Flawed Statistics

Statistics and I don't always get along well. I'm getting better at detecting fishy conclusions drawn from statistics, though. Take this article about abortion among Catholic women for instance.

Almost half of the clinic's 6000 patients last year identified their religion and of this group almost 40% said they were Catholic. A further 23% identified themselves as "Christian", while fewer than 5% said they were Protestant. Seven% were Muslim and 5% were Buddhist.

Nowhere does this article mention what percentage of women in the general population consider themselves Catholic. All it says is that 40% of those women who (1) have an abortion and (2) identify their religion, are Catholic. If Catholics outnumber Protestants in Australia, such a disparity is to be expected, all other things being equal.

Let's simplify the numbers a bit to clarify this. Suppose 100 women have an abortion. 40 are Catholic, 23 are generically Christian, 5 are Protestant, 7 are Muslim, 5 are Buddhist, and the remaining 20 are something else. Let's divide the 23 generic Christians equally between Catholics and Protestants, since we have no data to support a more lopsided grouping. That makes 52 Catholics and 16 Protestants. Let X denote the number of Catholic women in Australia and Y the number of Protestant women. The percentage of Catholic women who had an abortion is 100*52/X. The percentage of Protestant women who had an abortion is 100*16/Y. These percentages will be equal when X = 3.25 * Y. If the multiple is smaller than 3.25, the percentage goes up and vice versa. In other words, if Catholic women outnumber Protestant women by less than 3.25:1, Catholics women are "more likely" to have an abortion than Protestant women. Too bad the article doesn't give us a population breakdown. To make matters worse, only about 50% of those women having abortions identified their religion. The numbers given are essentially meaningless.

The Fallacy Files site has a good explanation of this kind of statistical goof.

Speaking of fallacies, this site is sort of a Cliffs Notes version of Fallacy Files.