The Precise Meaning of the Probability Value (3 of 3)
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The proper interpretation of the test is as follows: A person made a rather
extraordinary claim and should be able to provide strong evidence in support
of the claim if the claim is to believed. The test provided data consistent
with the null hypothesis that the person has no special ability since a
person with no special ability would be able to predict as well or better
more than 40% of the time. Therefore, there is no compelling reason to believe
the extraordinary claim. However, the test does not prove the person cannot
predict better than chance; it simply fails to provide evidence that he
or she can. The probability that the null hypothesis is true is not determined
by the statistical analysis conducted as part of hypothesis testing. Rather,
the probability computed is the probability of obtaining data as different
or more different from the null hypothesis (given that the null hypothesis
is true) as the data actually obtained.
Next section: At what level is H0 really rejected?