Dr ANDREI SEMIKHODSKI of Medical Genomics Ltd looks at some statistical misconceptions THE PROBATIVE value of DNA evidence is reflected by the value of the probability of a random match between DNA profiles from the crime scene sample and the accused.
Any probabilistic approach introduces uncertainly into the interpretation of scientific evidence which, if not properly understood, can give rise to misunderstanding of the evidence and inaccurate conclusions as to what the evidence really means. Some of those errors affect the way random match probability is calculated; others affect how DNA data is interpreted in court.
When DNA evidence is examined in court there is one issue that is crucial for determining how much weight should be given to it in the proceedings. The issue, though simple, is not trivial: is it possible to relate the DNA match between the accused and the crime stain, with the probability of the accused being the perpetrator of the crime he is being tried for? It is only for the judge and jury to assess the link between the evidence and the probability of guilt and not in any way the job of the prosecution DNA expert or the prosecutor to comment on it.
For example, when using DNA evidence in arriving at the decision as to the guilt of the accused, the jury may easily confuse the probability that the accused’s DNA profile would match that of the criminal, given that he is innocent, with the probability that the accused is innocent, given that their DNA profile matches that of the real criminal. That leads to probably the most common error of misinterpretation of evidence, called ‘the prosecutor’s fallacy’.
The prosecutor’s fallacy is a specific case of a logical error of the transposed conditional which arises when the probability of DNA evidence under a particular hypothesis is confused with the probability of the hypothesis given DNA evidence. That fallacy tends to favour the prosecution. There are two types of the prosecutor’s fallacy – the source probability error and the ultimate issue error.
The source probability error happens when the probability of DNA evidence is equated with the probability of the accused being the source of the crime stain sample. Equating these two probabilities tends to exaggerate the strength of the prosecution hypothesis and is detrimental to the defendant.
When the source probability error is extended to comment on the probability that the accused is guilty of the crime he is tried for, the prosecutor commits the ultimate issue error.
For example, when a probability of a random match between the accused and the crime samples is given as, say, 1 in 100 million, it may erroneously be interpreted as meaning that the probability of the accused being innocent is also 1 in 100 million. That type of reasoning also happens in the court room and has also been the subject of several successful appeals.