Hello Tom:
It is important to remember that the afni cdf program converts to and from
TAIL probabilities.
Taking your example with F[1,10] = 2:
First, let's calculate the probability of obtaining an F-value greater than 2:
cdf -t2p fift 2.0 1 10
yields:
p = 0.18767
This means that, if F ~ F[1,10], then Pr(F > 2) = 0.18767.
Now, let's find the value z for Z ~ N[0,1], such that
Pr(Z < -z) + Pr(Z > z) = 0.18767.
cdf -p2t fizt 0.18767
yields:
t = 1.3175
This means that Pr(Z < -1.3175) + Pr(Z > 1.3175) = 0.18767.
And, indeed, this is what we get by converting directly from the F-value
to the corresponding Z-value:
cdf -t2z fift 2.0 1 10
yields:
z = 1.3175
The result of the F to Z conversion is always a positive number. In the most
general case, it is not possible to assign a sign to the z-score obtained from
the F-value. However, for the special case where the numerator degrees of
freedom for the F-stat is 1 (e.g., F[1,10]), then it is possible to attach
a sign. For example, if the F-values came from a sub-brick produced by the
"-glt" option of 3dDeconvolve, where the GLT was a single linear combination,
then you can use 3dcalc to multiply by the sign of the corresponding linear
combination (e.g., the sign of the LC[0] coef. sub-brick).
Doug Ward
