Why P values are not measures of evidence

Muff et al. [1] propose to implement the recommendation ‘to regard P values as what they are, namely, continuous measures of statistical evidence’. This is a surprising recommendation, given that P values are not valid measures of evidence [2]. If the null-hypothesis is true, P values are uniformly distributed, and it is just as likely to observe a P value of 0.001 as it is to observe a P value of 0.999. Therefore, the interpretation of P = 0.001 as strong evidence cannot be defended just because the probability to observe this P value is small.