Statistics group, AgResearch, Lincoln
Room I1.09, I Block, University of Waikato (Note different start time from usual)
Well known multiple comparison procedures (MCP) include the Tukey, Bonferroni and Student-Newman-Keuls tests, Duncan's multiple range test, and Fisher's protected and unprotected LSD tests. In this paper I illustrate the differences between these six procedures by using each MCP to analyse an experiment with 32 treatments, firstly including all treatments in the analysis, then restricting the analysis to subgroups of 13, 4 and 2 treatments that are of interest to different clients. The differing results demonstrate the phenomenon of inconsistency (Saville 1990), or the very similar concept of familywise robustness (Holland and Cheung 2002), perhaps more aptly entitled family-size robustness. The procedure which performs best under both criteria is the unprotected LSD. I therefore advocate usage of this simple procedure in the minority of experiments when an MCP is appropriate, with the proviso that it be treated as an "hypothesis generator," not a procedure for simultaneous formulation and testing of hypotheses.