EXAMPLE 3.6.16

This situation actually occurred in Southern California a few years ago: a woman (we'll refer to her as "Nicole") was brutually murdered. The prime suspect was her ex-husband, a celebrity who had a record of domestic violence during their short-lived marriage. The ex-husband's defenders issued the following statistically reasonable statement: "Even if a woman has been the victim of domestic abuse at the hands of her husband, the probability that she will be murdered by her husband is only 1 in 1000. Therefore, it is extremely unlikely that [Mr. ex-Husband] committed the murder."

What, if anything, is wrong with this use of statistics?

SOLUTION

The statistic cited would be useful if Nicole were alive and we were interested in determining the likelihood that she would be murdered by her ex-husband. However, since she had already been murdered, it is meaningless to cite a statistic that will predict whether or not she will be murdered. A meaningful statistic would be one that begins with the phrase "given that the woman has been murdered..." For instance, "given that a woman has been murdered, what is the probability that the murderer wasn't her violent, abusive ex-husband?"
FBI statistics from 1996, for instance, indicate that 30% of women murder victims were murdered by a current or former boyfriend or husband, so "given that a woman has been murdered, the probability that the murderer was her her violent, abusive ex-husband" is certainly greater than .3, which is 300 out of 1000.

One should always be suspicious when we encounter a use of statistics that treats an event that has already occurred as if it were a random event that has yet to occur.

One more interesting note: an Internet search for statistical information about violence against women will turn up very few useful links, along with dozens of links to sites run by "men's lib" groups and devoted to denial of domestic abuse issues and to discussions of female violence against men.