient market is a prerequisite for certification.4 Without an initial demonstration of market efficiency, there is no assurance that the available material information concerning the stock translates into an effect on the market price and supports a classwide presumption of reliance. Absent an efficient market, individual reliance by each plaintiff must be proven, and the proposed class will fail the predominance requirement. Cf. Castano, 84 F.3d at 745. Because this inquiry can prove decisive for class certification, and because, given the realities of litigation costs, certification can compel settlements without trial, courts have frequently applied rigorous, though preliminary, standards of proof to the market efficiency determination. See, e.g., Gariety, 368 F.3d at 368-70; Newton, 259 F.3d at 167-69; Szabo, 249 F.3d at 675-77; Binder v. Gillespie, 184 F.3d 1059, 1064-65 (9th Cir.1999); In re Seagate Tech. II Sec. Litig., 843 F.Supp. 1341, 1354-55 (N.D.Cal.1994); Krogman, 202 F.R.D. at 473; Griffin, 196 F.R.D. at 303-05. Courts have [323]*323likened the degree of proof required to the standards used in preliminary injunction hearings, see Gariety, 368 F.3d at 366, or in Fed. Rule Civ. Proo. 12(b)(1) and 12(b)(2) jurisdiction contests, Szabo, 249 F.3d at 676. Although the court’s determination for class certification purposes may be revised (or wholly rejected) by the ultimate factfinder, the court may not simply presume the facts in favor of an efficient market.
Courts have relied on several factors to determine whether a stock traded in an “efficient market”: (1) the average weekly trading volume expressed as a percentage of total outstanding shares; (2) the number of securities analysts following and reporting on the stock; (3) the extent to which market makers and arbitrageurs trade in the stock; (4) the company’s eligibility to file SEC registration Form S-3 (as opposed to Form S-l or S-2);5 (5) the existence of empirical facts “showing a cause and effect relationship between unexpected corporate events or financial releases and an immediate response in the stock price”; (6) the company’s market capitalization; (7) the bid-ask spread for stock sales; and (8) float, the stock’s trading volume without counting insider-owned stock. See Cammer v. Bloom, 711 F.Supp. 1264, 1286-87 (D.N.J.1989) (using and discussing the first five factors); Krogman, 202 F.R.D. at 477-78 (using the last three factors). These tools for gauging market efficiency have been used by many courts throughout the country and within this circuit. See, e.g., Gariety, 368 F.3d at 368; Binder, 184 F.3d at 1064-65; Hayes v. Gross, 982 F.2d 104, 107 (3d Cir.1992); Freeman v. Laventhol & Horwath, 915 F.2d 193, 198-99 (6th Cir.1990); Lehocky, 220 F.R.D. at 505-09.
Although this does not represent an exhaustive list, and in some cases one of the above factors may be unnecessary, once a court endeavors to apply these factors, they must be weighed analytically, not merely counted, as each of them represents a distinct facet of market efficiency. Some courts have concluded that there is not an efficient market as a matter of law for stocks trading in the over-the-counter market. See In re Data Access Sys. Sec. Litig., 103 F.R.D. 130, 138 (D.N.J.1984), rev’d on other grounds by 843 F.2d 1537 (3d Cir.1988); Epstein v. Am. Reserve Corp., No. 79 C 4767, 1988 WL 40500 (N.D.Ill. Apr.21, 1988). We need not go so far here, but such holdings are indicative of the wide gulf between the type of market for stocks that trade millions of shares daily, e.g., Basic, 485 U.S. at 243-44, 108 S.Ct. at 990, and the much less active market for stocks like Amedisys.6
[324]*324Unfortunately, the district court in this case devoted insufficient attention to evaluating the market efficiency factors. The court’s determination that, during the time in question,-Amedisys stock traded in. an efficient market, was predicated on its finding of three factors: high stock trading volume, market makers trading the stock, and a cause-and-effect relationship between corporate events and price movement.
A high weekly stock trading volume suggests the presence of active, informed investors. In evaluating the stock trading volume, however, the district court never ascertained — and the plaintiffs never proved — the actual number of Amedisys shares being regularly traded. Accepting the plaintiffs’ naked claim as to this analytical starting point cannot yield a reliable result. The court first “found” that the average weekly trading volume was 3.9% of the outstanding shares, but then conceded that the figure could be cut in half. Because the court appears to have based its determination only on two printouts from the Internet, the court did not determine the mathematically correct average weekly trading volume. As commentators observe, however, trade volume can be grossly exaggerated on some exchanges through double-counting, sometimes by over fifty percent. M. Barclay & F. Tor-chio, A Comparison of Trading Models Used for Calculating Aggregate Damages in Securities Litigation, 64 Law & Con-temp. Probs. 105, 106 (Summer 2001). At the certification stage, reliance on unverifiable evidence is hardly better than relying on bare allegations.
The district court also found that the presence of twenty-two “market makers” for Amedisys stock weighed in favor of a finding of market efficiency. To support this conclusion, the court relied on a single Internet printout, coupled with affidavits by plaintiffs’ witnesses that were admitted without opportunity for cross-examination. Moreover, the court failed to acknowledge growing concern that the mere number of market makers, without further analysis, has little to do with market efficiency. See, e.g., Krogman, 202 F.R.D. at 476 (noting that the “number of market makers” factor has in practice proven an unreliable measure of market efficiency unless tied to trade volume and price); Griffin, 196 F.R.D. at 304; Serfaty v. Int’l Automated Sys., Inc., 180 F.R.D. 418, 422 (D.Utah 1998); O’Neil v. Appel 165 F.R.D. 479, 502 (W.D.Mich.1996) (“The economic literature has criticized reliance upon the number of market makers as an indicator of efficiency.”); see also Brad M. Barber, et al., The Fraud-on-the-Market Theory and Indicators of Common Stock’s Efficiency, 19 J. CoRP. L. 285, 307 (1994). The district court erred when it did not consider the questionable relevance of this finding.
The district court also found a causal connection between Amedisys corporate events and the movement of the stock price, but did not take into account the many other factors that could affect the price of Amedisys stock. The court correctly identified, the causal connection as one of the most important market-efficiency factors. It goes to the heart of the “fraud on the market” theory: In an efficient market, where information is nearly perfect, material misstatements alter a stock’s price almost immediately. In such circumstances, “it is easy to see how injury can befall a person who is unaware of the [325]*325deceit.” See Eckstein v. Balcor Film Investors, 8 F.3d 1121, 1129-30 (7th Cir.1993). Demonstrating that market reactions are caused by company press releases should not, however, be an exercise in post hoc, propter hoc logic. Many variables have the potential to and do affect a stock price — the daily market average; national, local and industry-specific economic news; competitors’ activities; and on and on. The overall volatility of the stock price and the speed of its reaction to company news may also be significant. See, e.g., Krogman, 202 F.R.D. at 477-78. To this end, expert testimony may be helpful because of the utility of statistical event analysis for this inquiry. See supra, n. 6.
Instead of recognizing the complexity of this cause-and-effect factor, the court relied on a showing that on March 1 and May 1, 2001, the stock price rose following positive announcements issued by Amedi-sys on those days, and the price dropped the day the company announced that its earnings would be restated. This evidence is no doubt worthwhile, but standing alone, it is insufficiently probative to determine, based on “empirical facts,” see Cammer, 711 F.Supp. at 1287, that a causal connection exists. In short, the court incorrectly used all three factors it found in favor of market efficiency as a checklist rather than an analytical tool.
Similarly, the court failed to evaluate the significance of the market-efficiency factors lacking in the instant case. For instance, the number of securities analysts following the stock is an important factor. See, e.g., Krogman, 202 F.R.D. at 475; Cammer, 711 F.Supp. at 1286-87. Hence, the fact that no analyst was reporting on Amedisys stock at the time in question should have been weighed against the rather scant utility of, for example, the number of “market makers.” Further, the court did not address the effect on the market efficiency determination of Amedi-sys’s ineligibility to file an SEC Form S-3 at the time in question (the other factor absent in this case).7 Because Rule 23 mandates a complete analysis of “fraud on the market” indicators, district courts must address and weigh factors both for and against market efficiency.
CONCLUSION
Although we owe considerable deference to district courts in reviewing certification decisions, we cannot affirm the order as it is presently supported. After a more thorough inquiry, however, certification may ultimately prove correct. When a court considers class certification based on the fraud on the market theory, it must engage in thorough analysis, weigh the relevant factors, require both parties to justify their allegations, and base its ruling on admissible evidence. Questions of market efficiency cannot be treated differently from other preliminary certification issues. Courts cannot make an informed decision based on bare allegations, one-sided affidavits, and unexplained Internet printouts.
For the foregoing reasons, the class certification order is VACATED and REMANDED for further proceedings consistent herewith.
VACATED AND REMANDED.