The F-distribution is the sampling distribution of the ratio of the variances of two samples drawn from a normal population. It is used directly to test to see if two samples come from populations with the same variance. Though you will occasionally see it used to test equality of variances, the more important use is in analysis of variance, (ANOVA). ANOVA, at least in its simplest form as presented in this chapter, is used to test to see if three or more samples come from populations with the same mean. By testing to see if the variance of the observations comes more from the variation of each observation from the mean of its sample or from the variation of the means of the samples from the grand mean, ANOVA tests to see if the samples come from populations with equal means or not.
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