Chapter 6: F-Test and One-Way ANOVA

Years ago, statisticians discovered that when pairs of samples are taken from a normal population, the ratios of the variances of the samples in each pair will always follow the same distribution. Not surprisingly, over the intervening years, statisticians have found that the ratio of sample variances collected in a number of different ways follow this same distribution, the F-distribution. Because we know that sampling distributions of the ratio of variances follow a known distribution, we can conduct hypothesis tests using the ratio of variances.

The F-statistic is simply:

$$F=s_1^2/s_2^2$$

where s₁² is the variance of sample 1. Remember that the sample variance is:

$$s^2=\sum (x-\bar{x}{)}^2/(n-1)$$