Two-way Fisher F-test calculator for analysis of variance (Anova)
Entirely free download of software

The F-test is used in analysis of variance (Anova) to test the difference between standard deviations under varying conditions.

The calculator program gives the probability of an F-test, given the F-value and
degrees of freedom of numerator (DF1) and denominator (DF2), and reversely
the value of the F-test given the probability.

For examples see: Anova table.

Screenprint of the two-way Fisher F-test calculator model:

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F-test calculator
F-distribution calculator

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            More examples of F-test model graphics in the F-test calculator software

            cumulative normal distribution
            In the F-test calculator model Fisher's cumulative
            F-distribution is used
            normal density distribution
            In the F-test calculator software Fishers's density
            F-distribution is used


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.

DF1 is even

        Pc = 1 - sn/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 . . . . . ]


s = n / (m+n.z), t = 1-s, m = DF1, n = DF2, z = reference value for the variable y following the F-distribution
      (like the F-test value itself),

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 = tn/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 . . . . . ]

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,n-1) 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,n-1) } / (1+w)

Using w=3 one finds a reasonable approximation.

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