Methods of controlling the Type I error and dependencies between point estimates when making multiple comparisons between effect means in a linear model.
||Purpose / Assumptions
|Student's t (Fisher's LSD)
||Compare the means of each pair of groups using the Student's t method.
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.
||Compare the means of all pairs of groups using the Tukey-Kramer method.
the error rate simultaneously for all k(k+1)/2 contrasts.
||Compare the means of all groups against the best of the other groups using the Hsu
Controls the error rate simultaneously for all k contrasts.
||Compare the means of all groups against a control using the Dunnett
Controls the error rate simultaneously for all k-1 contrasts.
||Compare the means of all groups against all other groups using the Scheffé F
Controls the error rate simultaneously for all possible
||Not a multiple comparisons method. It is an inequality useful in producing easy to compute multiple comparisons. In most scenarios, there are more powerful procedures such as Tukey, Dunnett, Hsu.
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.