Table 9.10.3: 0.975 Fractilesa of the F Distribution Associated with n1 and n2 degrees of Freedom F.975 (n1,n2) (Continued)

a The following equation may be used to compute 0.975 fractiles of the F distribution in lieu of using table values:

$\mathrm{F}_{.975} \approx \exp \left[2 \delta\left(1+\frac{z^{2}-1}{3}-\frac{4 \sigma^{2}}{3}\right)+2 \sigma z\left(1+\frac{\sigma^{2}\left(z^{2}-3\right)}{6}\right)^{1 / 2}\right]$

where

z = 1.96 δ = 0.5 [1/(γ₂ - 1) - 1/(γ₁ - 1)] σ² = 0.5 [(1/(γ₂ - 1) + 1(γ₁ - 1)] γ₁ = degrees of freedom for numerator γ₂ = degrees of freedom for denominator.

This approximation is accurate to within $0.4 \%$ for $\gamma_{1} \geq 10$ and $\gamma_{2} \geq 16$. See Reference 9.10.3.