Consider the following syllogism:
- If a person is an American, he is probably not a member of Congress.
- This person is a member of Congress.
- Therefore he is probably not American.
As John D. Cook writes:
We can’t reject a null hypothesis just because we’ve seen data that are rare under this hypothesis. Maybe our data are even more rare under the alternative. It is rare for an American to be in Congress, but it is even more rare for someone who is not American to be in the US Congress!