A measure of statistical evidence should permit the sample size determination so that the probability M of obtaining (strong) misleading evidence can be held as low as desired. On this desideratum the p-value fails completely, as it leads either to an arbitrary sample size if M >= 0.01 or no sample size at all, if M < 0.01.
Unlike the p-value, the ratio of likelihoods, the ratio of posteriors, as well as the Bayes Factor, permit controlling the probability of misleading evidence by the sample size.