The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances. The F distribution will be used in Chapter 4 when regression models are tested for significance. Figure 2.14 provides a graph of the F distribution. As with a graph for any continuous distribution, the area underneath the curve represents probability. Note that for a large value of F, the probability is very small.
The F statistic is the ratio of two sample variances from independent normal distributions. Every F distribution has two sets of degrees of freedom associated with it. One of the degrees of freedom is associated with the numerator of the ratio, and the other is associated with the denominator of the ratio. The degrees of freedom are based on the sample sizes used in calculating the numerator and denominator.
Appendix D provides values of F associated with the upper tail of the distribution for certain probabilities (denoted by
To find the F value that is associated with a particular probability and degrees of freedom, refer to Appendix D. The following notation will be used:
Consider the following example:
From Appendix D, we get
This means
The probability is very low (only 5%) that the F value will exceed 4.39. There is a 95% probability that it will not exceed 4.39. This is illustrated in Figure 2.15. Appendix D also provides F values associated with