according to Dr. Braddock, it is a common measurement used in his
field for identifying a student's SES[fn24a] (see id. at 1380),
and the State Defendants' expert, Dr. Rindskopf, used the same
measurement. We conclude, therefore, that though participation in
a subsidized lunch program is an imprecise measure of a student's
SES, it is not an inappropriate measure of that factor.
Similarly, we recognize that the regression analysis did not
control for all of the variables that contribute to a student's
academic performance. Dr. Braddock acknowledged, in fact, that
his study only accounted for 46.5% of the total variance, leaving
53.5% totally unexplained. The failure of a regression analysis
to account for every conceivable variable might render it less
probative than it otherwise might be, however the inclusion of
"the major factors" is sufficient for the analysis to be
acceptable as evidence of discrimination. Bazemore v. Friday,
478 U.S. 385, 400, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986); see
Bickerstaff v. Vassar College, 196 F.3d 435, 448-50 (2d Cir.
1999) (citing Koger v. Reno, 98 F.3d 631, 637 (D.C.Cir. 1996)),
cert. denied, ___ U.S. ___, 120 S.Ct. 2688, 147 L.Ed.2d 960
(2000). Moreover, we believe that Dr. Braddock's study was as
complete as possible, given the data which was available. (See
1993 Trial Tr. at 2146 (Steinberg).) Although there are
undoubtedly a whole range of variables that might affect a
student's academic performance, cf. People Who Care, 111 F.3d
at 537 ("The social scientific literature on educational
achievement identifies a number of other variables besides
poverty and discrimination that explain differences in scholastic
achievement, such as the educational attainments of the student's
parents and the extent of their involvement in their children's
schooling.") (citing David J. Armor, Forced Justice: School
Desegregation and the Law 96, 98; James S. Coleman, Equality of
Educational Opportunity 302 (1966)); (1993 Trial Tr. at 70-71,
106-09, 191-92 (Batista), 2131-32 (Steinberg)), Dr. Braddock
seems to have included in his analysis all of the factors that
were "measurable."[fn25a] Bazemore, 478 U.S. at 400, 106 S.Ct.
3000. Overall, therefore, the imprecision in some of Dr.
Braddock's variables, and the failure to consider every factor
that influences student achievement, weakens the force of Dr.
Braddock's conclusion, but does not render it totally
Third, Dr. Rindskopf's testimony fails to undermine our
confidence in Dr. Braddock's analysis. To the contrary, Dr.
Rindskopf's analysis actually confirms that conclusion. Until
Dr. Rindskopf controlled for census tract (which, as explained
below, improperly skewed his data), his results were consistent
with those of Dr. Braddock. Even using Dr. Rindskopf's
alternative methodology for controlling for variables, a racial
disparity was observed, when controlling for LEP status, special
education status, and participation in a subsidized lunch
We place little weight on the fact that the disparity
disappeared once census tract was used as a control, because the
use of that control variable reduced the sample size to such a
large extent that the resulting conclusions are not statistically
significant. Dr. Rindskopf's data accounts for approximately
800-1,000 students, out of a total of 12 to 13 thousand students
who took the exams in question. (See Trial Tr. at 2026-27
(Rindskopf).) In other words, his analysis only considered 8% of
the total population under consideration. (See id.) See Pollis
v. New Sch. for Social Research, 132 F.3d 115, 121-22 (2d Cir.
1997) ("The smaller the sample, the greater the likelihood that
an observed pattern is attributable to other factors and
accordingly the less persuasive the inference . . . to be drawn
from it.") (citing Mayor of Philadelphia v. Educational Equality
League, 415 U.S. 605, 621, 94 S.Ct. 1323, 39 L.Ed.2d 630 (1974);
Haskell v. Kaman Corp., 743 F.2d 113, 121 (2d Cir. 1984);
Coble v. Hot Springs Sch. Dist. No. 6, 682 F.2d 721, 733-34
(8th Cir. 1982)).[fn26a] Moreover, because the six census tracts
he examined were plainly not representative of the district as a
whole,[fn27a] the results observed for that 8% of the population
cannot be generalized as an explanation for the whole population.
Nor can it be shown that the census tract is a factor that
operates independently of race. (see Trial Tr. at 2141
(Steinberg)), especially in a city like Yonkers where unlawful
segregation permeated the low-income housing market for years.