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2.
Tools for Estimating the Strength of the Inference
We turn now to methods used to describe the strength of the relationship
between evidence and reference when a conclusion of individualization is
not possible. These methods are tools that help us decide for ourselves the
strength of the relationship, as well as to communicate this strength to inter-
ested parties. Several tools exist that can assist us in our evaluation of the
results. To determine which tool is best suited to the specific evidence under
consideration, the competent analyst must possess at least basic skills in
mathematics and statistics. These subjects should be an integral part of the
education and training of every forensic scientist.
It is useful to understand the concept of probability as our 
degree of belief
in a proposition. Another way of saying this is that we need tools to quantitate
the uncertainty or lack of knowledge about our conclusion. This mind-set
allows us to think more clearly about our task, to include both the capabilities
and limitations of our test into an expression of strength, and to communi-
cate more clearly our opinions, and the basis for them, to interested parties.
Two basic fields of study in statistics provide information about the
strength of evidence. One is 
frequency estimates
, where the number of times
the evidence is found in some defined population is used to relate the prob-
ability of finding the evidence as a random occurrence. The second is 
likeli-
hood ratios
(LRs) (usually in the context of Bayesian reasoning), where the
probability of competing hypotheses is compared, and the results are
expressed as how much more likely the evidence would be under one scenario
compared with another.
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Principles and Practice of Criminalistics