Asking the Right Questions, A Guide to Critical Thinking, 8th Ed

Are the Statistics Deceptive? 161
hair spray? As for the second statement, wouldn't you want to know how
many of those deaths would have been prevented if an SUV were not
involved, how many other motor vehicle fatalities not involving an SUV
there were, the number of SUVs on the road compared to how many
deaths they were involved in, and how many miles SUVs travel compared
to how many deaths occur in SUVs? With reference to the third statement,
how does the budget of one particular movie relate to the budget of other
movies, and is this one case highly unusual, or is it typical of the movie
industry?
When you encounter statistics, be sure to ask, "What relevant information
is missing?"
Risk Statistics and Omitted Information
"Daily use of Nepenthe brand aspirin will lower the chance of a second heart attack
by 55 percent."
"Routine physicals have been linked to finding early cures and lowering people's
likelihood of early death by 13 percent."
A common use of statistics in arguments—especially arguments about health
risks—is the reporting of risk reduction as a result of some intervention. Such
reports can be deceptive. The same amount of risk reduction can be reported
in relative or absolute terms, and these differences can greatly affect our
perceptions of the actual amount of risk reduction.
Imagine a 65-year-old woman who just had a stroke and is discussing
treatment options with her doctor. The doctor quotes statistics about three
treatment options:
(1) Treatment X will reduce the likelihood of a future stroke by 33 percent,
(2) Treatment Ywill reduce the risk by three percent, and
(3) With treatment Z, 94 percent of women are free of a second stroke for
10 years, compared to 91 percent of those who go untreated.
Which treatment should she choose? Our guess is that she will choose the
first. But all of these options refer to the same size treatment effect. They just
express the risk in different ways. The first (the 33 percent) is the "relative
risk reduction." If a treatment reduces the risk of heart attack from 9 in
100 to 6 in 100, the risk is reduced by one-third, or 33 percent. But the