E-Letter responses to:

p-forum: Ulrich Hoffrage, Samuel Lindsey, Ralph Hertwig, and Gerd Gigerenzer MEDICINE: Communicating Statistical Information Science 2000; 290: 2261-2262 [Summary] [Full text]

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Published E-Letter responses:

Response to "An Uninformative Example"

Ulrich Hoffrage   (26 January 2001)

An Uninformative Example

Philip Taylor   (17 January 2001)

Response to "An Uninformative Example" 26 January 2001
Ulrich Hoffrage Max Planck Institute for Human Development Respond to this E-Letter: Re: Response to "An Uninformative Example"	A Chain of Inference There is a chain of inference involved when using DNA evidence in court. From a reported match, one may want to infer (i) the probability that the person for whom the match is reported actually has the same DNA profile, (ii) the probability that this person is the source of the trace recovered from the crime scene, and finally (iii) that the person is guilty. In our study, which is briefly summarized in the Policy Forum of 22 December 2000, we tested participants for both the first and the second type of inference. For the first type of inference, one does not need to know the “size of the pool of people from whom the actual criminal might be found,” to use Philip Taylor’s phrase. What one needs, instead, is the base rate of the profile in the population. For the second type of inference, one does indeed need to factor in the “size of the pool” of potential sources. We specified the size of this pool to the participants in our study, but due to space limitations, we did not mention this information in the Policy Forum. For the third type of inference, the probability of guilt given a reported DNA match, one has to specify the prior probability of guilt. Neither the DNA statistics, nor the “size of the pool of people from whom the actual criminal might be found,” nor the combination of both would be sufficient to calculate this prior probability, and thus allow an inference of the probability of guilt. To see why, imagine one would know for certain that a particular person is the source of a DNA sample recovered from a crime scene. Thus, this probability (source given match) would equal 1, but it is still possible that the person left the DNA sample there without being the perpetrator of the crime, or that someone else planted it there. Ulrich Hoffrage, Samuel Lindsey, Ralph Hertwig, Gerd Gigerenzer
An Uninformative Example 17 January 2001
Philip Taylor, Physicist Case Western Reserve University Respond to this E-Letter: Re: An Uninformative Example	In the legal example given in this article, the authors go to some length to describe the parameters of the problem. They list the sensitivity, the base rate for DNA matching, and the false-positive rate. All this information, however, is meaningless without a specification of the size of the pool of people from whom the actual criminal might be found. There can only be a "correct" inference within the context of an assumption about this number. With a pool of only two suspects, the probability of guilt is 99.7%, but with a pool of 80 million it drops to 4 millionths. In the absence of any mention of this fact, the tabulation of how many professionals and students would have rendered a verdict of "guilty" is not very enlightening.