[R] nested anova and multiple comparisons

Stephen Cole swbcole at gmail.com
Sat Apr 26 19:29:53 CEST 2008

Hello R List:

My problem is with a nested anova.  I have read the r-help and it has
answered some of my questions but i still need some help on this one.
I have also posted for help on this data set before, so i apologize in
advance for any repetition.

My design is as follows:

response: Quadrat Counts (individuals per quadrat)

Explanatory: Region (3 regions)
                 Locations (4 locations nested within each region
for a total of 12)
                 Site (4 sites nested within each location within
each region for a total of 48)

I want to analyse this data set as an observational study where i am
interested if 1) There is significant variation at each scale in the

                                           2) partition the variance
components for each scale.

                                           3) Conduct multiple
comparisons at the highest level in the study (region)

I have managed to accomplish my first two goals by analyzing the data
as a 3 level nested Anova with the following code

mod1 <- aov(Count~Region/Location/Site, data=data)

This allows me to get the MS for a Anova table.   However R does not
compute the correct F-statistics (because it uses the residual MS for
the denominator in all calculations which it shouldnt) so i manually
computed the F-stats and variance components by hand.

>From reading the help guide i learned about and tried using the
Error(Region/Location/Site) command but then i can only get MS and no
F-statistics and still hand to compute the rest by hand.

My problem now is that i would liek to use TukeyHSD for multiple
comparisons.  Howeber since R is unable to compute the correct F
statistics in this nested design i also think it is using the wrong MS
and df in calculating tukeys q. for example when i use

TukeyHSD(mod1, "Region")  i will get values however i do not think
they have been calculated correctly.

Furthermore when i use the Error(Region/Location/Site) term i can then
no longer use TukeyHSD as i get the error message that there is no
applicable use of tukey on this object.

i am just wondering if there is any way to use Multiple comparisons
with R in a nested design like mine.

I have thought about using lme or lmer but if i understand them right
with a balanced design i should be able to get the same result using


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