Significance of a DNA match
44.21 Once a match has been reported between two profiles it is necessary to interpret the significance of the match in order to give weight to the evidence. Scientists usually present their statistical calculations in one of two ways.
44.22 First, the ‘match probability’ assesses the probability of the matching having occurred by coincidence. This is the probability that a person other than the suspect, randomly selected from the population, will have the same profile as that found at the crime scene. The smaller the probability, the greater the likelihood that the two samples came from the same person. The forensic scientist needs some knowledge of the frequency with which the alleles occur within a population, and population databases are used for this calculation.
44.23 Second, the ‘likelihood ratio’ (LR) is the ratio of the probability of a match if the DNA in the crime scene sample and that from the suspect came from the same person, to the probability of a match if they came from different persons. For example, a likelihood ratio can be expressed as ‘an LR of 1,000’. This means the probability that the profiles are the same is 1,000 times as great if the samples came from the same person as if they came from different persons.
44.24 It has been suggested that in some circumstances a match probability may be unfairly prejudicial to a suspect because the calculation is based on a match involving a randomly selected, unknown, unrelated person. Where the actual offender and the suspect are members of the same family, or perhaps even from the same ethnic community, this could result in a higher than random probability that their DNA profiles will match. Justice Action, a prisoners’ rights group, has commented:
While the chance that a randomly selected Australian citizen may have a DNA profile matching a Brewarrina Aborigine may be a million to one, a randomly selected Brewarrina Aborigine may be at a much higher chance of matching.
44.25 It has also been suggested that match probabilities would be irrelevant, or unfairly prejudicial, where they are far smaller than the probability of tampering, laboratory error, contamination or other causes that might lead to a false positive. Several commentators have suggested that the possibility of error should be incorporated into DNA statistics.
Small match probabilities
44.26 The use of match probabilities has been criticised on the basis that jurors, as ordinary members of the community, generally do not understand probabilities and infinitesimal match probabilities (eg ‘one in 90 billion’) will so dazzle jurors that they will not be able to evaluate the evidence fairly and critically.
44.27 Evett and others have commented that probabilities of the order of one in trillions, following from calculations based on ten locus profiles, require assumptions that cannot be evaluated by statistical experiment in the light of the size of existing databases. Such very small numbers are not necessarily incorrect as a technical matter of mathematics, but are without any real meaning and lack credibility in the context of criminal proceedings. They have also cautioned against what they call the widespread misconception that there is a real statistical probability to be assigned to any profile:
There appears to be a fairly widespread misconception that there is a real statistical probability to be assigned to a profile but this is not the case. There is an infinite range of ways of carrying out the calculation that underlies the figure given. The method chosen in the individual case must be seen to be as much a matter of opinion as one given in other areas of forensic science. The match probability is ‘personal’. It is based on what the scientist considers to be the most appropriate calculation given the circumstances of the case.
The ‘prosecutor’s fallacy’
44.28 The ‘prosecutor’s fallacy’ is an error in relation to probabilities that usually favours the prosecution. The forensic scientist could make the error in presenting DNA evidence by misrepresenting its probative value. Alternatively, the evidence initially may be presented correctly but the judge or counsel inadvertently could commit the error in summing up. A third possibility is that the jury could make an error in applying the evidence even though the evidence has been presented and summed up correctly.
44.29 Two different questions may be asked regarding evidence of a match between a defendant’s profile and the profile obtained from a crime scene. First, what is the probability that the defendant’s DNA profile matches the crime scene sample profile, given that he or she is innocent? Second, what is the probability that the defendant is innocent, given that his or her DNA profile matches the crime scene sample profile? The first question assumes the innocence of the defendant and asks about the chances of getting a match; the second assumes that the defendant’s profile matches and asks about guilt or innocence. The ‘prosecutor’s fallacy’ consists of mistakenly giving the answer to the first question as the answer to the second.
44.30 In R v Keir, the New South Wales Court of Criminal Appeal considered whether the ‘prosecutor’s fallacy’ had arisen during a criminal trial. The case involved the presumed murder of a woman in circumstances in which bone fragments were found buried under her house some years after her disappearance. DNA taken from the fragments was compared with her parents’ DNA for the purpose of identification.
44.31 An expert witness gave evidence that it was 660,000 times more likely to obtain the particular DNA profile found in the bones if it came from a child of the missing woman’s parents, rather than from a child of a random mating in the Australian population. However, in his directions, the trial judge (restating the prosecution’s submissions) referred to the DNA evidence as providing a ‘660,000 to one’ chance that the bones were those of the missing woman, and therefore a ‘660,000 to one’ chance that alleged visual identifications of the woman after her disappearance were not correct. The Court held that the Crown had fallen into the ‘prosecutor’s fallacy’, and the trial judge had repeated the Crown’s submissions. The Court noted that neither defence counsel nor the trial judge had recognised the fallacy at trial.
44.32 Even if the prosecution or the trial judge does not make this error, there is a danger that the jury will fall into this error in its consideration of the evidence.
National Research Council, The Evaluation of Forensic DNA Evidence (1996) National Academy Press, Washington, 127.
 See generally, Legislative Council Standing Committee on Law and Justice, Review of the Crimes (Forensic Procedures) Act 2000, Report No 18 (2002), Parliament of NSW, Sydney Ch 3.
Ibid [3.35], citing submission by Justice Action.
D Kaye and G Sensabaugh Jr, ‘Reference Guide on DNA Evidence’ in Federal Judicial Center (ed), Reference Manual on Scientific Evidence (2000) Washington DC, 485, 540.
 For example, see J Koehler, ‘Why DNA Likelihood Ratios Should Account for Error (Even When A National Research Council Report Says They Should Not)’ (1997) 37 Jurimetrics 425; M Goode, ‘Some Observations on Evidence of DNA Frequency’ (2002) 23 Adelaide Law Review 45, 55–57. Compare National Research Council, The Evaluation of Forensic DNA Evidence (1996) National Academy Press, Washington, 87.
 For example, see D Kaye and G Sensabaugh Jr, ‘Reference Guide on DNA Evidence’ in Federal Judicial Center (ed), Reference Manual on Scientific Evidence (2000) Washington DC, 485, 537–538.
I Evett and others, ‘DNA Profiling: A Discussion of Issues Relating to the Reporting of Very Small Match Probabilities’ (2000) Criminal Law Review 341, 347–348.
Ibid, 346. See also M Goode, ‘Some Observations on Evidence of DNA Frequency’ (2002) 23 Adelaide Law Review 45, 69.
D Balding and P Donnelly, ‘The Prosecutor’s Fallacy and DNA Evidence’ (1994) Criminal Law Review 711, 711–712. See R v Doheny v Adams  1 Cr App R 369; R v Keir (Unreported, NSW Court of Criminal Appeal, Giles JA; Greg James and McClellan JJ, 28 February 2002); R v GK (Unreported, NSW Court of Criminal Appeal, Mason P; Sully and Dowd JJ, 16 October 2001); R v Galli (Unreported, NSW Court of Criminal Appeal, Spigelman CJ; Sully and Adams JJ, 12 December 2001); R v Karger (Unreported, Supreme Court of South Australia Court of Criminal Appeal, Doyle CJ and Prior & Gray JJ, 30 August 2002).
D Balding and P Donnelly, ‘The Prosecutor’s Fallacy and DNA Evidence’ (1994) Criminal Law Review 711, 716–717.
R v Keir (Unreported, NSW Court of Criminal Appeal, Giles JA; Greg James and McClellan JJ, 28 February 2002).
 For example, see R v Galli (Unreported, NSW Court of Criminal Appeal, Spigelman CJ; Sully and Adams JJ, 12 December 2001) , in which the Court held that although a direction about the prosecutor’s fallacy might not be necessary in all cases where DNA evidence is admitted, a warning would have been desirable in the circumstances.