Last night, Emily Rooney’s Greater Boston included a segment on truancy in the Boston public schools. One of her guests, Suffolk County Sheriff Andrea Cabral, whom I usually admire and respect, claimed that 50% of high-school dropouts (from Boston public schools) become criminals. In support of this claim, Cabral asserted that when young inmates are interviewed in local jails and prisons, half of them turn out to be high-school dropouts.
Let’s examine this reasoning. Since I don’t have the actual figures, I’ll just give an example. Here is a typical two-by-two table for an imaginary school system:
As I say, these are made-up numbers, but they clearly illustrate a plausible situation where 50% of criminals are indeed drop-outs, but only 25% of drop-outs are criminals. So it’s a classic case of the fallacy of the converse in the context of conditional probability.
Barbara thinks I’m a geek because I exclaimed, “fallacy of the converse!” as soon as I heard Cabral’s claim while we were watching her on TV. Doesn’t sound geekish to me; just sounds normal.