Comparing means across three or more groups
One-way ANOVA tests whether the means of three or more independent groups differ significantly. It answers: do these three drug treatments yield different average symptom reduction, or are observed differences just noise? The left side of the diagram shows three overlapping distributions with their group means marked, making the apparent differences concrete.
ANOVA avoids the multiple-testing problem of running pairwise t-tests, which inflate false positive rates when you have many groups to compare.
The F-statistic and rejection region
The right side displays the F-distribution, a right-skewed probability distribution. The F-statistic (a ratio of between-group variance to within-group variance) is plotted on this axis. Large F-values are rare under the null hypothesis, so they fall into the shaded rejection region at the tail. If your computed F falls there, you reject the null and conclude at least one group mean truly differs from the others.