Full opinion text
OPINION SAND, District Judge. PREFACE This Opinion was prepared and ready for filing this past August. However, apprised of ongoing settlement discussions, the Court, on August 21, 2000, issued the following Order: The Court notes that Governor George E. Pataki has issued a statement asserting the State’s commitment to a consensual resolution of the pending school litigation and the payment of a $10,000,000 advance toward such settlement. In light of the foregoing, this Court will withhold its response to the Court of Appeals remand pending submission to it of a proposed settlement agreement. If at any time any party shall be of the opinion that progress toward achieving a settlement is not being made at a satisfactory pace or that settlement efforts are at an impasse, this Court shall be promptly advised of such circumstances. SO ORDERED. On November 29, 2000, the Court received a letter from the NAACP urging that the Court “issue its vestiges remand decision at the earliest possible occasion and move the process of final resolution forward.” OPINION Plaintiffs brought this action alleging that public housing and education in the City of Yonkers had been unlawfully segregated according to race. The Court finds that, as of 1997, vestiges of segregation existed in the Yonkers public schools. We therefore refer the matter to the Court-appointed School Monitor to report and recommend, after appropriate proceedings, as to a suitable remedy. I. BACKGROUND A. Procedural History In 1985, this Court found that the City of Yonkers (“the City”) and the Yonkers Board of Education (“the YBE”) had intentionally segregated the Yonkers public schools (“the YPS”). See United States v. Yonkers Bd. of Educ., 624 F.Supp. 1276, 1376-1545 (S.D.N.Y.1985) (“Yonkers I”) , aff'd, 837 F.2d 1181 (2d Cir.1987) (“Yonkers III ”). The following year, we ordered a remedy, which came to be known as the “educational improvement plan,” or “EIP I.” See United States v. Yonkers Bd. of Educ., 635 F.Supp. 1538 (S.D.N.Y.1986) (“Yonkers II”), aff'd, 837 F.2d 1181 (2d Cir.1987). The centerpiece of EIP I was a voluntary magnet school program that was designed to eliminate the severe racial imbalance that had previously existed with respect to student and faculty assignments, as well as to alleviate inequalities in facilities and extracurricular offerings. See id. By all accounts, the plan — which organized schools and programs around particular themes and assigned students based on their thematic and programmatic preferences — was a dramatic success. School enrollments were totally desegregated within one year of EIP I’s implementation and, moreover, “[t]he transition took place in a relatively smooth and peaceful manner, without the disturbances and disruption which plagued desegregating school districts elsewhere in this country.” United States v. City of Yonkers, 833 F.Supp. 214, 216 (S.D.NY.1993) (“Yonkers IV”). Despite EIP I’s obvious successes, local school officials in Yonkers came to believe that it had only partially remedied the many entrenched problems which, they believed, were the legacy of the prior segregation. These officials were unable to implement more thorough reform, however, because all available funds were being used to implement EIP I. The YBE, therefore, in 1987, filed a cross-claim against the State of New York and various state agencies and officials (collectively, “the State Defendants”), seeking a contribution of state funds that could be used to eradicate all remaining vestiges of public school segregation in Yonkers. After the State Defendants’ motions to dismiss and for summary judgment were denied, the Court commenced a trial, which was to be conducted in three stages. Because the State Defendants would not be liable for remedial funding if segregation had been completely eradicated by EIP I, the first stage (“the 1993 trial”) sought to determine whether or not there were vestiges of segregation. Our conclusion — that vestiges of segregation remained — was premised upon two findings of fact. We found, first, that a disparity existed with respect to the level of academic achievement attained by minority and non-minority students, see Yonkers IV, 833 F.Supp. at 220-22; and second, that the causes of that disparity were a combination of low teacher expectations for minority students and a curriculum that predated desegregation and had become anachronistic, see id. at 222. Having found that vestiges existed, the Court then turned, in the trial’s second phase (“the 1994 trial”), to the question of whether or not the State could be held liable for the pre-1985 segregation of the YPS and, therefore, required to contribute to the remedy. At the conclusion of that phase, we found that, as a matter of fact, the State Defendants’ conduct had been a contributing cause to the pre-1985 segregation, but nevertheless concluded, following Arthur v. Nyquist, 573 F.2d 134 (2d Cir.1978), that the State Defendants could not be held liable for their role in that violation. See United States v. City of Yonkers, 880 F.Supp. 212 (S.D.N.Y.1995). The Court of Appeals affirmed our factual finding (i.e., that the State Defendants’ conduct had contributed to the pre-1985 segregation), but reversed our legal conclusion. The court held that the State Defendants were liable, along with the City and the YBE, for the prior segregation of the YPS and that the State Defendants’ could therefore be required to contribute funding for remedial measures. See United States v. City of Yonkers, 96 F.3d 600 (2d Cir.1996) (“Yonkers V”). The court’s decision in Yonkers V required this Court to proceed to the third, and final, stage of the trial that had begun in 1993. The principal focus of the third stage (“the 1997 trial”) was to determine an appropriate remedy. However, because four years had by that time elapsed since our initial finding that vestiges of segregation remained, the parties were also permitted to present evidence as to whether or not any vestiges continued to exist as of 1997. At the conclusion of the trial’s third stage, we re-affirmed our prior finding that vestiges of segregation remained and ordered the state to contribute funding for additional remedial measures, which came to be known as “EIP II.” See United States v. Yonkers Bd. of Educ., 984 F.Supp. 687 (S.D.N.Y.1997) (“Yonkers VI”). The State Defendants and the City appealed, but sought no stay of our order, which was therefore in effect from October 8, 1997 until the Court of Appeals’ stay order of August 5, 1999. Because it believed that we had not articulated in detail all of the reasoning that underlay our findings, nor provided a detailed summary of the evidence, the Court of Appeals characterized our findings with respect to vestiges as “vague.” See United States v. City of Yonkers, 197 F.3d 41, 51 (2d Cir.1999) (“Yonkers VII”). Nevertheless, a majority of the appellate panel was able to discern two vestiges that, it believed, we had identified. It characterized those vestiges as (1) that “Yonkers’ curriculum and teaching techniques are insufficiently multi-cul-tural,” id. at 51; and (2) “low teacher expectations for minority students,” id. at 52. The majority found the record to be legally insufficient to support those findings, and, therefore, reversed. The majority also explained that it had scrutinized the record and (at least initially) determined that it could support no “alternative findings” of vestiges. See id. at 45. The third member of the panel, Judge Sack, filed an opinion concurring in part and dissenting in part. Although Judge Sack agreed that this Court had not set forth an adequate basis to support our finding of vestiges, he dissented on the ground that it would have been preferable for the Court to remand for further factual findings, rather than to reverse the findings we had made, scrutinize the record, and foreclose the possibility of any alternative findings of vestiges. See United States v. City of Yonkers, 181 F.3d 301, 321-30 (2d Cir.1999) (Sack, J., concurring in part and dissenting in part). After the NAACP sought reargument and an en banc hearing, the majority, for reasons that are not disclosed, came to agree with Judge Sack’s views. It, therefore, vacated its prior opinion and remanded the case. The “limited purpose” of the remand was to permit this Court to make further findings on the present record and in light of this opinion as to whether — or not — there are remaining vestiges of segregation in the Yonkers school system, and if so what they are and what record evidence is relied on for support. Yonkers VII, 197 F.3d at 46. B. Scope of Remand It is not without some trepidation that we now approach that limited task. We have been directed to render more detailed findings of fact in support of a conclusion that two members of the panel that will hear this case on appeal have expressly rejected. According to a published, though withdrawn, opinion, those two have “conducted [their] own careful scrutiny of the record, to see if it could support findings of vestigefs] ...” and, after that careful study, were “convinced that a remand would waste judicial resources and put off what in the end would be the same result.” United States v. City of Yonkers, 181 F.3d at 313 n. 3 Our trepidation is enhanced by the fact that, despite our best efforts and the guidance of the parties, we are genuinely puzzled as to the scope of the issues that have been remanded. Judge Sack’s view — of which the majority says it ultimately became convinced, see Yonkers VII, 197 F.3d at 46 — was that our findings were insufficiently detailed, as required by Federal Rule of Civil Procedure 52(a). See United States v. City of Yonkers, 181 F.3d at 322-25. Ordinarily, when findings are vacated on Rule 52(a) grounds, the purpose of the remand is to permit the district court to either supplement its findings or to conclude that in light of the Court of Appeals’ analysis, its findings are unsustainable. See Davis v. New York City Housing Authority, 166 F.3d 432, 435 (2d Cir.1999) (citations omitted); Inverness Corp. v. Whitehall Labs., 819 F.2d 48, 50-51 (2d Cir.1987). The passage quoted above, which describes the purpose of the remand as being to provide this Court with an opportunity “to make further findings on the present record and in light of this opinion,” Yonkers VII, 197 F.3d at 46, seems consistent with this view. The panel also characterizes its opinion as being “carefully limited to a review of the findings actually made by the district court and of the record evidence cited by the Board of Education and the NAACP,” id. at 49, which suggests, as well, that the panel has rejected its prior decision to scrutinize the record and has decided, instead, to limit its review to an analysis of the adequacy of our findings. Those two passages, read in light of the fact that the panel claims to have been persuaded by Judge Sack’s analysis, would lead us to conclude that the panel wishes us to reexamine the record and either render more detailed findings in support of our conclusion that vestiges of segregation remained as of 1997, or to conclude that no such finding is possible in light of the panel’s reasoning. Other portions of the remanding opinion, however, indicate that, at least with respect to some issues, no amount of elaboration or explanation would suffice. The introductory paragraph of the majority’s discussion of what it calls the “educational theory” vestige concludes with the following sentence: Our review is somewhat hampered by the district court’s failure to make specific factual findings on the subject, but because we do not want to prolong unnecessarily this already-lengthy litigation, we look to the record ourselves (and specifically to passages highlighted by the Board) rather than remand the case for a further articulation of findings on this particular issue. Id. at 51 (citing Wessmann v. Gittens, 160 F.3d 790, 802 (1st Cir.1998)) (emphasis added); see also id. at 45 (indicating that the panel adheres to its prior conclusion “that there was insufficient record support for the only two vestiges found by the district court....”) Although this passage strikes us as inconsistent with the panel’s decision to remand (which necessarily entails a prolongation of this “already-lengthy litigation”), and with the majority’s characterization of its opinion as being limited to a review of our findings, we must acknowledge that the sentence is included in the panel’s second, substituted opinion and is, therefore, legally binding upon this Court. See United States v. Tenzer, 213 F.3d 34, 40 (2d Cir.2000). The remanding panel has definitively resolved, therefore, that the record cannot support any findings that vestiges of segregation existed in the Yonkers public schools as of 1997 with respect to curriculum or teaching techniques. We therefore do not address those issues in this opinion. The panel’s discussion of the “teacher expectations” vestige, by contrast, is summarized with the following observation: [T]he evidence that teachers have low expectations of minority students is entirely based on scattered anecdotes, and the evidence supporting a causal link between these low expectations and pri- or de jure segregation is a set of subjective, intuitive, impressions. This is not enough. Id. at 53 (citations omitted). The State Defendants read this passage to mean that the panel has also adhered to its conclusion that the record cannot support a finding that low teacher expectations are a vestige of segregation. (See State Defendants’ Reply Memorandum of Law on Remand, Pursuant to the November 16, 1999 Order of the Court of Appeals for the Second Circuit (“State Reply”) at 5-6.) We agree. See Yonkers VII, 197 F.3d at 45 (indicating that the second opinion adheres to the conclusion that the two vestiges (educational theory and teacher expectations) discussed in the earlier opinion were insupportable). But the State Defendants also read this passage to signify that this Court may not in any way, directly or indirectly, refer to “teacher expectations,” nor the evidence in the record on that subject. (See State Reply at 16; State Defendants’ Proposed Findings of Fact and Conclusions of Law on Remand Pursuant to the November 16, 1999 Order of the Court of Appeals for the Second Circuit (“State Proposed Findings”) at 61, ¶ 7.) With this interpretation of the panel’s discussion, we do not agree. The remanding panel, apparently, held that the record failed to support our finding that low teacher expectations for minority students are a vestige of segregation. It said nothing, however, about whether evidence of teacher expectations, when considered in conjunction with other evidence, might support a finding that an alternative vestige of segregation exists. Similarly, the panel’s opinion addressed the disparity in achievement test scores, upon which this Court placed great reliance in our earlier opinions. The court noted that “using achievement test scores as a measure, either direct or indirect, of a school system’s movement away from segregation is deeply problematic.”, Yonkers VII, 197 F.3d at 54 (citing Missouri v. Jenkins, 515 U.S. 70, 101, 115 S.Ct. 2038, 132 L.Ed.2d 63 (1995); People Who Care v. Rockford Bd. of Educ., 111 F.3d 528, 537 (7th Cir.1997); Coalition to Save Our Children v. State Bd. of Educ., 90 F.3d 752, 776-78 (3d Cir.1996)). However, the court did not examine the propriety of our reliance on such a measure because it reasoned that even “[a]ccepting arguendo the study’s conclusion of a racial disparity, the study fails to show that the disparity was caused by pre-1986 segregation in Yonkers, as opposed to, for example, generalized ‘societal discrimination.’ ” Id. at 54-55 (citing Wessmann, 160 F.3d at 803-04; Swann v. Charlotte-Mecklenburg Bd. of Educ., 402 U.S. at 1, 22, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971)). “In short,” the court concluded, “a finding of prior segregation coupled with a finding of present day racial differences in educational achievement, is an insufficient positive test for the presence of residual segregative effects.” Id. at 55 (citing Wessmann, 160 F.3d at 801). The State Defendants’ argue that these passages indicate that the Court of Appeals has foreclosed any consideration of the demonstrated gap in minority achievement in Yonkers. {See State Reply at 5-7; State Proposed Findings at 61, ¶ 7.) We, however, read the panel’s discussion of this issue far more narrowly. We adhere to the panel’s conclusion that statistical anal-yses of test scores, standing alone, fail to establish the existence of vestiges, but we do not believe that the panel’s conclusion on this point implies that statistical analy-ses of test scores may not be an evidentia-ry factor weighed by the Court along with other evidence in reaching a conclusion that vestiges of segregation existed. We understand, of course, that “[t]his Court does not function as an appellate court from the Court of Appeals.” (State Reply at 4.) We have no desire or inclination to contradict or somehow evade the rulings of that court. But this case was remanded because the appellate panel came to believe that it was “worthwhile ... to ensure” that it had “the full benefit” of our views. Yonkers VII, 197 F.3d at 46. We have attempted, in the pages that follow, to provide the panel with that “full benefit,” though we recognize that some of our views have already been rejected. We do not therefore consider, in this opinion, whether educational theories, teacher expectations, or disparate test results are themselves vestiges of segregation — the remanding panel has foreclosed any such consideration. But for us to determine whether or not alternative vestiges existed and to explain the evidentiary basis of any such finding, it is necessary for us to consider evidence with respect to disparities in test scores and teacher expectations. That evidence is part of the record in this case. The Court of Appeals’ conclusion that it provides insufficient support for certain findings does not render it inadmissible. Our consideration of test scores and teacher expectations is not therefore, as the City and the State Defendants would have it, an attempt to “indirectly” overrule or evade the Court of Appeals’ ruling. To the contrary, it is the only way we can complete meaningfully the task that court has assigned us. II. LEGAL STANDARDS A vestige of segregation is a policy or practice which is traceable to the prior de jure system of segregation and which continues to have discriminatory effects. See United States v. Fordice, 505 U.S. 717, 727-28, 112 S.Ct. 2727, 120 L.Ed.2d 575 (1992); Freeman v. Pitts, 503 U.S. 467, 495-96, 112 S.Ct. 1430, 118 L.Ed.2d 108 (1992). This Court’s approach to the question of vestiges, both in our prior opinion and as amplified below, is to focus, first, on whether or not current policies or practices in Yonkers were, as of 1997, having a segregative effect in the public schools. As courts do in a variety of legal contexts that involve intricate and subtle questions of causation, we examine the question of segregative effect inferentially. The Supreme Court’s approach in employment discrimination eases provides perhaps the most familiar analogy. See, e.g., St. Mary’s Honor Ctr. v. Hicks, 509 U.S. 502, 113 S.Ct. 2742, 125 L.Ed.2d 407 (1993); Texas Dep’t of Community Affairs v. Burdine, 450 U.S. 248, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1981); McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). Gross statistical disparities in hiring data may justify an inference of discrimination because “absent explanation, it is ordinarily to be expected that nondiscriminatory hiring practices will in time result in a work force more or less representative of the racial and ethnic composition of the population in the community from which employees are hired.” Hazelwood Sch. District v. United States, 433 U.S. 299, 307, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977) (citations and internal quotation marks omitted). A prima facie showing of a discriminatory employment practice “raises an inference of discrimination ... because we presume those acts, if otherwise unexplained, are more likely than not based on the consideration of impermissible factors.” Burdine, 450 U.S. at 254, 101 S.Ct. 1089 (quoting Furnco Construction Corp. v. Waters, 438 U.S. 567, 577, 98 S.Ct. 2943, 57 L.Ed.2d 957 (1978) (internal quotation marks omitted)). A similar approach is followed in disparate impact cases, see Connecticut v. Teal, 457 U.S. 440, 446, 102 S.Ct. 2525, 73 L.Ed.2d 130 (1982); Albemarle Paper Co. v. Moody, 422 U.S. 405, 425, 95 S.Ct. 2362, 45 L.Ed.2d 280 (1975); Dothard v. Rawlinson, 433 U.S. 321, 329, 97 S.Ct. 2720, 53 L.Ed.2d 786 (1977); Griggs v. Duke Power Co., 401 U.S. 424, 431, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971), which we find particularly instructive here, since the question we are addressing is remarkably similar to the one addressed in that context. See Griggs, 401 U.S. at 430-31, 91 S.Ct. 849 (describing goal of disparate impact section of Title YII as being “to achieve equality of employment opportunities and remove barriers that have operated in the past to favor an identifiable group of white employees over other employees.”) We begin, in this case, with two premises shared by all parties: (1) the function of schools is to teach; and (2) all children can learn, without regard to their ethnic or racial heritage. The implication of those premises is that, absent some explanation, one would expect students of different races to achieve similar levels of academic success. If statistical data demonstrates a racial disparity in academic achievement, as the record in this case indisputably does, then an explanation is required, just as a prima facie showing of a discriminatory employment practice requires an employer to come forward with an explanation for the apparent disparity. The employer’s burden in that context, and the City and the State Defendants’ burden here, is one of production only, i.e., the burden of coming forward with a nondiscriminatory, or non-segregative, explanation. See Reeves v. Sanderson Plumbing Products, Inc., 530 U.S. 133, 120 S.Ct. 2097, 147 L.Ed.2d 105 (2000); Burdine, 450 U.S. at 254-56, 101 S.Ct. 1089; Meiri v. Dacon, 759 F.2d 989, 996-97 (2d Cir.1985). The YBE and NAACP have attempted to demonstrate that the explanation for the shortfall in minority achievement in Yonkers is a cluster of policies and practices that have a disparate, negative impact on minority students. The City and the State Defendants maintain that the explanation is a combination of non-racial factors (such as socioeconomic status, birth weight, and levels of parental education) that disproportionately disadvantage minority students, as well as ambient societal discrimination, as reflected by the fact that an achievement gap exists in several other districts that have not been the subject of a judicial finding of unlawful segregation. Although we address in detail the parties’ arguments on these issues below, we note in advance that we recognize the temptation to ascribe the shortfall in minority achievement to a concept as amorphous and imperceptible as “ambient societal discrimination” — a problem for which no individual or group bears any particular responsibility. It is similarly tempting to attribute the disparity to certain entrenched realities of this nation’s economic and social history — such as the levels of parental education in, and socioeconomic status of, Latino and African-American households — which are simply beyond the remedial reach of courts, schools, or other government officials. We believe, however, that it is essential for this Court, having already found a constitutional violation which we have attempted to remedy, to insure that these tempting explanations are not accepted as a more palatable surrogate for what is, in reality, a denial of our aforementioned fundamental premise that all children can learn. To provide a degree of assurance that the City and the State Defendants are advancing a tangible and credible explanation for the shortfall in minority achievement, rather than merely sloughing off responsibility under the guise of “ambient societal discrimination,” we assign those parties the burden of producing evidence that might explain the shortfall in minority achievement and exclude the explanation urged by the YBE and NAACP. Cf. Burdine, 450 U.S. at 255 n. 8, 101 S.Ct. 1089 (“[Assessing the burden of production helps the judge determine whether the litigants have created an issue of fact to be decided.... In a Title VIL case, the allocation of burdens and the creation of a presumption by the establishment of a prima facie case is intended progressively to sharpen the inquiry into the elusive factual question of intentional discrimination.”). In other words, the combination of our fundamental premise that all children can learn with the demonstrated shortfall in minority achievement, leads the Court to allocate the City and the State Defendants, if not the ultimate burden of persuasion, at least a burden of production. See Fleming James, Jr. et al., Civil Procedure § 7.15, at 342 (“Allocation of the burden of production is determined by rules extrinsic to the rules of evidence and trial procedure. These rules are specific to various issues and generally are correlated with the allocation of the burden of pleading.’). The State Defendants rely, for example, on the fact that four districts other than Yonkers which are said to be comparable demographically to Yonkers, have never been judicially determined to have engaged in racial discrimination and have some achievement test scores (PEP scores) which are comparable to Yonkers in terms of their racial disparity. The State proffers, nothing more concerning these four districts which it selected for comparison. That is, it offered nothing to show that these districts are indeed comparable or that, despite the absence of a judicial decree, they did not engage in de jure segregative practices. If any burden is placed on the party with the readiest access to information on the contested issue, see Fleming James, Jr. et al., Civil Procedure § 716, at 344, cited in United States v. City of Yonkers, 181 F.3d at 310, then with respect to this particular issue, the State surely bears a burden of production. Moreover, if one rejects the State’s reliance on those four other school districts about which they have produced relatively little information (as we do, for the reasons set forth below, see infra Part 111(A)(2)), their defense is reduced to a totally ineffective statistical presentation and anecdotal testimony by persons totally unfamiliar with the YPS. Such a defense fails to sustain even the minimal burden of production described above and therefore fails to rebut the presumption — grounded in the premise that all children can learn and the statistical evidence of a significant gap in minority achievement — that existing disparities in educational quality are the effect of segregative practices. Of course, for the Court to conclude that vestiges of segregation existed, it is also necessary for the YBE and the NAACP to identify those segregative policies and practices and to establish that they are “traceable” to the prior segregation. Although a policy or practice must “have a causal link to the de jure violation” in order to constitute a vestige, Freeman, 503 U.S. at 496, 112 S.Ct. 1430, that link need not be the exclusive cause for the policy in question. “Traceable” does not mean “exclusively caused by,” or even “predominantly caused by.” So long as the current policy had its roots in the prior regime, or had an antecedent in the prior regime, it may constitute a vestige of segregation if it has a segregative effect. At its core, the question of whether or not vestiges of segregation existed in Yonkers as of 1997 is a question about the adequacy of prior remedial measures. We certainly understand that this Court’s remedial authority extends only so far as the constitutional violation to which it is addressed. See Milliken v. Bradley, 418 U.S. 717, 744, 94 S.Ct. 3112, 41 L.Ed.2d 1069 (1974); Swann, 402 U.S. at 22, 91 S.Ct. 1267 (“One vehicle can carry only a limited amount of baggage.”). But before we abandon all remedial efforts and conclude that any existing disparities in the Yonkers public schools are the inevitable consequence of intractable social and economic inequalities, it is incumbent upon all interested parties to be certain that there is nothing further that can be done, practicably, to address the problems caused by the City and the State Defendants’ past violations. “Ambient societal discrimination” is an acceptable residual position if but only if all feasible remedies have been exhausted. It is this Court’s view, after twenty years of intense involvement with this case, that we have not yet reached that point. III. FINDINGS OF FACT A. The Disparity in Academic Achievement In our earlier opinions, we explained that this Court has found that “minority students (black and Hispanic) lag behind majority students (for these purposes, white and Asian students) in reading and math ... and that to a statistically significant extent, race is a factor with regard to levels of academic achievement in the Yonkers public schools.” Yonkers TV, 833 F.Supp. at 221; see Yonkers VI, 984 F.Supp. at 690. The evidentiary basis for that finding was our conclusion that the statistical expert proffered by the YBE, Dr. Jomills Braddock, presented a more credible and persuasive explanation of the test score data than did the State Defendants’ expert, Dr. David Rindskopf. Moreover, we found that upon close scrutiny, Dr. Rindskopfs analysis actually corroborated Dr. Braddock’s conclusion. See Yonkers TV, 833 F.Supp. at 221-22. The remanding panel did not disturb our finding on this subject. It believed it was unnecessary to address the issue, reasoning that a finding of a racial disparity in test scores failed to support the conclusion that vestiges of segregation remained. See Yonkers VII, 197 F.3d at 54-55 (“Accepting arguendo the study’s conclusion of a racial disparity, the study fails to show that the disparity was caused by pre-1986 segregation in Yonkers, as opposed to, for example, generalized ‘societal discrimination.’ ”) (citations omitted). Upon remand, for the reasons set forth in Appendix A, we re-affirm and elaborate upon our finding that race is a statistically significant factor in explaining the gap in achievement between minority and non-minority students in Yonkers. We take this opportunity to explain further, in light of the remanding panel’s concerns, the significance of that finding in our reasoning as to the existence of vestiges. We agree with the remanding panel that “a finding of prior segregation, coupled with a finding of present day racial differences in educational achievement, is an insufficient positive test for the presence of residual segregative effects.” Yonkers VII, 197 F.3d at 55 (citing Wessmann, 160 F.3d at 801). Such a test has never been applied by this Court. However, when one begins with the premise that all children can learn, a “finding of present day racial differences in educational achievement” creates a strong basis for inferring that, in some way, the school district is failing to teach minority students. Because the State Defendants have failed to come forward with any evidence that might rebut that inference, we find that some set of policies or practices in the Yonkers public schools, which inadequately serves the needs of minority students, must be responsible for the shortfall in minority achievement. The more closely that shortfall is correlated with the students’ racial or ethnic heritage, the more confident we are in the reliability of that inference. The Court has received testimony about a variety of different measures of academic achievement: (1) Metropolitan Achievement Test (“MAT”) scores; (2) Pupil Evaluation Program (“PEP”) scores; (3) dropout and graduation rates; and (4) the rates at which students pursue post-secondary education. Because MAT scores have been the subject of two detailed studies by statistical experts, they necessarily occupy a prominent place in our reasoning. It is, principally, due to the disparity in MAT scores and the statistical analyses’ thereof that we conclude that the record demonstrates a correlation between the gap in minority achievement and the students’ ethnic or racial heritage. Because all of the other measures of academic achievement manifest a gap in minority achievement that is consistent with the gap in MAT scores, we believe those measures provide additional corroborative support for our finding of a correlation between the achievement gap and students’ race. That finding, however, rests principally on the detailed analyses’ of MAT scores discussed below in Appendix A. The State Defendants argue, repeatedly, that any statistical evidence we have received that has not been the subject of an expert’s scrutiny evidence about all measures other than MAT scores) is utterly worthless. Without a regression analysis or some other method of isolating the effect attributable to race, they maintain, evidence of a statistical disparity with respect to an educational outcome is meaningless. We believe this contention mis-pereeives the nature of statistical evidence. Cf. Bazemore v. Friday, 478 U.S. 385, 400, 106 S.Ct. 3000, 92 L.Ed.2d 315 (explaining that regression analysis may be sufficient to establish Title YII plaintiffs case even if it does not establish proof of discrimination “with scientific certainty”). The purpose of the experts’ analyses is to establish an explanation for a disparity in student outcomes; if that explanation holds, then we believe it is plausible to presume that it holds regardless of which measure of student performance is used. Approached somewhat differently, for the State Defendants argument to be at all persuasive, it is incumbent upon them, at the very least, to suggest some reason that socioeconomic status, or any other variable, might fail to account for the disparity in MAT scores, yet nevertheless account for a similar disparity in, for example, PEP scores. Because they have not suggested any such reason, we presume that the explanatory value of the experts’ analyses of MAT scores is applicable to the other measures of student achievement as to which we have received evidence. 1. MAT Scores The MAT has been administered annually to almost every student in the Yonkers public school system, from the time of this Court’s initial remedial decree in 1986 until 1996. The only students who did not take the MAT were those students in a special education program whose individual learning plan did not include standardized tests, and students who demonstrated limited proficiency in English (“LEP”) and had received less than 20 months of instruction in English. (See 1993 Trial Tr. at 208-09 (Batista).) The exam is administered each May to students in grades 1 through 9. (See 1993 Tr. 350 (Wein-berger).) Similar or identical forms of the test are given to students in grades 1 and 2, grades 3 and 4, grades 5 and 6, and grades 7 through 9. (See 1993 State Trial Ex. N at 14.) The test measures student achievement in three categories' — Reading, Mathematics, and Language. (See id.) Because the “MAT was the outcome for which the widest set of data was available over time,” all of the experts who testified at trial agreed that it was “one of the key indicators through which” the district’s performance can be assessed. (See 1993 Tr. at 1378 (Braddock).) One method of measuring a student’s performance on the MAT is to compare the student’s performance to that which would be expected of a hypothetical average student, based on national norms, at that particular grade level. (See 1993 Tr. at 350 (Weinberger).) Because the examination occurs in May, which is the eighth month of a ten-month school year, the norm for a first grader taking the exam, for example, would be the performance that would be expected of a student who had completed one year and eight months of school, which is represented numerically as 1.8. (See id.) This numerical representation of the performance expected of an average student at a particular grade level are referred to as a “grade equivalent.” (See id.) Educators and administrators use grade equivalents data to determine how their students’ performance compares to that of other students nationwide. Dr. David Weinberger, the YBE’s Director of Research and Evaluation, testified that for every single grade level in the YPS, between the years 1987 and 1996, the average MAT scores of white students was consistently higher than the national norm, but that the average MAT score of minority students was consistently lower than national norms. (See 1997 YBE Ex. 4, at ¶¶ 9-11 & Tabs 3-4; 1993 Trial Tr. at 352-55 (Weinberger); 1993 YBE Exs. 5A-5F.) Moreover, the disparity in grade equivalents was greater in the higher grades than in the lower grades. (See 1997 YBE Ex. 4, at ¶¶ 9, 11 & Tabs 3-4; 1993 YBE Exs. 5A-5F.) For example, focusing on the 1991-92 test, when the students’ performance on all three of the test’s components — reading, language, and math— were combined (producing a figure referred to as “total battery”), white first graders in Yonkers scored % of a grade above grade equivalent (i.e.; as second graders in their third month), but minority students performed slightly below grade equivalent. (See 1993 YBE Ex. 5A.) The disparity among first graders, therefore, was approximately one whole grade level. By comparison, white ninth graders, however, performed almost a whole grade level higher than their grade equivalents (ie., as tenth graders), while black ninth graders performed over a grade level below expected and Hispanic ninth graders performed two grade levels lower than expected. (See id.; 1993 Trial Tr. at 354-55 (Weinberger).) The disparity among ninth graders, therefore, was between two and three grade levels. These trends of widening gaps from expected grade level, upwards for white students and downward for blacks and Hispanics, was consistently found in Yonkers between 1987-88 and 1996-97, on all three components of the MAT (or CAT) and in terms of total battery. (See 1997 YBE Ex. 4, at 9-12 and Tabs 3-4; YBE 1993 Trial Exs. 5A-5F; 1993 Trial Tr. at 356-57 (Wein-berger).) Moreover, the disparity does not appear to be abating over time; the largest disparity is observed in 1994-95, in which “the gap between both non-minority and Black achievement and nonminority and Hispanic achievement grew to 2 grade equivalents by grade 3; was at 3 grade equivalents by grade 6; and reached between 3.5 and 4.0 grade equivalents by grades 8 and 9.” (1997 YBE Ex. 4, at ¶ 12 and Tabs 3-4.) This evidence of a gap in minority achievement, as explained and analyzed by the statistical experts, see infra Appendix A, provides the principal evidentiary basis for our finding that, as of 1997, race was meaningfully correlated with the disparity in academic achievement in the Yonkers public schools. 2. PEP Scores Virtually all students in the State of New York were, as of 1997, required to take an exam called the Pupil Evaluation Program (“PEP”). (See 1997 YBE Ex. 4, at ¶ 17; 1993 Trial Tr. at 365 (Wein-berger).) The PEP consists of reading and math tests that are given to 3rd and 6th graders and a writing test that is administered to 5th graders. (See 1993 Trial Tr. at 365 (Weinberger).) The test measures whether a student has acquired competence in certain basic skills. It does not rank students against each other; it only reports whether a student has passed certain thresholds. (See 1997 YBE Ex. 4, at ¶ 18; 1993 Trial Tr. at 365 (Wein-berger).) The thresholds are a state reference point (“SRP”), which represents the number of questions a student must answer correctly to be considered minimally competent, and a mastery level, which represents the number of questions that a student must answer correctly to be considered to have mastered the skills being tested. (See 1997 YBE Ex. 4, at ¶ 18; 1993 Trial Tr. at 365 (Weinberger).) The YBE and the NAACP presented evidence disaggregating by race the Yonkers’ students’ performance on the PEP for the years 1992 through 1997. (See 1997 YBE Ex. 4, at Tabs 6-7; 1993 YBE Ex. 6A-6B.) The data reveal a consistent racial disparity in the rates with which students meet the SRP. (See 1997 YBE Ex. 4, at ¶¶ 19-20.) For all six years presented, on all 5 of the individual tests, a significantly lower percentage of white students than minority students failed to achieve the SRP level. (See 1993 YBE Ex. 6A-6B.) Minority students were at least twice as likely to fail to achieve the SRP as were non-minority students, and on many of the tests, they were almost three times as likely to fail. Between 1993 and 1997, students in the YPS improved, overall, in their performance on the PEP tests, but the racial disparity remained consistent, with African-American and Latino students failing at rates between two and four times higher than those for non-minority students. (See 1997 YBE Ex. 4, at ¶20 and Tab 7.) The disparity is even greater when one focuses on the rates at which students achieve the mastery level, with non-minority students achieving that level approximately twice as frequently than minority students and, on some tests, as much as five times more frequently. (See id. at ¶ 21 and Tab 8.) With respect to the 1992 data, Dr. Weinberger determined that the observed disparity was statistically significant to a factor of pc.001. (See 1993 Trial Tr. at 447.) The Defendants’ principal response to the PEP data is their claim that a similar disparity exists in four other school districts — New York City, two community school districts within New York City, and Freeport — the racial demographics of which are allegedly similar to that found in Yonkers. (See Ct.Ex. A of 9/16/97.) In a prior opinion, we explained that we found this argument unpersuasive because we felt it inappropriate to assume that no segregation had occurred in those districts merely because they had not been the subject of a judicial finding of unlawful segregation. See Yonkers VI, 984 F.Supp. at 690. The Court of Appeals found our reasoning to be flawed, noting that “the district court’s approach would invalidate reality-checking comparisons with any and all other districts.” Yonkers VII, 197 F.3d at 55. In light of the Court of Appeals’ opinion, we have considered the Defendants’ argument anew, but still find it to be, ultimately, unpersuasive. We are troubled by the fact that the analysis was presented in terms of PEP scores. The PEP only measures whether or not a student has passed a certain threshold; it does not say by how much. We are unable to conclude on the basis of this evidence, therefore, that the disparity in achievement in these other four districts is of a similar magnitude as that observed in Yonkers. Moreover, even if the disparity in Freeport and New York City was of a similar magnitude, the object of this Court’s remedy order was not to raise Yonkers schools to the level of other districts which were not adequately meeting the needs of their minority students, but to the level that would have obtained had there been no unlawful segregation. For all these reasons, the Court finds that the Yonkers’ students PEP scores provide additional evidentiary support, in corroboration of the MAT data, for a finding that, as of 1997, there was a meaningful racial disparity with respect to the levels of academic achievement found among students in the Yonkers public schools. That four districts outside Yonkers, not shown to be highly comparable or to have been free of de jure segregation, does not negate this finding. 3. Dropout and Graduation Rates The New York State Education Department (“SED”) defines a dropout as a student over the age of compulsory attendance (17 years old) who has not transferred to another district or to an approved education program. (See 1993 Trial Tr. at 388 (Weinberger); 1993 YBE Ex. 12, at n. *; 1997 YBE Ex. 4, at ¶ 30.) The YPS only considers a student to be a dropout if it can confirm that the student is older than the age of compulsory attendance and that the student has not entered another approved program. For example, a student who left school at the age of 16 or younger, or one who left without any indication of his future plans would not be considered a formal dropout, even though it is possible that the student will never return to school again. (See 1997 YBE Ex. 4, at ¶ 30.) Between 1987 and 1997, African-American and Latino students dropped out of the YPS at a higher rate than white students. (See 1997 YBE Ex. 4, at ¶ 30 & tab 18; 1993 YBE Ex. 12; 1993 Trial Tr. at 388 (Weinberger).) The African-American and Latino dropout rates ranged from approximately 4 to 9% over the ten years for which evidence is available, with an average in the 6 to 7% range. (See 1997 YBE Ex. 4, at Tab 18; 1993 YBE Ex. 12.) Over the same period, the white students’ dropout rate only exceeded 4% in one year (1992) and seems to have averaged, approximately 2.5% to 3.5%. (See id.) Among those students who remained in school long enough to begin their senior year, the graduation rate among African-American and Latino students was substantially lower than it was for white students. (See 1997 YBE Ex. 4, at ¶¶ 30-31 & Tab 18; 1993 YBE Ex. 13; 1993 Trial Tr. at 396-97 (Weinberger).) Throughout the ten year period examined, the minority students were 1.5 to 2 times more likely not to graduate than were white students; the minority graduation rate, for those -students who earned enough credits to be qualified as seniors, ranged between 20 and 30% while the white graduation rate remained within the 10% to 15% range. CSee 1997 YBE Ex. 4, at ¶¶ 30-31 & Tab 18; 1993 YBE Ex. 13; 1993 Trial Tr. at 396-97 (Weinberger).) Poor academic performance is, obviously, not the only reason that a student might drop out of high school. Any number of other factors could, conceivably, motivate that decision. A student’s economic circumstances, work schedule, or immigration status are just a few examples of noneducational factors that might influence a decision to drop out of high school. However, we believe that the evidence of a disparity in dropout rates does, to a limited degree, account for such factors. If a student leaves the YPS prior to reaching the age of seventeen, which is likely an accurate description of some of the most transient students upon whom the State Defendants focus, he would not be counted as a dropout, due to the narrow way that dropouts are defined. Moreover, the YBE supplemented its report of a disparity in raw dropout rates, by showing that the data was consistent when refined to include only those students who earned enough credits to be classified as seniors. Certainly, some of the students whose dropouts were caused by transient lifestyles or persistent economic disruption would not be able to earn enough credits to be classified as seniors and would, therefore, have been excluded from this analysis. (See NAACP’s Reply Submission on Vestiges, Ex. 1, at ¶ 230 (“Even those black and Hispanic students who have the desire and support to remain in school into their senior year lack the credits or skills needed to graduate.”).) Although the evidence is not sufficiently refined to support a conclusion that poor academic performance is the exclusive cause of the racial disparity in dropout rates, it is persuasive enough, in light of our findings with respect to MAT and PEP scores, to provide additional, corroborative support for a finding that, as of 1997, a racial disparity existed in the YPS with respect to the levels of academic achievement. The Defendants argue that the disparity is consistent with national trends. However, the very witness upon whose testimony they rely for that argument, Professor Darling-Hammond, (see State Defendants’ Proposed Findings of Fact at ¶ J(8)) explained that the reason for that national disparity is that educational policies or practices nationwide have a disparate impact on racial minorities. (See Darling-Hammond 8/13/97 dep. at 92.) Her testimony, therefore, further supports our finding, and even supports the inference we draw therefrom. 4. PosNSecondary Education The disparate impact of the YPS’s educational policies and practices is also reflected, to a very limited degree, in the disparity, as of 1997, between minority and non-minority students’ rates of applying, and of being accepted by, post-secondary educational programs. Between 1988 and 1996, approximately 55% of the African-American students in the YPS applied to post-secondary programs. (See 1997 YBE Ex. 4, at Tab 22.) For Latino students, the application rate demonstrated a downward trend over the same period, declining from approximately 68% in 1988 to approximately 55% in 1996. (See id.) During those years, the application rate among white students increased dramatically, from a low of approximately 55% in 1990, to a high of almost 90% in 1995, and averaging somewhere between 60 and 70%. (See id.) While, as of 1997, the rate at which students from the YPS had been accepted into post-secondary educational programs had declined for all three ethnic groups, the overall rate was significantly lower (approximately 10%) for minority students than it was for non-minority students. (See id.) We recognize, as the State argues, that many students who do, in fact, apply to post-secondary educational programs and who are accepted will not be captured in the YBE’s data. The data only accounts for those students who applied for, and were accepted by, post-secondary programs while they were seniors in the Yonkers school system. (See 1993 Trial Tr. at 484-85 (Weinberger).) If a student waited for a year, after graduating from high school, before applying, the student would not be reflected in the Board’s data. However, we have no reason to assume that any particular racial or ethnic group will fall into this category at a higher rate than another. The Defendants argue that waiting to apply for post-secondary education is more common among poor students, who are disproportionately minority, but we decline to engage in such speculation. Evidence of a disparity in the rates with which students pursued post-secondary education would not be sufficiently probative, taken alone, to support an inference of a segregative effect. However, we believe that this evidence provides some additional corroboration of our finding, based on the test score data and dropout rates, that there was, as of 1997, a racial disparity with respect to the quality of education offered to students in the Yonkers public schools. 5. Conclusion All of the evidence of academic achievement outcomes indicates, consistently, that, as of 1997, a disparity existed between the academic performance of minority and non-minority students in Yonkers. Regardless of the measure that is used, white students were, as of 1997, performing at higher levels than minority students. Expert analyses of some of the numerical data convinces us that race is a statistically meaningful variable in explaining the disparity. The Court finds, therefore, by a preponderance of the evidence, that, as of 1997, a racial disparity in academic performance existed in the Yonkers Public Schools. Given our premise that all children can learn, and the City and the State Defendants’ total failure to establish an alternative explanation for that gap, we infér that the cause of the disparity was a set of policies and practices that existed in the Yonkers public schools as of 1997, an issue which we address next. B. Current Policies and Practices Notwithstanding our inference that educational policies and practices were responsible for the gap in minority performance, to conclude that vestiges of segregation existed, we must identify those practices and determine whether or not they are traceable to the prior segregation. Below, we address five of the policies and practices suggested by the YBE and the NAACP — (1) tracking; (2) disciplinary practices; (3) special education referrals; (4) inadequate provision of pupil personnel services; and (5) inadequate services for LEP students. Before summarizing and analyzing the record with respect to each of those five policies and practices, we note that it is not alleged that any of the putative vestiges is the product of intentional discrimination, nor that any of the policies or practices operate in an openly discriminatory manner. Rather, the YBE’s and NAACP’s claim is that racism is so embedded in the YPS, as a result of what occurred prior to 1985, that teachers and other administrators . unintentionally administer facially neutral policies in a racially discriminatory manner, or, at least, without sufficient sensitivity to the disparate negative impact that they have on minority students. The evidence offered in support of this position consists primarily of testimony from educators in the Yonkers public schools as to their perception of the attitudes of their colleagues, and their understanding of the sources of those attitudes. Many YPS administrators, almost all of whom had formerly been teachers in the YPS, testified that they believed non-minority teachers had lower expectations for minority students than they did for non-minority students. (See 1993 Trial Tr. at 234-37 (Batista), 542, 545-47 (Pack), 804-05 (Duncan), 878 (Jamieson); 972 (Cardo-na-Zuckerman)). Those judgments were formed after classroom visits (see id. at 731-42 (Pack), 809-11 (Duncan)), reviews of teacher evaluations (see id. at 958 (Jamieson)), reviews of reports prepared by outside consultants {see id. at 58 (Batista)), and conversations with teachers and students {see, e.g., id. at 234-37 (Batista), 878 (Jamieson), 804-07 (Duncan)). The low expectations were demonstrated in a lack of homework assigned to minority students (see id. at 1047 (Fries)), seating patterns in classrooms (see id. at 809-10 (Duncan)), and a general lack of concern for minority students’ inattentiveness in class (see id. at 731-42 (Pack)). The witnesses testified that, in their judgment, the improper attitudes they observed were rooted in the district’s history of segregation and its attempts to integrate. {See id. at 551 (Pack); 1191 (Car-dona-Zuekerman).) Dr. Gladys Pack, the YPS’s Assistant Superintendent for Restructuring, explained one way in which the district’s history of segregation influenced teachers’ current attitudes — the move away from neighborhood schools (because of the segregation caused thereby) required some parents to travel some distance to attend parent-teacher conferences; minority parents, many of whom were poor, often lacked the resources to undertake such travel; some non-minority teachers, unaware of the parents’ hardships, inferred that the parents were not interested in their children’s schooling and, consequently, developed low expectations for those students. (See id. at 552-53; see also id. at 70-81 (Batista).) That schools that had previously been identified as minority schools had also been perceived to be inferior schools, has also, according to the witnesses, left many non-minority teachers with the impression that minority students are unable to achieve at high levels. (See id. at 972 (Cardona-Zucker-man); 878 (Jamieson).) We find this testimony to be highly credible and persuasive. The racism that existed in Yonkers prior to 1985 — which was demonstrated overwhelmingly to this Court in the course of literally hundreds of days of trial and hearings — was invidious and pervasive. Our liability opinion contains numerous examples of the ways in which blatantly racist attitudes were exhibited in the administration of school policies. See, e.g., Yonkers I, 624 F.Supp. at 1454-62 (describing pervasive racist attitudes exhibited in the administration of special education program). In light of that history, the testimony of local school officials who perceive the continuation of racist expectations and attitudes in the Yonkers public schools is highly credible and persuasive. See Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 267-68, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977) (noting that historical background is an “evidentiary source” that can be used to interpret other forms of evidence); Brown v. Bd. of Educ., 978 F.2d 585, 590 (10th Cir.1992) (“To expect the effects of legally mandated segregation to magically dissolve is to expect too much.”). The Court of Appeals rejected the testimony about teacher expectations on the ground that it was nothing more than “scattered anecdotes” and “subjective, intuitive impressions.” Yonkers VII, 197 F.3d at 53 (citations omitted). We do not deny that much of the evidence is, obviously, anecdotal. But it is anecdotal evidence that is fully consistent with the history and background of this case, and with all of the available quantitative evidence. Cf. Wessmann v. Gittens, 160 F.3d at 806 (“[Ajnecdotal evidence may prove powerful when proffered in conjunction with admissions or valid statistical evidence ....”) (citation omitted). Moreover, it is evidence that was provided, without contradiction, by a group of educators who, collectively, have decades of experience in the Yonkers public schools. The Court of Appeals doubted the credibility of those witnesses, reasoning that they have a financial incentive to exaggerate the effects of the prior segregation. See Yonkers VII, 197 F.3d at 54 (“[I]t is clear enough that the Board has no incentive to rid itself of that taint so long as its self-accusation generates a flow of state remedial funds through this litigation.”). But none of the YBE’s witnesses have any personal, financial interest in the outcome of this litigation. To the contrary, they have demonstrated themselves, over the course of the last several years, to be committed educators. They have testified before this Court that, in their experienced judgment, racist attitudes and expectations affect the administration of a variety of YPS policies. Cf. People Who Care, 111 F.3d at 536 (reasoning that “consensus of ... educational authorities ... deserves some consideration by a federal court”). Because the City and the State Defendants did not call a single witness who had any degree of experience in the YPS to contradict that testimony, and because (as we have indicated) we find it credible, the Court finds that, as of 1997, there were teachers and administrators, in the YPS who exhibited reduced expectations for minority students and that those expectations are traceable to the pre-1985 segregation of the YPS. Although we do not consider those expectations, themselves, to be a vestige of segregation, they play an integral role in our assessment of the five policies and practices that the YBE and the NAACP suggest are vestiges of segregation. We turn now to an analysis of the record with respect to those five policies and practices. 1. Tracking Like many other school districts; the YPS, as of 1997, separated its students into discrete groups based on some assessment of the students’ abilities. At the top of the spectrum is the Century Honors program, which provides enrichment programs to a select group of students who have demonstrated high academic ability. The students participate in these enrichment programs as a group and their participation is supplemental to their other courses. {See 1993 Trial Tr. at 90-91, 258 (Batista).) Students apply for participation in the Century Honors program and are selected on the basis o