The test
of a given statistical hypothesis entails an assessment of whether or not our
sample (or samples) have yielded a statistic that is among those cases that would
only occur alpha proportion of the time if the hypothesis tested is true.
In
these circumstances we know the probability of rejecting the hypothesis tested
when it is true (that probability is equal to alpha) but unless we have also specified
an alternative hypothesis to the hypothesis tested, we have no idea of the probability
of being in error, if our test has failed to yield a value that enables us to
reject the hypothesis tested.
