One-way ANOVAs, along with a number of other statistical tests, use the F distribution. Earlier in this course you learned about the \(z\) and \(t\) distributions. You computed \(z\) and \(t\) test statistics and used those values to look up p-values using statistical software. Similarly, in this lesson you are going to compute F test statistics. The F test statistic can be used to determine the p-value for a one-way ANOVA.

The video below gives a brief introduction to the F distribution and walks you through two examples of using Minitab to find the p-values for given F test statistics. The steps for creating a distribution plot to find the area under the F distribution are the same as the steps for finding the area under the \(z\) or \(t\) distribution. For the F distribution we will always be looking for a right-tailed probability. Later in this lesson we will see that this area is the p-value.

The F distribution has two different degrees of freedom: between groups and within groups. Minitab will call these the numerator and denominator degrees of freedom, respectively. Within groups is also referred to as error.