FALLACIES AND FANTASIES

• Jurisdiction: Australia

FALLACIES AND FANTASIES

The danger of misusing statistics ................................................................. [80A.1200]

Prosecutor's fallacy ....................................................................................... [80A.1220]

Defence fallacy.............................................................................................. [80A.1240]

The meaning of frequencies ......................................................................... [80A.1260]

Database searches ....................................................................................... [80A.1280]

Uniqueness and individualisation ................................................................. [80A.1300]

[80A.1200] The danger of misusing statistics

In statistics, propositions and conditional probabilities must be formulated with precision. Changing the formulation can change the end result. Different formulations, that mean essentially the same thing in everyday language, can have divergent meanings in mathematics and statistics. It is therefore important that results are expressed correctly.

It is easy, and common, for non-scientific people to fail to appreciate these distinctions. However, the importance of framing the conclusions correctly is underscored by several judicial decisions in the United Kingdom that overturned verdicts because of a concern that the juries were misled: R v Deen (unreported, English Court of Appeal, 1993), cited in Matthews (1994); Doheny and Adams v The Queen [1997] 1 Cr App R 369. The errors in these cases are examples of what is known as the transposed conditional or prosecutor's fallacy. (Evett and Weir (1998) discuss these and other appeal court decisions in some detail.)

Recall that it was pointed out at [80A.100] that "a match" does not identify the suspect as the source of the crime scene material that he matches because we cannot be sure that no one else has the same set of matching characteristics (alleles). Moreover, it tells us nothing about how or when the DNA came to be at the crime scene and it does not tell us who else could have been the source of the DNA.

Non-statisticians (and thus many prosecutors and defence lawyers) can lose sight of these limitations and misstate the results. This gives rise to two aptly named misstatements the Prosecutor's fallacy and the Defence fallacy. These are now explained.

As before the symbols have these meanings:

• Gc = genotype of the crime sample
• Gs = genotype of the suspect
• Hp = prosecution hypothesis (the suspect left the crime stain)
• Hd =

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