Radiation-induced leukemia is riding high again, promoted by quacks who know less about statistics than a baby baboon knows about Social Security deductions. I have previously reported on how the "child leukemia clusters near three British nuclear estab-lishments" can as well and better be explained as "leukemia clusters near British motorways" [AtE May 87], and how a study by the British Natl. Radiation Protection Board completely rejected such conclusions. Nevertheless, assorted quacks are now riding a new gimmick: double and triple the average! Sounds really damn-ing when it refers to child leukemia near nuclear facilities, espe-cially since it is probably quite correct. However, such double and triple leukemia clusters can also be found near symphony orchestras, pet cemeteries and railroad museums. The secret is in the behavior of rare events or states with low probabilities.
If you take a group of randomly selected people, you would ex-pect half of them to be women. If some group has a large deviation from the average of 50%, it most likely is because either the group was too small (nothing remarkable about both of two randomly picked persons being women) or something went wrong with the selection, which was not random after all. If you observe 100% (double the average in other groups) of 50 persons to be women, it could be because the group is taken not from the general popula-tion but from the listeners exiting after a lecture on prenatal care. In the first case the method of measurement is flawed; in the second there is statistical indication that the result is not acciden-tal, but that there is a significant connection between gender and the composition of the group. (The probability of 50 randomly per-sons just happening to be women by accident is very close to zero: ½ to the power 50 or 0.00000000000000088 or 8.8E-16).
So in this example, the average (50% of the total) cannot be doubled accidentally (100%), and it cannot be tripled at all (150%).
But what if we take something with a much smaller average, like the number of left-handed chess players called Jonathan per 100,000 population? Let's say the average number (I really have no idea) is 5. Then in a group of 20,000 people we would expect to find one such Jonathan
¾meaning that in very many groups of 20,000 the average will be one per group. But in any single group there may very well be two such Jonathans or three or none at all, because the real world consists of fluctuations about averages. And what is the probability of finding double (2) or triple (3) the average (1) of such Jonathans in the group?That's not quite as simple as the case of the women; if you really want to know how it's done, see the reference below, but the num-bers for this case are the following. The probability of finding double the average (2 such Jonathans) in the group amounts to about 90% of the probability of finding the average (1); and the probability of finding triple the average in the group amounts to about 67% of the probability of finding the average. If, therefore, you find three left-handed chess playing Jonathans, or triple the expected number, in a group of 20,000, it does not mean you have run into a colony of left-handed chess players; it means nothing whatsoever, it is statistically insignificant
¾just as insignificant as the "leukemia dusters." Why?Because the rate of child leukemia in the US is of the same order as in this example: for children under 10 it is 3.1 per 100,000.
[More: P. Beckmann, Elements of Applied Probability Theory (1967), $7.50 from Golem Press, Box 1342, Boulder, CO 80302. Warning! Assumes familiarity with college-level calculus.]
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Vol. 16, No. 5
Newsletter: Access to Energy Newsletter Archive Volume: Issues Issue/No.: Vol. 16, No. 5 Date: December 01, 2004 02:20 PM Title: The privilege of irresponsibility
Copyright © 2004 - Access to Energy Newsletter Archive
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