F-test calculator

Reference: Abramowitz and Stegun, page 946

A numerical solution of Fisher's F- probability distribution is obtained when either DF1 or DF2 is even.
When both are even, use the smallest. When both are uneven (odd) an approximate solution is to be found.

Pe = s^n/2 [ 1 + n.t / 2 + n (n+2) t² / 8 + n (n+2) (n+4) t³ / 48 + n (n+2 ) (n+4) (n+6) t⁴ / 384 . . . . . ]

where:

s = n / (n+m.f), t = 1-s, m = DF1, n = DF2, f = F-test value determined from measurements.

Pe = probability of exceedance of the true F-test value over the reference (measured) F-test.

The series of denominators 2, 8, 48, 384 . . . equals the series 2, 2x4, 2x4x6, 2x4x6x8 . . .

The number of terms between the parentheses [ ] to be used is n / 2.

        Pe = 1-t^n/2 [ 1 + n.s / 2 + n (n+2) s² / 8 + n (n+2) (n+4) s³ / 48 + n (n+2) (n+4) (n+6) s⁴ / 384 . . . . . ]

The above equations for Pe are, apart of f, a function of m and n, and can be represented as Pe(m,n).

When DF1=m and DF2=n are both uneven (odd), the ecxceedance probability Pe(m,n) can be approximated by non linear interpolation between Pe(m,n-1) and Pe(m,n+1).
The interpolation can be done with a weight factor (w):

        Pe(m,n) = { w.Pe(m,n+1) + Pe(m,n-1) } / (1+w)

Using w=3 one finds a reasonable approximation.