Feeling the future: A meta-analysis of 90 experiments on the anomalous anticipation of random future events

In 2011, one of the authors (DJB) published a report of nine experiments in the Journal of Personality and Social Psychology purporting to demonstrate that an individual's cognitive and affective responses can be influenced by randomly selected stimulus events that do not occur until after his or her responses have already been made and recorded, a generalized variant of the phenomenon traditionally denoted by the term precognition. To encourage replications, all materials needed to conduct them were made available on request. We here report a meta-analysis of 90 experiments from 33 laboratories in 14 countries which yielded an overall effect greater than 6 sigma, z = 6.40, p = 1.2 × 10 (-10 ) with an effect size (Hedges' g) of 0.09. A Bayesian analysis yielded a Bayes Factor of 5.1 × 10 (9), greatly exceeding the criterion value of 100 for "decisive evidence" in support of the experimental hypothesis. When DJB's original experiments are excluded, the combined effect size for replications by independent investigators is 0.06, z = 4.16, p = 1.1 × 10 (-5), and the BF value is 3,853, again exceeding the criterion for "decisive evidence." The number of potentially unretrieved experiments required to reduce the overall effect size of the complete database to a trivial value of 0.01 is 544, and seven of eight additional statistical tests support the conclusion that the database is not significantly compromised by either selection bias or by intense " p-hacking"-the selective suppression of findings or analyses that failed to yield statistical significance. P-curve analysis, a recently introduced statistical technique, estimates the true effect size of the experiments to be 0.20 for the complete database and 0.24 for the independent replications, virtually identical to the effect size of DJB's original experiments (0.22) and the closely related "presentiment" experiments (0.21). We discuss the controversial status of precognition and other anomalous effects collectively known as psi.