The Precise Meaning of the Probability Value (2 of 3)
To illustrate that the probability is not the probability of the hypothesis, consider a test of a person who claims to be able to predict whether a coin will come up heads or tails. One should take a rather skeptical attitude toward this claim and require strong evidence to believe in its validity. The null hypothesis is that the person can predict correctly half the time (H0: π = 0.5). In the test, a coin is flipped 20 times and the person is correct 11 times. If the person has no special ability (H0 is true), then the probability of being correct 11 or more times out of 20 is 0.41. Would someone who was originally skeptical now believe that there is only a 0.41 chance that the null hypothesis is true? They almost certainly would not since they probably originally thought H0 had a very high probability of being true (perhaps as high as 0.9999). There is no logical reason for them to decrease their belief in the validity of the null hypothesis since the outcome was perfectly consistent with the null hypothesis.