Bayes’s theorem) runs the risk of backlash; the defense
attorney’s fallacy combined with expert Bayesian
instruction may increase guilty verdicts.
Even nonfallacious presentations of statistical evi-
dence pose challenges for jurors, particularly when they
are evaluating low-probability events. Compare DNA
incidence rates presented as 0.1 out of 10,000, 1 out of
100,000, or 2 out of 200,000. Mathematically, these
rates are identical, but psychologically, they differ;
jurors are more likely to find for the defendant in the lat-
ter two cases. Why? The first, fractional incidence rate
contains no cues that people other than the defendant
might match the DNA. Each of the other rates contains
at least one exemplar within it, which encourages jurors
to think about other people who might match. This
effect may rest in part on the size of a broader reference
group; it is easier to generate exemplars with an inci-
dence rate of 1 in 100,000 when considering a city of
500,000 people than when considering a town of 500.
Jurors’ task becomes more difficult when they face
both a random match probability (RMP) (e.g., there is
a 1 in 1 million chance that the defendant’s DNA sam-
ple would match that of the perpetrator if the defendant
is innocent) and a laboratory error rate (LE) (e.g., the
laboratory makes a mistake in 2 of every 100 cases).
The probability that a match occurred due either to
chance or to lab error is roughly 2 in 100. Yet jurors
who hear the separate RMP and LE (as recommended
by the National Research Council) convict the defen-
dant as often as those who hear only the much more
incriminating RMP.
Why do jurors fail in combining an RMP and an LE?
Traditional explanations point to various logical or math-
ematical errors. Another explanation suggests that jurors’
interpretation of statistical evidence necessarily reflects
their expectancies about such data. Consider jurors who
receive extremely small RMP estimates (1 in a billion)
and comparatively large LE estimates (2 in 100), com-
pared with those who receive comparatively large RMP
estimates (2 in 100) and extremely small LE estimates
(1 in a billion). Logical (e.g., we are more convinced by
more vivid evidence, like 1 in a billion) or mathematical
(e.g., we average probabilities) explanations for juror
errors make identical predictions in the two cases. But
instead, mock jurors are more likely to convict in the
large RMP paired with small LE condition. Similarly,
they are more likely to convict when presented with
extremely small LE estimates and no RMP estimate than
when presented with only an extremely small RMP esti-
mate and no LE estimate. This difference may reflectjurors’ preexisting expectancies that the likelihood of a
random match is extremely small and that of laboratory
error is relatively large.
Some forms of statistical evidence (e.g., bullet lead
analysis) illustrate that jurors must consider not just the
reliability of statistical evidence but also its diagnostic-
ity (usefulness). The value of a forensic match (e.g., the
defendant’s DNA profile is the same as that of blood
found at the crime scene) depends on reliability of the
evidence (did the laboratory correctly perform the test?)
and also its diagnosticity (could the match be a coinci-
dence?). One study gave the same information about hit
rate and false-positive rate to all jurors. It varied a third
statistical piece of information: the diagnostic value of
the evidence. Some jurors learned that all sample bullets
taken from the defendant matched the composition of
the murder bullet, while no bullets taken from a com-
munity sample matched (strong diagnostic evidence).
Others learned that the matching rate for the defendant’s
bullets was the same as that for bullets taken from a
community sample (worthless diagnostic evidence).
Jurors who received the strong diagnostic evidence were
more likely to believe the defendant guilty. However,
this effect held only for mock jurors who were relatively
confident in their ability to draw conclusions from
numerical data. Jurors who were less confident did not
differ across conditions. Furthermore, jurors who heard
the worthless diagnostic evidence tended to give it some
weight before they deliberated; deliberation eliminated
the effect.How Jurors Combine
Statistical Evidence With
Nonstatistical Evidence
How do jurors combine numerous pieces of evidence
(not necessarily statistical) to make decisions? Both
mathematical (e.g., probability theory) and explana-
tion-based (e.g., story model) approaches have been
proposed. Research specifically examining the use of
statistical evidence has generally followed a mathemat-
ical approach and has compared jurors’ probabilities
(typically the probability that the defendant committed
the crime) with probabilities calculated using Bayes’s
theorem.
Bayes’s theorem prescribes how a decision maker
should combine statistical evidence with prior evi-
dence. Prior odds (the defendant’s odds of guilt, based
on all previously presented evidence) are multiplied
by the likelihood ratio (the probability that the newStatistical Information, Impact on Juries——— 763S-Cutler (Encyc)-45463.qxd 11/18/2007 12:44 PM Page 763