The F-statistic in the context of ANOVA allows us to test the null hypothesis that there are no differences across groups relative to the alternative hypothesis that there are differences between groups with respect to the mean of the continuous response. $F = \frac{SS_{treat}/(J-1)}{SS_{resid}/(n-J)}$ Note that this F-statistic is equivalent to the F-statistic in the context of [[base/R/linear regression]]. In [[R]], ANOVA can be run with `aov()`, wrap with `anova()` to get more information. ```R anova(aov(y ~ x, data = df)) ``` The residual standard error from the report is calculated as $\hat \sigma = \sqrt{\frac{SS_{resid}}{df_{resid}}}$