All the commonly used statistical tests assume that the only information available for performing the test is the data used in the test itself. Where there is other information, such as other studies or theory, this assumption is incorrect and the resulting p-values are also incorrect. The nature of the error in this instance is that where the p-value leading to a conclusion that is contrary to the other evidence then the p-value is smaller than it should be and vice versa. Bayesian statistics provides tools for incorporating other information into statistical testing.
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