In the

United States Court of Appeals

For the Seventh Circuit ____________

No. 06-2213

ELEANOR BAYLIE and FRANCES L. SMITH,

Plaintiffs-Appellants,

v.

FEDERAL RESERVE BANK OF CHICAGO,

Defendant-Appellee.

____________

Appeal from the United States District Court for the

Northern District of Illinois, Eastern Division.

No. 98 C 1186—William J. Hibbler, Judge.

____________

ARGUED JANUARY 3, 2007—DECIDED FEBRUARY 14, 2007

____________

Before EASTERBROOK, Chief Judge, and POSNER and

WOOD, Circuit Judges.

EASTERBROOK, Chief Judge. This appeal presents the

tail end of a class action in which employees accused the

Federal Reserve Bank of Chicago of race, sex, and age

discrimination. Four years ago the district court decertified the class and allowed employees to pursue individual claims. Only two remain for resolution on this appeal.

The district judge concluded that these two had not

established even a prima facie case of discrimination and

granted summary judgment to the Bank.
2 No. 06-2213

Although only two employees’ claims remain for decision,

their brief proceeds largely as if a class continued to seek

systemic relief. Plaintiffs rely heavily on the report of an

expert who concluded that black employees were less

likely to be promoted than white employees. They maintain that this report is enough by itself to require a trial.

Going to the opposite extreme, the Bank contends that

statistical evidence is never relevant outside a class

action or a suit by a public agency on behalf of employees

as a group. Both of these positions misunderstand the

role of statistical inference.

Most contentions in litigation are empirical rather than

axiomatic. Propositions of fact are arrived at by inductive

rather than deductive means. All inferences are statistical—whether implicitly or explicitly does not matter. A

plaintiff who accuses Supervisor X of discrimination

because he never has promoted a black person, and often

says disparaging things about black workers, is drawing

a statistical inference: that if X has been indifferent to

race, then selections from the pool of employees eligible

for promotion would have included some black workers,

and in particular would have included the plaintiff.

Likewise the proposition “9 of 10 people exposed to sarin

die within 20 minutes, so sarin is deadly” is a statistical

inference, one so obvious that no expert is needed to

show causation. But the inference often may be elusive,

and then someone trained in the analysis of numbers

will help.

Professional statistics is a rigorous means to analyze

large numbers of events and inquire whether what appear to be patterns really are the result of chance (and, if

not, which variables are associated with which outcomes).

Suppose we know that 20,000 of 100,000 persons exposed

to high dosage x-rays eventually develop cancer, and that

19,500 of 100,000 persons not so exposed develop cancer.

Should we attribute the apparent excess risk of 500
No. 06-2213 3

cancers to the x-ray, or might it have some other cause? Is

this excess risk real or an illusion caused by errors in

measurement and analysis, the sort of variance that

may occur by chance? A statistical analysis may be able

to answer these questions—and, if the answer is yes, the

knowledge that high-dosage x-rays increase the risk of

cancer may inform a decision whether the benefits of

the procedure are worth the extra risk. But it will not

tell us whether a given person who develops cancer did

so because of the x-ray; only 2.5% of cancers can be attributed to the radiation, so 97.5% of all cancers, even

among persons exposed to high-dosage x-rays, have other

causes. This is the sense in which statistics are more

helpful in a pattern-or-practice case, where a judge will

be asked to direct the employer to change how it makes

hiring or promotion decisions.

In individual cases, studies of probabilities are less

helpful. Suppose 1,000 employees apply for 100 promotions; 150 of the workers are black and 850 white. If all

are equally qualified and the employer ignores race, then

85 white workers and 15 black workers will be promoted,

plus or minus some variation that can be chalked up to

chance. Suppose only 10 black workers are promoted. Is

that the result of discrimination or chance? Econometric

analysis (an application of statistical techniques) may

suggest the answer by taking into account both other

potentially explanatory variables and the rate of random variance. See Mister v. Illinois Central Gulf R.R.,

832 F.2d 1427 (7th Cir. 1987); Federal Judicial Center,

Reference Manual on Scientific Evidence 83-227 (2d ed.

2000); Paul Meier, Jerome Sacks & Sandy L. Zabell, What

Happened in Hazelwood: Statistics, Employment Discrimination, and the 80% Rule, 1984 Am. Bar Foundation

Research J. 139, 158-70; Thomas J. Campbell, Regression

Analysis in Title VII Cases, 36 Stan. L. Rev. 1299 (1984).
4 No. 06-2213

When the answer is positive (discrimination occurred;

the conclusion is statistically significant) it cannot reveal

with certainty whether any given person suffered. In

this example, 150 black workers applied for promotion;

10 were promoted and the other 140 were not. But for

discrimination, 15 would have been promoted and 135 not.

Which of the 140 non-promoted employees would have

received the other 5 promotions? The statistical analysis

does not tell us—and in civil litigation, where the plaintiff’s burden is to show more likely than not that he was

harmed by a legal wrong, data of this kind will not get

a worker over that threshold.

Statistical analysis is relevant in the technical sense

that it “has a tendency to make the existence of [a material] fact . . . more probable or less probable than it would

be without the evidence.” Fed. R. Evid. 401. But data

showing a small increase in the probability of discrimination cannot by itself get a plaintiff over the more-likelythan-not threshold; it must be coupled with other evidence,

which does most of the work. A disappointed worker

could ask for damages measured by the lost opportunity:

each of the 140 disappointed workers might receive as

damages 5/140 of the extra income enjoyed by those who

received promotions. That’s the loss-of-a-chance measure

of damages. See Doll v. Brown, 75 F.3d 1200 (7th Cir.

1996). But it is more suited to class-wide litigation, and

our two plaintiffs have not requested this remedy.

What statistics did these plaintiffs offer—the kind that

permit a sound inference in an individual case (our

examples of Supervisor X and exposure to sarin) or the

kind that may support class-wide equitable relief but are

only marginally relevant when an individual plaintiff

seeks an award of damages? Plaintiffs’ expert analyzed all

non-managerial workers at the Bank between 1995 and

2000. Workers as a whole enjoyed a probability of about

0.25 of being promoted to a higher pay grade each year
No. 06-2213 5

(stated otherwise, the average worker was promoted once

every four years). Coefficients in an econometric regression

implied that black workers had about a 0.20 probability

and white workers about a 0.27 probability, and after

controlling for other variables the expert concluded that

5/7 of this difference (or a 0.05 chance of promotion each

year) was unaccounted for by any hypothesis other than

race. In other words, the average white worker received

an extra promotion every 20th year compared with the

average black worker, holding constant factors (such as

education) other than race. The Bank’s experts questioned

whether this result is statistically significant (that is,

whether the difference is a result of chance rather than

race) and whether it is meaningful for most of the workers.

It turns out that the most frequent “promotion” is from

temporary to full-time work. If the analysis is limited to

persons (such as plaintiffs) already working at the

Bank full time, then black workers are slightly more

likely than white workers to be promoted in any given

year.

Given the consequence of restricting the data set to fulltime workers, this econometric analysis offers our two

plaintiffs no support. Even presented as plaintiffs’ expert

did, rolling the temporary-to-full-time promotions into

the data, the study doesn’t provide plaintiffs with much

assistance. These two plaintiffs applied for several promotions annually. If race affects one promotion every

20 years, and workers seek three promotional opportunities a year, then there is one chance in 60 that a given

application would have been successful if the applicant

were white rather than black. Over many years and

many employees this effect could be substantial—which

is why such analysis is helpful in class actions—but in a

single employee’s case it does very little to get the claim

over the more-likely-than-not threshold. A worker can’t

say simply: “I’ve been here 20 years, so I’m entitled to one
6 No. 06-2213

extra promotion.” All of that time except the most recent

300 days falls outside Title VII’s statute of limitations. See

National Railroad Passenger Corp. v. Morgan, 536 U.S.

101 (2002). Analysis thus must proceed vacancy-byvacancy in an individual case, not career-by-career.

If a plaintiff had evidence suggesting that the probability that race accounted for a given turn-down was (say)

49.8%, then the addition of the statistical analysis would

push the probability past 50%. In other words, the expert’s conclusion in this litigation could serve as a tiebreaker. But first there would have to be a tie—and

plaintiffs’ evidence does not come close to making this

case a tossup that statistics might decide in their favor. Cf.

Sun v. University of Illinois, No. 06-2438 (7th Cir. Jan. 16,

2007), slip op. 23-26 (considering statistical evidence in

an individual case but finding that the data did not

create a material dispute).

Frances Smith began as a staff assistant in 1977 and

after multiple promotions reached the rank of “senior

examiner” in 1994. Smith’s applications for further

advancement have been denied, and her principal argument is that she is no less qualified for promotion than

white “senior examiners” who the Bank did promote to

higher grades (though not different titles; “senior examiner” is the highest in the progression). In addition to

contending that the econometric analysis is enough to

create a jury issue, Smith maintains that the district

judge was too demanding in requiring her to show that

the white employees to whom she compared herself were

comparable in every respect.

The judge may well have asked too much of comparability analysis, see Crawford v. Indiana Harbor Belt R.R.,

461 F.3d 844 (7th Cir. 2006), but that doesn’t matter. The

Bank explained why it passed Smith over: pay grades

higher than Smith’s are awarded only to examiners who
No. 06-2213 7

do substantial field work (that is, examine books in the

banks that the Federal Reserve regulates), and Smith has

declined to accept a position as a full-time field examiner.

Nothing in the record suggests that this explanation is

a lie, so, even if Smith has made out a prima facie case, no

reasonable jury could find the Bank’s explanation to be

a pretext for discrimination. The case is not close; the

statistical study cannot tip the balance.

Eleanor Baylie has worked for the Bank as a secretary

since 1964; her most recent promotion, to a grade 9

position, was in 1988. Since then she has applied for

multiple positions, none of which is secretarial, in grades

10 and above. The positions for which she was passed

over have titles such as “control specialist” and “production

coordinator"; it is impossible to tell from these titles, or

the parties’ briefs, the duties of these positions and

whether Baylie would be competent to perform them.

Baylie asserts that she is at least as well qualified as the

workers who received these promotions, but her brief

contains no details about who received the promotions,

after what process. It does not contain citations to the

portions of the record bearing on her individual claim (as

opposed to the statistical analysis). There is accordingly

no reason to believe that race or sex played a role in the

decisions.

Although, as we observed in Crawford, a district judge

should not insist that the other employees to whom a

plaintiff compares herself be identically situated, there

must be a reasoned basis for thinking the comparator

close enough in material ways so that a reasonable factfinder could think that race (sex, or another covered

attribute) was the difference that the employer perceived. When despite ample opportunity for discovery the

plaintiff makes no serious effort to show that the favored

worker was similarly situated except with respect to race

(sex, and so on), the district judge properly concludes that
8 No. 06-2213

a prima facie case of discrimination has not been established.

So it is here. Baylie’s opening brief does not tell us who

received the promotions she sought or in what respects the

applicants were like (or unlike) her. Her reply brief

devotes one page to that subject, but the effort is too little

and too late. Baylie obviously believes in her own skills,

but employers make comparative rather than absolute

judgments. Because Baylie has not tried to show in the

necessary detail that race rather than an employer’s

honest evaluation of comparative skills accounts for the

decisions, the Bank was entitled to summary judgment

in its favor.

Plaintiffs’ other arguments have been considered but do

not require discussion. The judgment is affirmed.

A true Copy:

Teste: 

 ________________________________

Clerk of the United States Court of

Appeals for the Seventh Circuit 

USCA-02-C-0072—2-14-07