I guess I'm one of the few "numerate" people around--at the end of "Deep Impact" when the comet the size of Mt. Everest was blown up into a million pieces, I conjecture that I was the only person in the theater to figure out that each piece still weighed one million tons.
This doesn't seem necessarily that interesting a skill but it does
have some personal benefits. For example, I can easily address the
well meaning yet annoying relatives who insist that I should wear a
helmet whenever I ride my bicycle. My response is that they
are incorrectly applying the "ergodic hypothesis" which asserts that the
statistical history of a single individual reflects the statistical
average of the whole system at a given time. In particular, since I've
never crashed in the 50,000 miles I've ridden in the last 7 years, I
probably won't crash in the future either, no matter what most other
people's experience is. A more persuasive argument against the ergodic
hypothesis is to design what I call a "statistical thought
experiment," i.e., a study which would never be made because its
premise is inherently flawed. In this case:
"Since 10% of the population is over 6ft. tall, I will be over 6ft. tall for 10% of my life."
That was a somewhat inconsequential example, but such thought
experiments can have an important function in casting doubt on entire
scientific fields, especially if they predict correct results.
For example, the pitfalls of epidemeology
are highlighted by the following correct thought experiment:
"Smoking reduces a woman's chance of dying of breast cancer."
In fact, one can easily generate numerous "correct" flawed studies:
Collecting such fallacies was a hobby of mine, but I've recently
become aware of many existing studies which exhibit such inherent
flaws. A recent example which got me going was heard on National
Public Radio (usually a goldmine of disinformation, as educational
radio and TV are often the only news sources to go into enough
depth to get things really wrong). The claim was that a study showed
that cigar smokers had an even higher rate of heart disease than
cigarette smokers. My immediate reaction was the
undoubtedly correct thought experiment:
"Driving a Cadillac causes heart disease."
This got me to start wondering about the risks of smoking. In particular, it seems clear to me that smoking in the U.S.A. is highly correlated to poor diet, lack of exercise, and poverty, so any study correlating smoking to heart disease should take these factors into account (I'm assuming that smoking doesn't actually cause these factors). The relevant thought experiment in this case is the plausible:
"Heart disease among smokers in Switzerland is lower than the instance of heart disease in the general U.S. population."
The moral is, as always when dealing with statistical studies, to spot the hidden agenda motivating the study and see how it leads to skewed results.
Challenge Problem: Design your own statistical thought experiment.