After fitting a linear regression model using lm, we can feed that into the anova function. Thus, we get the corresponding sum of squares and F-tests. But since analysis of variance (ANOVA) relies on a sum of squares (or linear regression residuals) it also suffers from the presence of outliers.

The mechanics here are quite similar to the non-robust/standard way: first, we do the robust regression model, and then we pass the estimated model into the anova.lmrob function.