A Bayes factor meta-analysis of recent extrasensory perception experiments: comment on Storm, Tressoldi, and Di Risio (2010).

Psi phenomena, such as mental telepathy, precognition, and clairvoyance, have garnered much recent attention. We reassess the evidence for psi effects from Storm, Tressoldi, and Di Risio's (2010) meta-analysis. Our analysis differs from Storm et al.'s in that we rely on Bayes factors, a Bayesian approach for stating the evidence from data for competing theoretical positions. In contrast to more conventional analyses, inference by Bayes factors allows the analyst to state evidence for the no-psi-effect null as well as for a psi-effect alternative. We find that the evidence from Storm et al.'s presented data set favors the existence of psi by a factor of about 6 billion to 1, which is noteworthy even for a skeptical reader. Much of this effect, however, may reflect difficulties in randomization: Studies with computerized randomization have smaller psi effects than those with manual randomization. When the manually randomized studies are excluded and omitted studies included, the Bayes factor evidence is at most 330 to 1, a greatly attenuated value. We argue that this value is unpersuasive in the context of psi because there is no plausible mechanism and because there are almost certainly omitted replication failures.