 United States Court of Appeals
         FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued November 6, 2013           Decided December 27, 2013

                       No. 13-5071

                IN RE: NAVY CHAPLAINCY,

      CHAPLAINCY OF FULL GOSPEL CHURCHES, ET AL.,
                     APPELLANTS

                             v.

               UNITED STATES NAVY, ET AL.,
                       APPELLEES


        Appeal from the United States District Court
                for the District of Columbia
                    (No. 1:07-mc-00269)


     Arthur A. Schulcz Sr., argued the cause and filed the
briefs for appellants.

    Sushma Soni, Attorney, U.S. Department of Justice,
argued the cause for appellees. With her on the brief were
Stuart F. Delery, Assistant Attorney General, Ronald C.
Machen Jr., U.S. Attorney, and Marleigh D. Dover, Attorney.

   Before: TATEL and KAVANAUGH, Circuit Judges, and
WILLIAMS, Senior Circuit Judge.
                              2

   Opinion for the Court filed by Senior Circuit Judge
WILLIAMS.

     WILLIAMS, Senior Circuit Judge: Plaintiffs, whom we’ll
call simply the chaplains, are a group of current and former
officers in the Navy Chaplain Corps who identify themselves
as non-liturgical Christians, plus two chaplain-endorsing
agencies. They sued in district court, claiming (among other
things) that several of the Navy’s policies for promoting
chaplains prefer Catholics and liturgical Protestants at the
expense of various non-liturgical denominations. The basic
argument is that the policies amount to disparate treatment of
the non-liturgical chaplains, violating the equal protection
component of the Fifth Amendment and the Establishment
Clause of the First Amendment.

     The case has already been before this court several times.
See In re Navy Chaplaincy, 697 F.3d 1171 (D.C. Cir. 2012);
In re Navy Chaplaincy, 534 F.3d 756 (D.C. Cir. 2008);
Chaplaincy of Full Gospel Churches v. England, 454 F.3d
290 (D.C. Cir. 2006). The judgment now on review is that of
the district court denying plaintiffs’ motion for a preliminary
injunction against the Navy’s use of the challenged practices.
In re Navy Chaplaincy, 928 F. Supp. 2d 26 (D.D.C. 2013).
The district court reviewed the statistical evidence offered by
the plaintiffs to show inter-denominational discrimination, and
found it wanting. We affirm.


                            * * *

    The Navy uses “selection boards” to choose officers for
promotion. See 10 U.S.C. § 611(a). By law, such boards
must have at least five members. 10 U.S.C. § 612(a)(1).
Except in certain circumstances not at issue here, at least one
member of a selection board for a competitive category—
                               3

here, the Chaplain Corps—must be from that competitive
category. 10 U.S.C. § 612(a)(2)(A). Selection boards for
chaplains before fiscal year 2003 consisted of five or more
members, at least one of whom was not a chaplain. Under a
change in Navy regulation, boards for fiscal year 2003 and
thereafter are composed of seven officers, two of whom are
chaplains “nominated without regard to religious affiliation.”
SECNAVINST 1401.3A, Encl. (1), ¶ 1.c.(1)(f). Either the
Chief of Chaplains or one of his two deputies serves as
selection board president.        According to a Defense
Department Inspector General report cited by plaintiffs,
“sleeves” hide the board members’ hands as they depress
buttons reflecting their votes, making them secret ballots.
According to the chaplains, the boards take an initial secret
vote and then the board president recommends two score cut-
offs: candidates above the higher score are treated as clearly
deserving promotion, and ones below the lower score are
treated as deserving no further consideration. Candidates who
fall between the two are re-evaluated for the remaining
available promotions.

     The chaplains asked the district court to enjoin three
current Navy selection board policies—(1) staffing the seven-
member selection boards with two chaplains, (2) enabling
members to keep their votes secret via the “sleeves,” and (3)
allowing the Chief of Chaplains or his deputy to serve as the
selection board president—that they claim result in disparate
treatment of the non-liturgical candidates. Plaintiffs’ (July 22,
2011) Motion for a Preliminary Injunction 1. The disparate
treatment, they say, is shown by various statistical data, which
we’ll consider shortly.

    The chaplains’ theory is that a candidate is more likely to
be promoted if he or she shares a religious denomination with
one of the chaplains on the selection board, or with the Chief
of Chaplains. The bottom line is an advantage in promotion
                               4

rates for Catholics and liturgical Protestants over non-
liturgical Christians. The chaplains posit that the small board
size, combined with secret votes, enables each board’s
chaplains to ensure that a particular candidate will not be
promoted, thus increasing the odds for their preferred (and
discriminatory) results.

     Pending resolution of their summary judgment motion,
the chaplains asked the district court for a preliminary
injunction halting the challenged policies. The district court
denied the request, but we vacated the denial and remanded
for the district court to clarify its reasoning on the chaplains’
likelihood of success on the merits; we were unsure whether
the district court viewed the insufficiency of the chaplains’
claims to be legal or factual. See In re Navy Chaplaincy, 697
F.3d at 1180. On remand, the district court concluded that the
chaplains were unlikely to succeed on the merits of either
claim because the statistics they offered failed to show any
discriminatory intent behind the challenged policies or the
resulting outcomes. In re Navy Chaplaincy, 928 F. Supp. 2d
at 36-37.

     The chaplains appeal to us again, claiming that the court
erred in requiring a showing of intent to prove either an equal
protection or establishment clause violation. We find that the
chaplains’ equal protection attack on the Navy’s facially
neutral policy could prevail only if they showed a likelihood
of success in proving an intent to discriminate (which they
have not shown) or the lack of a rational basis for the policies
(which they have not claimed). As to the Establishment
Clause, the chaplains have not shown a likelihood of success
under any test that they have asked the court to apply. We
therefore affirm the district court’s denial of the preliminary
injunction.
                                5

                             * * *

     In order to determine whether to issue a preliminary
injunction, the district court applies four familiar criteria: (1)
likelihood of success on the merits; (2) irreparable injury; (3)
lack of substantial injury to other parties; and (4) furthering
the public interest. Chaplaincy of Full Gospel Churches, 454
F.3d at 297. We have already found an absence of any error
in the district court’s analysis of the last three factors, and
have made clear that the only unresolved issue is whether the
chaplains have shown a likelihood of success on the merits.
In re Navy Chaplaincy, 697 F.3d at 1179. The chaplains in
effect argue that the district court used improper legal
standards on that issue. But the record and the district court’s
findings allow us to resolve the question of likelihood of
success on the merits on our own, and we accordingly do so.
See Chaplaincy of Full Gospel Churches, 454 F.3d at 297
(legal conclusions upon which denial of preliminary
injunction relies are reviewable de novo).

     Equal protection. The chaplains argue that the three
challenged policies result in disparate treatment of non-
liturgical chaplains. But none of the challenged practices on
its face prefers any religious denomination. The regulation
behind the practice of staffing boards with two chaplains
explicitly requires denominational neutrality. “Chaplain
Corps board members shall be nominated without regard to
religious affiliation.” SECNAVINST 1401.3A Encl. (1),
¶ 1.c.(1)(f) (Dec. 20, 2005). Thus, even if one of the
chaplains always serves as board president (as the chaplains
allege), the board president, necessarily a board member, must
be a person chosen for the board without regard to religious
affiliation. Finally, the practice of secret voting is neutral on
its face. All three policies together, then, are facially neutral
with respect to denomination.
                              6

     The chaplains nonetheless claim that the policies either
were adopted with discriminatory intent or have been applied
in such a manner as to favor denominations other than the
non-liturgical ones. As the district court found, the chaplains
have presented no evidence of discriminatory intent in the
policies’ enactment. Nor have they shown a current pattern of
disparate     outcomes      from     which     unconstitutional
discriminatory intent could be inferred under the prevailing
understanding of equal protection. For such claims, “Absent a
pattern as stark as that in Gomillion or Yick Wo, impact alone
is not determinative.” Village of Arlington Heights v.
Metropolitan Housing Development Corp., 429 U.S. 252, 266
(1977) (citing Gomillion v. Lightfoot, 364 U.S. 339 (1960);
Yick Wo v. Hopkins, 118 U.S. 356 (1886)). The district court
found, at best, only a 10% advantage in promotion rates for
officers of the same denomination as the Chief of Chaplains
(the difference between a 73.3% promotion rate for candidates
of different denominations and an 83.3% rate for candidates
of the same denomination). In re Navy Chaplaincy, 928 F.
Supp. 2d at 37.

     There is some internal contradiction in the chaplains’
position on these figures. Their brief states that they cover
promotions in the period 2003-2012, when the current
procedures were in place (Appellants’ Br. at 15), but it cites
Joint Appendix (“J.A.”) 1107, an affidavit that situates the
data in 1981-2000, before the proportion of chaplains on the
selection boards was decreased. Giving the chaplains the
benefit of the doubt, we assume the data apply to the later
period, the one governed by the rules they seek to enjoin. The
chaplains’ only efforts to show a larger disparity rely on data
for selections occurring before the 2003 changes.

     The district court correctly noted that the disparity
between 73.3% and 83.3% does not remotely approach the
stark character of the disparities in Gomillion or Yick Wo. Id.
                               7

     For reinforcement, plaintiffs cite their expert’s opinion
that this disparity is statistically significant. The record does
not explain the reasoning behind the choice of one set of
statistical tests for significance over another (e.g., a “simple
binomial” test versus a standard test of the differences in
proportions), or demonstrate the actual calculations. See, e.g.,
Appellants’ Br. at 15. But assuming arguendo that the
methodology for determining statistical significance is
reasonable, the finding does little for our analysis.
“Correlation is not causation.” Tagatz v. Marquette Univ.,
861 F.2d 1040, 1044 (7th Cir. 1988). 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. (That statement must be
qualified by recognition that time in service is broadly
reflected in occasional references to whether the candidates
were “in zone” (i.e., were within a group of a predetermined
number of the most senior officers who had not previously
been considered for promotion to a given grade) or “above
zone” (i.e., had previously been considered for promotion to a
given grade). See, e.g., J.A. 1468-70 (chaplains’ tables noting
comparisons of in zone candidates, and of in zone and above
zone candidates); J.A. 1289-92 (Navy employee affidavit
describing the zone compositions).)              Thus the label
“statistically significant” does nothing to elevate plaintiffs’
figures into the realm of Yick Wo or Gomillion.

     Given facially neutral policies and no showing of intent
to discriminate, the chaplains’ equal protection attack on the
Navy’s specific policies could succeed only with an argument
that the policies lack a rational basis. See Washington v.
Davis, 426 U.S. 229, 242 (1976); United States v. Thompson,
27 F.3d 671, 678 (D.C. Cir. 1994). The chaplains attempt no
                               8

such argument. So we agree with the district court that they
have not shown the requisite likelihood of success.

     Establishment. The chaplains say that under Larson v.
Valente, 456 U.S. 228 (1982), we must subject the challenged
selection methods to strict scrutiny on the ground that they
“grant[] a denominational preference,” id. at 246, or, failing
that, find that they run afoul of Lemon v. Kurtzman, 403 U.S.
602 (1971), notably the element of Lemon now generally
described as the “endorsement” test.

      The chaplains’ proposed analytical sequence matches the
structure laid down by the Supreme Court for measures
assailed as denominational preferences. “Larson teaches that,
when it is claimed that a denominational preference exists, the
initial inquiry is whether the law facially differentiates among
religions. If no such facial preference exists, we proceed to
apply the customary three-pronged Establishment Clause
inquiry derived from Lemon v. Kurtzman, 403 U.S. 602
(1971).” Hernandez v. Comm’r of Internal Revenue, 490 U.S.
680, 695 (1989). As the challenged policies are facially
neutral, Larson doesn’t trigger strict scrutiny, and we proceed
to Lemon.

     Lemon presents us again with a multipart test: “In order to
pass constitutional muster under the Lemon test, laws and
government practices involving religion must: (1) have a
secular legislative purpose; (2) have a principal or primary
effect that neither advances nor inhibits religion; and (3) not
result in excessive entanglement with religion or religious
institutions.” Bonham v. D.C. Library Admin., 989 F.2d 1242,
1244 (D.C. Cir. 1993) (citing Lemon, 403 U.S. at 612-13).
The chaplains naturally do not challenge the chaplaincy
program as a whole; the Second Circuit has found it
compatible with the Establishment Clause, in an opinion that
does not precisely track Lemon. Katcoff v. Marsh, 755 F.2d
                               9

223 (2d Cir. 1985). Nor do the chaplains claim that the first
or third element of Lemon cuts against the disputed selection
procedures.

     Rather they claim that the challenged policies have the
“effect” of advancing particular denominations, which at least
in this context entails application of the “endorsement” test.
Bonham, 989 F.2d at 1245. That in turn takes us to the
question of whether the selection policies appear to endorse
religion in the eyes of a “reasonable observer,” who “‘must be
deemed aware’ of the ‘history and context’ underlying a
challenged program.” Zelman v. Simmons-Harris, 536 U.S.
639, 655 (2002) (quoting Good News Club v. Milford Central
School, 533 U.S. 98 (2001)). As the policies themselves are
facially neutral, the chaplains under this theory argue in effect
that a reasonable observer, contemplating the results of the
policies (as gathered in the chaplains’ statistical evidence),
would infer that the government had as a practical matter
endorsed the liturgical denominations.

     Assuming arguendo that it is proper to see the
“reasonable observer” as a hypothetical person reviewing an
array of statistics (the observer is already a judicial construct
rather than a human being), the figures in this case would not
lead him to perceive endorsement. Here the plaintiffs’
statistics fail to show government endorsement of particular
religions under the reasonable observer test for the same
reason that, in the equal protection context, they failed to
show intentional discrimination paralleling that of Gomillion
or Yick Wo. The only new wrinkle, perhaps, is that we must
impute to the reasonable observer either enough grasp of
statistics not to be misled by the assertion of “statistical
significance,” or at least the modesty not to leap to a
conclusion about the data without making an elementary
inquiry on the subject. We feel confident that when
reasonable observers find that the term means only that there
                               10

is little likelihood that the “discrepancy” is due to chance, they
are most unlikely to believe that the policies convey a
message of government endorsement.

     Plaintiffs cite Title VII cases in which we found that
statistically significant “disparities” in such matters as hiring
and pay were enough to support district court findings of
racial discrimination. See, e.g., Berger v. Iron Workers
Reinforced Rodmen Local 201, 843 F.2d 1395 (D.C. Cir.
1988); Segar v. Smith, 738 F.2d 1249, 1277-79, 1286-87
(D.C. Cir. 1984). But in these cases the court found liability
only after being satisfied that the statistical evidence properly
controlled for confounding variables. See, e.g., Berger, 843
F.2d at 1413-21 (reviewing potential non-discriminatory
explanations); id. at 1419 (reasoning that the “entire notion of
employing statistical proof is to eliminate non-discriminatory
causes” of the disparities); Segar, 738 F.2d at 1274-77. Here,
as we observed in the equal protection analysis, the chaplains
point to no serious effort at such controls for any of their
statistical comparisons. Accordingly, even assuming that a
court could properly impute a belief in denominational
favoritism to the reasonable observer simply on the basis of
statistics that might satisfy a plaintiff’s Title VII burden, the
chaplains’ data fail to meet that standard and thus fail to show
a likelihood of success on the merits.

     Finally, the chaplains point to our observation in Bonham
that there is no “de minimis exception to traditional
Establishment Clause analysis.” 989 F.2d at 1245. But the de
minimis defense that we rejected there was a notion that state
actions could be excused, even though a reasonable observer
would have regarded them as endorsing religion, so long as
the action in question had only a trivial impact, for example,
an action affecting “only a single day of the year.” It was,
obviously, not a suggestion that the “reasonable observer”
should be deemed to spot “endorsement” on a bare surmise.
                             11

     The district court’s order denying the chaplains’ motion
for preliminary injunction is therefore

                                   Affirmed.
