In the October 2015 edition of the Forensic Foundations’ newsletter (http://alined.createsend.com/t/ViewEmailArchive/r/FE030E89152E034C2540EF23F30FEDED/C67FD2F38AC4859C/) I highlighted the potential problem when you translate one language to another. In the article, I focused on translating from Mathematics into English and from Greek into English.
On 29th May 2017, John Silvester publish an excellent article in The Age newspaper. The article describes the apprehension of Gregory Keith Davies for the abduction, rape and murder of six year old Kylie Maybury in 1984 (http://www.theage.com.au/victoria/kylie-mayburys-killer-trapped-by-mix-of-newage-science-oldfashioned-policing-20170529-gwfe06.html). I was involved with this case in the early days of my forensic science career and it is gratifying to see it finally resolved.
However, I do take issue with one comment made by John Silvester. He has fallen into the trap of the prosecutor’s fallacy. In his article, he states: ‘In 2016 he (Davies) was approached for a DNA sample. It proved positive to the one in the Maybury case. The science shows that the odds of it being anyone other than Davies was 100 billion to one. Faced with the maths Davies had no choice but to plead guilty.’
I have highlighted the prosecutor’s fallacy in the quote above. What the science would have actually shown was that ‘The DNA profile associated with the Maybury case would be 100 billion times more likely if it originated from Davies than if it had originated from another unrelated man.’
So, what is the difference between these two statements – it’s still a huge number? Does it matter? Well yes, it does, it is an incorrect translation of Mathematical language into English. The first statement is talking about the probability (or odds) of it being another person, whereas the second (and correct) statement talks about the probability of the DNA profile.
As I explained in 2015, we have two mathematical expressions which look similar - Pr(4|C) and Pr(C|4). The first expression equates to the 'Probability that an animal has four legs, given it is a cow' which is 1 or very close to 1 - there are not that many cows with more or less than four legs. The second expression equates to 'Probability that an animal is a cow, given that it has four legs' which of course is very low - it could be dog, a cat, a rat.
Using this example, rather than a DNA example incorporating huge numbers, we can clearly see the difference in the two statements.
If you are interested in what cauliflowers have to do with it, you have to read the October 2015 newsletter article.
If you are interested in reading another unfortunately worded translation, go to https://www.hotelnewsresource.com/article77377.html.
If you are interested in learning more about the application of statistics to forensic science or translating Mathematics to English, download our brochure here. https://www.forensicfoundations.com.au/wp-content/uploads/statistics-brochure-web.pdf