A new standard is proposed for the evidential assessment of replication studies. The approach combines a specific reverse-Bayes technique with prior-predictive tail probabilities to define replication success. The method gives rise to a quantitative measure for rep- lication success, called the skeptical p-value. The skeptical p -value integrates traditional significance of both the original and replication study with a comparison of the respective effect sizes. It incorporates the uncertainty of both the original and replication effect estimates and reduces to the ordinary p -value of the replication study if the uncertainty of the original effect estimate is ignored. The proposed framework can also be used to determine the power or the required replication sample size to achieve replication success. Numerical cal- culations highlight the difficulty to achieve replication success if the evidence from the original study is only suggestive. An application to data from the Open Science Collaboration project on the replicability of psychological science illustrates the proposed methodology.