Can statistics alone prove
By Marc W. Pearce, JD, PhD, and Kimberly S. Dellapaolera • University of Nebraska–Lincoln
The case In re Navy Chaplaincy involves a group of current and former non-liturgical Protestant chaplains in the
U.S. Navy who sued the Department of the Navy, alleging that
it discriminated against them on the basis of their religion
by using quotas and religious preferences in their promotion
decisions. The chaplains argued that the Navy’s promotion
practices discriminated against candidates who had different
faiths than the chaplains on the promotion selection board
or the Chief of Chaplains, who served as the selection board
president. Specifically, the claimants said that the small size of
the selection board, combined with the board’s secret voting
process, led to more promotions for Catholics and liturgical
Protestants than for non-liturgical Christians.
To attempt to prove that the Navy’s promotion practices
were applied unfairly, the chaplains presented evidence showing
that the difference between the 83. 3 percent promotion rate for
candidates of the same denomination as the chief of chaplains
and the 73. 3 percent promotion rate for candidates of different
denominations was statistically significant.
The Court of Appeals rejected the chaplains’ claim for two
reasons. First, the court observed that the magnitude of the
difference in promotion rates “does not remotely approach the
stark character of the disparities in Gomillion or Yick Wo,” two
precedents that set the threshold for allowing statistical impact
alone to establish an equal protection claim. Second, the court
criticized the chaplains’ statistical methodology, stating:
“Assuming arguendo that the methodology for determining
statistical significance is reasonable, the finding does little
for our analysis. ‘Correlation is not causation.’ Statistical
significance, assuming it has been shown, indicates only a low
probability for one possible cause of the alleged disparities
— random chance. The chaplains have made no attempt to
control for potential confounding factors, such as promotion
ratings, education, or time in service. Thus the label ‘statistically
significant’ does nothing to elevate [the chaplains’] figures into
the realm of Yick Wo or Gomillion.”
On Oct. 6, the U.S. Supreme Court denied the chaplains’
petition to review this decision. Thus, it stands as the final word
on the lack of sufficiency of the chaplains’ statistical proof.
In re Navy Chaplaincy provides a potent reminder about
the difference between the thresholds for statistically and
legally meaningful empirical findings. It is well-established
that the magnitude of a relevant difference, and not merely its
statistical significance, should be considered when determining
whether a plaintiff has met his or her burden of proof (e.g.,
Bregant & Robennolt, 2012). Courts do recognize that the
magnitude of the difference in treatment of two groups
can be so great that the only plausible explanation for the
difference is discrimination. For example, in Yick Wo, a city
board denied licenses to 100 percent of all Chinese applicants,
but denied only one of 80 applications from other applicants.
In Gomillion, all but five African-American voters — but no
white voters — were excluded from a voting district. When
the magnitude is not so great, however, parties must do more
than establish a statistically significant disparity: The statistics
must be supplemented with other evidence showing intent to
It is also well-established that statistical evidence can be
proof of discrimination if major confounding factors are
accounted for. In Bazemore v. Friday (1986), the Supreme Court
explained that although the omission of some variables from a
regression analysis may make the analysis less probative than it
might otherwise be, claimants “need not prove discrimination
with scientific certainty,” but rather by a preponderance of the
evidence taken as a whole. The chaplains’ failure to account for
major confounds, combined with their failure to provide other
evidence of discrimination, doomed their case. n
“Judicial Notebook” is a project of APA Div. 9 (Society for the
Psychological Study of Social Issues).
Bazemore v. Friday, 478 U.S. 385 (1986).
Bregant, J. & Robennolt, J. K., Statistical significance
in court. Monitor on Psychology. 2012. 43 ( 1): 28.
Gomillion v. Lightfoot, 364 U.S. 339 (1960).
In re Navy Chaplaincy, 738 F.3d 425 (D.C. Cir. 2013).
Yick Wo v. Hopkins, 118 U.S. 356 (1886).