Methods of controlling the Type I error and dependencies between parameters when making multiple comparisons between many means/medians of independent samples.
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.
Control the type I error rate is for each contrast.
Control the type I error rate 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 k-1 comparisons.
Controls the error rate simultaneously for all possible contrasts.
As discussed in Hsu (1996) it is not a confident inequalities method and cannot be recommended.
A joint-ranking nonparametric method but as discussed in Hsu (1996) it is not a confident inequalities method and cannot be recommended. Use the Dwass-Steel-Critchlow-Fligner or Steel test instead.
As discussed in Hsu (1996) applying parametric methods to the rank-transformed data may not produce a confident inequalities method even if the parametric equivalent it mimics is. Use the Dwass-Steel-Critchlow-Fligner or Steel test instead.
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.
