Friday, October 1, 2010

Lies, damned lies and statistics

A story I read in the "Lifestyle" magazine fascinated me.  A woman was told that she would be granted three wishes but that her husband would get ten times more or better than whatever she wished for.  For the first two wishes, she wanted to become the richest and the most beautiful woman in the world, and both were granted.  Her third wish was malicious: "I'd like a mild heart attack."

Of course, the woman had a mild heart attack, but what would the husband have got for the third wish?  He would certainly have had a heart attack.  But would it have been ten times severer or ten times milder than the wife's? 

That depends on how we interpret the condition in relation to the wish.  And if we are required to generalize the "sample" (one woman) to the "population" (all women), what conclusion can we come to about women in general?  That also depends on our interpretation.  If our interpretation is that the husband's heart attack was ten times severer, then women are clever indeed.  If, on the contrary, our interpretation is that it was ten times milder, women are dumb, though they think they are smart.  Most women might argue that the first interpretation is the correct one, and most men, the second.  Truth, it is said, "will out".  But it looks as though there are no truths; there are only interpretations.

If you think I am splitting hairs, you are right.  And I am splitting hairs because I have just finished reading two books about statistics in which there is plenty of hair-splitting: How to Lie with Statistics, written more than forty years ago, and Damned Lies and Statistics, published in 2001.

Joel Best, the author of the second book, talks about the following statistic he once came across in an article in a prestigious journal: "Every year since 1950, the number of American children gunned down has doubled."  What does it mean?  Well, let's assume that the number of American children gunned down in 1950 was one.  If the number doubled each year, there must have been two children gunned down in 1951, four in 1952, eight in 1953, and so on.  By 1980, the number would have been one billion (more than four times the total US population that year).  By 1995, when the article was published in the journal, the annual number of children gunned down in America would have been over 35 trillion.  Absurd!  Actually, the author of the journal article had borrowed the statistic from a 1994 yearbook in which the information had been given as follows: "The number of American children killed each year by guns has doubled since 1950."  In other words, the deaths in 1994 were twice as many as in 1950.  But the statistic had got garbled in the journal article. And considering the reputation of the journal, the statistic must have been uncritically accepted and quoted by several researchers.

Let me go back to the point I made with reference to that funny story with a clever punchline: you can prove anything with statistics if only you know the "art" of interpretation.  Benjamin Disraeli was not wide of the mark when he said: "There are three kinds of lies: lies, damned lies and statistics."

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