False precision 77
Both mathematics and science make widespread use of
numbers, and both have prestige as sources of authority. The
extension of exact numbers into areas quite inappropriate to
them is often little more than the attempt to invest certain
statements with the aura and prestige attaching to mathematics
and science.
The fallacy derives from the use of unjustified material, and
from the attempt to impart more confidence in the assertions
than the evidence for them actually merits.
Our mouthwash is twice as good, yes two times as good, as its leading
competitor.
(On what instrument, do you suppose, can one read off the quality of
a mouthwash; and in what units?)There are several versions of this fallacy, all of which have it in
common that the numbers used give a misleading impression of
the confidence one can place in the claim.
Four out of five people can't tell margarine from butter.
(It may be true, but how is it established? If large numbers on a one-
against-one test repeatedly fail to distinguish them, we might be
impressed. If smaller numbers fail to pick out the one margarine
sample from a plateful of crackers covered with different types of
butter, we might be rather less impressed.)Yet another version might talk about quantity, where quality was
a highly important factor.
Kills 99 per cent of all household germs.
(A worthy claim, unless the rest happen to be typhoid.)