According to the New Scientist, Daryl Bern has a paper to appear in Journal of Personality and Social Psychology, which claims that the participants in psychological experiments are able to predict the future. A preprint of this paper is available online. Here's a quote from the New Scientist article:

In one experiment, students were shown a list of words and then asked to recall words from it, after which they were told to type words that were randomly selected from the same list. Spookily, the students were better at recalling words that they would later type.

In another study, Bem adapted research on "priming" – the effect of a subliminally presented word on a person's response to an image. For instance, if someone is momentarily flashed the word "ugly", it will take them longer to decide that a picture of a kitten is pleasant than if "beautiful" had been flashed. Running the experiment back-to-front, Bem found that the priming effect seemed to work backwards in time as well as forwards.

Question: even assuming the methodology is sound, given experimenter bias, publication bias and your priors on the existence of psi, what sort of p-values would you need to see in that paper in order to believe with, say, 50% probability that the effect measured is real?