LIAR, DAMNED LIAR, STATISTICS

I believe the comparison above is due to Mark Twain, a man whom I dearly love, but on this occasion he was wrong. Statistics becomes a liar only if you don't know how to handle it, or if, like the late Mayor Beame, you know how to handle it all too well. (Panhandling for funds, he lamented that half of New York's population had an income below the national median¾failing to add that the income of the other half was above it.)

Now compare this with a rare phenomenon, such as a randomly picked child having leukemia. Cancer is, by and large, an old man's disease; it is rare for children to have it, and the special case of leukemia is, of course, even rarer¾in the US, there are only 3.1 cases per 100,000 children under age 10. If you take a sample of 50 as before, it is extremely unlikely to include any leukemias, so you would observe an incidence of zero, which is an error ratio of no less than infinity. But even if you take a sample of 100,000 children, you have quite a low probability of having exactly 3 leukemias in it: that particular group of 100,000 may have 2, or 4, or 1 case in it, all of which, when interpreted as probability ratios, are wide off the mark. And with a "mere" 100,000, you cannot get the correct value of 3.1 cases.