  Both the Bayes factor and the relative belief ratio satisfy the principle of
evidence and so can be seen to be valid measures of statistical evidence.
Certainly Bayes factors are regularly employed. The question then is: which of
these measures of evidence is more appropriate? It is argued here that there
are questions concerning the validity of a current commonly used definition of
the Bayes factor based on a mixture prior and, when all is considered, the
relative belief ratio has better properties as a measure of evidence. It is
further shown that, when a natural restriction on the mixture prior is imposed,
the Bayes factor equals the relative belief ratio obtained without using the
mixture prior. Even with this restriction, this still leaves open the question
of how the strength of evidence is to be measured. It is argued here that the
current practice of using the size of the Bayes factor to measure strength is
not correct and a solution to this issue is presented. Several general
criticisms of these measures of evidence are also discussed and addressed.
