Methods of controlling the Type I error and dependencies between point estimates when making multiple comparisons between effect means in a linear model.
When making all pairwise comparisons this procedure is also known as unprotected Fisher's LSD, or when only performed following significant ANOVA F -test known as protected Fisher's LSD.
Controls the Type I error rate individually for each contrast.
Controls the error rate simultaneously for all k(k+1)/2 contrasts.
Controls the error rate simultaneously for all k contrasts.
Controls the error rate simultaneously for all k-1 contrasts.
Controls the error rate simultaneously for all possible contrasts.
A useful application of Bonferroni inequality is when there are a small number of pre-planned comparisons. In this case, use the Student's t (LSD) method with the significance level (alpha) set to the Bonferroni inequality (alpha divided by the number of comparisons). In this scenario, it is usually less conservative than using Scheffé all contrast comparisons.
