EDWARD C. PRADO, Circuit Judge:

This school-redistricting equal protection case is now before us for the second time. In the first appeal, in 2011, a divided panel of this Court reversed summary judgment in favor of Defendant-Appellee Ascension Parish School Board ("Board"), holding that material fact issues surrounded the discriminatory purpose and effect of the Board's adoption of a redistricting plan that concentrated economically disadvantaged students in a majority-nonwhite school district. Lewis v. Ascension Par. Sch. Bd., 662 F.3d 343 (5th Cir.2011) (per curiam). On remand, the district court held a three-day bench trial and entered judgment for the Board. It concluded that the plan was facially race neutral, that the plaintiffs had failed to prove the redistricting plan treated similarly situated students of different races differently, and that, even if he had made this threshold showing, he failed to establish that the plan had a discriminatory effect. Discerning no material infirmities in the court's legal conclusions and no clear error in its findings of fact, we affirm the judgment.

I. FACTUAL AND PROCEDURAL BACKGROUND

A. Factual Background1

The Ascension Parish School District ("the District") operates four high schools in southeast Louisiana—Donaldsonville High School on the west bank of the Mississippi River, and East Ascension High School, Dutchtown High School,2 and St. Amant High School on the east bank. Since at least 1972, the District has assigned students to these schools through an attendance-zone-based "feeder plan," whereby specified elementary schools "feed" into specified middle schools, which in turn "feed" into one of the high schools. This organization allows students to matriculate together to middle school and high school.

In 2004, a federal district court dismissed the District's longstanding desegregation case and declared the District unitary after finding that all vestiges of the prior compulsory dual school system had been eliminated to the extent practicable.

Later that year, in response to dramatic population growth in the Dutchtown area, the Board convened a "Growth Impact Committee." Troy Gautreau, Sr., a Board member and chairman of the Committee, presented the Board with a "Growth Impact Charter," which included the following "objectives": (1) "develop a plan to address the growth with minimal impact on residents"; (2) "ensure equal facilities and instructional quality for all children"; (3) attain "enrollment maximums" established for the elementary, middle, and high school levels; and (4) "maintain unitary status." (alterations omitted). According to then-Superintendent Donald Songy, the District sought to move approximately 450 students from Dutchtown Middle School, and thus out of Dutchtown High School's feeder zone, to other east bank schools with capacity for growth.

To facilitate the Board's consideration of various rezoning options, Superintendent Songy, Gautreau, and other Board members requested that Demographics Application Specialist David Duplechein generate demographic data for several plans. Using the District's "Edulog" computer program—which "geographically code[d] all students actually enrolled in the school system based on their physical residential addresses"—Duplechein projected the demographic effects of various prospective rezoning plans. Ultimately, the Board, which governs the District, narrowed its consideration down to four rezoning plans, referred to as Options 1, 2, 2f, and 3.

Between 2004 and 2007, Gautreau delivered several PowerPoint presentations to the Board on the topic of rezoning. In a 2004 presentation, Gautreau discussed the persistent overcrowding issues in several of the District's primary and middle schools. The presentation indicated that, since the implementation of the 2002 feeder plan that accompanied the construction of Dutchtown High School, the percentage of at-risk students3 at the primary and middle schools in the East Ascension High School feeder zone had increased and the average School Performance Scores ("SPS")4 at those schools had decreased. It further highlighted a decline in student enrollment, SPS, and standardized test scores, and an increase in the percentage of at-risk students, at East Ascension High School. In addition, the presentation delineated the negative effects of a higher at-risk student population, emphasizing that "the concentration of poverty within a school can be shown to be harmful to all students in that school whether or not an individual student comes from a poor background." It concluded that "a higher percentage of majority students should increase at[-]risk achievement." It is unclear whether the presentation incorporated demographic data derived from Edulog.

By 2006, the enrollment of Dutchtown Middle School, a Dutchtown High School feeder school, had risen to over 1,000 students, causing severe overcrowding. No other east bank middle school had more than 730 students enrolled. Accordingly, in 2006 or 2007 Gautreau prepared another PowerPoint presentation that examined Options 2f and 3 in detail. The presentation compared then-current racial demographics at each of the high schools, projected total enrollment at several primary and middle schools, projected percentages of "black" and "white" students at several primary and middle schools, and projected percentage of "Title I"5 and "fully paid" students at several primary and middle schools. It concluded that Option 3 "clearly offers the best opportunity for all students in Ascension Parish and avoids putting an undue burden on one particular school by increasing the at[-]risk student population." (alteration omitted). As with Gautreau's 2004 presentation, it is unclear whether the 2006-2007 presentation incorporated Edulog data.

Sometime after 2007, Gautreau created a chart using Edulog data that projected the total enrollment and the percentages of "minority" and at-risk students at each of the three east bank high schools under each of the rezoning options under consideration. The chart indicated, in relevant part, that: (1) under current conditions, with no redistricting, (a) the enrollment of Dutchtown High School would increase from 1695 students in 2007 to 2072 students in 2012, a total student population exceeding the 2012 projections at East Ascension High School and St. Amant High School by 700 students and 400 students, respectively, and (b) the percentage of at-risk students in all three high schools would increase, with the largest jump occurring at East Ascension High School; and (2) under each of Options 2, 2f, and 3, (a) the total enrollment in all three schools would increase but would approach parity, and (b) the percentage of at-risk students in all three high schools would increase, again with the largest jump occurring at East Ascension High School.6

In 2008, Superintendent Songy also compiled a chart with Edulog data, titled "Statistical Analysis of Options 1, 2, 2f and 3," and presented it to the Board for consideration. The chart listed the current enrollment, percentage of African-American students, and percentage of at-risk students at each school in the district, then projected the enrollment, percentage of African-American students, and percentage of at-risk students at each school under each of the four rezoning options. Unlike Gautreau's chart, Songy's chart did not project data beyond the 2007-2008 school year. Songy's chart indicated, in relevant part, that: (1) the current African-American population at East Ascension High School exceeded that of the other high schools, but would decrease at East Ascension High School and would increase at the remaining schools under any plan; (2) the at-risk population at East Ascension High School would decrease under any plan, with the greatest drop under Option 3 and the second greatest drop under Option 2f; (3) the at-risk populations at Dutchtown High School and St. Amant High School would increase under any plan; and (4) the total student enrollment would increase at East Ascension High School and St. Amant High School, but not at Dutchtown High School, under any plan.7

At its January 15, 2008 meeting, Gautreau discussed the School Board's redistricting efforts and, according to the meeting minutes, told the School Board and audience that "the criteria most concentrated on was [sic] maintaining our current unitary status with the Department of Justice and moving the least amount of kids as possible." Lewis, 662 F.3d at 345. Gautreau also "informed the public that Option 2f or Option 3 needed to be passed by the School Board that night, and that some people would be upset with the School Board's decision."8 Following remarks by each of the eleven Board members and by nineteen members of the public, the Board voted on Options 2f and 3.9 Option 3 failed by a vote of six to four, then Option 2f passed by a vote of the same margin, with precisely the same voting blocs on either side. Each Board member was in possession of Songy's chart at the time of the vote, but it is unclear which Board members, if any, were in possession of Gautreau's chart or presentations. Four of the six Board members who voted in favor of Option 2f testified at the bench trial, and each Board member who testified stated that, at the time of the vote, they were aware of the demographic projections and of the correlation between at-risk status and lower academic achievement.

Option 2f employed several means to shift the student population among the east bank schools. First, it redrew the District's geographic attendance lines so that a number of students were moved from the Dutchtown and St. Amant High School feeder zones to the East Ascension High School feeder zone. In total, Option 2f moved 339 students into different feeder zones during the 2008-2009 school year. Second, Option 2f moved Duplessis Primary School, a Title I school, from the Dutchtown feeder zone to the East Ascension feeder zone. As a result, all five of the primary schools in the East Ascension feeder zone were now Title I schools. Third, Option 2f assigned one new primary school and one new middle school to the East Ascension feeder zone, two new primary schools to the Dutchtown feeder zone, and three new primary schools to the St. Amant feeder zone.

According to data collected by the Louisiana Department of Education, since the implementation of Option 2f, total student enrollment has increased at all three east bank high schools; the percentage of at-risk students has increased at all three east bank high schools; and East Ascension High School has maintained the highest percentages of nonwhite students and at-risk students among the east bank high schools, and those percentages have each grown from 2007 to 2013. In addition, the percentages of both nonwhite students and at-risk students at each primary school and middle school in the East Ascension feeder zone have increased during this time.

Further, it is undisputed that, since the adoption of Option 2f the majority of the District's nonwhite students and a majority of the District's at-risk students attend schools in the East Ascension feeder zone; East Ascension High School is the only majority nonwhite and majority at-risk high school in the District; a majority of the East Ascension feeder schools are majority nonwhite, unlike the Dutchtown and St. Amant feeder schools; and all of the East Ascension feeder schools are majority at-risk, unlike the Dutchtown and St. Amant feeder schools.

The evidence of academic performance under Option 2f is mixed. The average ACT score for the 2013 graduating class at East Ascension was 19.4, lower than St. Amant's average score of 20.3 and Dutchtown's average score of 21.3, and lower than the state's average score of 19.5, but average ACT scores also declined for all three schools during this time. Additionally, Dutchtown and St. Amant high school students performed better than East Ascension students on Advanced Placement ("AP") exams in the 2011-2012 academic year. Dutchtown also attained superior SPS to East Ascension High School, both before and after the implementation of Option 2f. In the 2007-2008 school year, East Ascension's SPS was 95.1, compared to Dutchtown's SPS of 109.8. In the 2012-2013 school year—after the Department of Education revised the SPS scale from 150 points to 200 points—East Ascension's SPS was 135.2, compared to Dutchtown's SPS of 163.3 and St. Amant's SPS of 149.7. On the other hand, East Ascension's SPS has gradually increased since the implementation of Option 2f, and its state school ranking and graduation rate are now at all-time highs.

B. Procedural Background

1. The Suit

Shortly after the adoption of Option 2f, Lewis, the father of two African-American school children assigned to the East Ascension feeder zone both pre- and post-Option 2f, filed suit against the Board in Louisiana state court. Lewis, 662 F.3d at 345. Lewis sued under 42 U.S.C. § 1983, asserting violations of his children's Fourteenth Amendment rights to equal protection. Id. at 346. He essentially raised two challenges to Option 2f: first, he alleged that the Board adopted Option 2f "to ensure that East Ascension High School [and its feeder schools] would maintain a disproportionately large non-white minority population, leaving the remaining two East Bank schools as predominantly white" (the "racial balancing" claim), id. (alteration in original) (internal quotation marks omitted); and second, he alleged that because Option 2f placed a disproportionate number of at-risk students in the East Ascension feeder zone, "Option 2f `would ensure that the nonwhite minority students at East Ascension High School [and in its feeder system] would not, now and in the future, be afforded educational opportunities equal to those available to the students at either Dutchtown High School or St. Amant High School" (the "funneling" claim), id. (alteration in original).

The Board removed the action to federal court and successfully moved for summary judgment. Id. The district court found Option 2f facially race neutral and concluded that Lewis had not presented competent evidence of both discriminatory intent and discriminatory effect so as to invoke strict scrutiny. Id. It then upheld the plan on rational basis review because the Board had a legitimate government interest in reducing overcrowding. Id.

2. The First Appeal

A divided panel of this Court reversed. Id. at 352. The Court held, first, that Lewis's racial-balancing claim was not preserved and that Lewis's only live claims were his funneling claim and his claim that Option 2f employs explicit racial classifications. Id. at 348 & n. 11. It then criticized the district court's analysis, which relied in part on evidence that the Board "considered [the race of reassigned students] in an effort at maintaining the racial balance already existing among the schools in East Ascension Parish and in maintaining the school district's unitary status, not as part of a racially discriminatory motive to allocate a `disproportionate number' of African-American students to the East Ascension school zone." Id. at 349. The Court raised two concerns with this reasoning: first, "it is unclear how, on the record before us, the court could make a factual finding as a matter of law about the Board's lack of discriminatory purpose"; and second, "the court's assumption that it might be justifiable to use racially-based decisions for the `benign' purpose of maintaining post-unitary `racial balance' among the schools in the system is at least in tension with the Supreme Court's decision in Parents Involved." Id.

The Court then identified several pieces of evidence that created a genuine issue of material fact concerning the Board's discriminatory purpose. Id. at 350-52. First, the Court cited the Board's reliance on Edulog data, noting that Edulog "coded each enrolled student in order to predict the `statistical effects' of Option 2f's boundary assignments" and that, in turn, "it is unclear how a student assignment plan could calculate the percentage of black students at each school without classifying individual students by race." Id. at 350. The Court rejected the Board's explanation "that the Statistical Analysis underlying Option 2f . . . does not constitute Option 2f itself" because "to accept that self-serving, summary allegation would be to allow a school district to skew reality by selectively including documents in the record and labeling only those documents its `plan.'" Id. This, the Court said, it could not countenance on review of a summary judgment. Id.

Next, the Court quoted the testimony of Superintendent Songy and various Board members that "suggest[ed] that the District relied upon the race of the individual students residing in different geographic locations when it re-zoned its schools." Id. at 350-51. The Court also cited an excerpt from the District's website that referred to "alter[ing] the racial balance" and "balanc[ing] the demograph[ics]" at East Ascension. Id. at 351 (second alteration in original). In response to the district court's finding that "`only' 339 students, in a district population of 18,000, were affected by Option 2f," the Court observed that, "[i]n light of the testimony, this seems to be a group identifiable and identified principally on racial grounds (whether minority or not) for assignment to particular schools." Id.

Lastly, the Court concluded that there were material questions of fact surrounding the discriminatory effect of Option 2f. Id. Criticizing the district court for basing its finding on a statistical analysis of Option 2f's impact on only the east bank high schools, the Court pointed out that Lewis alleged a discriminatory effect on the East Ascension feeder system. Id. The statistics in the record, the Court said, "provide some support" for Lewis's funneling claim. Id. at 352. The Court gave particular attention to statistics showing disparities between the percentage of the total east bank student population enrolled in each feeder system and the percentage of the east bank's total at-risk student population and total nonwhite student population in each feeder system. Id. at 351-52.10 In any event, the Court declined to identify the pertinent standard of review, holding that the determination of whether to apply strict scrutiny or rational basis review "turns on the factual questions of discriminatory motive and impact." Id. at 352.

3. Remand, Pretrial Motions, and the Bench Trial

On remand, the district court permitted additional discovery; then both parties moved for summary judgment. The district court denied Lewis's motion and granted in part and denied in part the Board's motion. Two aspects of the district court's ruling are relevant here. First, the district court "conclude[d] that the School Board's consideration of projected racial and socioeconomic data prior to voting does not amount to a racial classification." It correspondingly denied "Lewis'[s] request that the Court review Option 2f under strict scrutiny on this basis" and granted "[t]he School Board's request that the Court dismiss Lewis'[s] claim that Option 2f employs a racial classification." Second, the district court denied "the School Board's request that the Court dismiss Lewis'[s] remaining Equal Protection claim on th[e] basis" that "Lewis cannot establish that [his children] were treated differently than similarly situated students of a different race"—namely, white students in the Dutchtown and St. Amant feeder zones. Despite announcing that it was "unable to consider all of the evidence presented until after a full trial on the merits," the district court "conclude[d]," based on "the evidence presented here, [the] context of this matter, and factors considered by the School Board when it adopted Option 2f," that the plaintiff's children "are, in fact, similarly situated to white students in the Dutchtown High School and St. Amant High School feeder zones."

The case proceeded to a three-day bench trial. At the opening of the trial, the Board orally requested that the district court reconsider several of its rulings in its summary-judgment order, including its conclusion on the "similarly situated" issue. The district court denied the Board's requests without prejudice to the Board's right to reurge them in its post-trial briefs. Lewis made no request that the district court reconsider its ruling that Option 2f did not employ racial classifications.

At trial, Lewis called ten witnesses: five members of the Board who voted on Option 2f, Demographics Application Specialist Duplechein, Lewis, Lewis's son, Bridget Thomas (a "concerned parent" who compiled statistics on the rezoning options), and Dr. Percy Bates (an expert witness in educational psychology). The Board, in turn, called two witnesses: Patrice Pujol, current Superintendent of the Board, and former Superintendent Songy.

Following post-trial briefing, the district court issued Rule 52 findings of fact and conclusions of law. The court's findings of fact are summarized in Part I(A), supra. The court opened its conclusions of law with a summary of Lewis's theory:

The court then held that: (1) Option 2f does not employ explicit racial classifications, (2) Lewis failed to prove that non-white students in the East Ascension attendance zone are similarly situated to white students in the Dutchtown and St. Amant attendance zones, and, in turn, that Option 2f accords disparate treatment to similarly situated students of a different race, and (3) even if Lewis had proven that Option 2f treats similarly situated students differently on the basis of race, the record evidence does not support the conclusion that Option 2f has had a discriminatory effect on nonwhite students in the East Ascension feeder zone. Accordingly, the court omitted discussion of whether the Board acted with a discriminatory purpose. In addition, the court did not identify the level of scrutiny it would apply to Lewis's challenge to Option 2f; it held only that "Lewis has not satisfied his burden of proving by a preponderance of the evidence that [the Board's] adoption of Option 2f violates the Equal Protection Clause." Lewis timely appealed.

II. JURISDICTION AND STANDARD OF REVIEW

The district court had jurisdiction over Lewis's suit pursuant to 28 U.S.C. § 1331. This Court has jurisdiction to review the district court's final judgment pursuant to 28 U.S.C. § 1291.

"The standard of review for a bench trial is well established: findings of fact are reviewed for clear error and legal issues are reviewed de novo." Bd. of Trs. New Orleans Emp'rs Int'l Longshoremen's Ass'n v. Gabriel, Roeder, Smith & Co., 529 F.3d 506, 509 (5th Cir.2008) (quoting Water Craft Mgmt. LLC v. Mercury Marine, 457 F.3d 484, 488 (5th Cir.2006)). "A finding is clearly erroneous if it is without substantial evidence to support it, the court misinterpreted the effect of the evidence, or this court is convinced that the findings are against the preponderance of credible testimony." Id.

III. DISCUSSION

The Equal Protection Clause of the Fourteenth Amendment mandates that "[n]o State shall . . . deny to any person within its jurisdiction the equal protection of the laws." U.S. Const. amend. XIV, § 1. "Its central purpose is to prevent the States from purposefully discriminating between individuals on the basis of race." Shaw v. Reno, 509 U.S. 630, 642, 113 S.Ct. 2816, 125 L.Ed.2d 511 (1993). Accordingly, "[l]aws that explicitly distinguish between individuals on racial grounds fall within the core of that prohibition," id., and are subject to strict scrutiny, Hunt v. Cromartie, 526 U.S. 541, 546, 119 S.Ct. 1545, 143 L.Ed.2d 731 (1999). "Strict scrutiny also applies to government action that is `ostensibly neutral,' but only if the neutral law has a `disproportionately adverse effect' that `can be traced to a discriminatory purpose.'" Lewis, 662 F.3d at 348 (quoting Pers. Adm'r of Mass. v. Feeney, 442 U.S. 256, 272, 99 S.Ct. 2282, 60 L.Ed.2d 870 (1979)).11 Under strict scrutiny, "the burden [is] on the government to prove that its actions are narrowly tailored to achieve a compelling government interest." Id. By contrast, where there is no proof of either discriminatory purpose or discriminatory effect, the government action is subject to rational basis review, id., and the burden is on the challenger to rebut the "strong presumption of validity" accorded the action and prove that the action is not rationally related to a legitimate government purpose, Heller v. Doe, 509 U.S. 312, 319-20, 113 S.Ct. 2637, 125 L.Ed.2d 257 (1993).

At trial, Lewis mounted a two-pronged attack on Option 2f: he alleged that Option 2f was subject to strict scrutiny (1) because it contains explicit racial classifications, and, alternatively, (2) because its funneling feature was motivated by racial animus and had a disproportionately adverse impact on nonwhite students in the East Ascension feeder zone. On appeal, he contends that the district court committed numerous errors in entering judgment against him. We address each claim of error in turn.

A. Option 2f and Explicit Racial Classifications

Lewis first urges that the district court erred in holding that Option 2f does not explicitly classify students on the basis of race.

Although the district court granted summary judgment to the Board on Lewis's claim that Option 2f should be subjected to strict scrutiny because it employs express racial classifications, it rejected this argument anew in its Rule 52 findings of fact and conclusions of law. It cited three grounds for its decision: (1) the court had previously ruled against Lewis, and Lewis had not requested reconsideration; (2) "a review of the evidence supports the conclusion that Option 2f does not employ an explicit racial classification" because the plan is facially race neutral and "Lewis failed to point to any provision of Option 2f that classifies students on the basis of race[] or uses race as a factor in school assignment"; and (3) "the School Board's consideration of the projected enrollment and percentage of nonwhite and `at-risk' students . . . does not amount to a rezoning plan that assigns students on the basis of race."

Given these ostensible alternative rulings—one procedural and one on the merits—we requested supplemental briefing on the ruling subject to appeal and the corresponding standard of review. The parties agreed that the district court reconsidered its summary judgment ruling sua sponte when it announced a post-trial merits holding, see, e.g., Zarnow v. City of Wichita Falls, Tex., 614 F.3d 161, 171 (5th Cir.2010), and our standard of review therefore tracks that applicable to an ordinary bench trial: we review findings of fact for clear error and legal issues de novo, Bd. of Trs., 529 F.3d at 509.

"It is well established that when the government distributes burdens or benefits on the basis of individual racial classifications, that action is reviewed under strict scrutiny." Parents Involved in Cmty. Schs. v. Seattle Sch. Dist. No. 1, 551 U.S. 701, 720, 127 S.Ct. 2738, 168 L.Ed.2d 508 (2007). "A statute or policy utilizes a `racial classification' when, on its face, it explicitly distinguishes between people on the basis of some protected category." Hayden v. Cty. of Nassau, 180 F.3d 42, 48 (2d Cir.1999) (citing Adarand Constructors, Inc. v. Pena, 515 U.S. 200, 227, 115 S.Ct. 2097, 132 L.Ed.2d 158 (1995); Wygant v. Jackson Bd. of Educ., 476 U.S. 267, 282-84, 106 S.Ct. 1842, 90 L.Ed.2d 260 (1986); Loving v. Virginia, 388 U.S. 1, 11-12, 87 S.Ct. 1817, 18 L.Ed.2d 1010 (1967)).

Although the Supreme Court has not addressed the facial neutrality of school district boundaries in the context of a post-desegregation equal protection challenge,12 we find its precedents on electoral redistricting instructive. In this context, the Court has repeatedly made clear that redistricting plans do not classify individuals and are therefore facially race neutral.13 As a result, "a more searching inquiry is necessary before strict scrutiny can be found applicable in redistricting cases than in cases of `classifications based explicitly on race.'" Bush, 517 U.S. at 958, 116 S.Ct. 1941. Moreover, the Court has unequivocally stated that a legislative body's mere awareness or consideration of racial demographics in drawing district boundaries will not alone trigger strict scrutiny.14 To the contrary, the challenger must demonstrate that race was "the predominant factor motivating the legislature's decision." Miller, 515 U.S. at 916, 115 S.Ct. 2475. To make this showing, the challenger is obligated to prove—using direct or circumstantial evidence, or a combination of the two—"that `the legislature subordinated traditional race-neutral districting principles, including . . . compactness, contiguity, and respect for political subdivisions or communities defined by actual shared interests, to racial considerations[.]'" Hunt, 526 U.S. at 547, 119 S.Ct. 1545 (quoting Miller, 515 U.S. at 916, 115 S.Ct. 2475). One form of circumstantial evidence is the shape of the district, which may, in some cases, be so "bizarre" or "highly irregular that, on its face, it rationally cannot be understood as anything other than an effort to segregat[e] . . . voters on the basis of race." Miller, 515 U.S. at 914, 115 S.Ct. 2475 (alteration and ellipsis in original) (quoting Shaw, 509 U.S. at 646-47, 113 S.Ct. 2816) (internal quotation marks omitted).15

While there is no post-Parents Involved law in this Circuit assessing whether school redistricting plans like Option 2f contain express racial classifications, the Third and Sixth Circuits have recently held that school zoning plans that divide the student population by geography are facially race neutral. See Spurlock v. Fox, 716 F.3d 383, 394-96 (6th Cir.2013); Doe ex rel. Doe v. Lower Merion Sch. Dist., 665 F.3d 524, 545-48 (3d Cir.2011). Importantly, both of these cases affirmed bench-trial verdicts in favor of the school districts, Spurlock, 716 F.3d at 385; Lower Merion, 665 F.3d at 539, 558, and both cases were decided after this Court issued its first opinion in Lewis. In both Spurlock and Lower Merion, the courts distinguished Parents Involved as a case speaking only to student-assignment plans that explicitly use a student's race as a factor in assignments; a plan that, on its face, relies exclusively on a student's home address is necessarily race neutral, and Parents Involved has no application. Spurlock, 716 F.3d at 394; Lower Merion, 665 F.3d at 545-46. Additionally, both courts rejected the students' arguments that the rezoning bodies' consideration of racial demographic data in formulating the district boundaries amounted to an express racial classification.16 To this end, the Third Circuit relied in part on the Supreme Court's electoral redistricting precedents. See Lower Merion, 665 F.3d at 547. And, notably, the Sixth Circuit held that its conclusion was not inconsistent with this Court's opinion in Lewis. Spurlock, 716 F.3d at 395-96.17

Before this Court, Lewis contends that the record evidence and the trial court's findings of fact "clearly show that race was an important stand alone [sic] factor in the adoption of Option 2f and that a main goal of Option 2f was to keep a specific balance of racial groups in each East Bank school in order to maintain unitary status." This, Lewis says, is contrary to Parents Involved, in which the Court "held that a unitary school district's decision to classify students by race and to rely on that classification in determining school assignments is subject to strict scrutiny." Lewis's position hinges on the premise that Option 2f is more than the maps and written descriptions laying out the geographic boundaries of the feeder zones; in his view, the demographic analysis underlying Option 2f classifies students on the basis of race, and this data, as well as the race-conscious motives of the Board members, evince express racial classifications in the plan.

The Board counters that the district court correctly looked only to the face of Option 2f to assess its race neutrality, and it contends that the court's finding that none of the documents that make up Option 2f include any reference to race is not clearly erroneous. The Board urges this Court to follow the Third and Sixth Circuits and hold that a school zoning plan that assigns students to schools based on their home addresses is facially race neutral, and the rezoning body's consideration of demographic data in drawing the relevant geographic boundaries does not amount to making an express classification. Lastly, the Board posits that even if Option 2f incorporated Gautreau's or Songy's statistical analysis, the plan would still not contain any express racial classifications because there is no provision that "identif[ies] any classification by individual student or group for purposes of school assignment" or that "require[s] the consideration of race when enrolling students in any school."

We agree with the Board and find no error in the district court's ruling that Option 2f contains no explicit racial classifications. Lewis provides no basis for this Court to conclude that the district court's factual finding that Option 2f is facially race neutral and assigns students to schools on the sole basis of geography is clearly erroneous. The only evidence he points to on appeal relates to the Board's awareness of racial demographics and its alleged desire to maintain the District's unitary status through racial balancing. Under the Supreme Court's electoral-redistricting precedents, and consistent with the Third and Sixth Circuit's reasoning, this evidence has no bearing on the facial neutrality of the Board's action—at least absent evidence that the geographic boundaries are explicable only as the product of intentional segregation, see Miller, 515 U.S. at 914, 115 S.Ct. 2475; see also supra note 16; cf. Spurlock, 716 F.3d at 394; Lower Merion, 665 F.3d at 548. Even accepting Lewis's position that Option 2f incorporated the demographic data and projections, this does not establish that the plan explicitly classified students by race; it shows only that the Board considered the same sort of data that the Supreme Court has refused to equate to a facial racial classification, albeit in the electoral context.18 See Bush, 517 U.S. at 958, 116 S.Ct. 1941; Miller, 515 U.S. at 916, 115 S.Ct. 2475; Shaw, 509 U.S. at 646, 113 S.Ct. 2816. It also does not bring the plan within the ambit of Parents Involved, as that case addressed individualized student assignments that took into account the student's race and the overall racial makeup of the school. See supra note 13.

Likewise, the district court's legal conclusion that the Board's consideration of demographic data in formulating Option 2f "does not amount to [adopting] a rezoning plan that assigns students on the basis of race" conforms to Supreme Court case law, see, e.g., Bush, 517 U.S. at 958, 116 S.Ct. 1941, and is in accord with the decisions of this Court's sister circuits, see Spurlock, 716 F.3d at 394; Lower Merion, 665 F.3d at 548. Accordingly, we hold that the district court did not err in concluding that Option 2f does not make express racial classifications and so is not subject to strict scrutiny on that basis.

B. The Discriminatory Purpose and Effect of Option 2f

Lewis next contends that the district court erred in rejecting his alternative theory that, despite Option 2f's facial neutrality, the redistricting plan's funneling feature is nevertheless subject to strict scrutiny because it had both a discriminatory purpose and a discriminatory effect. See Vill. of Arlington Heights v. Metro. Hous. Dev. Corp., 429 U.S. 252, 264-66, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977) (holding that an equal protection claim premised on an outwardly neutral law requires proof of both a discriminatory effect and a discriminatory purpose). Relevant to this determination, the district court first found that the pertinent comparator group for Lewis's equal protection claim was white students within the East Ascension feeder zone—not white students in the other feeder zones, as it had originally ruled on post-remand summary judgment. It then found that, even if Lewis had successfully established that nonwhite students in the East Ascension feeder zone were similarly situated to their white counterparts in the other feeder zones, he had not proven that Option 2f had a discriminatory adverse effect on nonwhite students in the East Ascension feeder zone. Lewis urges that the district court erred in both regards.

Because we resolve the district court's treatment of Lewis's alternative equal protection theory on the discriminatory-effect finding, we need not address either the court's similarly situated finding or Lewis's proffered evidence of discriminatory purpose. See id.; Palmer v. Thompson, 403 U.S. 217, 224, 91 S.Ct. 1940, 29 L.Ed.2d 438 (1971) ("[N]o case in this Court has held that a legislative act may violate equal protection solely because of the motivations of the men who voted for it."); Lower Merion, 665 F.3d at 549-50 ("[D]iscriminatory impact must be shown to establish an equal protection violation because `plaintiffs must show that they have been injured as a result' of the governmental action to ensure that courts `can impose a meaningful remedy.'" (quoting Garza v. Cty. of Los Angeles, 918 F.2d 763, 771 (9th Cir.1990))). We simply assume without deciding that it was Lewis's burden to identify a similarly situated comparator group and that he met this burden,19 and we proceed to the district court's finding on the issue of discriminatory impact.

As a preliminary matter, we note a disagreement between the parties concerning the standard of review applicable to the district court's determination. On one hand, there is general agreement that a finding of discriminatory effect is a finding of fact subject to review for clear error.20 On the other hand, there is authority for the proposition that where, as here, the facts are essentially undisputed, the question of whether those facts evince a discriminatory effect is ultimately one of law that this Court reviews de novo.21 We assume without deciding that our review is de novo, as affirmance under this standard compels the same result as under the more deferential alternative standard.

To subject a facially race neutral government action to strict scrutiny, the plaintiff must establish both discriminatory intent and a disproportionate adverse effect upon the targeted group. Feeney, 442 U.S. at 272, 99 S.Ct. 2282. The discriminatory-impact element of an equal protection claim may be satisfied with statistical evidence. See, e.g., Chavez v. Ill. State Police, 251 F.3d 612, 638 (7th Cir.2001) ("While few opinions directly acknowledge that statistics may be used to prove discriminatory effect, the Court has repeatedly relied on statistics to do just that." (citing Yick Wo, 118 U.S. at 374, 6 S.Ct. 1064 and Hunter v. Underwood, 471 U.S. 222, 227, 105 S.Ct. 1916, 85 L.Ed.2d 222 (1985))); accord Bennett v. City of Eastpointe, 410 F.3d 810, 818 (6th Cir.2005). "Of course, parties may not prove discrimination merely by providing the court with statistical analyses. The statistics proffered must address the crucial question of whether one class is being treated differently from another class that is otherwise similarly situated." Chavez, 251 F.3d at 638. Further, statistical analysis, like other expert testimony, must be "both relevant and reliable," and "[d]etermining the validity and value of statistical evidence is firmly within the discretion of the district court." Id. at 641.

Although this Court has not spoken on the quantum of evidence sufficient to prove discriminatory impact as a matter of law, cases from other circuits shed some light on the subject. In Chavez, the Seventh Circuit affirmed summary judgment in favor of the state-police defendants in a class action alleging that the officers "utilize[d] impermissible racial classifications in determining whom to stop, detain, and search." 251 F.3d at 635. The plaintiffs had obtained records of citations and police field reports, which were used to document traffic stops, and had compared the race of the targets with various population benchmarks, including the Census and the Nationwide Personal Transportation Survey. Id. at 642-44. After holding that the plaintiffs could utilize statistics to show discriminatory effect, id. at 640, the court independently reviewed the proffered statistics and found them inadequate as a matter of law to carry the plaintiffs' burden, id. at 641, 645. As relevant here, the court cited the absence of evidence of the total number of field reports prepared (or even the number analyzed by the plaintiffs) and the lack of an adequate population benchmark against which to measure whether the plaintiffs' racial groups were stopped at a rate disproportionate to their representation in the driving population. Id. at 643-44.

Similarly, in a case with facts closer to those presented here, the First Circuit in Anderson affirmed a bench-trial judgment in favor of the city defendant in an equal protection challenge to a school-rezoning plan. 375 F.3d at 74, 79. To establish the discriminatory effect of the rezoning plan, the plaintiffs relied exclusively on the testimony of a single witness. Id. at 88. The witness, who lacked formal training in statistical analysis, "testified that she reviewed admissions data from `every school in the city,' [but] she only presented data for the 2002-03 admission rounds for one class in each of three schools." Id. The witness prepared charts for each of these schools, comparing the racial demographics of students admitted under the new plan with those of students who would have been eligible for admission under an alternative plan. Id. at 88-89. These charts showed that "in the three elementary schools—out of the 85 or so in the [public school] system—a total of twenty white students . . . were not admitted under the actual [plan]." Id. at 89. Further, the plaintiffs declined to "engage in any systemwide analysis of the racial impact" of the plan, resting instead on the "individual examples of the racial effect" evident in the witness's charts. Id. The First Circuit held this evidence insufficient to show discriminatory effect—and, as a corollary, discriminatory purpose inferable from a gross statistical disparity. Id.

Here, the district court held that Lewis's proffered evidence failed to establish that Option 2f worked a discriminatory effect on nonwhite students in the East Ascension feeder zone by funneling a disproportionate number of at-risk students to their schools. Even accepting the undisputed evidence that the percentage of at-risk students in the East Ascension feeder zone increased after the implementation of Option 2f, the court found that this was insufficient, standing alone, to carry Lewis's burden. The court found that the objective evidence of student performance adduced at trial—ACT scores, SPS, and AP classes and exam results—was unpersuasive. Lewis only offered average ACT scores for a single year; although the scores placed East Ascension 0.1 point below the state average, 0.9 point below St. Amant, and 1.9 points below Dutchtown, these results were neither broadly representative of student performance nor relevant to the educational experiences of students in the East Ascension feeder zone's primary and middle schools. East Ascension High School's SPS had "gradually increased since the implementation of Option 2f," and although it was outpaced by Dutchtown's and St. Amant's SPS—by 28.1 points and 14.5 points, respectively—"Lewis failed to introduce evidence to establish that these differences are statistically significant, or that such differences are the result of unequal educational opportunities[.]" The AP scores were similarly unavailing: Lewis presented evidence of inferior performance by East Ascension High School students in one academic year, but he again failed to establish statistical significance. And, as with the ACT scores, the SPS and AP performance related only to East Ascension High School and not its feeders.

Finally, the court rejected the opinion of Lewis's expert, Dr. Percy Bates, as "meaningless." Although Dr. Bates was qualified as "an expert on the impact of a disproportionate number of at-risk students on an academic environment," he based his expert report solely on "the general research findings of other experts, student performance scores from 2006 and 2007, iLEAP test scores from 2006 and 2007, and Gautreau's projections."22 He claimed that his opinion was confirmed—and, indeed, strengthened—by the evidence he observed at trial, but he conceded that he had not considered any post-Option 2f data in rendering his opinion in the first instance. In particular, he acknowledged that he had not researched the quality of instruction or the course offerings in the East Ascension schools relative to their counterparts in the other feeder zones, he had not interviewed Lewis's children, and he had not done any calculations of the actual effect of Option 2f on the at-risk population. As for Dr. Bates's "research findings in other districts" and his consideration of "the general research findings of other experts," the court noted that this research could be "instructive," but "his failure to conduct an independent analysis in this case renders his opinion meaningless."

Lewis essentially makes two arguments on appeal. First, he contends that the objective evidence of student performance he presented at trial, coupled with Dr. Bates's expert testimony, proved as a matter of law that Option 2f's funneling caused a disproportionate adverse effect on the nonwhite population in the East Ascension feeder zone. Second, he asserts that the district court committed legal error by faulting him for failing to prove discriminatory purpose, despite the court declining to reach that issue in the first instance.

We find that Lewis failed to prove as a matter of law that Option 2f's funneling feature had a racially discriminatory effect. Lewis's statistical evidence is stronger than that offered in Anderson, as it at least offers a glance at the system-wide effects of Option 2f, but it suffers from many of the same flaws identified in Chavez (e.g., nonrepresentativity and difficulty isolating the operative factor). Many of the statistics are limited in scope (e.g., one year of ACT and AP scores), and those that are not (e.g., SPS) do not clearly support Lewis's theory.23 In addition, the statistical evidence of at-risk-population figures is only inferentially related, at best, to the conditions at the East Ascension feeder schools. Importantly, the district court observed that Lewis offered no evidence of statistical significance at trial,24 and he makes no colorable argument to the contrary on appeal—nor, for that matter, does he cite any case law in support of his contention that his evidence proved discriminatory impact as a matter of law. Moreover, we agree with the district court that the expert testimony of Dr. Bates was not specific enough to establish discriminatory impact. Dr. Bates based his conclusions on general research findings from other school districts and the findings of other experts, and failed to evaluate the specific impact of Option 2f on the non-white population in the East Ascension feeder zone. This general evidence is insufficient to establish discriminatory impact as a matter of law.

Lewis's claim of legal error is similarly unavailing. It is true that the district court's discussion could be read to suggest that statistical evidence of racial disparities cannot prove discriminatory effect absent evidence of discriminatory purpose. Indeed, while explaining that "evidence of an increase in the percentage of nonwhite and at-risk students at schools in the East Ascension High School zone, without more, is insufficient to establish disparate impact[,]" the district court cited portions of Feeney and Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), that indicate that a violation of equal protection cannot be founded solely on disparate impact. This construction provides the impetus for Lewis's claim that "[t]he `more' referenced by the Trial Court is `discriminatory intent' . . . [and] not additional `disparate impact.'" However, immediately after making this pronouncement, the court proceeded to assess the remainder of Lewis's evidence of discriminatory effect and it ultimately held that Lewis failed to carry his burden to prove a discriminatory impact. Accordingly, viewed in the context of its entire discussion, the district court's legal framework is sound, and we affirm its determination on this dispositive issue.

C. Lewis's Other Claims of Error

Lewis's remaining arguments—that the district court erroneously failed to consider his racial balancing and de jure segregation arguments—relate to claims not properly before us. In the first appeal, this Court held that Lewis's claim of racial balancing or racial gerrymandering was not preserved. Lewis, 662 F.3d at 348 & n. 11. The waiver doctrine barred the district court from considering this claim anew on remand, and it bars this Court's review now. See Lindquist v. City of Pasadena, Tex., 669 F.3d 225, 239 (5th Cir.2012) ("The waiver doctrine holds that an issue that could have been but was not raised on appeal is forfeited and may not be revisited by the district court on remand. The doctrine also prevents us from considering such an issue during a second appeal." (footnote and internal quotation marks omitted)). As for Lewis's de jure segregation claim, Lewis never advanced this theory of relief in the district court, and he correspondingly cannot do so now. See, e.g., Leverette v. Louisville Ladder Co., 183 F.3d 339, 342 (5th Cir.1999) (per curiam).

D. The Appropriate Level of Scrutiny

Although the district court did not announce the level of scrutiny it was applying to Lewis's equal protection claim, it may be inferred from the court's subsidiary rulings that it deemed rational basis review appropriate. When a government action is facially race neutral and there is no proof of either discriminatory purpose or discriminatory effect, that action is subject to rational basis review. See Lewis, 662 F.3d at 348. On rational basis review, the burden is on the challenger to rebut the "strong presumption of validity" accorded the action and prove that the action is not rationally related to a legitimate government purpose. Heller, 509 U.S. at 319-20, 113 S.Ct. 2637. We agree with the district court that rational basis review applies to the funneling aspect of Option 2f and that the plan survives this limited scrutiny. Given that the Board has cited at least one legitimate governmental purpose animating its adoption of Option 2f— alleviating overcrowding in the Dutchtown feeder zone25 —and Lewis has made no effort to "negative every conceivable basis which might support" the Board's action, id. at 320, 113 S.Ct. 2637, we concur in the district court's conclusion that rational basis review is satisfied.

IV. CONCLUSION

For the foregoing reasons, we AFFIRM the district court's judgment.