On Graphical Procedures for Multiple Comparisons
Yosef Hochberg, Gideon Weiss and Sergiu Hart
In a graphical procedure for comparing k treatment means
in a one-way ANOVA, one displays
uncertainty intervals around the sample means and judges
any pair to be significantly different if and only if
their uncertainty intervals do not overlap.
A graphical procedure is a Multiple Comparison Procedure
(MCP) if and only if it controls the experimentwise error rate.
In this paper we consider some new
graphical MCP's for the unbalanced one-way ANOVA design.
These procedures are based on different
approximations to the Tukey-Kramer (TK) procedure
(e.g., Kramer 1956). As such, they constitute
alternatives to Gabriel (1978) (and its modification by
Andrews, Snee, and Sarner 1980), which is based
on approximating a less efficient MCP (the GT2 of Hochberg 1974).
Two of the four procedures
considered here are based on best and simple upper bounds
to all the confidence-interval lengths of the
TK method and hence must be conservative.
The other two procedures are based on approximations
(here too we have the best vs. the simple procedure),
but simulations were used to find that their true
experimentwise error rates are less than the nominal ones;
that is, these procedures are still on the
conservative side. The choice of a particular procedure
will depend then on the relative importance of
simplicity, efficiency, and the security of having a
controlled experimentwise error rate.
Analysis of variance, Simultaneous pairwise comparisons, Graphical display
Journal of the American Statistical Association 77 (1982), 380,