Duke Lacrosse Statistics

Below is taken from Stephen Dubner and Steven Levitt at their Freakonomics blog. It is fairly interesting, and like Levitt, I am not sure what to make of it.

Here is something that I don’t quite know how to interpret.

In the Duke lacrosse sexual assault case, the police made the 46 players come down to the police station to have their pictures taken. Then these 46 pictures were shown to the women who has accused the lacrosse players of sexually assaulting her.

She was shown the pictures one-by-one. The three players that she positively identified were the fourth, fifth, and seventh pictures that she saw. These are the only three positive identifications that were made.

Statistically this is quite strange. The chance of any one player being positively identified is 3/46, or about .065. I did the calculations, and if the order of the pictures was randomly chosen, the probability that 3 of the first 7 pictures would be positive identifications is less than 1 in 100.

This suggests one of three possibilities:

1) Rare events happen and maybe this is the one time in 100 that a distribution this unusual occurred.

2) The police intentionally or unintentionally stacked the deck so that these three pictures were in the beginning.

3) There was some sort of bias that led the accuser to be inclined to give positive identifications early in the process.

I’m not trying to side with either party on this matter, at all. Indeed, I haven’t even been paying close attention to what has been happening. I just raise this as a statistical curiosity for the conspiracy theorists among you to argue about.

(Thanks to Brian Sullivan for bringing this issue to my attention and passing along the Motion to Dismiss which contains this information. I don’t have an online version of it to link to. I’m sure someone reading this blog will be able to provide such a link.)