Hierarchical Model as an ANOVA

[simonbrauer]

@Isabela_Castro

The frequentist method ANOVA is not suitable because it usually does not give a significant p-value. Sometimes the difference is so small that it does not seem important (but it is!).

Note that the partial-pooling/random effects ANOVA approach is more conservative than the no-pooling approach (assuming you don’t adjust for multiple tests, e.g. Bonferroni) because it shrinks the treatment means toward each other. So it wouldn’t achieve that specific goal.