278 F.3d 64
Pauline DAVIS, Cynthia Williams, Cornelia Simmons, and Kim Rivera, on behalf of themselves and all others similarly situated, Plaintiffs-Appellees,v.NEW YORK CITY HOUSING AUTHORITY, Defendant-Appellant.
Docket No. 99-6238.
United States Court of Appeals, Second Circuit.
Argued February 16, 2000.
Final briefs submitted July 28, 2000.
Decided January 3, 2002.

COPYRIGHT MATERIAL OMITTED Scott A. Rosenberg, New York, New York (Helaine Barnett, The Legal Aid Society, Civil Division, Civil Appeals & Law Reform Unit, New York, New York, on the brief), for Plaintiffs-Appellees.
Henry Schoenfeld, New York, New York (Jeffrey Schanback, General Counsel, Nancy M. Harnett, Stephen W. Goodman, Steven J. Rappaport, on the brief), for Defendant-Appellant.
Before WALKER, Chief Judge, KEARSE and POOLER, Circuit Judges.
KEARSE, Circuit Judge.


1
This case returns to us following remands in 1999 and 2000 to the United States District Court for the Southern District of New York, Robert W. Sweet, Judge, for further findings, clarification, and supplementation of the record in connection with its issuance of injunctions prohibiting defendant New York City Housing Authority ("NYCHA" or the "Authority") from implementing proposed changes in its method of complying with a 1992 consent decree (the "Consent Decree" or "Decree") settling actions alleging that, in accepting tenants for public housing in New York City, the Authority had discriminated against Latinos and African Americans on the basis of race. The district court found that NYCHA's proposed introduction of a working-family preference into the tenant acceptance procedures would cause a significant perpetuation of past segregation at 20 NYCHA low-income housing projects, and in 1999 it permanently enjoined NYCHA from implementing that preference at those projects. NYCHA appeals, contending principally that the district court erred (a) in its view of what constitutes segregation, and (b) in finding that segregation would be significantly perpetuated. For the reasons that follow, we affirm with respect to 14 of the housing projects, and we reverse with respect to the remaining six.

I. BACKGROUND

2
The factual background of this litigation has been chronicled in several opinions, familiarity with which is assumed. The prior proceedings are summarized below.

A. The Consent Decree (Davis I)

3
NYCHA, an independent public corporation created by New York State Law, operates 322 public housing projects in New York City. In the early 1990s, parallel actions were brought by the United States and by plaintiffs Pauline Davis et al. on behalf of themselves and others similarly situated, alleging that NYCHA had engaged in discrimination in violation of, inter alia, 42 U.S.C. §§ 1981, 1982, and 1983 and the Fair Housing Act of 1968, as amended, 42 U.S.C. § 3601 et seq. ("FHA"), by assigning applicants for public housing to particular housing projects on the basis of race. NYCHA ultimately acknowledged that it had engaged in, inter alia, "racial steering" (NYCHA Memorandum of Law in Support of the Fairness and Adequacy of the Davis Settlement and the Entry of the Consent Decree and in Response to Comments Submitted by Interested Persons, dated October 30, 1992 ("NYCHA Memorandum Supporting Consent Decree" or "NYCHA Memorandum"), at 21), and it stated that "[t]he Housing Authority concluded that the complaint had merit" (id. at 22).


4
The parties agreed to settle both actions in 1992 by entering into the Consent Decree. See Davis v. New York City Housing Authority, 1992 WL 420923 (S.D.N.Y. Dec.31, 1992) ("Davis I"). In urging the district court to enter the Decree, NYCHA admitted that


5
[t]he Housing Authority engaged in a number of policies and practices that had the effect of discriminating against Black and Hispanic applicants. Because the Housing Authority was convinced that these policies were wrong, and indeed in most instances were stopped well before the lawsuits were brought, the Housing Authority believed that the responsible course was to settle these suits to remedy these past practices in as fair a manner as possible.


6
(NYCHA Memorandum at 21.) Describing "a few of these policies" (id.), the NYCHA Memorandum stated, inter alia, that the Authority in 1960 adopted an "integration program" whose "racial steering component ... continued at a few predominantly white projects until January, 1988, resulting in a higher proportion of whites than would have resulted from a race neutral admissions policy" (id.), and that until 1990, some NYCHA "employees would expedite applications and send them to projects to which they would not otherwise have been sent[,] [o]ften ... favor[ing] white applicants who sought an apartment at a predominantly white project" (id. at 22).


7
Following a fairness hearing, then-District Judge Pierre N. Leval, to whom the case was then assigned, approved the Consent Decree, making findings of fact and conclusions of law that included the following:


8
Plaintiffs' evidence supports their allegations that during specified periods of time the Housing Authority selected and assigned applicants for public housing, and tenants requesting transfers, to certain housing projects using methods that resulted in unlawful discrimination against Blacks and Hispanics. These methods included (1) the intermittent use of codes denoting housing projects to which only white families could be assigned; (2) the use of zip code and other geographic restrictions on admission to projects; (3) the use of racial goals or targets when new projects were "rented up" and on an ongoing basis thereafter; and (4) the assignment of families to projects where vacancies were not expected to arise.


9
Davis I, 1992 WL 420923, at *2. The Consent Decree


10
permanently enjoined [NYCHA] from engaging in any act or practice which denies equal access to its housing ... on the basis of race, color, or national origin, including[] adopting and implementing any tenant application, selection, assignment, and transfer plan, or any such policy or process, which gives preference to Applicants or tenants on the basis of race, color, or national origin.


11
Consent Decree ¶ 4(a). Other provisions permanently enjoined NYCHA from, inter alia, basing denials of transfers on racial considerations, see id. ¶ 4(b), making statements indicating a preference or limitation based on race, see id. ¶ 4(c), and falsely representing, because of an applicant's race, that certain projects were not anticipating vacancies when in fact such vacancies were anticipated, see id. ¶ 4(d). Although parts of the Decree were to be dissolved 8½ years after its date of entry, the provision for such dissolution expressly excluded "the permanent injunctive provisions." Id. ¶ 50.


12
As part of the injunctive relief granted, the Consent Decree also required NYCHA to implement a new three-stage tenant selection and assignment plan ("TSAP") that substantially revised the Authority's prior procedures for granting applications for public housing. After explicitly incorporating the TSAP by reference, the Decree stated that "[t]he TSAP will be implemented by the Housing Authority to prevent any unlawful discrimination on the basis of race, color, or national origin, in compliance with the Housing Authority's obligations therewith under Title VI, the Fair Housing Act and the implementing regulations and requirements of" the United States Department of Housing and Urban Development ("HUD"). Consent Decree ¶ 5. HUD "approved the TSAP for a five-year period as meeting the requirements of," inter alia, HUD's "regulations governing non-discrimination on the basis of race, color, or national origin." Consent Decree page 5, ¶ WHEREAS.


13
In the TSAP, NYCHA recognizes "federal" preferences for certain categories of applicants, as required by certain federal laws, and employs certain of its own preferences ("local preferences"). In the first stage of the TSAP, applicants are chosen from the overall applicant pool for interviews as to their eligibility for public housing. In the second stage, those interviewed who are found eligible are assigned to waiting lists for vacancies and are divided into three "Tiers." Tier III families have the highest incomes; Tier I families have the lowest. In the final stage of the TSAP, NYCHA attempts to allocate 25% of the vacancies to Tier III and to divide the remaining 75% evenly between Tiers I and II. Under the original TSAP's local preferences, priority is given to families on the basis of housing need.

The Decree also provided that

14
[n]o Applicant will be barred or disqualified from any Project tenanted under the TSAP because of any minimum income requirements that result in discrimination on the basis of race, color, or national origin in violation of Title VI or the Fair Housing Act; provided, however, that consistent with HUD's general occupancy standards, the Housing Authority may seek to achieve a tenant body in each Project composed of families with a broad range of incomes, generally representative of the range of incomes and rent-paying abilities of lower income families in its geographic operating area to the extent permitted under 42 U.S.C. § 1437d(c)(4)(A)(iv), 24 C.F.R. § 960.205, and 24 C.F.R. Part 913.... If any new minimum income requirements are added to existing [conventional housing projects administered by NYCHA], plaintiffs shall have the right to challenge such a change during the five-year period [after full implementation of the TSAP] or thereafter....


15
Consent Decree ¶ 8.


16
NYCHA was required to have the TSAP fully implemented within one year after entry of the Decree. See id. ¶ 6(a). If, during the five-year period after full implementation of the TSAP, NYCHA proposed to modify any provision of the TSAP, it was to give at least 60 days' notice to plaintiffs, who were given "the right ... to move the court to enjoin the proposed modification as inconsistent with the terms of th[e] Consent Decree." Id. ¶ 6(b). The Decree also provided that for three years following that five-year period, plaintiffs were allowed to ask the district court to "modify or otherwise enjoin any aspect of any TSAP implemented by the Housing Authority on the ground that it violates the Fair Housing Act, Title VI and/or HUD implementing regulations." Id. ¶ 6(c).


17
B. NYCHA's Proposed Working-Family Preference (Davis II-IV)


18
In 1995, NYCHA sought to modify the local preferences recognized under the TSAP. To the extent material here, it proposed to introduce a working-family preference ("WFP"), altering the factors determining whether an applicant for public housing is even granted an interview. Under the WFP, federal preference holders who are working or disabled would receive a priority over those who are not; as to local preferences, Tier III families and Tier II families would receive priority, in that order; thereafter, Tier I applicants who are working or are disabled would be given priority, but other Tier I applicants would have no priority. See Davis v. New York City Housing Authority, 1997 WL 407250, at *4 (S.D.N.Y. July 18, 1997) ("Davis II"). The proposed WFP would eliminate applicant housing need as a local priority concern and instead give preference to families who can pay the most. NYCHA's goals in proposing this change are to increase the number of working families in public housing and increase income integration in public housing, in order to promote financial and social stability in such housing. See id. at *14.


19
Plaintiffs opposed NYCHA's proposed changes and moved before Judge Sweet, to whom the case had been reassigned, for an injunction. While conceding that NYCHA's interest in financial stability was legitimate, plaintiffs contended, supported by affidavits from their expert Dr. Leonard Cupingood, that the WFP would favor the admission of white families and thereby have the effect of perpetuating racial segregation. Plaintiffs suggested that the WFP be modified so that, while continuing to give the lowest preference to Tier I (i.e., lowest-income) families, NYCHA would give all Tier I applicants equal preference. Under plaintiffs' proposed alternative, Tier I families would continue to rank below Tier II and Tier III families; and thus, because Tier II and III families by definition have higher incomes than Tier I families, the number of rentals to higher-income families would still increase; but desegregation of the housing projects would be less adversely affected. NYCHA conceded that plaintiffs' suggested alternative might increase income integration but rejected it, stating that it would frustrate the goal of increasing the proportion of rentals to working families. See Davis II, 1997 WL 407250, at *15.


20
The district court noted the legitimacy of NYCHA's concerns and goals and stated that there was no dispute that an increase in the proportion of tenants with higher incomes was needed in order to safeguard the projects' stability:


21
Historically, public housing applicants in the lowest income categories accounted for approximately 1/3 of all NYCHA rentals. Since 1990, however, an increase in homeless families applying for housing has resulted in a significant increase in the number of rentals to the lowest income applicants. By 1995, these lowest income applicants accounted for 77.6% of new admissions. NYCHA states, and plaintiffs do not dispute, that unless a higher proportion of applicants with higher incomes receive rentals, the stability of the projects will be jeopardized.


22
Id. at *4. The court also noted that NYCHA had submitted its proposed WFP, along with another proposed modification called "Project Choice," to HUD for approval. Although HUD approved Project Choice as "`not likely to affect the racial identifiability of developments in New York City,'" Davis II, 1997 WL 407250, at *5 (quoting HUD letter to NYCHA dated October 24, 1996), HUD's response to the proposed WFP, in contrast, was as follows:


23
"HUD does not approve local preferences, and thus NYCHA may create these local preferences, so long as notice and comment requirements are met. However, NYCHA should be mindful of the injunctive relief provided for by the Davis consent decree and its responsibilities under civil rights statutes."


24
Davis II, 1997 WL 407250, at *5 (quoting HUD letter to NYCHA dated July 31, 1996) (emphasis ours).


25
The district court proceeded to consider the likely effects of the WFP on NYCHA's performance of its obligations under the Decree. Noting that in 1995, under the TSAP's scheme of priorities, only some 15% of all applicants for public housing even reached the stage of being granted interviews, see Davis II, 1997 WL 407250, at *3, the court found that implementation of the WFP would significantly change


26
the racial composition of the top 15% of applicants, who are those likely to be called for interviews. Under the current TSAP, only 7.2% of the top 15% of applicants are white. If the new Working Family Preference were implemented, there would be a statistically significant increase in the percentage of white families in the top 15% of the list of applicants. These conclusions are not disputed by NYCHA.


27
Id. at *5. The court noted further that Dr. Cupingood had concluded that if the WFP were implemented at the 11 projects that as of June 1996 remained more than 50% white, the process of desegregation would be significantly slowed at three of the projects, completely stopped at four projects, and indeed reversed at four projects. See id.


28
The court noted, however, that the WFP's desegregative effects could easily be lessened:


29
It also appears that NYCHA could eliminate the objectionable perpetuation of discrimination by making revisions to their plan that are even less drastic than those proposed by plaintiffs. The Working Family Preference could be instituted in essentially the proposed form, provided white applicants selected under the preference are not placed in projects in which whites are over-represented relative to the applicant pool. The extent to which such a modification would be administratively feasible or desirable is, of course, a question for NYCHA.


30
Id. at *15 (emphases added).


31
Accepting the projections made by Dr. Cupingood, the district court found that plaintiffs were likely to succeed on the merits of their WFP challenge with respect to the housing projects whose tenant populations remained predominantly white. The court entered a preliminary injunction prohibiting implementation of the WFP at all 322 NYCHA projects, but it invited NYCHA to offer suggestions for modifications that would limit the injunction to the disproportionately white projects. See id. at *18.


32
Thereafter, the parties "agree[d] that the WFP considered in Davis [II] w[ould] not perpetuate past discrimination at any of the NYCHA projects other than the 21 projects where greater than 30% of the apartments are rented to whites (the `Disproportionate Projects')," Davis v. New York City Housing Authority, 1997 WL 711360, at *4 (S.D.N.Y. Nov. 13, 1997, as amended Nov. 20, 1997) ("Davis III"), and "agree[d] that the WFP should go forward for the non-Disproportionate Projects," id. at *5. Accordingly, in Davis III, the court narrowed its prior order and enjoined use of the WFP at only those 21 housing projects where white families then occupied more than 30% of the apartments.


33
NYCHA appealed. This Court was unable to resolve the merits of the appeal, however, as we concluded that the district court had not provided an adequate explanation for finding that plaintiffs would likely succeed in showing that the WFP would perpetuate segregation at the projects to which the injunction applied. See Davis v. New York City Housing Authority, 166 F.3d 432, 437 (2d Cir.1999) ("Davis IV"). We stated that although the opinions in Davis II and Davis III were


34
not entirely devoid of detail, Judge Sweet failed to adequately explain the subsidiary facts and methodology underlying the ultimate finding. For instance, Judge Sweet refers to "existing trends demonstrat[ing] that many of the[] additional white families [admitted under the proposed modification] will be concentrated in predominantly white developments," but does not discuss or attempt to explain these trends or the data reflecting them. He also fails to address the time period during which the purported impact of the proposed TSAP was assessed and/or how future "trends" might affect application of the TSAP to developments that are not currently, but subsequently become, predominantly white. Further, while he focuses on the racial imbalance the proposed TSAP will cause at specific developments within the NYCHA system, he does not identify them by name or state the number, fraction or percentage of additional white families who will be admitted to each of the 21 developments as a result of the proposed TSAP.


35
Davis IV, 166 F.3d at 436 (footnotes omitted). We also noted that Dr. Cupingood "d[id] not cite to any precise numerical data underlying his opinion." Id. at 437.


36
Accordingly, while leaving the preliminary injunction undisturbed, we remanded for the district court to address these matters, stating that "[t]he proper standard to be applied on remand is whether the proposed use of the working family preference will significantly perpetuate segregation at the relevant NYCHA developments." Id. at 438 (emphasis in original).


37
C. The WFP as Significantly Perpetuating Segregation (Davis V)


38
Following the remand in Davis IV, the district court conducted a hearing, received additional evidence and arguments, and addressed, both broadly and in considerable detail, (1) whether there is a basis on which to conclude that there is segregation to be dealt with under the Consent Decree, and (2) whether the WFP would significantly perpetuate segregation. In an opinion dated August 11, 1999, the court rendered a final decision, answering both questions in the affirmative and concluding that plaintiffs were entitled to a permanent injunction prohibiting NYCHA from implementing the WFP at 20 housing projects. See Davis v. New York City Housing Authority, 60 F.Supp.2d 220 (S.D.N.Y.1999) ("Davis V").


39
First, as to the existence of segregation, the court ruled that, for purposes of this litigation, it is appropriate to deem a project segregated if white families occupy more than 30% of its apartments. It pointed out that


40
throughout this litigation projects have been deemed "disproportionate" or "predominantly white" if more than 30 percent of the parties residing there are white. See, e.g., Davis II, 1997 WL 407250 at *12.


41
Davis V, 60 F.Supp.2d at 231 (footnote omitted). The court noted that this benchmark was reflected in the TSAP, which was incorporated by reference into the Consent Decree. See, e.g., id. at 232 n. 9 ("[T]he TSAP identifies housing projects that are 30 percent white as infected by past segregation."). The TSAP contains a "Borrowing Provision" that can be used by a housing project that has more vacancies than willing applicants. Such a project is allowed to "borrow[]" applications from another project, id. at 231; but "`if the borrowing project's tenant body is more than 30% white, [the NYCHA decisionmaker] shall not select a project whose tenant body is also more than 30% white,'" id. at 232 (quoting TSAP at 29). The court pointed out that the 30% benchmark was


42
not, as NYCHA urges, an arbitrary number, but a negotiated figure that implies that the parties and the Court believed that a project was disproportionately white if more than 30 percent of its families are white.... An examination of Exhibit A to the Consent Decree, a list of projects where it was alleged that discriminatory practices occurred in statistically significant amounts, reveals that during the time in question most of these projects were at least 30 percent white.


43
Davis V, 60 F.Supp.2d at 232. Further, the court noted that the injunctive relief ordered was necessarily premised on a finding that a white tenant population above the 30% level constituted segregation:


44
The TSAP must be read as in harmony with existing law.... Under existing law, borrowing of applications could not have been prohibited at projects more than 30 percent white (without regard for claimant relief) unless those projects were still tainted by past segregation.... [R]emedies containing race-conscious relief "must be substantially related to the objective of eliminating the alleged instance of discrimination,... and must not unnecessarily trammel the interests of affected third parties." Kirkland v. New York State Dept. of Correctional Serv., 711 F.2d 1117, 1132 (2d Cir.1983). Thus, had there been no finding that housing projects that are greater than 30 percent white were affected by past segregation, the Borrowing Provision would be unlawful.


45
Davis V, 60 F.Supp.2d at 232. Accordingly, having previously "held that `[u]nder the TSAP, a project is considered disproportionately white if more than 30 percent of its families are white,'" the court concluded that "30 percent will continue to be employed as a measure to identify segregation in this case." Davis V, 60 F.Supp.2d at 232 (quoting Davis II, 1997 WL 407250 at *12).


46
Second, as to the impacts of the WFP on the desegregation of the disproportionately white projects, the district court, largely crediting the analysis of Dr. Cupingood, made extensive findings. The court noted that, in predicting the effects of the WFP on the racial mix of those likely to move into public housing projects ("move-ins"), Dr. Cupingood relied on data for the period 1991-1994 because 1991 is "the first year that is free of distortion caused by NYCHA's own discrimination," and 1994 is the "last year that is free of distortion [caused] by" the initial implementation of the Consent Decree remedies, to wit, the "Davis move-ins." Davis V, 60 F.Supp.2d at 226. Dr. Cupingood relied on NYCHA's records of move-ins and move-outs by race for each project, and he proceeded on the assumption that families of each race will make decisions about which projects to choose in the same manner, and with the same probabilities, as families of that race have done in the past. The court concluded that "[w]hile projections about the future, are by definition, subject to some uncertainty, Dr. Cupingood has taken reasonable steps, such as the use of historical averages, to minimize the impact of possible uncertainties." Id. at 239 n. 17.


47
The court credited Dr. Cupingood's view that the WFP would have significant impacts on the disproportionately white projects, either by increasing the percentage of a project's white population or by detrimentally affecting the degree or timing of the project's desegregation. The Davis V opinion included tables showing, for each disproportionately white project, inter alia, "Race Distribution of 1995 Rentals Under Original TSAP and WFP" (Table 1); "Effect of WFP at Disproportionate Projects After Five Years Assuming Historical [T]urnover by Race" (Table 3); "Relative Percentage Reduction in Number of White Families [D]ue to WFP After Five [Y]ears Assuming Historical Turnover by Race" (Table 4); "Change in Percentage White Occupancy At Disproportionate Projects After Five Years Assuming Historical Turnover by Race" (Table 5); "Effect of WFP at Disproportionate Projects After Five Years Assuming Historical Turnover by Race" (Table 7), and "[same] After Ten Years" (Table 6). See Davis V, 60 F.Supp.2d at 225-31.


48
In discussing the anticipated percentages of apartments that would be occupied by white families at each Disproportionate Project after five years, with and without the WFP, the court noted that,


49
[a]ssuming historical turnover by race, after five years under the WFP, the percentage of white families at Middletown Plaza would rise from 51.85 to 60.1% (instead of falling to 49.4%). At the remaining Disproportionate Projects, white occupancy percentages would either stabilize or fall more slowly under the WFP than under the original TSAP. For example, at Cassidy Lafayette, after five years the percentage of white families in occupancy would inch down from 53.6% to 50.4% (instead of falling to 42.4%).


50
Id. at 228-29. These figures were reflected in Table 5:


51
                               Table 5
               Change in Percentage White Occupancy At
             Disproportionate Projects After Five Years
                 Assuming Historical Turnover by Race

                     Initial           5 Years after Davis Move-Ins
Project Name         % White        Original TSAP                WFP

Bay View              34.5%             22.9%                  24.7%
Berry                 56.2%             45.0%                  50.4%
Cassidy-Lafayette     53.6%             42.4%                  50.4%
Forest Hills          51.7%             41.3%                  44.4%
Glenwood              30.0%             18.1%                  18.9%
Haber                 53.0%             39.6%                  46.4%
Holmes Towers         26.6%             18.6%                  21.8%
Independence             9% [sic]       63.9%                  64.8%
Isaacs                33.1%             24.8%                  27.9%
Middletown Plaza      51.8%             49.4%                  60.1%
New Lane              73.0%             64.8%                  71.1%
Nostrand              41.9%             30.0%                  32.9%
Pelham Parkway        31.8%             22.1%                  23.5%
Pomonok               41.5%             33.3%                  36.5%
Robbins Plaza         53.4%             42.6%                  52.0%
Sheepshead Bay        35.2%             24.0%                  26.8%
South Beach           53.1%             41.6%                  47.6%
Straus                28.5%             27.4% [sic]            20.9%
Taylor-Wythe          54.4%             51.0%                  52.1%
Todt Hill             46.7%             35.7%                  39.7%
Williams              61.6%             57.5%                  58.2%


52
Davis V, 60 F.Supp.2d at 229; see also id. at 227, Table 3 (at Independence, 493 of 715 apartments were initially occupied by white families, a percentage of 68.95; at Straus, under the original TSAP five years after the Davis move-ins, white families would occupy 48 of 263 apartments, a percentage of 18.3); id. at 233, Table 8 (as of June 1998, before Davis move-ins, Holmes Towers and Straus were above the 30% level, at 30.6% and 30.4%, respectively). The court noted that Table 6 showed that


53
[s]imilar trends exist after ten years, except that at Disproportionate Projects where desegregation would not essentially stop, the magnitude of the impact of the WFP would generally become larger. For example, at Middletown Plaza, where segregation would increase under the WFP, the white population would climb to 108 instead of falling to 81. At Berry Houses, where desegregation would be significantly slowed, the white population would fall to 231 instead of 186. In the aggregate, after ten years under the WFP (again assuming historical turnover by race), the Disproportionate Projects would be occupied by 722 more white families than would have resided in those projects in the absence of the WFP.


54
Davis V, 60 F.Supp.2d at 229.


55
NYCHA, proffering the views of its own expert Dr. David Peterson, argued that Dr. Cupingood's analysis was flawed because it was based on the assumption that, in the absence of the Consent Decree's injunction, the percentage of white families admitted to NYCHA's public housing in 1998 would have risen from 4.2% to 9.9%. The Authority contended that the percentage admitted would have risen only to 6.48%. However, the district court found that there were substantial flaws in Dr. Peterson's methodology:


56
[I]n addition to a number of other errors, Dr. Peterson did not account for the fact that several thousand families who moved into NYCHA housing during 1998 were selected for interviews and/or certified to project waiting lists before the WFP went into operation. Because families selected under the old TSAP are still working their way through the "pipeline," the white admission rate in 1998 was significantly lower than would have occurred if all families had been selected for interviews and certified pursuant to the WFP. Moreover, Dr. Peterson['s] conclusion is based on an under-representation of 1998 move-ins. Significantly, even accepting Dr. Peterson's methodology, and adjusting only for the undercount of families to the 21 projects, one obtains a corrected figure of 8.53 percent white among families who were placed in 1998 and were "allegedly untainted by the Pipeline Effect" (Cupingood Sixth Aff. ¶ 9).


57
Davis V, 60 F.Supp.2d at 239 n. 16. Accordingly, the court rejected Dr. Peterson's analysis and credited that of Dr. Cupingood.


58
The court also rejected NYCHA's contention "that so long as the white occupancy rates would decline under the WFP, regardless of the rate of decline, then the WFP cannot be said to perpetuate segregation." Id. at 238. The court noted that to "`perpetuate' means to extend in time," id. (other internal quotation marks omitted), and that that is precisely the effect that the WFP will have. Although at the outset of housing discrimination litigation "the adverse impact of an applicant selection process ... is determined by whether minority applicants are chosen at a rate lower than their proportional representation in the overall applicant pool," once remedies for segregation have been ordered and the defendant proposes to change its method of compliance "[t]he query ... is not whether the [change] would have an adverse impact on minority applicants, but whether it will significantly perpetuate segregation." Davis V, 60 F.Supp.2d at 237 n. 14 (emphasis omitted).


59
Where a court-ordered plan intended to eradicate past segregation is in effect, and where, as here, a proposed change to the plan is alleged to perpetuate past segregation, the Supreme Court has compared the results under the proposed plan with those under the original, court-ordered plan.


60
. . . .


61
Accordingly, in evaluating whether the WFP significantly perpetuates segregation, the relevant comparison will be the desegregation that would be achieved under the original TSAP with the projected effect of the WFP.


62
....


63
The relevant inquiry here is not whether desegregation will occur eventually, but whether the WFP will significantly delay desegregation at the Disproportionate Projects. See Monroe v. Board of Commissioners, 391 U.S. 450, 459, 88 S.Ct. 1700, 20 L.Ed.2d 733 (1968) ("if it cannot be shown that such a plan will further rather than delay conversion to a unitary, nonracial, nondiscriminatory school system, it must be held unacceptable."); Wright [v. Council of the City of Emporia], 407 U.S. [451,] 460, 92 S.Ct. 2196, 33 L.Ed.2d 51 [(1972)] ("if the proposal would impede the dismantling of the dual system, then the district court ... may enjoin it from being carried out").


64
Davis V, 60 F.Supp.2d at 237-38 (emphasis in original).


65
The district court concluded that the WFP would significantly impede desegregation at NYCHA's 20 disproportionately white projects, see Davis V, 60 F.Supp.2d at 231 n. 7 (of the 21 projects covered by the preliminary injunction pursuant to Davis III, Glenwood was omitted because prior to June 1998 it had fallen "below the 30% threshold"). The court reached this conclusion because the WFP will "more than double white admission rates," and "because existing trends demonstrate that many of these additional white families will be concentrated in predominantly white developments." Davis V, 60 F.Supp.2d at 238-39 (internal quotation marks omitted). It found these effects to have both "[s]tatistical significance," which "measures whether a particular phenomenon is the cause of a specific set of effects," and "[l]egal significance," which "measures whether, assuming the phenomenon was the cause of those effects, those effects have any legal import." Id. at 239. As to statistical significance, the court stated as follows:


66
A standard tool for assessing statistical significance is the two-standard deviation test. The test is used to determine whether a deviation from the expected norm is small enough to be attributable to chance, or so large that random chance could not reasonably account for the outcome. "The greater the number of standard deviations, the less likely it is that chance is the cause of any difference between the expected and observed results." Ottaviani [v. State Univ. at New Paltz, 875 F.2d 365, 371 (2d Cir.1989), cert. denied, 493 U.S. 1021, 110 S.Ct. 721, 107 L.Ed.2d 740 (1990)]. Courts have frequently adopted a standard of two to three standard deviations as constituting statistical significance. See Hazelwood School District v. United States, 433 U.S. 299, 311 n. 17, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977) ("if the difference between the expected value and observed number is greater than two or three standard deviations, then the hypothesis that employees were hired without regard to race would be suspect."); Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977).


67
Davis V, 60 F.Supp.2d at 239 (footnote omitted). The court noted that, in terms of the total number of apartments affected by the WFP in the disproportionately white projects, the magnitude of the effects would be well in excess of two standard deviations:


68
For the five year-period, and assuming historical turnover trends for each race, the WFP would result in a total of approximately 1,139 white move-ins at the Disproportionate Projects, as compared to only 625 without the WFP. The difference between these figures — some 514 excess white move-ins — represents 15.39 standard deviation units and is highly significant.


69
Id. at 239-40 (footnote omitted). And over a period of "ten years, assuming historical turnover rates for each race, the WFP would increase white move-ins from 1,217 to approximately 2,240 — an increase of 1,023 white move-ins. The difference represents 21.92 standard deviation units." Id. at 240 n. 19. The court found that the magnitude would also be statistically significant when assessed in terms of individual projects:


70
[A]fter five years, 18 of the 21 Disproportionate Projects would have statistically significant white move-in differential caused by the WFP. At the ten year mark, again using historical turnover rates for each race, 20 of the 21 Disproportionate Projects would have statistically significant reductions in desegregation. At Holmes Towers, for example, the WFP would result in approximately 75 white move-ins as opposed to 34 without the WFP, a disparity representing 4.3 standard deviation units. At Pomonok, there would be approximately 287 white move-ins with the WFP and 138 without the WFP in place, a difference constituting 8.21 standard deviation units.


71
Id. at 240.


72
Finally, as to the legal significance of the WFP's retardation of desegregation, the court noted that


73
[w]hile ... many of the cases cited by the parties involve larger discrepancies than in the instant case, "small" percentage-point differences can result in significant perpetuation of segregation. At the Pomonok project, for example, where the WFP would increase the white occupancy rate by 3.2 percentage points after five years, and 5.5 percentage points after ten years, (see Cupingood Third Aff. [Cupingood's] Tables 4 and 6), every percentage point increase in the white population means relinquishing 20 apartments to white families that would have gone to African American and Hispanic families. At Pomonok alone, the WFP would deprive non-white families of 66 apartments after five years (see id. [Cupingood's] Table 5) and 114 apartments after ten years (see id. [Cupingood's] Table 7).


74
....


75
These figures are significant in sheer magnitude.... Perhaps more importantly, they are significant to the families affected. To be sure, the WFP has numerous benefits, but with respect to the Disproportionate Projects, these are outweighed by its adverse effects. The WFP markedly inhibits the rate at which desegregation will occur, adversely affects the ratios at the Disproportionate Projects, and contravenes the purposes of the Consent Decree. In short, the WFP significantly perpetuates segregation.


76
Davis V, 60 F.Supp.2d at 240-41 (footnotes omitted).


77
Accordingly, having determined that the effects of the WFP in slowing the pace of desegregation at the disproportionately white projects would be significant, the court enjoined NYCHA from implementing the WFP at the 20 relevant developments, making its preliminary injunction permanent.


78
D. Comparisons of the TSAP With and Without the WFP (Davis VI-VII)


79
NYCHA again appealed. This Court again remanded without resolving the merits, asking for additional information. See Davis v. New York City Housing Authority, 2000 WL 232191 (2d Cir. Feb.23, 2000) ("Davis VI"). Given that the WFP had been implemented in 1998 at some 302 projects, i.e., all but the 20 projects covered by the injunction, we stated that we would benefit from knowing (1) whether and to what extent actual tenant move-outs correspond with projected move-outs, and whether and to what extent the actual numbers would alter the experts' conclusions; (2) at each of the 20 covered projects, how many months it is expected to take to achieve a white family occupancy rate below 30% with and without the WFP; and (3) whether figures presented in the Davis V tables based on Dr. Cupingood's estimate of a 9.9% white admissions rate under the WFP should be revised to reflect a rate of 8.53%, as it appeared Dr. Cupingood might have suggested in one affidavit, or a rate of 8.28% as NYCHA suggested.


80
In June 2000, the district court responded to the questions posed by Davis VI. As to our first question, the court found that the expert witnesses for both sides opined that the use of actual move-out rates for 1998 would not necessarily increase the accuracy of the white admissions rate projections. See Davis v. New York City Housing Authority, 103 F.Supp.2d 228, 229 (S.D.N.Y.2000) ("Davis VII"). As to our last question, the court found that the reference in Dr. Cupingood's prior affidavit to a rate of 8.53% was the result of a copying error and that the intended reference was to a rate of 8.28%. Id. at 231. However, the court found that Dr. Cupingood's rationale for using the rate of 9.9% for white move-ins rather than a rate of 8.28% was more persuasive than that proffered by Dr. Peterson for the lower rate. Id. at 232. The court also found that use of the 8.28% rate would not show any significant decrease in the WFP's effects of delaying desegregation in the 20 projects. Id. "Thus, adoption of the 8.28% rate, and revision of the calculations, would not change this Court's prior conclusion that implementation of the WFP at the Disproportionate Projects would result in a significant perpetuation of discrimination." Id.


81
As to our second question, requesting a comparison of the estimated times for desegregation under the TSAP with and without the WFP, the court set forth the following table:


82
                         Months to Reach 30%     Months to Reach 30%
Project                      Without WFP               With WFP

Bay View                           17                       21
Berry                             195             Will never reach 30%
Cassidy-Lafayette                 195             Will never reach 30%
Forest Hills                      149                      246
Haber                             146             Will never reach 30%
Holmes Towers            Already below 30%*      Already below 30%*


83
Independence                      620                      899
Isaacs                             18                       29
Middletown Plaza         Will never reach 30%     Will never reach 30%
New Lane                 Will never reach 30%     Will never reach 30%
Nostrand                           57                       85
Pelham Parkway                      6                        8
Pomonok                            84                      171
Robbins Plaza                     355             Will never reach 30%
Sheepshead Bay                     23                       35
South Beach                       163             Will never reach 30%
Straus                   Already below 30%*      Already below 30%*
Taylor St./Wythe Ave.             649                     1323
Todt Hill                         103                      198
Williams                          707                     1066


84
Id. at 231.


85
Following these findings, the appeal by NYCHA was reinstated.

II. DISCUSSION

86
On appeal, NYCHA contends principally (1) that neither the Consent Decree nor the TSAP defined housing projects with more than 30% white tenant populations as segregated, and that the district court therefore erred in using that standard in finding the 20 projects in question to be segregated; (2) that the district court erred in its findings as to the WFP's desegregation delays because the court (a) accepted the view of Dr. Cupingood rather than that of Dr. Peterson, (b) failed to do a project-by-project analysis, and (c) analyzed the "wrong comparables"; and (3) that the court erred in concluding that the differences in white tenancy percentages with and without the WFP are legally significant. For the reasons that follow, we reject most of NYCHA's contentions, finding merit only in its challenge to the ruling as to the legal significance of the WFP's effects at six projects.

A. Standard of Review

87
The standard of review is well established. In reviewing the district court's judgment and its issuance of a permanent injunction, we may overturn the court's findings of fact only if they are clearly erroneous. See Fed.R.Civ.P. 52(a).


88
Although the meaning of the phrase "clearly erroneous" is not immediately apparent, certain general principles governing the exercise of the appellate court's power to overturn findings of a district court may be derived from [Supreme Court] cases. The foremost of these principles ... is that "[a] finding is `clearly erroneous' when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed." United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948). This standard plainly does not entitle a reviewing court to reverse the finding of the trier of fact simply because it is convinced that it would have decided the case differently. The reviewing court oversteps the bounds of its duty under Rule 52(a) if it undertakes to duplicate the role of the lower court. "In applying the clearly erroneous standard to the findings of a district court sitting without a jury, appellate courts must constantly have in mind that their function is not to decide factual issues de novo." Zenith Radio Corp. v. Hazeltine Research, Inc., 395 U.S. 100, 123, 89 S.Ct. 1562, 23 L.Ed.2d 129 (1969). If the district court's account of the evidence is plausible in light of the record viewed in its entirety, the court of appeals may not reverse it even though convinced that had it been sitting as the trier of fact, it would have weighed the evidence differently. Where there are two permissible views of the evidence, the factfinder's choice between them cannot be clearly erroneous. United States v. Yellow Cab Co., 338 U.S. 338, 342, 70 S.Ct. 177, 94 L.Ed. 150 (1949); see also Inwood Laboratories, Inc. v. Ives Laboratories, Inc., 456 U.S. 844, 102 S.Ct. 2182, 72 L.Ed.2d 606 (1982).


89
Anderson v. Bessemer City, 470 U.S. 564, 573-74, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985); see also id. at 577, 105 S.Ct. 1504 (the question is not whether a contrary finding by the court of appeals would be clearly erroneous, but only whether the finding made by the district court was clearly erroneous). These standards apply whether the district court's findings are based on oral testimony or solely on documentary evidence. See, e.g., id. at 574, 105 S.Ct. 1504; Fed.R.Civ.P. 52(a).


90
Determinations as to the existence and cause of racial discrimination are findings of fact, and hence are subject to the clearly-erroneous standard of review. See, e.g., Anderson v. Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985); Pullman-Standard v. Swint, 456 U.S. 273, 287-90, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982); United States v. Yonkers Board of Education, 837 F.2d 1181, 1218 (2d Cir.1987), cert. denied, 486 U.S. 1055, 108 S.Ct. 2821, 100 L.Ed.2d 922 (1988). We apply no different standard for the district court's findings as to the likely future discriminatory effects of actual or proposed conduct. Even as to past events, a trial judge


91
cannot always be confident that he "knows" what happened. Often, he can only determine whether the plaintiff has succeeded in presenting an account of the facts that is more likely to be true than not.


92
Anderson v. Bessemer City, 470 U.S. at 580, 105 S.Ct. 1504. Our task as an "appellate tribunal[ ] ... is more limited still: we must determine whether the trial judge's conclusions are clearly erroneous." Id. at 580-81, 105 S.Ct. 1504. We similarly review only for clear error the district court's findings as to whether particular conduct will more likely than not perpetuate discrimination.


93
The district court's conclusions as to questions of law, or as to mixed questions of fact and law, are reviewed de novo. See, e.g., St. Johnsbury Academy v. D.H., 240 F.3d 163, 168 (2d Cir.2001); United States v. City of Yonkers, 197 F.3d 41, 49 (2d Cir.1999), cert. denied, 529 U.S. 1130, 120 S.Ct. 2005, 146 L.Ed.2d 956 (2000). A determination of the legal significance of the effects that the court has found likely to occur is a conclusion of law. The interpretation of a consent decree is also an issue of law that is freely reviewable by the court of appeals. See, e.g., United States v. O'Rourke, 943 F.2d 180, 186 (2d Cir.1991); United States v. International Brotherhood of Teamsters, 931 F.2d 177, 182-83 n. 1 (2d Cir.1991); Berger v. Heckler, 771 F.2d 1556, 1568 (2d Cir.1985); see also id. at 1567-68 ("Consent decrees are a hybrid in the sense that they are ... construed largely as contracts, but are enforced as orders.").


94
The propriety of relief in the form of a permanent injunction is reviewable for abuse of discretion. See, e.g., Knox v. Salinas, 193 F.3d 123, 128-29 (2d Cir.1999) (per curiam); General Media Communications, Inc. v. Cohen, 131 F.3d 273, 278 (2d Cir.1997), cert. denied, 524 U.S. 951, 118 S.Ct. 2367, 141 L.Ed.2d 736 (1998); Schulz v. Williams, 44 F.3d 48, 53 (2d Cir.1994). And "though a court cannot randomly expand or contract the terms agreed upon in a consent decree, judicial discretion in flexing its supervisory and enforcement muscles is broad." EEOC v. Local 580, International Association of Bridge, Structural & Ornamental Ironworkers, 925 F.2d 588, 593 (2d Cir.1991); see also Berger v. Heckler, 771 F.2d at 1568 (court's interest in protecting the integrity of a judicially approved consent decree "justifies any reasonable action taken by the court to secure compliance" (internal quotes omitted)).


95
B. The 30-Percent Level as the Measure of Segregation


96
For several reasons, we reject NYCHA's contention that the district court erred in using the 30% white family population level as the standard for whether a NYCHA public housing project should be deemed segregated.


97
First, the district court drew the 30% figure directly from the Consent Decree and the litigation surrounding it. As set out in Part I.C. above, the TSAP's Borrowing Provision allows an undersubscribed public housing project to borrow applications from another project; but it explicitly forbids an undersubscribed project whose tenant population is more than 30% white from borrowing applications from another project whose tenant population is also more than 30% white. Thus, the Consent Decree, which expressly incorporated the TSAP by reference, treated 30% as the significant level.


98
Second, the Decree identified 31 projects as "Affected Developments," see Consent Decree ¶ 1(b) & Exhibit A, and required NYCHA to give priority placement at those 31 projects to some 1,990 families who had been "adversely affected by discrimination since 1985," Davis I, 1992 WL 420923, at *2. When Davis I was entered, 24 of those 31 projects, or more than 77%, had white family populations in excess of 30% (with three of the remaining seven having white tenant populations of 29-29.9%). (See NYCHA Tenant Statistics by Race as of Dec. 31, 1992.) And those 24 projects constituted 80% of the 30 NYCHA projects whose white tenant populations exceeded 30%. (Id.) Thus, it was reasonable for the district court to use the 30% figure as a reflection of which projects the parties had agreed were infected by past segregation.


99
Third, although NYCHA contends that none of its projects should be considered "segregated" under the Consent Decree once NYCHA has provided the relief that the Decree ordered for individual applicants, that contention is belied by the Decree itself. The Decree (a) allowed plaintiffs, within the first five years of the TSAP's operation, to seek an injunction against any proposal to modify the TSAP on the ground that the modification would be inconsistent with the Decree or with the FHA, and (b) allowed plaintiffs, within the three years following that five-year period, to request modification of the Decree on the ground that NYCHA's implementation of the TSAP was violating the FHA. Accordingly, the existence of segregation in New York City public housing may properly be measured by FHA standards, not solely by whether NYCHA has provided the individualized relief ordered for specific victims of prior discriminatory practices.


100
Fourth, when Davis V was decided, NYCHA data showed that, overall, white families in NYCHA housing projects constituted just 7.0% of the tenant population. (N.Y.CHA Research and Policy Development Special Tabulation of Tenant Characteristics as of Jan. 1, 1999 ("NYCHA 1999 Tenant Characteristics Tabulation"), at 1). Thus, in using the 30% level as the pertinent measure of segregation, the court generally considered a project to be segregated only if its white population was at least 23 percentage points higher than the average white tenant population system-wide, or more than four times the system-wide average.


101
The court's treatment of such wide discrepancies as indicative of segregation was entirely consistent with existing law. In United States v. Yonkers Board of Education, for example, we upheld findings that housing in the city of Yonkers was segregated in 1980 where minorities constituted 40.4% of the residents of one quadrant of the city, but only 18.8% of the city's total population. See 837 F.2d at 1185, 1218; see also id. at 1185-86 (in five of the 10 real estate tracts within that quadrant, minorities constituted more than 50% of the residents). We concluded that there was no error in the district court's findings that the city's decision to concentrate low-income housing, occupied principally by minorities, in that quadrant had a discriminatory effect. See id. at 1219-20. Cf. Brown v. Board of Education, 892 F.2d 851, 870 & n. 54 (10th Cir.1989) (comparing minority enrollment in particular schools against system-wide figures and finding vestiges of segregation where the difference in minority representation between the actual population and the student population exceeded 15 percentage points), vacated, 503 U.S. 978, 112 S.Ct. 1657, 118 L.Ed.2d 381 (1992), reinstated in full, 978 F.2d 585 (10th Cir.1992), and cert. denied, 509 U.S. 903, 113 S.Ct. 2994, 125 L.Ed.2d 688 (1993); Penick v. Columbus Board of Education, 583 F.2d 787, 799 (6th Cir.1978) (same), aff'd, 443 U.S. 449, 99 S.Ct. 2941, 61 L.Ed.2d 666 (1979).


102
NYCHA attempts to distinguish such authorities by pointing out that the present litigation was resolved without a trial on the merits and that the Consent Decree recited that NYCHA did not concede liability. This approach is unpersuasive. To establish a violation of the FHA, a plaintiff need not show discriminatory intent but need only prove that the challenged practice has a discriminatory effect. See Huntington Branch, NAACP v. Town of Huntington, 844 F.2d 926, 936 (2d Cir.), aff'd, 488 U.S. 15, 109 S.Ct. 276, 102 L.Ed.2d 180 (1988) (per curiam); United States v. Yonkers Board of Education, 837 F.2d at 1217. The FHA prohibits such practices and authorizes courts to order "affirmative action to erase the effects of past segregation and desegregate housing patterns." Otero v. New York City Housing Authority, 484 F.2d 1122, 1133 (2d Cir.1973). Here, NYCHA's own records plainly show segregative housing patterns. In 1992, NYCHA operated more than 320 public housing projects. Some 62.66% of the white families (9,731 of 15,530) lived in the 31 projects that were defined in the Consent Decree as Affected Developments. (See NYCHA Tenant Statistics by Race as of Dec. 31, 1992.) In addition, there are four projects (Haber, Independence, Taylor-Wythe, and Williams) that were not defined as Affected Developments but are covered by the present injunction, whose respective white tenant populations at the end of 1992 ranged from 42% to 65% (see NYCHA Tenant Statistics by Race as of Dec. 31, 1992) and in 1998 ranged from 53% to 61.6%, see Davis V, 60 F.Supp.2d at 227, Table 3; id. at 229, Table 5. As of December 31, 1992, those four projects housed an additional 1,298 white families. (See NYCHA Tenant Statistics by Race as of Dec. 31, 1992.) Thus, when Davis I was decided, NYCHA had placed more than 71% of the white public-housing population in 35 of its 320-odd projects.


103
In approving the Consent Decree, the district court found that plaintiffs' evidence supported their allegations that NYCHA had selected, assigned, and transferred applicants for public housing to particular projects using methods that resulted in unlawful discrimination on the basis of race. Davis I, 1992 WL 420923, at *2. NYCHA did not appeal those findings. Nor could it legitimately have done so. In urging the district court to approve the Consent Decree, NYCHA stated that it had engaged in a number of practices, some dating back to 1960, and some lasting until 1990, "that had the effect of discriminating against Black and Hispanic applicants." (N.Y.CHA Memorandum Supporting Consent Decree at 21-22.) NYCHA stated that those policies included racial steering and favoring white applicants for predominantly white housing projects (id. at 22), that "these policies were wrong" (id. at 21), and that "[t]he Housing Authority concluded that the complaint had merit" (id. at 22). See Part I.A. above. Having made those statements to the court in order to secure judicial approval of the Decree, NYCHA cannot now disavow them.


104
In sum, only 7% of the families in NYCHA housing projects system-wide are white; the TSAP, incorporated into the Consent Decree, treated 30% white family occupancy as a threshold signifying segregation; when the Decree was entered, more than 62% of the white public-housing population lived in fewer than 10% of the NYCHA projects; and nearly all of the projects whose tenant populations were more than 30% white were targeted by the Decree for placement of individual applicants who had been the victims of past discrimination. We see no clear error in the district court's finding that in negotiating and approving the Consent Decree, the parties and the court, respectively, had regarded projects more than 30% of whose apartments were rented to white families as segregated, nor any error in the court's use of the 30%-level as a reasonable standard.


105
C. The District Court's Findings of Fact as to the WFP's Effects


106
Nor do we see clear error in the district court's findings as to the likely percentages of white tenant populations in the 20 covered projects with and without the WFP. NYCHA attacks those findings principally by arguing that the court should have adopted the views presented by Dr. Peterson rather than those of Dr. Cupingood; that the court failed to conduct a project-by-project analysis; and that it erred in comparing the projected effects under the WFP to the projected effects under the original TSAP rather than to the then-current racial composition of the projects. We disagree.


107
As discussed in Part II.A. above, decisions as to which witness to credit and which of two permissible inferences to draw lie strictly within the province of the district court as factfinder. As discussed in Parts I.C. and D. above, the district court found that Dr. Cupingood had extrapolated data from a reasonable period — one that was free of distortion either by NYCHA's discriminatory practices or by the implementation of decretal remedies for those practices — and that his assumptions, "us[ing] historical averages, to minimize the impact of possible uncertainties," Davis V, 60 F.Supp.2d at 239 n. 17, were reasonable. Further, in response to the remand in Davis VI, both sides' experts agreed that use of actual turnover data for the available period would not change their views as to the likely effects of the WFP in the future. Although predictive analysis is generally more speculative than statistical analysis of existing data — which the district court recognized, see, e.g., Davis V, 60 F.Supp.2d at 239 n. 17 ("projections about the future, are by definition, subject to some uncertainty") — the need for predictions in this case, in order to determine the WFP's likely effects, was inescapable.


108
The district court found that Dr. Peterson's analysis was flawed in several respects. It is immaterial to appellate review whether the views proffered by Dr. Peterson were nonetheless permissible. The views proffered by Dr. Cupingood were permissible, and we thus see no basis on which to conclude that the court's acceptance of his analysis, rather than that of Dr. Peterson, is clearly erroneous.


109
NYCHA also contends that Dr. Cupingood's analysis is flawed because it would automatically produce statistical significance over time. We disagree because the present inquiry falls outside the realm in which ordinary statistical analysis, and the need for inquiry into significance from a purely statistical standpoint, are needed. Ordinarily, such an inquiry is used when observable data are compared against expected data, or when two sets of observations are compared, and the question is whether the differences between the two data sets are attributable to a factor other than chance. In the present case, there is no question as to what causes the differences between the projections of the pace of desegregation with and without the WFP: the differences are caused simply by the contrasting hypotheses.


110
Nor is there any merit in NYCHA's contention that the district court failed to analyze the likely effects of the WFP on a project-by-project basis. Most of the district court's analyses were conducted at both the project level and the aggregate level. See, e.g., Davis V, 60 F.Supp.2d at 240 ("Statistical significance can also be analyzed at the project level.") Although the court did not discuss every project in detail, its inclusion of the numerous tables in Davis V and Davis VII, showing the levels of white-family concentration at each project for various time periods, provides adequate assurance that each project was considered individually. Thus, while we disagree with some of the court's conclusions as to the legal significance of the WFP differential at certain of the projects, see Part II.D. below, we see no indication that the court failed to give each project individual attention.


111
Finally, the court did not err in comparing the anticipated desegregation effects under the WFP against the anticipated effects under the original TSAP rather than against the racial composition of the projects without the TSAP. The remedies implemented under the TSAP were designed to alleviate past racial discrimination. It was both consistent with Supreme Court cases, as the district court discussed in Davis V, 60 F.Supp.2d at 237, and eminently reasonable for the court to compare the effects of NYCHA's proposed changes against the anticipated status of the projects under the original TSAP.


112
D. The Legal Significance of the WFP's Effects


113
The matter of whether the differences in the pace of desegregation under the original TSAP and the TSAP as it would be modified by the WFP are legally significant is a question of law that we review de novo. The caselaw give us little guidance as to what constitutes legal significance. The district court focused primarily on the issue of desegregation and the differences between the existing and the proposed procedures in achieving desegregation. In so doing, the court adopted the reasonable premise that past segregation may be perpetuated by actions that slow the pace of desegregation, even though they do not reverse it, see, e.g., Arthur v. Nyquist, 712 F.2d 816, 822 (2d Cir.1983) (affirming suspension of hiring and layoff rules that delayed desegregation of public school faculty), cert. denied, 467 U.S. 1259, 104 S.Ct. 3555, 82 L.Ed.2d 856 (1984); Sarabia v. Toledo Police Patrolman's Ass'n, 601 F.2d 914 (6th Cir.1979) (affirming suspension of civil service rule that restrained growth in African American representation on the police force). Were the court not to consider the effects of proposed conduct on the pace of desegregation, desegregation could be delayed to such an extent that it effectively would never be achieved. And were there no worthy countervailing considerations, the court's correct findings that proposed modifications would substantially delay desegregation would likely end our inquiry.


114
In the present case, however, NYCHA has proposed the WFP in pursuit of a valid countervailing interest that is, to some extent, in tension with the goal of expeditious desegregation and that is worthy of consideration. As discussed in Part I.B. above, NYCHA's goal in proposing a preference for working families is to increase the number of such families, increase income integration in public housing, and thereby promote financial and social stability in such housing. There can be no doubt that this is a legitimate objective. In providing federal funding for low-income housing, Congress has prohibited recipient public housing agencies from "concentrat[ing] very low-income families (or other families with relatively low incomes) in public housing dwelling units in certain public housing projects or certain buildings within projects," 42 U.S.C. § 1437n(a)(3)(A) (Supp. V 1999), and has required such agencies to adopt plans for deconcentration:


115
A public housing agency shall submit with its annual public housing agency plan ... an admissions policy designed to provide for deconcentration of poverty and income-mixing by bringing higher income tenants into lower income projects and lower income tenants into higher income projects. This clause may not be construed to impose or require any specific income or racial quotas for any project or projects,


116
42 U.S.C. § 1437n(a)(3)(B)(i) (Supp. V 1999). See also 42 U.S.C. § 1437d(c)(4)(A)(iv) (1994) (which, at the time the WFP was proposed, provided that public housing authorities "to the maximum extent feasible, ... will include families with a broad range of incomes and will avoid concentrations of low-income and deprived families with serious social problems"), repealed, Balanced Budget Down-payment Act, I, Pub.L. No. 104-99, § 402(d)(1), 110 Stat. 26, 41 (1996). As amended in 1998, § 1437n provides that "[a] public housing agency may establish and utilize income-mix criteria for the selection of residents for dwelling units in public housing projects, subject to the requirements of this section," 42 U.S.C. § 1437n(a)(1) (Supp. V 1999).


117
Consistent with these statutory provisions, HUD regulations explicitly permit a preference for "working families." See 24 C.F.R. § 960.205(a) (2001); 24 C.F.R. § 960.206(b)(2) (2001). In issuing § 960.205(a), HUD commented that "[t]he Department is convinced that housing agencies must have the flexibility to give preference to working families to assure diversity in the residency of projects and to include families who can serve as role models for other families." 59 Fed.Reg. 36,618 (July 18, 1994).


118
Notwithstanding that conviction, HUD did not endorse NYCHA's proposed WFP. Nor, however, despite having responsibility under § 602 of Title VI of the Civil Rights Act of 1964 to review plans for federally funded public housing to ensure compliance with federal civil rights law, see 42 U.S.C. § 2000d-1 (1994), did HUD criticize the WFP. Rather, when NYCHA sought HUD's approval for the WFP and Project Choice, HUD's response with respect to the WFP — unlike its reaction to Project Choice, which HUD found "`not likely to affect the racial identifiability of developments in New York City for the remaining period of the Davis TSAP,'" Davis II, 1997 WL 407250, at *5 (quoting HUD letter to NYCHA dated October 24, 1996) — was to remind NYCHA that it must give notice of the proposed WFP and that it must "`be mindful of the injunctive relief provided for by the Davis consent decree and its responsibilities under civil rights statutes.'" Davis II, 1997 WL 407250, at *5 (quoting HUD letter to NYCHA dated July 31, 1996).


119
We too are mindful of NYCHA's responsibilities under the Decree and the civil rights laws, and we conclude that the assessment of whether the effects of the WFP are legally significant involves a balancing of the interest in eradicating the past effects of segregation against the interest in achieving financial stability in public housing. The latter is reflected in the public housing statutes discussed above. The district court acknowledged that interest, see Davis II, 1997 WL 407250, at *14, as well as the existence of cause for concern on the part of NYCHA, see id. at *4 (noting that the percentage of applications from families who are homeless or in the lowest income category had risen from approximately 33% to 77.6%). And plaintiffs did "not dispute, that unless a higher proportion of applicants with higher incomes receive rentals, the stability of the [NYCHA] projects will be jeopardized." Id.


120
At the same time, we think it plain that Congress did not mean to cause public housing agencies to implement plans for financial deconcentration in a way that would violate the civil rights laws. And we take into account the fact that, in the present case, the concentration of most of the white families in a small percentage of the projects was the consequence of NYCHA policies and practices that — as acknowledged by NYCHA in urging judicial approval of the Consent Decree — included racial steering, withholding of information that could have led minority applicants to rent apartments in predominantly or disproportionately white projects, misrepresentations that deterred such integrated rentals, and favorable treatment for white applicants seeking housing in predominantly or disproportionately white projects. As a result, when the Decree was entered, NYCHA had placed more than 71% of its white families in 35 of its 320-odd projects. (See NYCHA Tenant Statistics by Race as of Dec. 31, 1992.) More than 51% of the white families (7,929 of 15,530) lived in the 20 projects that are at issue on this appeal (see id.); and that concentration level declined little after the implementation of the TSAP. As of January 1, 1999, there were a total of 12,185 white families residing in NYCHA projects (see NYCHA 1999 Tenant Characteristics Tabulation at 1), and 5771 of them lived in the 20 projects covered by the injunction (see id. at 25, 29, 59, 104, 119, 126, 133, 136, 177, 192, 193, 203, 207, 223, 236, 241, 251, 258, 262, 297). Thus, when the permanent injunction was entered, 20 of NYCHA's 322 housing projects (6.2%) still housed 47.36% of the white families.


121
Balancing all of the factors, we conclude that in the circumstances of this litigation, the district court determined correctly, with respect to most — although not all — of the 20 projects in question, that the desegregation delays that would be caused by implementation of the WFP are legally significant. In reaching this conclusion, we consider the delays not just in terms of percentages but also as real-time intervals. With that focus, which is somewhat broader than that of the district court, we see significant distinctions between certain categories of projects: There are two projects that were in effect desegregated prior to the entry of the permanent injunction, four projects at which the WFP is predicted to delay the achievement of desegregation by very small intervals of real time, several others at which desegregation will be delayed for a large number of years, still others that would otherwise eventually be desegregated but that will never reach the 30% level under the WFP, and two projects that will never reach the 30% level with or without the WFP.


122
The projects covered by the injunction, see Part I.D. above, and Davis VII, 103 F.Supp.2d at 231, are ranked below in order of the time it will take their white tenant populations to decline to the 30% level under the WFP, with the last column showing the differential between that time and the time each would need to reach that level without the WFP.


123
                         Months to              Months to
                         Reach 30%              Reach 30%
Project                 Without WFP             With WFP         Differential

Holmes Towers         Already below 30            None                   n/a
Straus                Already below 30            None                   n/a
Pelham Parkway                6                      8              2 months
Bay View                     17                     21              4 months
Isaacs                       18                     29             11 months
Sheepshead Bay               23                     35             12 months
Nostrand                     57                     85             2.33 years
Pomonok                      84                    171             7.25 years
Todt Hill                   103                    198             7.92 years
Forest Hills                149                    246             8.08 years
Independence                620                    899            23.25 years
Williams                    707                   1066            29.92 years
Taylor/Wythe                649                   1323            56.17 years
Haber                       146           Will never reach 30%
South Beach                 163           Will never reach 30%
Berry                       195           Will never reach 30%
Cassidy-Lafayette           195           Will never reach 30%
Robbins Plaza               355           Will never reach 30%
Middletown Plaza         Never 30%        Will never reach 30%
New Lane                 Never 30%        Will never reach 30%


124
Although Holmes Towers and Straus, respectively, had white populations of 30.6% and 30.4% as of June 1998, see Davis V, 60 F.Supp.2d at 233, Table 8, they were, factoring in the Davis move-ins, at 26.6% and 28.5% respectively, by the time the injunction was made permanent, see id. at 229, Table 5; Davis VII, 103 F.Supp.2d at 231. There was no prediction that the white tenant populations in those two projects would rise above the 30% level as a result of the WFP. In Davis III, plaintiffs agreed that the WFP should not be enjoined at projects whose white tenant population was not above 30%. See 1997 WL 711360, at *4-*5. More importantly, 30% has been used by the district court throughout as the measure of segregation. In the circumstances, we conclude that Holmes Towers and Straus should not have been deemed still segregated. The effects of the WFP in delaying further integration of those projects should not have been found legally significant, and implementation of the WFP at those projects should not have been enjoined.


125
At four projects, the desegregation delays caused by implementation of the WFP would range from two months to 12 months. The delays of two months and four months for Pelham Parkway and Bay View, respectively, are not legally significant but rather are de minimis. Nor do we view the delays of 11 and 12 months for Isaacs and Sheepshead Bay, respectively, as impermissibly long. Substantial strides in desegregating those projects have been made since entry of the Consent Decree, causing them to approach the 30% level. Thus, whereas on December 31, 1992, Isaacs and Sheepshead Bay, respectively, had white tenant populations of 52.9% and 54.1% (see NYCHA Tenant Statistics by Race as of Dec. 31, 1992), by January 1, 1999, their respective white tenant populations were 36.3% and 35.0% (see NYCHA 1999 Tenant Characteristics Tabulation at 136, 236). Given this history and the valid objective of financial stability, we conclude that the delays of 11 and 12 months at those two projects are not legally significant. In sum, we conclude that implementation of the WFP at Pelham Parkway, Bay View, Isaacs, and Sheepshead Bay should not be enjoined.


126
The WFP's effects at the 14 remaining projects, substantially delaying their desegregation, are legally significant. Although the law tolerates some "reasonable delay" in achieving desegregation, nearly a decade has passed without these projects' nearing the 30% desegregation level. All of these 14 projects had white tenant populations substantially in excess of 30% when the Consent Decree was entered in 1992, and they still had white populations substantially in excess of 30% in 1999. Indeed, nine of them remain more than 50% white. The anticipated pace of desegregation under the original TSAP in most cases already provided for additional "reasonable" delay. For example, even without the WFP, the projected time remaining after 1999 for desegregation of the Pomonok and Todt Hill projects was some seven or eight years, i.e., some 13-14 years after entry of the Decree. We regard NYCHA's proposed expanded delays, most ranging from more than seven years to eternity, as legally significant, and we see no abuse of discretion in the district court's permanent injunction against implementation of the desegregation-delaying WFP at these remaining projects.


127
We recognize that it is predicted that three projects (Independence, Williams, and Taylor/Wythe) even under the original TSAP would not be desegregated for more than a half-century. Those target dates are indeed distant. But the WFP's impact, delaying the ultimate desegregation of those projects for an additional 23-56 years, is a perpetuation of desegregation that we cannot deem insignificant. Further, though the anticipated dates of desegregation of five projects (South Beach, Berry, Cassidy Lafayette, Robbins Plaza, and Haber) are also more than a decade away without the WFP, under the WFP desegregation would never be achieved. We cannot view such "delays" as not legally significant.


128
Lastly, at Middletown Plaza and New Lane, a reduction to the 30% level is not expected under either plan. Although the WFP thus would not prevent the actual desegregation of those projects, its implementation would have legal significance, for it would impede or reverse the expected five-year decreases in white-family concentration. According to Table 5 in Davis V, 60 F.Supp.2d at 229, white family tenancy at New Lane would decrease from 73% to 64.8% without the WFP; but it would decline only to 71.1% with the WFP. And at Middletown Plaza, which is projected for only a modest decrease from 51.8% to 49.4% without the WFP, adoption of the WFP would actually increase the percentage of white families from 51.8% to 60.1%. Thus, though Middletown Plaza and New Lane would not reach desegregated levels even without the WFP, the degree of segregation would be significantly greater with the WFP.


129
In sum, we conclude that at those six projects where the WFP will not delay the reduction of the white tenant population to 30% either at all or by more than 12 months, the effects of the WFP are not legally significant. At the remaining 14 projects, the delays that would be caused by the WFP are legally significant, and implementation of the WFP at those projects was properly enjoined.


130
It is, of course, well established that a district court has the power, in the exercise of its discretion, to modify its past injunctive decrees in order to accommodate changed circumstances. See, e.g., United States v. United Shoe Machinery Corp., 391 U.S. 244, 248-49, 251, 88 S.Ct. 1496, 20 L.Ed.2d 562 (1968); System Federation No. 91, Railway Employees' Department v. Wright, 364 U.S. 642, 646-48, 81 S.Ct. 368, 5 L.Ed.2d 349 (1961); Fed.R.Civ.P. 60(b)(5). It remains open to NYCHA to move for a modification of the present injunction against implementation of the WFP at any of the remaining 14 projects in the event that the number of apartments rented to white families at such project declines to the 30% level.

CONCLUSION

131
We have considered all of NYCHA's contentions on this appeal and, except as indicated above, have found them to be without merit. The order of the district court is reversed to the extent that it enjoined NYCHA from implementing the WFP at the Bay View, Holmes Towers, Isaacs, Pelham Parkway, Sheepshead Bay, and Straus projects; in all other respects, the injunction is affirmed.



Notes:


*
 After Davis Move-Ins


JOHN M. WALKER, JR., Chief Judge, dissenting:

132
I am concerned that the majority, in its effort to more rapidly rectify the past discriminatory practices of the New York City Housing Authority ("NYCHA"), has endorsed a questionable attempt at social engineering and, in doing so, has reached a decision that may well have the practical effect of making several of the housing projects in New York City worse. Although the majority acknowledges the importance of working families to the financial and social stability of public housing, its treatment of the working family preference ("WFP") leaves the impression that those interests must always yield to a desegregation remedy, however crafted. I disagree with any such implication, and with the majority's rejection of the position in favor of the WFP taken by the NYCHA.


133
As the agency charged with administering public housing, the NYCHA should generally be allowed to implement critical objectives such as the WFP even though it might slow the pace of desegregation somewhat. The NYCHA has acknowledged the wrongfulness of its past practices of segregation and is now working to promote desegregation. In my opinion, the WFP represents a good faith effort by the NYCHA to maintain the viability of public housing in New York City by striking a balance between rapid desegregation and the values promoted by social and financial stability. That such a balance needs to be struck cannot be doubted. As Congress found in the "Findings and Purposes" section of the Quality Housing and Work Responsibility Act of 1998, "the public housing system is plagued by a series of problems, including the concentration of very poor people in very poor neighborhoods and disincentives for economic self-sufficiency." Pub.L. No. 105-276, § 502(a)(3), 112 Stat. 2518, 2520. Congress further made the significant finding that the "public interest[ ] will best be served by a reformed public housing program that," among other things, "vests in public housing agencies that perform well the maximum feasible authority, discretion, and control with appropriate accountability... [and that] rewards employment and economic self-sufficiency of public housing residents." Id. § 502(a)(5)(C) & (D), 112 Stat. at 2521 (emphasis added).


134
The plaintiffs themselves have acknowledged the important values promoted by the WFP in the consent decree. The consent decree authorizes the NYCHA to "seek to achieve a tenant body in each Project composed of families with a broad range of incomes, generally representative of the range of incomes and rent-paying abilities of lower income families in its geographic operating area to the extent permitted under 42 U.S.C. § 1437d(c)(4)(A)(iv), 24 C.F.R. § 960.205, and 24 C.F.R. Part 913." (Majority Op. at 68 (quoting Consent Decree ¶ 8)). Section 1437d(c)(4)(A)(iv) in turn requires every contract for contribution to provide that the public housing agency will comply with requirements prescribed by the Secretary of Housing and Urban Development, including the selection of tenant criteria that "are designed to ensure that, to the maximum extent feasible, the projects of an agency will include families with a broad range of incomes and will avoid concentrations of low-income families and deprived families with serious social problems." 42 U.S.C. § 1437d(c)(4)(A)(iv) (1992) (emphasis added). Similarly, 24 C.F.R. § 960.205 mandates that tenant selection criteria "shall be reasonably related to individual attributes and behavior of an applicant and shall not be related to those which may be imputed to a particular group or category of persons of which an applicant may be a member." 24 C.F.R. § 960.205 (1992) (emphasis added).


135
Although we should never blindly defer to agency decisions, I do not think that the NYCHA's congressionally-authorized WFP should be enjoined without a project-by-project and in-depth examination of the relative importance of project stability and the other values promoted by the WFP, on the one hand, and the rate at which desegregation targets are met, on the other. The majority's adherence to the district court's talismanic number of 30% for whites is no substitute for such an examination. While the 30% figure was accepted by the NYCHA as an aspirational goal in the consent decree, that was long before it could have been known that the 30% figure would be a barrier to the implementation of the WFP. The 30% number seems to have been picked out of thin air. Why not 25% or 35% or 40%? Why not a different number for different projects? In my view, the 30% figure amounts to an arbitrary number that is being used to frustrate the considered policy of the NYCHA. Putting aside the counter-intuitive notion that permeates the district court's analysis, affirmed by the majority, that a project with more than 30% white-occupied apartments is "predominantly white" (Majority Op. at 71) and thus is segregated, it is clear that the color-blind WFP would not perpetuate such "segregation" but, except for Middletown Plaza which is located in a largely white area, would reduce it, albeit more slowly than under the tenant selection and assignment plan ("TSAP"). Moreover, under the district court's and the majority's holdings, the 30% figure sheds its aspirational character and effectively becomes a quota which, should the NYCHA fail to meet it with sufficient dispatch, penalizes a housing project by denying to it the WFP.


136
In sum, the practical effect of the majority's decision is to deny housing to people who deserve it because of their hard work or other merit solely on the basis of their race or ancestry, to frustrate the worthwhile efforts of the NYCHA to reward and promote employment and economic self-sufficiency in its tenants, and to deny the existing tenants the obvious benefit of having working families as their neighbors. I am concerned that by overriding the NYCHA's policy decision for the sake of more rapid desegregation, the majority's decision could result in the deterioration of the New York City housing projects that remain under the injunction to the point where the achievement of its desegregation targets would be a Pyrrhic victory.


137
I respectfully dissent.

