Interpreting Evidence

Ignoring the limitations of its small sample size, what can we learn from this study? There are two categories of errors that can occur in methods used to match suspects to evidence from a crime scene, whether this evidence be fingerprints, tissue samples containing DNA, eyewitness accounts, or odors on objects identified by dogs. These errors are false positive identification, in which an innocent suspect is conv icted because of an incorrect match between the ev idence and the suspect, and false negative identification, in which a guilty suspect is acquitted because of failure to make a match between the evidence and the suspect. The general principle of jurisprudence, that a person is considered innocent until proven guilty beyond a reasonable doubt, implies that the first type of error is considered more serious than the second, at least in contemporary Western society. McCauliff (1982) surveyed 171 judges and found that the most common interpretation of "beyond a reasonable doubt" was that the chance of false positive identification was 10%. This means that innocent suspects might be convicted as frequently as 10% of the time, or, said another way, that conv iction is reasonable if the likelihood of guilt is greater than 90%. Of course, in our legal system of trial by jury, the ultimate determinant of the meaning of "beyond a reasonable doubt" is the collective opinion of the jurors.

Before applying these ideas to the problem of scent identification, I'd like to discuss a seemingly different but in fact perfectly parallel problem, which is easier to analyze because fewer assumpt ions are necessar y. Consider a diagnostic test for a disease, such as the occult-stool test for colorectal cancer in which blood in the stool is used as an indicat ion that a person might have cancer in the lower portion of the digestive tract (Hoffrage et al. 2000). We can summarize the values needed for our calculations in a 2 X 2 table in which the two columns represent people with and without the disease and the two rows represent positive and negative results of the test ( Table 3.1). The sensitivity of the test is 50%; that is, if a person has the disease, the chance of a positive test result is 50%. This means that the occult-stool test misses 50% of the cases of colorectal cancer. These are false negatives, represented by the value of 0.5 in the lower-left cell of the table.

The upper-right cell of the table shows the probability of a false posit ive test result: an occult-stool reading that indicates colorectal cancer in a person who does not actually have the disease. This probability is only 3%. In other words, for a person who is not afflicted with colorectal cancer, the chances are 97% that the occult-stool test would correctly be negat ive. But the most important issue is how to interpret a positive test result for someone whose

Table 3.1. The occult-stool test for colorectal cancer.
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