Often data is gathered across several groups and we wish to make inferences about the population means for those groups. Rather than conducting multiple hypothesis tests to compare two means, an Analysis of Variance (or ANOVA) is conducted. This requires a new statistic, known as the F statistic, and a new distribution, known as the F distribution. For example, based on these boxplots for the GPAs of a random sample of students at four colleges, do we think the mean GPAs are different at these colleges? Although we can see differences within the plots, an ANOVA would need to be done to completely answer this question.