Empirical replication has long been considered the final arbiter of phenomena in science, but replication is undermined when there is evidence for publication bias. Evidence for publication bias in a set of experiments can be found when the observed number of rejections of the null hypothesis exceeds the expected number of rejections. Application of this test reveals evidence of publication bias in two prominent investigations from experimental psychology that have purported to reveal evidence of extrasensory perception and to indicate severe limitations of the scientific method. The presence of publication bias suggests that those investigations cannot be taken as proper scientific studies of such phenomena, because critical data are not available to the field. Publication bias could partly be avoided if experimental psychologists started using Bayesian data analysis techniques.