Freakonomics guy Steven Levitt takes a look at the “Arizona DNA database” issue raised by a recent L.A. Times article, and pronounces himself surprised to learn that the numbers . . . aren’t surprising:
When I heard about this, I wondered if the F.B.I. is totally off its rocker when it comes to the probabilities it gives about DNA matches. Is it possible that the F.B.I. is right about the statistics it cites, and that there could be 122 nine-out-of-13 matches in Arizonas database?
Perhaps surprisingly, the answer turns out to be yes.
Of course, it shouldn’t be surprising at all. Levitt reveals that you would expect to find about 100 matches at nine loci. Instead, 122 were found, which is likely an inconsequential difference given the magnitude of the numbers we’re discussing.
But these numbers are set forth in the article. So why did Levitt, an experienced statistician, wonder whether the FBI was “totally off its rocker”?
The answer lies in the overly dramatic way the issue was portrayed by the L.A. Times.
On the front page, the paper portrayed the findings as surprising, announcing with great fanfare that dozens of matches were found with probabilities like 1 in 113 billion. It seemed to defy impossible odds, we were told.
Only on page A20 were we told that most of these stunningly unexpected matches were, in fact, expected — because the analyst was comparing every pair to every other pair. As Levitt explains, that means that about 1.4 trillion comparisons were done, making a 1 in 113 billion match anything but unexpected..
This sort of manipulation of the readership helps dramatize a story and sell papers. But it also has real-world consequences, as the last link shows.
More details to come in the comments.