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b.
Hypothesis Testing and Likelihood Ratios
Consideration of more than one hypothesis to account for the physical evi-
dence forces the criminalist to think more rigorously and discourages bias
in evaluating the results of analyses. LRs not only allow, but specifically
require the simultaneous evaluation of the competing hypotheses. If the
analyst has been considering alternate causes from the inception of the anal-
ysis, it is natural to continue this comparison using LRs as a tool. This brings
us to a subtle distinction between hypothesis testing and Bayesian statistics.
In classical hypothesis testing, we attempt to falsify the null hypothesis.
Only two outcomes are possible from this predicate. Failing to falsify it, we
accept the null hypothesis, or, disproving the null hypothesis, we must accept
an alternate hypothesis. However, in the common scheme where no specific
alternate hypothesis is defined, the analyst is left with the unsatisfying and
unhelpful conclusion merely that the null hypothesis is incorrect. For events
connected to a crime, however, this is rarely satisfactory. If cause A did not
effect the event, then some other specific cause must have. While a defendant
might appreciate the conclusion that he did not cause the event, the detective
who wants to solve the crime needs not only to figure out what did not
happen, but what did happen. Even if a specific alternate explanation for the
evidence is proposed, we can, again, only falsify or fail to falsify it. The
statistics are all directed at the null hypothesis. No quantitative information
is gathered about any alternatives, so we have no idea if yet another expla-
nation might be more likely. In falsifying a null hypothesis, we must blindly
accept the alternate hypothesis, and we are essentially blindsided into accept-
ing it as the “right” answer. Thinking stops.
* We are aware of some jurisdictions, such as New Zealand, where criminalists typically
present testimony in Bayesian terms.
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Principles and Practice of Criminalistics
Construction of LRs in Bayesian statistics encourages the comparison of
uncertainty for specific competing hypotheses. This allows for the simulta-
neous evaluation of different causes of an event, and results in a quantitative
statement about which cause the physical evidence favors. We still do not
know for sure which one is “right,” but the quantitative information resulting
from the comparison helps us determine which might be more likely. Because
the physical evidence is not the only evidence used to determine the cause
of an event, it, in and of itself, does not equate to the probability of the event.
A full Bayesian treatment forces an explication of assumptions and inferences
before the fact finder incorporates the physical evidence into a comment on
the ultimate issue. Whatever new information is proffered is used to update
our certainty about the cause of an event. We reiterate the mathematical form
of this verbal expression:
Prior odds 
×
LR = posterior odds
The use of Bayes’ theorem recognizes the circumstantial, and therefore infer-
ential, nature of physical evidence. It does not usurp the fact-finding role,
but contributes information to a specific proposition. It is a natural fit with
the purposes of evidence in law.