Let’s Summarize

• The null hypothesis is that all the group population means are the same. The alternative hypothesis is that at least one pair of means is different.
• A one-way ANOVA uses variances to help determine if the means are equal or not.

• The F-statistic (or ratio) has two degrees of freedom associated with it.
• The F-statistic compares the variability between groups and the variability within groups. If these variabilities are similar, the F-statistic ratio is close to 1.
• A one-way ANOVA is always a right-tail test.
• Another test that follows an F distribution is a test of two variances, which may be one-tailed or two-tailed.