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NO EVIDENCE FOR PSI

8

>

100

0 Extreme evidence for H

30

100

0 Very Strong evidence for H

10

30

0 Strong evidence for H

3

10

0 Substantial evidence for H

1

3

0 Anecdotal evidence for H

1

No evidence

1/3

1

1 Anecdotal evidence for H

1/10

1/3

1 Substantial evidence for H

1/30

1/10

1 Strong evidence for H

1/100

1/30

1 Very strong evidence for H

<

1/100

1 Extreme evidence for H

Table 1: Classification scheme for the Bayes factor, as proposed by Jeffreys (1961). We replaced the labels “worth no more than a bare mention” with “anecdotal”, and “decisive” with “extreme”.

B a y e s f a c t o r , B F 0 1

Interpretation

makers & Gr¨unwald, 2006), particularly in the context of psi (e.g., Bayarri & Berger, 1991; Jaynes, 2003, Chap. 5; Jefferys, 1990).

To illustrate the extent to which Bem’s conclusions depend on the statistical test that was used, we have reanalyzed the Bem experiments with a default Bayesian t-test (G¨onen e t a l . , 2 0 0 5 ; R o u d e r e t a l . , 2 0 0 9 ) . T h i s t e s t c o m p u t e s t h e B a y e s f a c t o r f o r H 0 v e r s u s H 1 , a it is important to note that the prior model odds plays no role whatsoever in its calculation (see also Equations 1 and 2). One of the advantages of this Bayesian test is that it also allows researchers to quantify the evidence in favor of the null hypothesis, something that is impossible with traditional p-values. Another advantage of the Bayesian test that it is consistent: as the number of participants grows large, the probability of discovering the true hypothesis approaches 1. n d

The Bayesian t-Test

Ignoring for the moment our concerns about the exploratory nature of the Bem stud- ies, and the prior odds in favor of the null hypothesis, we can wonder how convincing the statistical results from the Bem studies really are. After all, each of the Bem studies fea- tured at least 100 participants, but nonetheless in several experiments Bem had to report one-sided (not two-sided) p-values in order to claim significance at the .05 level. One might intuit that such data do not constitute compelling evidence for precognition.

I n o r d e r t o a s s e s s t h e s t r e n g t h o f e v i d e n c e f o r H 0 ( i . e . , n o p r e c o g n i t i o n ) v e r s u s (i.e., precognition) we computed a default Bayesian t-test for the critical tests reported in Bem (in press). This default test is based on general considerations that represent a lack of knowledge about the effect size under study (G¨onen et al., 2005; Rouder et al., 2009; for a generalization to regression see Liang, Paulo, Molina, Clyde, & Berger, 2008). More specific assumptions about the effect size of psi would result in a different test. We decided to first apply the default test because we did not feel qualified to make these more specific assumptions, especially not in an area as contentious as psi. H 1

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