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Jon Carroll Banner
Stupidity is a curable disease

Jon Carroll
  Thursday, June 14, 2001

I REALIZED SOME time ago that I did not understand statistics well enough to evaluate them. My solution was to stop repeating statistics in my column. Surely we can agree that homelessness is a problem that needs to be addressed, whether the number of homeless in the United States is 300,000 or 3 million.

Numbers are often reported as facts; they look like facts, very hard and specific. But they're not. They need to be cross-examined: Where did the numbers come from? How was "homeless" defined -- people on the street for one night, one week, one month, what? Who counted them, and when?

Even if I knew the answers to those questions, I would be no closer to divining the truth. I have never taken a course in statistics. I am, to use the jargon, "innumerate," which is to math what "illiterate" is to reading. Knowing a little something about statistics would help me find the small lies, the mistakes and misinterpretations. (The big lies, where people just make up the data, cannot be uncovered by just looking at the studies. That's why we need whistle-blowers.)

So I asked around and finally settled upon two books, one old ("The Cartoon Guide to Statistics" by Larry Gonick and Woolcott Smith) and one new ("Damned Lies and Statistics," by Joel Best).

I KNEW I was in the right place when I hit Page 46 of the cartoon guide. The text presented a hypothetical problem. Suppose there is a new disease infecting one person out of every thousand in the population. Suppose there is a test for that disease.

If a person has the disease, the test comes back positive 99 percent of the time. Regrettably, the test also produces some false positives -- 2 percent of uninfected people test positive for the disease.

I just tested positive. Should I pay for the expensive treatment, which involves bombarding my body with pearl onions accelerated at high speeds?

Now me, I'd think there are 99 chances out of a hundred that I have the disease. Wait, no, 2 percent false positives -- OK, 98 percent chance. I almost certainly have it. Bring on the pearl onions.

Alas, the truth is that less than 5 percent of those who test positive for the disease actually have it. There is math to back that up, but the trick is to consider that 999 people do not have the disease, and that 2 percent of them is a much greater number than 99 percent of the .01 percent who do have the disease.

It's nonintuitive -- that's why it's called the False Positive Paradox -- but it's true. It points out how careful we have to be in handling numbers even when we know the numbers to be entirely accurate.

SOMETIMES, THOUGH, WE don't even know that. We have to watch out for other things: Sample size (the smaller the sample, the more anomalous the results are likely to be), true randomness (phone polls, for instance, discriminate against people who don't have phones and against people who hate pollsters) and even the agenda of the people promoting the statistics.

Note: Agenda and motive are not the same thing. Good people can use bad numbers. For an instructive example of this, see the discussion of the epidemic of church bombings in the South in Chapter 2 of Best's book.

"Damned Lies and Statistics" is a sort of catalog of errors, divided by type, with famous examples. In "The Worst Social Statistic Ever," the introduction of the book, Best nominates this sentence, found on numerous Web sites and journal articles: "Every year since 1950, the number of American children gunned down has doubled."

Assuming just one child gunned down in 1950, that would mean that, by 1987, 137 billion American children would have died in the gruesome manner, more than the estimated number of humans that have ever lived on Earth.


Trying to be smarter, I selected packages of knowledge called books.

Stop all this weeping, swallow your pride; you will not die, it's not jcarroll@sfchronicle.com.


 
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Stupidity is a curable disease
06/14/2001

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06/13/2001

I enjoy being a virus
06/12/2001

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