# Re: [R] Question about Tukey HSD (stat package)

From: JRG <loesljrg_at_verizon.net>
Date: Tue 15 Mar 2005 - 06:38:10 EST

On 14 Mar 2005 at 17:22, Peter Dalgaard wrote:

> "JRG" <loesljrg@verizon.net> writes:
>
> > On 14 Mar 2005 at 16:13, Peter Dalgaard wrote:
> >
> > > Alice Le Bars <alice.le-bars@nantes.inserm.fr> writes:
> > >
> > > > Dear all,
> > > >
> > > > I would be glad if someone could tell me if Tukey HSD (function of
> > > > stats library) accept the NA values and could correct the unbalanced
> > > > design (different number of sample in each group)
> > >
> > > I don't think the *theory* of the HSD allows this. There is some more
> > > or less well-founded speculation that if the imbalance is not too bad,
> > > then the HSD results are somewhat useful anyway, but please consider
> > > using the multcomp package, which is specifically designed to get
> > > these things right.
> > >
> >
> > I believe that Hayter (JASA, 1984, 12, 61--75) proves that the so-called Tukey-Kramer method is guarnateed to be conservative for
> > any set of cell sizes --- under the usual ANOVA model, of course.
>
> Make that Annals of Statistics, not JASA.
>
> Hayter proves that simultaneous confidence intervals based on using
> the Studentized range distribution with (1/ni+1/nj)/2 instead of 1/n
> will have coverage at least (1 - \alpha). He doesn't say *how*
> conservative it is, though, and it doesn't change the fact that
> multcomp has a better idea.
>

Whoops, let it be Annals. However, there is a paper by Dunnett (ca 1981) which I again believe to be JASA which shows that the degree of conservativism is pretty slight, over a broad range of cell sizes. Your point about multcomp stands.

---JRG
> --
> O__ ---- Peter Dalgaard Blegdamsvej 3
> c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
> (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
> ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907

John R. Gleason
Associate Professor

Syracuse University

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