Evidence of a DNA "match" between two samples is impossible to understand and interpret without knowing the probability that a match would be declared if the samples are from different individuals. A match based on the fact that both the suspect’s blood and blood at the crime scene contain hemoglobin, for example, would be meaningless because all blood contains hemoglobin. A “match” provides useful evidence of identity only to the extent that different people are unlikely to match. Thus, the question for statisticians is to determine whether the match is as common as a Chevy or as rare as a stillrunning Edsel. Many commentators consider the ability to quantify the probability of a “match” between samples from different people to be crucial to the admissibility of DNA- derived evidence: "without being informed of such background statistics, the jury is left to its own speculations." McCormick, Evidence, 655 (Cleary ed.).26
When DNA evidence is offered in the courtroom, it is usually accompanied by an estimate of the frequency of the matching DNA profile in a reference population. The frequency is assumed to represent the probability of a coincidental match between a given individual and another member of the same population. Suppose, for example, that a “match” was declared between a suspect’s DNA profile and the profile of a rapist’s semen. If the matching profile is found in only one person in a million, then the probability that an innocent suspect would, by coincidence, happen to match the rapist was assumed to be one in a million. Courts in most jurisdictions refused to admit DNA evidence unless it was accompanied by frequency estimates, and much of the controversy surrounding the admissibility of DNA evidence has concerned the scientific validity of the methods used to estimate DNA profile frequencies.
Of course, frequency statistics do not tell the whole story. When assessing the value of DNA evidence for proving two samples have a common source, the trier-of-fact must consider the reliability of the test as well. A DNA “match” between different individuals can occur in two ways: there may be a coincidental match between two people who happen to have the same genotypes, or there may be a false positive--that is, a false match due to an error in collecting, handling, processing or typing the samples. The potential for false positives can greatly reduce the probative value of DNA evidence.27 However, courts have not required forensic experts to present estimates of the false positive rate of laboratories— perhaps because these error rates are difficult to estimate.
If no match has been declared between a reference and evidentiary sample, then the inquiry ends there. Exclusions in DNA testing require no statistical probabilities. They are considered absolute.
26 Appellate courts in most jurisdictions have required that DNA evidence be accompanied by appropriate statistics as a condition of admissibility, see, e.g., People v. Barney, 10 Cal.Rptr.2d 731, 742 ("The statistical calculation step is the pivotal element of DNA analysis, for the evidence means nothing without a determination of the statistical significance of a match of DNA patterns."); People v. Axell (1991) 235 Cal.App.3d 836, 866 1 Cal.Rptr.2d 411, 430 ("We find that...a match between two DNA samples means little without data on probability...); People v. Wallace (1993) 17 Cal.Rptr.2d 721, n. 3 (without valid statistics DNA evidence is "meaningless"); Commonwealth v. Curnin, 409 Mass. 218, 526 N.E.2d 440 (1991)("It is apparent from the basis on which we decide the DNA testing issue that we would not permit the admission of test results showing a DNA match (a positive result) without telling the jury anything about the likelihood of that match occurring"); Ex Parte Perry, 586 So.2d 242, 254 (Ala. 1991); State v. Cauthron, 846 P.2d 502 (Wash. 1993)("[t]estimony of a match in DNA samples, without the statistical background or probability estimates, is neither based on a generally accepted scientific theory nor helpful to the trier of fact."); Nelson v. State, 628 A.2d 69 76 (Del. 1993)(trial court's exclusion of match frequency "inherently inconsisitent" with its admission of testimony of a match, because "without the necessary statistical calculations, the evidence of the match was 'meaningless' to the jury."); State v. Brown, 470 N.W.2d 30 (Iowa 1991)("Without statistical evidence, the ultimate results of DNA testing would become a matter of speculation."); State v. Vandebogart, 616 A.2d 483, 494 (N.H. 1992)("A match is virtually meaningless without a statistical probability expressing the frequency with which a match would occur.").
27 See, Thompson, Taroni & Aitken, How the probability of a false positive affects the value of DNA evidence. 48 J. Forensic Sci. 47 (2003).
National Resource Council (NRC) (1996). The Evaluation of Forensic DNA Evidence. National Academy Press, Washington DC. (on-line)
National Resource Council (NRC) (1996). NRC II Executive Summary. National Academy Press, Washington DC.
Balding, D.J. (1997). Errors and misunderstandings in the second NRC report. Jurimetrics. 37: 469-476.
Mueller, L. D. (1999). The DNA typing controversy and NRC II. In Statistics in Genetics, M. E. Halloran and S. Geisser (eds), pgs. 1-23, Springer-Verlag, New York.
Mueller, L.D. (1993). The use of DNA typing in forensic science. Accountability in Research. 3: 55-67.
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