  Statistical tests are needed to determine experimentally whether a
hypothetical theory based on local realism can be an acceptable alternative to
quantum mechanics. It is impossible to rule out local realism by a single test,
as often claimed erroneously. The ``strength'' of a particular Bell inequality
is measured by the number of trials that are needed to invalidate local realism
at a given confidence level. Various versions of Bell's inequality are compared
from this point of view. It is shown that Mermin's inequality for
Greenberger-Horne-Zeilinger states requires fewer tests than the
Clauser-Horne-Shimony-Holt inequality or than its chained variants applied to a
singlet state, and also than Hardy's proof of nonlocality.
