Key Concepts

• 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.
• The null hypothesis states all samples come from populations having the same normal distribution. The alternate hypothesis states at least two of the samples come from populations with different normal distributions.
• A one-way ANOVA is always a right-tail test.

Glossary

F-Ratio: a ratio used as the test statistic in a one-way ANOVA; the formula is [latex]F= \frac{MS_ \mathrm{between}}{MS_ \mathrm{within}}[/latex].

NOTE: [latex]MS_ \mathrm{between} = \frac{SS_ \mathrm{between}}{df_ \mathrm{between}} = \frac{SS_ \mathrm{between}}{k-1}[/latex], [latex]MS_ \mathrm{within} = \frac{SS_ \mathrm{within}}{df_ \mathrm{within}} = \frac{SS_ \mathrm{within}}{n-k}[/latex], where [latex]n[/latex] is the total sample size, [latex]k[/latex] is the number of groups (or factors), [latex]SS_ \mathrm{between}[/latex] is a measure of variability between groups and [latex]SS_ \mathrm{within}[/latex] is a measure of variability within a group.