Date: Mon, 29 Jun 2009 12:28:11 -0400
Reply-To: Susan Durham <sdurham@BIOLOGY.USU.EDU>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Susan Durham <sdurham@BIOLOGY.USU.EDU>
Subject: Re: Fisher's Protected LSD versus Tukey's HSD
On Mon, 29 Jun 2009 10:12:39 -0400, Kevin Viel <citam.sasl@GMAIL.COM> wrote:
> I performed a one-factor ANOVA with approximately 8 levels and 100
>observations (unbalanced). The omnibus F test suggested that at least one
>mean is different. An investigator requested Fisher's protected LSD.
>Originally, I used the Tukey's HSD.
> For a few comparisons, there is a difference. Does anyone have an
>opinion concerning which test is more appropriate?
>Atlanta, Georgia, USA
Such a can of worms!
A useful reference for the standard multiple comparison methods is
RW Day & GP Quinn, 1989, Comparisons of treatments after an analysis of
variance in ecology, Ecological Monographs 59(4), 433-463.
On pp450-451, Day and Quinn say "Carmer and Swanson (1973) and others have
claimed that the Fisher's protected LSD test controls the EER
[experiment-wise error rate] at the specified level by virtue of the
preliminary overall F test. This will only be true when there are no real
differences between treatments, as shown by Carmer and Swanson's (1973) own
simulation results.... Where some mean differ, the protected test functions
as a simple LSD test for comparisons within groups; it has a per-comparison
type I error rate...."
In contrast, Tukey's HSD does control EER, although conservatively. Day &
Quinn's simulations indicate that Tukey's comes in at about half the nominal
rate in some comparisons (see their Fig. 1), so it is possible to have an
overall test significant at <0.05 but no pairwise comparisons significant at
<0.05, as Peter notes in his response to your post.
A choice between Fisher's protected LSD and Tukey's HSD is a choice between
apples and oranges: the former controls comparison-wise Type I error, and
the latter controls experiment-wise Type I error. Since you originally used
Tukey's, you can argue that you've chosen to control EER, which the
protected LSD doesn't do.
Utah State University
Logan, UT 84322-5205