Post-hoc testing of ANOVAs
Multiple comparison procedures are commonly used in an analysis of variance after obtaining a significant omnibus test result, like the ANOVA F-test. The significant ANOVA result suggests rejecting the global null hypothesis H0 that the means are the same across the groups being compared. Multiple comparison procedures are then used to determine which means differ. In a one-way ANOVA involving K group means, there are K(K − 1)/2 pairwise comparisons.
A number of methods have been proposed for this problem, some of which are:
- Tukey–Kramer method (Tukey's HSD) (1951)
- Scheffe method (1953)
Multi-step procedures based on Studentized range statistic
- Duncan's new multiple range test (1955)
The Nemenyi test is similar to Tukey's range test in ANOVA.
The Bonferroni–Dunn test allows comparisons, controlling the familywise error rate.[vague]
- Student Newman-Keuls post-hoc analysis
- Dunnett's test (1955) for comparison of number of treatments to a single control group.
I was wondering what "single-step" and "multi-step" mean here?
Are they both for pairwise comparisons for every two groups, right?
Thanks and regards!