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MATHEMATICS A numerical solution of Fisher's F probability distribution is obtained when either DF1 or DF2 are even. (See reference below.) When both are even, use the smallest. When both are uneven (odd) an approximate solution is to be found. DF1 is even Pc = 1  s^{n/2} [ 1 + n.t / 2 + n (n+2) t^{2} / 8 + n (n+2) (n+4) t^{3} / 48 + n (n+2 ) (n+4) (n+6) t^{4} / 384 . . . . . ] where:
s = n / (m+n.z), t = 1s, m = DF1, n = DF2, z =
reference value for the variable y following the
Fdistribution Pc = cumulative probability that can also be represented by the probability P(y<z) that y is less than z. 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. DF2 is even
Pc = t^{n/2} [ 1 + n.s / 2 + n (n+2)
s^{2}) / 8 + n (n+2) (n+4) s^{3} /
48 + n (n+2) (n+4) (n+6) s^{4} /
384 . . . . . ] DF1 and DF2 are uneven (odd) The above equations for Pc are, apart of z, a function of m and n, and can be represented as Pc(m,n). When DF1=m and DF2=n are both uneven (odd), the cumulative probability Pc(m,n) can be approximated by non linear interpolation between Pc(m,n1) and Pc(m,n+1). The interpolation can be done with a weight factor (w): Pc(m,n) = { w.Pc(m,n+1) + Pc(m,n1) } / (1+w) Using w=3 one finds a reasonable approximation. Reference: Casio, 1990. "Program library". Manual for Casio's programmable calculators. See online.

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