11.9 The F Distribution

The F distribution is another family of curves whose shape differs according to the degrees of freedom. The pdf of the F distribution is

These curves differ not only according to the size of the samples, but also on how many samples are being compared. The F distribution has two sets of degrees of freedom, df ₁(degrees of freedom for the numerator) and df ₂ (degrees of freedom for the denominator). The designation of an F distribution with 10 degrees of freedom for the numerator, and 15 degrees of freedom for the denominator is df = ( df ₁, df ₂) = ( 10, 15).

Figure 11.21 shows two F distributions, one with df( 8, 40), and the other with df( 8, 4).

Figure 11.21: The F distribution for different degrees of freedom.

The mean ? of the F distribution is given by

Thus, for the F distribution with df( 8, 40),

and for the other with df( 8, 4),

The variance of the F distribution is given by

Percentile values of the F distribution for different degrees of freedom are denoted as F _p and can be found in math tables such as the CRC Standard Mathematical Tables. The tables give values of x for the cdf

The F distribution tables are based on the df ₁ and df ₂ degrees...