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DNA Evidence, False Positives,
and "Natural Frequencies"

Editor's Preface
Jurimetrics, The Journal of Law, Science, and Technology
Volume 43, No. 2, January 2003, pp. vii-ix

© 2003 D.H. Kaye

This issue of Jurimetrics, The Journal of Law, Science, and Technology includes articles on the psychology of evidence, medical records and privacy, genetic research and bioethics, and the computation of lost profits in patent infringement cases. Inasmuch as these papers confront difficult issues and stake out new positions, we expect them to prompt further debate and a better understanding of the questions they seek to answer.

The many legally trained readers of Jurimetrics should appreciate the merits of the legal and ethical arguments in several of these articles with no further editorial gloss. However, the psychological experiment, previously reported in substantially less detail in Science, may be less accessible to the modal reader. In Communicating Statistical DNA Evidence, Samuel Lindsey, Ralph Hertwig, and Gerd Gigerenzer discuss the presentation of probabilities associated with DNA and other trace evidence. They propose using “natural frequencies” rather than decimals or percentages, especially when a defendant has been identified by searching through a database of DNA profiles from convicted offenders. The authors’ research adds to our understanding of how the manner in which trace evidence is presented affects assessments of that evidence. They report that mock jurors return fewer guilty verdicts and arrive at the correct figure for particular probabilities much more often when relevant probabilities are presented as “natural frequencies.”

In interpreting this finding, the precise meaning of “natural frequencies” must be appreciated. The experiment involves more than the translation of decimal numbers such as 0.0001% into fractions such as 1 in a million. The subjects in the “frequency condition” were told the number of men in the population who actually possessed the incriminating DNA type —- that is, the number of true positives. They were told how many men who did not possess the type would be erroneously reported to have it —- the number of false positives. Because they were provided such numbers rather than mere frequencies, they did not have to understand the tricky concept of conditional probability to find the posterior probability. In contrast, the subjects in the “probability condition” were given no cues as to how to transpose a conditional probability. Whether merely presenting the statistical information as frequencies expressed as natural numbers would have the same effect as giving the numbers of true and false positives in a particular population remains unknown.

A second facet of the paper also warrants a brief comment. The authors suggest that the probative value of a DNA match depends greatly on (1) whether the defendant is identified by searching a database of DNA types of convicted offenders, as opposed to (2) whether the defendant is identified on the basis of non-DNA evidence, and then the DNA match is made. They write that in the database-search case, “the population frequency should be multiplied by the size of the databank to reflect the new chance of a coincidental match,” and an accompanying footnote states that they believe that “the correct conditional probability of the defendant’s being the source of the evidentiary sample” requires multiplication by the “databank size.” As discussed in a symposium in this journal, however, this supposed correction is controversial at best. Thoughtful statisticians have argued strongly that when the hypothesis in question is whether the defendant is the source, such multiplication is grossly incorrect.

These statistical and psychological issues, like the bioethical and economic questions in the other articles in this issue, are far from trivial. They require careful analysis and explication for the legal system intelligently to regulate science and technology and to apply scientific methods to its own needs. As such, we look forward to publishing further dialogue on these and other topics at the intersection between law and science.

March 2003 —-D.H. Kaye, Editor