Full opinion text
MEMORANDUM & ORDER PAULEY, District Judge. This action involves class-based allegations that certain policies and practices of the New York City Human Resources Administration, the New York State Office of Temporary and Disability Assistance, and the New York State Department of Health have the effect of preventing eligible individuals from applying for and timely receiving food stamps, Medicaid and cash assistance benefits. This memorandum and order addresses three motions. First, New York City Mayor Rudolph Giuliani and Jason Turner, Commissioner of the New York City Human Resources Administration (the “City defendants”), move to vacate the preliminary injunction entered by this Court on January 25, 1999 and modified on May .24, 1999. Additionally, defendants Brian J. Wing, Commissioner of the New York State Office of Temporary and Disability Assistance, and Barbara DeBuono, Commissioner of the New York State Department of Health (the “State defendants”), move for an order, pursuant to Fed.R.Civ.P. 12(b)(6), dismissing the complaint as against them. Finally, plaintiffs Lakisha Reynolds, Georgina Bonilla, April Smiley, Lue Garlick, Adriana Calabrese, Jenny Cuevas and El-ston Richards move for an order, pursuant to Fed.R.Civ.P. 23, certifying as class plaintiffs “[a]ll New York City residents who have sought, are seeking, or will seek to apply for food stamps, Medicaid, and/or cash assistance from City defendants at Job Centers.” (Compl. ¶ 61) The facts of this case, together with the statutory and regulatory framework underlying plaintiffs’ claims, are set forth in two prior memoranda and orders of this Court, familiarity with which is assumed. See Reynolds v. Giuliani, 35 F.Supp.2d 331 (S.D.N.Y.1999) (“Reynolds I”); Reynolds v. Giuliani, 43 F.Supp.2d 492 (S.D.N.Y.1999) (“Reynolds II”). However, given the complexity of this litigation and the substantial evidentiary record that the parties have amassed, it is useful to summarize the factual background and procedural posture of the action before turning to the pending motions. Background Until March 1998, New York City’s Human Resources Administration (“HRA”) accepted and processed applications for public assistance at offices known as income support centers. Thereafter, HRA began converting its 31 income support centers to “job centers” in an effort to implement the changes in federal and State welfare policy wrought by the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 (“PRWORA”), Pub.L. No. 104-193, 110 Stat. 2105 (Aug. 22,1996). PRWORA changed welfare programs in New York and around the country by, among other things, ending the Aid to Families with Dependent Children (“AFDC”) program and replacing it with a block grant program known as the Temporary Assistance to Needy Families (“TANF”). TANF introduces mandatory work requirements and limits the amount of time that a person can collect benefits. See, e.g., 42 U.S.C. § 607 (detailing mandatory work requirements for those receiving TANF benefits); 42 U.S.C. § 602(a)(l)(A)(ii) (requiring TANF recipients to work when they are determined to be ready to work, or after twenty-four months of benefits, whichever is earlier); 42 U.S.C. § 608(a)(1)(B) (forbidding states from using TANF money to assist a family if an adult in the family has received assistance for sixty months). New York passed its own welfare reform legislation in August 1997 and participates in TANF through two cash assistance programs: Family Assistance, which is available to pregnant women and families with a minor child, and Safety Net Assistance, which is available to childless adults. See N.Y. Social Services Law §§ 158 and 349. In New York City, these public assistance programs are administered by HRA’s Family Independence Administration (“FIA”). Since public assistance recipients are generally eligible for food stamps and Medicaid, FIA oversees the application process for individuals seeking a combination of benefits. (Smith Decl. ¶ 2) However, FIA is not directly responsible for eligibility determinations for food stamps or Medicaid. Instead, applicants seeking these benefits at job centers or income support centers are referred to separate agencies for eligibility determinations. {Id.) This division of responsibility for processing non-public and public assistance applications predates HRA’s program of converting income support centers to job centers. {Id.) Another important division within HRA is the Office of Quality Assurance (“OQA”), which is responsible for “preserving the quality, efficiency, and financial integrity of FIA’s programs.” (Abdullah Decl. ¶ 2) One of OQA’s functions is to replicate the quality control reviews of food stamp eligibility conducted by federal and state agencies. Under the federal food stamps program, states with relatively high error rates may face sanctions by way of a reduction in federal funding. See 7 U.S.C.A. § 2025(d). OQA- sends monitoring personnel out to centers to attempt to predict and minimize HRA’s payment error rate. At the present time, HRA operates twelve income support centers and sixteen job centers. In 1999, FIA merged four income support centers into two, converted three income support centers into job centers, and closed one income support center. The application process for public assistance at job centers is more rigorous than at income support centers, as job centers place greater emphasis on job search and employment activities for those able to work. Last year, HRA’s job centers and income support centers received and processed approximately 168,000 public assistance applications and assisted approximately 350,000 individuals in engaging in employment activities. (Smith Decl. ¶ 3) Procedural History Plaintiffs commenced this action by order to show cause in December 1998 seeking, inter alia, a temporary restraining order enjoining the conversion of additional income support centers to job centers. Plaintiffs alleged that HRA’s staff at job centers were routinely preventing prospective applicants from applying for benefits during their first visit to a job center, pressuring applicants to withdraw their applications, improperly denying combined applications for cash assistance, food stamps and Medicaid when only cash assistance had been denied, and failing to provide adequate notice of determinations. The complaint asserted private rights of action under federal food stamps and Medicaid statutes and regulations, including the right to apply for such benefits without delay and to receive timely determinations of eligibility. The complaint also set forth claims under 42 U.S.C. § 1983 based on alleged violations of these statutes and regulations as well as plaintiffs’ federal due process rights. Following a period of expedited discovery, this Court conducted a three-day evi-dentiary hearing in January 1999. On January 25, 1999, this Court held in Reynolds I that plaintiffs had established irreparable harm and a likelihood of success on their claims. The Court rejected the City defendants’ argument that the errors and deficiencies at job centers were isolated problems. On the contrary, the evidence pointed to system-wide failures resulting from HRA’s hurried conversions of income support centers to job centers and its incremental, post hoc responses to what appeared to be an array of serious and interrelated problems. At the hearing, the Court heard evidence that HRA had opened its first job center in March 1998 as a test-bed with the intention of addressing problems as they arose. See Reynolds I, 35 F.Supp.2d at 341. The evidence demonstrated that problems abounded. Data proffered by plaintiffs revealed sharp declines in applicants being approved for benefits after an income support center was converted to a job center. Those declines appeared attributable to the efforts of job center personnel to deter applicants from applying for food stamps, Medicaid and cash assistance. See Reynolds I, 35 F.Supp.2d at 343. By way of example, a monthly average of 48.96% of all applicants were diverted from seeking assistance at the Jamaica Job Center. Id. Figures for other job centers were equally alarming. Other evidence confirmed what might be fairly characterized as a culture of improper deterrence at job centers, including summary reports prepared by job centers tracking the number of applicants diverted. Id. at 344-45. Plaintiffs also presented evidence that job centers were failing to comply with certain statutory and regulatory requirements for administering food stamps and Medicaid benefits. For example, the evidence indicated that job centers were failing to timely process applications, failing to separate eligibility determinations, erroneously denying food stamps and Medicaid applications, failing to allow individuals to apply for benefits on their first visit to a job center, and failing to provide adequate notice of determinations. See Reynolds I, 35 F.Supp.2d at 345-47. Based on these findings, the Court granted plaintiffs’ application for a preliminary injunction and directed the City defendants to: • allow plaintiffs and all persons applying for food stamps, Medicaid and cash assistance, including expedited food stamps and temporary pre-in-vestigation grants to apply for such benefits on the first day that they visit a Job Center; • process all applications for expedited food stamps and temporary pre-in-vestigation grants at Job Centers within the time frames required by law; • make eligibility determinations regarding food stamps and Medicaid applications at Job Centers separate from the eligibility determinations regarding cash assistance applications; and ® send plaintiffs and all persons applying for food stamps, Medicaid and cash assistance, including expedited food stamps and temporary pre-in-vestigation grants at Job Centers timely and adequate written notice of determinations of their eligibility for all benefits which they seek. Reynolds I, 35 F.Supp.2d at 347-48. The Court enjoined the City defendants from opening new job centers and from converting existing income support centers to job centers, pending a hearing and determination on the adequacy of a corrective plan addressing remedial training and procedures for job center personnel. At a minimum, the corrective action plan was to address the following issues: • Procedures to permit applicants to file an application for food stamps, Medicaid or cash assistance on the first day of contact with a Job Center; • Procedures for separate determinations on an applicant’s request for food stamps, Medicaid and cash assistance; • Procedures for processing applications for expedited food stamps within seven days from the date the application is submitted; • Procedures for processing applications for pre-investigation immediate needs cash assistance in a manner consistent with State law; • Procedures for processing applications for food stamps and/or Medicaid where applicants fail to comply with work requirements; [and] • Procedures for providing written notice to applicants denied food stamps, Medicaid and/or cash assistance together with the basis for those denials and an opportunity to request a fair hearing. Reynolds I, 35 F.Supp.2d at 348. The Court was (and remains) sensitive to intruding on HRA’s ability to freely exercise its managerial prerogatives and to implement policy, but nevertheless observed: In its quest to enhance the delivery of food stamps, Medicaid and cash assistance benefits to the City’s most needy residents, the City cannot lose sight of the requirements imposed by federal statutes and regulations. Because some of the City’s neediest residents continue to fall through the safety net at job centers, this Court is impelled to ensure that remedial steps are taken on a specified time-line and that the effects of the revisions to job center procedures are measured to ascertain whether they are working. Reynolds I, 35 F.Supp.2d at 341. Thereafter, the City defendants set out to formulate a comprehensive corrective action plan and to retrain its front-line personnel at job centers and income support centers. After a series of revisions that were shaped in part by plaintiffs’ suggestions and criticisms, the City defendants submitted a proposed corrective action plan and moved for an order lifting the stay on job center conversions. On May 24, 1999, this Court approved the corrective action plan and modified the preliminary injunction to allow the City defendants to convert three more income support centers to job centers. See Reynolds II, 43 F.Supp.2d at 492. The Court declined to permit additional job center conversions because the City defendants’ proof was inconclusive as to whether its corrective action plan and other remedial measures were having salutary effects at job centers. At that time, FIA had audited its job centers and income support centers for the months of January and February 1999 in an effort to monitor their performance in a number of critical areas. While the City defendants argued that the audit data demonstrated improved accuracy in processing applications at job centers, plaintiffs drew contrary conclusions from the same data set and raised doubts about the reliability of FIA’s audit procedures. See Reynolds II, 43 F.Supp.2d at 498. Those issues could not be resolved on the record as it existed at that time. The Court observed: “The disparities between the parties’ calculations underscores the need for reliable, uniform audit procedures and statistically valid monitoring protocols. While data may always be subject to differing interpretations, the parties cannot even agree on the validity of the data set.” Reynolds II, 43 F.Supp.2d at 498. Accordingly, this Court ruled that it would consider a further modification of the preliminary injunction “after a hearing and determination on the adequacy of the City defendants’ auditing procedures for job centers and an analysis of the data collected pursuant to those procedures.” Reynolds II, 43 F.Supp.2d at 498. The City defendants were invited to amend or supplement their audit procedures, or to demonstrate that their existing procedures were reliable and valid. Id. In either event, the Court envisioned that additional data for the months of March, April, and May 1999 would be available for analysis so that it could be more fully informed “as to whether the reforms contemplated by the corrective action plan are translating into practice.” Id. Following Reynolds II, the parties engaged in additional discovery as the City defendants prepared to bring on a further application to modify the preliminary injunction. An evidentiary hearing was scheduled by this Court for July 26, 1999. On the eve of that hearing, after voluminous submissions had been filed with the Court, the City defendants requested that the hearing be adjourned. During a telephone conference conducted on July 26, 1999, the City conceded that it was not prepared to defend the reliability of their existing audit procedures. By order dated July 26, 1999, this Court denied the City defendants’ motion to modify the preliminary injunction without prejudice to its renewal upon further application to the Court. The City defendants balked at that time because they apparently recognized that the results of the audits conducted by FIA in anticipation of the hearing were materially flawed. One of the principal criticisms leveled by plaintiffs expert was that FIA sampling protocol — which involved manually selecting cases from batches of application control cards that are maintained at job and income support centers — generated a hopelessly biased sample in which accepted cases were over-represented. (Faust 1st Rpt. ¶ 59; Faust 2d Rpt. ¶ 19) During the months of August and September 1999, the City defendants conducted another audit of applications filed in May, June and July 1999 using a newly-designed audit instrument (the “Reynolds Audit”). Although plaintiffs suggested to the City defendants that then* respective experts collaborate on the design of the new audit instrument, their overture was rejected. On September 22, 1999, this Court conducted a status conference at which the City defendants indicated their intention to renew their motion to dissolve the preliminary injunction. Since plaintiffs had not participated in designing the Reynolds Audit, they sought time to conduct discovery. The Court acceded to the City defendants’ request for a prompt hearing date and established tentative dates for the expeditious completion fact and expert discovery. During a further pretrial conference conducted on October 21, 1999, those tentative dates hardened into firm deadlines, and an evidentiary hearing was scheduled for December 15 and 16,1999. The hearing proceeded on December 15 and 16, 1999. A third and final day of testimony was taken on January 19, 2000, and thereafter the parties submitted post-hearing memoranda of law and proposed findings of fact. On March 2, 2000, the Court heard oral argument on the City defendants’ motion. By order dated May 18, 2000, the Court directed plaintiffs and the State defendants to submit additional memoranda of law concerning the State defendants’ motion to dismiss plaintiffs’ claims as against them. During the evidentiary hearing, the City defendants presented testimony from Patricia M. Smith, Executive Deputy Director for FIA; Jacqueline Flaumm, Assistant Deputy Commissioner for FIA; Rochelle L. Abdullah, Director of OQA; Andrew Bush, Executive Deputy Administrator of HRA’s Office Policy and Program Analysis (“OPPA”); Meyer Elbaz, HRA’s Assistant Deputy Administrator for Management Information Systems; and Dr. June E. O’Neill, an expert in statistical sampling and the use and interpretation of data. Plaintiffs’ sole witness was their statistician, Richard Faust. In addition to this testimony, the parties made extensive pre-hearing submissions. Notably, the City defendants offered a final version of their expert report, dated October 12,1999. (City Ex. 1) The analy-ses contained in this final version of Dr. O’Neill’s report included additional case files that were located and audited during the final weeks of the Reynolds Audit. Dr. O’Neill also submitted a lengthy supplemental declaration, dated January 7, 2000, containing a host of new tables and revised calculations. Plaintiffs’ expert submitted two reports in connection with the Reynolds Audit, the first dated December 6, 1999 (“Faust 2d Rpt.”), and the second dated January 17, 2000 (“Faust 3d Rpt.”). Plaintiffs’ January 17, 2000 expert report addressed the matters raised in Dr. O’Neill’s supplemental declaration of January 7, 2000. Discussion I. The City Defendants’ Motion To Vacate The Preliminary Injunction The purpose of the evidentiary hearing was to determine whether the corrective action plan approved in Reynolds II had translated into practice. The City defendants pointed to an array of initiatives and other items of proof in an effort to show that it had. Principally, the City defendants rely on the results of the Reynolds Audit in which HRA personnel audited 1,893 case files drawn from job centers and income support centers. The City defendants also contend that HRA has improved its other monitoring and oversight activities. In January 1999, OQA implemented Process Evaluation and Review Team (“PERT”) audits, in which a pair of FIA auditors conduct a week-long inspection and review of the operations at a particular job center. The City defendants also highlight OQA’s “QC [Quality Control] Doctor” program, in which several OQA personnel make repeated visits to a particular center to focus on and resolve particular problems. In addition, shortly after the preliminary injunction issued in Reynolds I, FIA began sending “spot-checkers” to job and income support centers. The spot-checkers posed as applicants in order to determine whether individuals were permitted to file for benefits on their first day of contact with a center. Apart from these oversight activities by HRA, centers are also subject to reviews by the New York State Office of Temporary and Disability Assistance (“OTDA”), as well as the United States Department of Agriculture (“USDA”). Additional monitoring activities have been undertaken in connection with this litigation. Pursuant to this Court’s order entered on April 5, 1999, plaintiffs’ counsel has been permitted to conduct one-day inspections of up to five job centers each month during discovery. The particular center to be inspected on any given day is identified by plaintiffs’ counsel 48 hours in advance. In addition, the parties have utilized an “informal intervention” procedure in which plaintiffs’ counsel may call HRA’s attention to particular cases of exigent need for expedited food stamps and/or emergency cash assistance. Finally, the City defendants have begun using the results of “fair hearing” appeals of agency determinations as a monitoring device for job center and income support center performance. By comparing HRA’s “win rates” for appeals taken from both job center and income support center eligibility determinations, the City defendants conclude that job centers generally perform better. Based on these efforts and the Reynolds Audit, the City defendants argue that there is no longer a basis for maintaining the preliminary injunction. (City Defs.’ Post-Hearing Mem. at 2) Before turning to the merits of the City defendants’ motion, the Court addresses the parties’ divergent views as to the standard governing the City’s application. A. The Applicable Standard This Court set out the applicable standard for modifying a preliminary injunction in Reynolds II. On such motions, “a court is charged with exercising the same discretion it exercised in granting or denying the injunction in the first instance.” Reynolds II, 43 F.Supp.2d at 494 (citing Sierra Club v. United States Army Corps of Engineers, 732 F.2d 253, 256 (2d Cir.1984)). “An injunction is an ambulatory remedy that marches along according to the nature of the proceeding. It is executory and subject to adaption as events may shape the need, except where rights are fully accrued or facts are so nearly permanent as to be substantially impervious to change.” Sierra Club, 732 F.2d at 256. Though both plaintiffs and the City defendants would accept this general standard as controlling, they join issue as to how it should be applied. At the outset, the Court observes that the City defendants’ motion seeks to vacate all portions of this Court’s January 25, 1999 preliminary injunction, including both the stay on job center conversions and those decretal paragraphs ordering that applications for food stamps, Medicaid and cash assistance be processed in conformity with applicable statutory mandates. Focusing on these two aspects of the order, the City defendants contend that there is no longer a factual or legal basis for continuing the injunction. Specifically, the City defendants argue that plaintiffs failed to prove during the evidentiary hearing that job center personnel continue to deter individuals from applying for benefits. The City defendants further contend that the Reynolds Audit demonstrated that job centers perform at least as well, and often better than, income support centers. Thus, as to job center conversions, the City defendants claim that the conditions that may have warranted preliminary injunctive relief in Reynolds I have abated, and they argue that plaintiffs have offered no evidentiary basis for its continuance. With respect to that branch of the preliminary injunction requiring HRA to comply with federal and state law, the City defendants assert that any errors in processing applications at job centers are isolated occurrences. Relying again on the results of the Reynolds Audit, the City defendants further claim that HRA is in “substantial compliance” with applicable statutory and regulatory requirements. Consequently, the City defendants argue that the balance of the preliminary injunction should be vacated because plaintiffs cannot establish a municipal “policy or custom” pursuant to Monell v. Department of Social Services of City of New York, 436 U.S. 658, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978). Plaintiffs attack the City defendants’ characterization of the parties’ respective burdens of proof at this juncture in the proceedings, and they dispute the applicability of Monell’s policy or custom requirement. Plaintiffs argue that since their class-action complaint seeks only prospective injunctive relief, Monell is inapplicable. Plaintiffs also argue that even if Monell applied, the proof in Reynolds I established the requisite policy or custom, and the City defendants have not met their burden of showing compliance with applicable laws or cessation of improper deterrence at job centers. Since it is a threshold issue that really underlies both of the aforementioned branches of the preliminary injunction, the Court turns first to the City defendants’ arguments concerning the relevancy of Monell. There is scant and conflicting authority as to whether Monell applies in actions where the only remedy demanded is prospective injunctive and declaratory relief. However, those courts which have squarely addressed the issue have concluded that it does not. The Ninth Circuit’s decision in Chaloux v. Killeen, 886 F.2d 247 (9th Cir.1989), is a leading example. In Chal-oux, the plaintiffs were recipients of social security disability benefits who challenged the constitutionality of Idaho’s statutory scheme of post-judgment execution and garnishment procedures. Their class action complaint alleged that the statute violated their due process rights and ran afoul of the Supremacy Clause because it permitted seizure of their federally exempt disability benefits. See Chaloux, 886 F.2d at 248-49. The plaintiffs invoked 42 U.S.C. § 1983 and sought prospective declaratory and injunctive relief. Id. at 250. On appeal from the district court’s order dismissing the complaint, the Ninth Circuit considered whether Monell’s official policy or custom requirement was applicable to claims against the defendant county sheriffs named in their official capacities. The court ruled that this requirement did not apply to “a suit for prospective relief against a county or its officials for enforcing allegedly unconstitutional state laws.” Chaloux, 886 F.2d at 250. The court explained: We reach this conclusion upon review of the policy justifications supporting the decision in Monell. The Monell Court set forth an “official policy or custom” requirement to limit § 1983 damage awards against municipalities. That limitation served to alleviate the imposition of financial liability on local governments based solely on a respondeat superior theory. We find no persuasive reasons for applying the Court’s “official policy or custom” requirement to suits against counties only for prospective relief. The justification for limiting an action for damages is notably absent when the relief sought is an injunction halting the enforcement of an unconstitutional state statutory scheme. The relief sought here, a declaration that the Idaho statutes are unconstitutional and an injunction against their enforcement, do not carry any threat of fiscal liability. Chaloux, 886 F.2d at 250-51 (citations and footnotes omitted); accord Los Angeles Police Protective League v. Gates, 995 F.2d 1469, 1472 (9th Cir.1993) (“[T]he City can be subject to prospective injunctive relief even if the constitutional violation was not the result of an official custom or policy.”) (internal quotation marks omitted); Nobby Lobby, Inc. v. City of Dallas, 767 F.Supp. 801, 810 (N.D.Tex.1991) (“The Court can find in the case law no reason to impose an official policy or custom requirement in a situation where prospective relief alone is at issue and there is no threat of municipal financial liability.”) (internal quotation marks omitted), aff'd on other grounds, 970 F.2d 82 (5th Cir.1992); Santiago v. Miles, 774 F.Supp. 775, 792-93 (W.D.N.Y.1991) (in action for prospective injunctive relief against State officials pursuant to Ex parte Young, plaintiffs were not required to prove that defendants acted pursuant to a policy or custom). Several courts have applied MonelVs policy or custom requirement in actions involving only prospective injunctive relief, but did so without analysis. See Bannum, Inc. v. City of Fort Lauderdale, 901 F.2d 989, 997 (11th Cir.1990); Salazar v. District of Columbia, 954 F.Supp. 278, 324 (D.D.C.1996); United States v. Commonwealth of Pennsylvania, 902 F.Supp. 565, 580, 649 (W.D.Pa.1995), aff'd, 96 F.3d 1436 (3d Cir.1996). Other cases cited by the City defendants are distinguishable in that they involved claims for both damages and injunctive relief, see, e.g., Barrett v. Harwood, 189 F.3d 297, 300, 303 (2d Cir.1999); Adkins v. Board of Educ. of Magoffin County, Ky., 982 F.2d 952, 957-59 (6th Cir.1993); Nix v. Norman, 879 F.2d 429, 433 (8th Cir.1989), or for retroactive declaratory relief, see Community Health Care Association of New York v. DeParle, 69 F.Supp.2d 463, 471-72, 474-75 (S.D.N.Y.1999); see generally Green v. Mansour, 474 U.S. 64, 73, 106 S.Ct. 423, 428, 88 L.Ed.2d 371 (1985). Notwithstanding the paucity of case law supporting the City’s position, its arguments are not without merit. Plaintiffs in this action seek broad-based, system-wide injunctive relief. Such relief would necessarily have some impact on the City’s expenditure of public funds, thereby undercutting the rationale of Chaloux and its progeny. Viewed through a different lens, the relief plaintiffs seek would only require the City to comply with applicable federal requirements, something it is already bound to do. See generally Rothstein v. Wyman, 467 F.2d 226, 232 (2d Cir.1972). This Court, however, need not decide whether the City’s argument concerning Monell — raised now for the first time — is correct. Whether or not Monell requires plaintiffs in this action to plead and prove a policy or custom, the evidence adduced in Reynolds I, see supra, was indicative of a widespread pattern of violations that would be actionable under Monell. See City of Canton, Ohio v. Harris, 489 U.S. 378, 388-89, 109 S.Ct. 1197, 1204-05, 103 L.Ed.2d 412 (1989); Walker v. City of New York, 974 F.2d 293, 297-98 (2d Cir.1992); Batista v. Rodriguez, 702 F.2d 393, 397 (2d Cir.1983); Turpin v. Mailet, 619 F.2d 196, 200 (2d Cir.1980). Accordingly, to obtain the relief they seek, the City defendants must show that the conditions warranting preliminary injunctive relief in Reynolds I have been remedied through their successful implementation of the corrective action plan or have otherwise abated. Plaintiffs, having met their burden in Reynolds I of establishing a risk of irreparable harm based on the City defendants’ failure to comply with federal law, are not required to re-prove their case for preliminary injunctive relief. The question for the Court is whether circumstances have changed, particularly since Reynolds II when the Court approved the City’s corrective action plan, such that continuation of the preliminary injunction is no longer warranted. The burden of establishing such changed circumstances rests squarely on the City defendants. The Court will not presume that the City’s corrective action plan has succeeded simply because it had all the right ingredients; the proof of the pudding is in the eating. With these precepts in mind, the Court turns to the City defendants’ motion. B. The Reynolds Audit 1. Overview of the Sampling Process and the Audit Instrument The City defendants’ describe the Reynolds Audit as a “massive undertaking” (City Defs.’ Posk-Hearing Mem. at 10), a characterization plaintiffs do not dispute. The City defendants embarked on this effort immediately after informing the Court on July 26, 1999 that it was unprepared to defend its existing audit procedures. First, the City defendants designed a series of protocols for selecting a random sample of cases from among the applications submitted at job centers and income support centers in May, June and July 1999. After drawing the sample, the City utilized a new audit instrument to review the sampled case files and measure performance in the following areas: “(a) providing immediate needs cash assistance where appropriate; (b) providing expedited food stamp service where appropriate; (c) timely providing immediate needs and expedited food stamps; and (d) making separate determinations or referrals for food stamps or Medicaid where cash assistance was denied or the application was withdrawn.” (O’Neill Rpt. ¶ 9) Additionally, the instrument sought to determine whether a notice of benefit determination was issued to an applicant. In order to select its random sample of case files, the City defendants initially decided to utilize HRA’s “NYCWAY” computerized database. HRA maintains over 100 different computer databases. (Elbaz Decl. ¶ 3) It uses the NYCWAY system to track appointments made for public assistance applicants in education, training and work programs. (Dep/Elbaz/154-55) Thus, the NYCWAY system focuses primarily on public assistance recipients rather than on applicants. (Elbaz Decl. ¶ 6) Information for the NYCWAY system is electronically transmitted from the State of New York Welfare Management System (“WMS”), a state-operated computer system used to maintain information on applicants for certain benefits, including food stamps, Medicaid and cash assistance. NYC WAY receives updated information from the WMS system every night so it is available to case workers the following morning. (Dep/Elbaz/63-64) The primary focus of the WMS system is on active public assistance recipients who have completed the application process, though it contains limited information regarding applicants for food stamps, Medicaid and cash assistance. (Elbaz Decl. ¶ 5) On or about August 5, 1999, the City defendants drew a sample of cases from the NYCWAY database. This was done with a computer program designed to select eases from job centers and income support centers in proportion to the number of applicants at each center. (O’Neill Rpt. ¶¶ 14, 16) The City defendants originally intended to include approximately 2,100 cases in the Reynolds Audit, consisting of an average of 25 cases per month for each center, with a minimum of 20 cases selected at any given center. (O’Neill Rpt. ¶ 14 and Ex. B) However, as HRA auditors began to review the sampled case files, they discovered that the NYCWAY data set was over-inclusive. For example, it contained applications by persons with AIDS under the “DASIS” (Division of Aids Services and Income Support) program. (O’Neill Rpt. ¶ 16) Additionally, HRA realized that the NYCWAY data set was under-inclusive because it replaced old information about applicants with any new information. (Dep/Elbaz/52) Once old information is over-written on the NYCWAY system, it cannot be retrieved. For example, if an applicant files more than one application, the newest application automatically purges any information about all earlier applications. (Dep/Elbaz/55-56) These shortcomings led the City defendants to draw a second sample from a different database known as the Eligibility Verification Review (“EVR”) information system. Like the NYCWAY system, the EVR database receives applicant-specific information from the state-run WMS system. (Dep/Elbaz/66) The EVR computer system is oriented around the eligibility verification review process, wherein the information and supporting documentation provided by applicants is screened for accuracy. (Elbaz Decl. ¶ 8) Once an EVR appointment is scheduled, the system tracks the applicant through the application process. In contrast to the NYCWAY system, the EVR system does not overwrite data, so every filing of an application is preserved. (Dep/Elbaz/87, 97,174) The second sample of cases was drawn from the EVR database on or about August 11, 1999. (O’Neill Rpt. ¶ 17) At that time, however, HRA auditors had already begun reviewing case files for May 1999 from the NYCWAY sample. Rather than start anew, the City defendants decided that for cases filed in May 1999, it would rely primarily on the NYC WAY sample and would draw additional cases from the EVR database only when a sufficient number of NYCWAY-selected case files could not be physically located and retrieved from the centers. (O’Neill Rpt. ¶ 17) However, since the EVR database was superior because it more closely “approximated the target group” (O’Neill Rpt. ¶ 17) of applicants, the City defendants made it the primary database when it drew sam-pies for the months of June and July 1999; for those months, the NYCWAY database was used as a supplement. Once the primary and secondary samples were drawn, the ease files were physically delivered to a central location at' HRA headquarters. (O’Neill Rpt. ¶ 20) There, the files were audited by OQA staff members. Of the ten auditors involved, some had prior experience in conducting such reviews while others did not. (Dep/Mortley/11; Dep/Ricks/13) The auditors used a newly-designed audit instrument that presented a series of questions in two stages. (O’Neill Rpt., City Ex. A) Stage one of the audit instrument contained several categories of questions focusing on whether applications were properly screened and processed for, inter alia, immediate needs cash and/or expedited food stamps eligibility. Stage two confined its questions to cases where an application was rejected (“RJ”) or “single/issue closed” (“SI/CL”) The SI/CL category refers to applicants who actually received emergency cash assistance or expedited food stamps. After the auditors finished their review, the case files and completed audit instruments were given a second-level review by selected staff members from job centers and income support centers. (Abdullah Decl. ¶ 22; Flaum Decl. ¶ 9) Thereafter, a third-level review was conducted by regional managers or their deputies. (Flaum Decl. ¶ 17) 2. Applicable Standards The City defendants do not dispute that they bear the burden of demonstrating that Reynolds Audit was conducted in conformity with generally accepted survey principles. When a sample is drawn for the purpose of generating data about a population to be offered for its truth, as the Reynolds Audit is being offered here, “[t]he methods used must conform to generally recognized statistical standards.” Manual for Complex Litigation, § 21.493 (3d ed.1997). Relevant factors include whether: • the population was properly chosen and defined; • the sample chosen was representative of that population; • the data gathered was accurately reported; and • the data was analyzed in accordance with accepted statistical principles. Manual for Complex Litigation, § 21.493. See generally Schering Corp. v. Pfizer Inc., 189 F.3d 218, 224-26 (2d Cir.1999). Both parties’ experts subscribe to the view that the representativeness of the sample is the primary concern of any researcher because without it, one cannot reliably project from the sample to the population. See Moore’s Federal Practice, Reference Manual on Scientific Evidence, at 237 (Matthew Bender 1997) (“Identification of a survey population must be followed by selection of a sample that accurately represents that population.”); accord Pittsburgh Press Club v. United States, 579 F.2d 751, 758 (3d Cir.1978); Rosado v. Wyman, 322 F.Supp. 1173, 1181-82 (E.D.N.Y.1970), aff'd, 437 F.2d 619 (2d Cir.1970), aff'd, 402 U.S. 991, 91 S.Ct. 2169, 29 L.Ed.2d 157 (1971). Representativeness can usually be assured when the source(s) from which the sample is drawn (i.e., the “sampling frame”) accurately reflects the target population. See Moore’s Federal Practice, Reference Manual on Scientific Evidence, at 235. In addition, the sampling protocol should be designed so that every element in the sampled population has a known, nonzero probability of being selected. Id. at 237. See also American Home Products Corp. v. Barr Laboratories, Inc., 656 F.Supp. 1058, 1070 (D.N.J.1987), aff'd, 834 F.2d 368 (3d Cir.1987); Dreyfus Fund, Inc. v. Royal Bank of Canada, 525 F.Supp. 1108, 1116 (S.D.N.Y.1981); Handbook of Recommended Procedures for the Trial of Protracted Cases, 25 F.R.D. 351, 429 (Judicial Conf.1960); Kevin H. Smith, External Validity: Representativeness and Projectability in the Probative Value of Sample Surveys, 39 Wayne L.Rev. 1433, 1484-87 (1993). Nevertheless, even where a survey is found to suffer from technical or methodological flaws, it may still be received in evidence subject to arguments about its weight and probative value. See Schering, 189 F.3d at 228; Bacardi & Co. Ltd. v. New York Lighter Co., Inc., 2000 WL 298915, at *5 (E.D.N.Y. Mar. 15, 2000) (97 Civ. 7140(JS)). For example, where a sampling frame is under-inclusive, “the survey’s value depends on the extent to which the excluded population is likely to react differently from the included population.” Reference Manual on Scientific Evidence, at 236; accord Champion v. Shalala, 33 F.3d 963, 966-67 (8th Cir.1994). Similarly, criticisms that a sampling protocol was not random or otherwise reliable, see, e.g., Debra P. v. Turlington, 730 F.2d 1405, 1408, 1411 n. 11 (11th Cir.1984), or resulted in a high non-response rate, see, e.g., Champion, 33 F.3d at 967, will not render a survey inadmissable. Rather, such shortcomings will undermine a survey’s reliability and erode its probative value. Of course, a combination of technical flaws or a single, fundamental defect may eviscerate the evidentiary force of a survey. See, e.g., Universal City Studios, Inc. v. Nintendo Co., Ltd., 746 F.2d 112, 118 (2d Cir.1984). Plaintiffs take the view that the Reynold Audit is fundamentally flawed in so many areas that it cannot be used to draw any reliable conclusions about the performance of job centers and income support centers. First, plaintiffs argue that the sampling frame for the Reynolds Audit, i.e., the NYCWAY and EVR computer databases, is under-inclusive of the population of applicants because it does not include applications that were withdrawn or rejected on the same day they were filed. Consequently, plaintiffs contend that the sampling frame is unrepresentative of the population. In addition, plaintiffs argue that the Reynolds Audit sample of 1,893 cases is not sufficiently representative of the NYCWAY and EVR databases from which it was drawn. Further, plaintiffs claim that an inordinately high number of cases could not be located and retrieved from centers or were erroneously excluded from the auditing process. Finally, plaintiffs contend that the two-stage audit instrument used to conduct the Reynolds Audit was poorly designed and failed to include necessary questions. The Court addresses • these issues seriatim. 3. The Absence of Certain Withdrawn and Rejected Cases From the Sampling Frame According to plaintiffs, the greatest fault with the Reynolds Audit is that its sampling frame excluded virtually all cases in which an application was withdrawn on the same day it was submitted. (Faust 2d Rpt. ¶¶ 29, 48-80) In fact, only 12 of the 1,893 cases in the Reynolds Audit sample are withdrawn cases. Relatedly, plaintiffs contend that an unknown number of cases rejected on the same day they were submitted are absent from the sampling frame, though plaintiffs acknowledge that this may present a lesser problem since the sample includes a substantial number of rejected cases. The City defendants do not dispute that the NYCWAY and EVR databases generally do not capture instances where an application is filed and withdrawn on the same day. (Bush Decl. ¶¶ 3-4) They argue, however, that the absence of withdrawn cases is largely immaterial because they do not impact the principal issues being audited and therefore could not have biased the survey results. (City PosWHearing Mem. at B-3) As for rejected cases, the City defendants appear to dispute that any significant number of rejected cases were improperly excluded. Before turning to the merits of these arguments, the Court addresses several preliminary points. First, the Reynolds Audit was apparently intended to include withdrawn cases, even though it failed to do so. In that regard, page one of the audit instrument required auditors to indicate the disposition of the application being reviewed. One of the six check boxes provided on the audit instrument was for “WD” (withdrawn) applications. Further, the City defendants’ expert report observed that “[t]he instrument was designed to capture Job Center and Income Support Center performance in ... (d) making separate determinations or referrals for Food Stamps or Medicaid where cash assistance was denied or the application was withdrawn. ” O’Neill 2d Rpt. ¶ 9 (emphasis added). Nevertheless, the expert reports submitted by the City defendants in advance of the evidentiary hearing failed to account for the absence of withdrawn cases from the NYCWAY and EVR databases. By way of illustration, Table I of the City defendants’ expert report (City Ex. 1) provided statistical breakdowns of dispositions for the job center and income support center samples, as well as comparative data on dispositions from the NYCWAY and EVR databases. The table lists only five of the six disposition categories: application pending, single-issue, acceptance, rejected, and single-issue closed. Withdrawn cases are not mentioned, even though the 12 cases that were included in the Reynolds Audit constituted 0.8% of the job center sample and 0.5% of the income support center sample. (Faust 2d Rpt. ¶ 60) . The City defendants claim that they decided to draw audit samples from the NYCWAY and EVR databases, knowing that they might be under-inclusive or otherwise imperfect, because HRA does not maintain a computer database capable of tracking applications that are withdrawn on the same day they are filed. See Smith Supp. Dec. ¶ 8 (“[Tjhere is no computer database that contains all incidents of applications filed at the Centers.”) (emphasis in original). Further, the City defendants hoped to avoid the pitfalls they experienced in connection with the aborted July 26, 1999 hearing where the audit samples were drawn manually using control cards. (Bush Decl. ¶¶ 4-5; Dep/Smith/20-23) Ultimately, the City defendants concluded that “the databases [were] the best available approximation of the universe of applicants,” (Smith Decl. ¶ 19), and that auditing withdrawn cases would not have yielded additional useful information. In the Court’s view, the Hobson’s Choice depicted by the City defendants was self-imposed. It is noteworthy that despite the City defendants’ acknowledgment on July 26, 1999 that their existing audit results were fundamentally flawed, HRA personnel were drawing cases from the NYC-WAY database less than two weeks later. While courts rarely find fault with a litigant who proceeds with alacrity, in this case the City defendants’ hastily-conceived sampling protocol spawned an array of complex statistical issues that might have been avoided. The City defendants acknowledge that “some of the peculiarities of the computer databases selected were not fully evident until the [] Reynolds audit was eom-plete[.]” (Smith Decl. ¶ 19) See also O’Neill Rpt. ¶ 19 (referring to the “significant time constraints [the City defendants] faced in completing the audit.”); Tr/ O’Neill/86 (“Q: But, Dr. O’Neill, it was your earlier testimony, wasn’t it, just a few minutes ago, that you in fact knew that withdrawn cases are purged at the time you prepared this report? Isn’t that correct? A: I said that I believed that I was conscious of something like that. Honestly, it was not something that I had focused on. It was something that was always a kind of fuzzy area.”); Dep/Elbaz/86-87 (“Q: Do you know why, on approximately August 11, a sample was selected from a second data set?” “... A: A lot of this happened very quickly because of the pressure that I was under to produce something right away.”). Against this backdrop, the City defendants’ reasons for relying exclusively on the NYCWAY and EVR databases for the Reynolds Audit have the earmarks of post hoc rationalization. This is most evident in Dr. O’Neill’s second supplemental declaration, dated January 7, 2000, in which she discusses for the first time various statistical approaches for testing and compensating for over- and under-representativeness in samples. Dr. O’Neill’s second supplemental declaration — which easily surpasses her main expert report in length and complexity — was precipitated by matters raised by plaintiffs during the portion of the evidentiary hearing conducted in December 1999. Plaintiffs, in turn, responded with a third expert report challenging the appropriateness of the corrective techniques employed by Dr. O’Neill as well as the results of her analy-ses. Such successive rounds of increasingly complex submissions would have been obviated had the City defendants taken the time to inform themselves of the “peculiarities” of the databases on which they chose to rely. Turning to the merits, it is useful to briefly explore why certain withdrawn and rejected cases may have been excluded from the sampling frame. New applications are initially entered into the State-run WMS database, which then transmits relevant information to the NYCWAY and EVR databases overnight on a daily basis. (Dep/Elbaz/63-67) However, applications withdrawn on the same day they are filed are automatically purged from the WMS system before a record of those applications is transferred to the NYCWAY or EVR databases. (Dep/Elbaz/194-97; Dep/Parker/110) On the other hand, if an EVR appointment is made for an applicant before his case is withdrawn, then the EVR system records (and preserves) the application without regard to the nightly WMS data transfer. Thus, there are only two ways in which a withdrawn application could enter the NYCWAY or EVR databases: (1) the application is not withdrawn on the WMS system on the same day it is entered into that system, in which case it will be transferred to the NYCWAY and EVR systems overnight; or (2) an EVR appointment is scheduled for an applicant before his application is withdrawn, in which case the EVR system will preserve a record of the application. (Faust 2d Rpt. ¶¶ 72, 73). Applications which are rejected on the same day they are filed may also be excluded from the NYC WAY and EVR databases, though the record is considerably murkier as to how and when that might occur. (Dep/Elba3/190-93 (opining that the answers to such questions lie within a labyrinth of computer programming code)) Ultimately, plaintiffs were unable to do more than speculate as to the number of rejected cases, if any, that may have been excluded. (Faust 2d Rpt. ¶ 29; Faust 3d Rpt. ¶ 41; Tr/Faust/367, 371-73) For that reason, the Court will focus instead on withdrawn cases and how their relative absence from the sample may have skewed the audit results. Nevertheless, the possibility that even a small number of rejected cases were inadvertently excluded from the sample raises concerns. According to the City defendants’ own calculations, over the three-month audit period rejected cases exhibited significantly higher rates of inappropriate denials of immediate needs cash grants than accepted cases (39.4% — 47.9% for rejected cases versus 8.8% — 14.7% for accepted cases). (O’Neill Sec. Supp. Decl., Tbl. 11; Tr/O’Neill/481) Inappropriate denials of expedited food stamp applications were also much more prevalent among rejected cases than accepted cases (30.8% — 41.0% versus 13.8% — 19.8%). {Id. at Tbl. 15) Thus, the use of a database which may have excluded a segment of rejected cases could be a source of error. The City defendants’ expert report does not address the potential impact of purging rejected cases from the sampling frame. (Tr/O’Neill/lOO) As mentioned earlier, only 12 withdrawn cases appeal* in the Reynolds Audit. Those cases constitute just 0.8% of the job center audit sample, a figure that plaintiffs demonstrated is grossly under-inclusive of the true population of withdrawn cases. Plaintiffs performed tabulations of the true population of withdrawn cases based on two different sources. One set of population disposition data was derived from Job Center Applicant Reports prepared by HRA’s Office Policy and Program Analysis (“OPPA”). A second set of tabulations was done by counting the number of withdrawn cases appearing on the Daily Activity Logs maintained by job centers. (Jeffrey Decl. ¶ 5) Tabulations from the OPPA reports indicate that for the three-month audit period, 27.8% of those persons categorized as seeking assistance did not continue their application past the financial planning interview. (Jeffrey Deck ¶ 7) Plaintiffs’ review of the Daily Activity Logs indicated that 17.5% of those seeking assistance withdrew their applications at or before the financial planning interview. {Id. at ¶ 14) These two figures of 17.5% and 27.8% are an upper and lower estimate of the true number of withdrawn applications at job centers. Plaintiffs’ expert performed a binomial test of statistical significance, for all categories of disposition, on the percentages generated by the Reynolds Audit sample and the OPPA reports. Plaintiffs’ expert similarly compared the percentage of withdrawn cases in the audit sample with the Daily Activity Log tabulations. The respective percentages may be summarized as follows: Disposition Status Audit Sample OPPA Rpts Activity Logs AP (pending) 3.2 3 - SI (single issue) 6.1 4 - AC (accepted) 46.6 28 - RJ (rejected) 19.5 18 - SI/CL (SI closed) 24.1 20 - WD (withdrawn) 0.8 28 17 For the AP (pending), SI (single issue), RJ (rejected) and SI/CL (single issue/closed) categories of disposition, there is little disparity between the sample and population figures, and the differences are not statistically significant. (Faust 2d Rpt. ¶ 64) However, for AC (accepted) cases and WD (withdrawn) cases, the differences (46.6% versus 28%, and 0.8% versus 17%-28%, respectively) are statistically significant beyond the 0.001 level. A finding that a disparity is statistically significant “at the 0.001 level” means that the chance is less than one in a thousand that the disparity occurred by chance. (Tr/Faust/286) As mentioned at the outset, the City defendants do not dispute that withdrawn cases were largely excluded from the Reynolds Audit sample. Rather, they argue that plaintiffs failed to demonstrate that the absence of withdrawn cases could have biased the audit results in favor of job centers. The City defendants further claim that withdrawn cases implicate, at most, only one of the several issues being audited. (City Defs.’ Post-Hearing Response Mem. at 17; O’Neill Sec. Supp. Decl. ¶ 5) This Court disagrees. The failure to capture withdrawn cases in the audit sample necessarily biases the results by over-representing the other dispositions, particularly accepted cases. (Faust 2d Rpt. ¶ 80) As indicated above, accepted cases have significantly lower rates of inappropriate denials for immediate needs cash grants and for expedited food stamps than rejected cases. For immediate needs cash grants, the difference in inappropriate denials is 8.8% — 14.7% for accepted cases versus 39.4% — 47.9% for rejected cases. For expedited food stamps, the figures are 13.8% — 19.8% versus 30.8% — 41.0%. Plaintiffs argue that inappropriate denials may well be more prevalent in withdrawn cases than accepted cases, and would likely occur more frequently in job centers given their more rigorous application process. Indeed, given this Court’s previous finding that job centers were improperly deterring individuals from submitting applications, see Reynolds I, 35 F.Supp.2d at 343, the absence of withdrawn cases raises serious concerns that the audit results are biased in favor of job centers. This concern is heightened by evidence presented by plaintiffs suggesting that some applicants are still improperly deterred from filing applications. The Daily Activity Logs from seven job centers contain handwritten entries suggesting that applicants withdrew their applications for assistance based on inaccurate information concerning eligibility criteria. (Jeffrey Supp. Decl., App. I) Some of the reasons listed for withdrawals, e.g., missing documents, applicant being under 21 years of age, or appearing at the job center without a spouse, echo problems discussed in Reynolds I. See Reynolds I, 35 F.Supp.2d at 344-45. It may be, as HRA Executive Deputy Director Patricia M. Smith asserted in her supplemental declaration dated January 7, 2000, that job center staff are simply noting legitimate issues of ineligibility in the Daily Activity Logs. (Smith Supp. Decl. ¶ 22) The City defendants argue that “it is not enough to simply look at the very brief annotations in the Job Center daily logs and conclude that unlawful diversion is occurring.” (City Defs.’ Post-Hearing Mem. at 12) That too, may be true, and the Court does not view the Daily Activity Logs as conclusive proof of unlawful diversion. However, the Court found such practices of unlawful diversion existed in Reynolds I; it is the City defendants’ burden on this motion to demonstrate that their corrective action plan and other remedial measures have put an end to those practices. At a minimum, the Daily Activity Logs raise doubts about whether unlawful deterrence continues to occur at job centers, and they compound the danger of having withdrawn cases essentially unrepresented in the audit sample. The City defendants have not adequately investigated and resolved these questions. Similarly, the City defendants failed to adequately support their theory that withdrawn cases are only relevant for examining issues of separate Medicaid and food stamps eligibility determinations. Applicants who withdraw applications for cash assistance but continue their applications for food stamps and Medicaid must be screened for eligibility for expedited food stamps; they are also entitled to notice of their eligibility for ongoing food stamps and Medicaid. (Compare Tr/Smith/22-26 with Tr/O’Neill/489-91) In fact, of the twelve withdrawn cases in the audit samT pie, seven were reviewed by auditors for whether a correct determination of eligibility for expedited food stamps had been made. OQA’s auditors found that in one of those instances, benefits had been wrongly denied. (Tr/Faust/417-18) One of the twelve withdrawn cases was evaluated for whether a correct determination of eligibility for an immediate needs grant had been made. In that case, the determination was correct. Id. While the City defendants suggest that such partial withdrawals are uncommon, (City Defs.’ Post-Hearing Mem. at B-4), they offer no concrete proof to substantiate that assertion. In sum, the Court finds that the absence of withdrawn cases from the audit sample significantly undermines the reliability of the audit results. J. The Sample Is Statistically Unrepresentative Of The NYCWAY And EVR Computer Databases From Which It Was Drawn The City defendants do not dispute that the Reynolds Audit sample is unrepresentative of the NYCWAY and EVR computer populations from which it was drawn. Instead, the City argues that the deviations between the sample and these populations are not large enough “to seriously influence the results of the audit” and that “for all practical purposes the audit sample provides a reliable representation of the population from which it is drawn.” (O’Neill Rpt. ¶ 27) The Court disagrees that the statistical deviations at issue are small enough to be treated lightly, and it declines the City’s invitation to take a leap of faith and presume that these deviations did not bias the sample results. The City defendants’ expert elected to perform chi-square tests of re