  A popular approach to significance testing proposes to decide whether the
given hypothesized statistical model is likely to be true (or false).
Statistical decision theory provides a basis for this approach by requiring
every significance test to make a decision about the truth of the
hypothesis/model under consideration. Unfortunately, many interesting and
useful models are obviously false (that is, not exactly true) even before
considering any data. Fortunately, in practice a significance test need only
gauge the consistency (or inconsistency) of the observed data with the assumed
hypothesis/model -- without enquiring as to whether the assumption is likely to
be true (or false), or whether some alternative is likely to be true (or
false). In this practical formulation, a significance test rejects a
hypothesis/model only if the observed data is highly improbable when
calculating the probability while assuming the hypothesis being tested; the
significance test only gauges whether the observed data likely invalidates the
assumed hypothesis, and cannot decide that the assumption -- however
unmistakably false -- is likely to be false a priori, without any data.
