I got intrigued by the numbers presented in this news article talking about the re-trial in the Amanda Knox case. The defendants, accused and initially convicted of murder, were acquitted in the appeal’s instance when the judge ruled that the forensic evidence was insufficiently conclusive. The appeals judge ignored the forensic scientist’s advice to retest a DNA sample, because

“The sum of the two results, both unreliable… cannot give a reliable result,” he wrote.

Now the acquittal has been overturned by Italy’s highest instance court and there is a re-trial. As the example illustrates, there can be considerably more information gained from a second test.

I’m reproducing the calculations which led to the resulting numbers of the example in the news article in this hands on tutorial. (make sure to click “hide toolbar” do be able to see the last lines.)

You can do it by yourself with pen and paper. I use a software called RStudio to write the example. Have a look at the source file (faircoins.Rmd) on my github.