I'm curious to know how the cdf program converts test statistics to p-values. The help file for cdf is somewhat terse. I've tried to figure this out on my own for the correlation coefficient and I came up with using Fisher's z transformation (Fisher 1920) to go from r to z and then 1-cumulative density function(z) to go from z to p. But the result doesn't exactly match that of the cdf program. One paper (Bandettini et al. 1993) suggested another equation, which seems to give a third value. Perhaps there is no perfect method to map [-1,+1] to (-inf,+inf), but I would like to know how cdf does it for r values (as well as other test statistics). Any and all references would be helpful.

By the way, I'm a grad student teaching myself fmri, and I was wondering: why does it seem like I need a PhD in statistics before I can get a PhD in fmri?


References

Bandettini PA, Jesmanowicz A, Wong EC, Hyde JS. 1993. Processing Strategies for Time-Course Data Sets in Functional MRI of the Human Brain. Mag. Reson. Med. 30: 161-173.

Fisher RA. 1920. On the "Probable Error" of a Coefficient of Correlation deduced from a Small Sample. Metron 1: 3-32.