Like other scientists, psychologists believe experimental replication to be the final arbiter for determining the validity of an empirical finding. Reports in psychology journals often attempt to prove the validity of a hypothesis or theory with multiple experiments that replicate a finding. Unfortunately, these efforts are sometimes misguided because in a field like experimental psychology, ever more successful replication does not necessarily ensure the validity of an empirical finding. When psychological experiments are analyzed with statistics, the rules of probability dictate that random samples should sometimes be selected that do not reject the null hypothesis, even if an effect is real. As a result, it is possible for a set of experiments to have too many successful replications. When there are too many successful replications for a given set of experiments, a skeptical scientist should be suspicious that null or negative findings have been suppressed, the experiments were run improperly, or the experiments were analyzed improperly. This article describes the implications of this observation and demonstrates how to test for too much successful replication by using a set of experiments from a recent research paper.