Hi:

On Thu, Oct 21, 2010 at 4:13 PM, mirick <mirick2@yahoo.com> wrote:

>
> Hello all,
> Can any of you R gurus help me out?  I’m not all that great at stats to
> begin with, and I’m also learning the R ropes (former SAS user).
>

Sounds like you need a support group :)


> Here’s what I need help with…  I have a nested sample design and ran a
> nested anova, but I don’t know how to interpret the results
> habitat (four different types) is nested in site (three types), and site is
> nested in gear (two types)
>  My  code:    pat2<-aov(catchrate~habitat/site/gear, data=pat)
> This created the following outcome:
>                               Df               Sum Sq           Mean Sq
> F value                      Pr(>F)
> habitat                   3                2.932              0.9774
> 0.9543               0.4155656
> habitat:site           8                18.716            2.3395
> 2.2842                0.0235207
> habitat:site:Gear  12             39.244            3.2704
> 3.1930                0.0003546
> Residuals              186 190.505  1.0242
>
>  What exactly does this outcome mean?   It looks like there are differences
> between gears and sites, but not among habitats.  Which gear is better,
> which site is better, which gear works better in each site, etc.?
> I’ve looked for some post hoc code to do this, but I can’t find anything
> and
> I am at wits end.
> Thanks,
> Rick M.
>
>
Firstly, in a nested design, one often treats nested factors as random. You
appear to want to treat them as fixed, which means that you are only
interested in comparisons among the 24 habitats in your study, which are
nested within the six sites which in turn are nested within the two types of
gear.  Is that correct?

Secondly, the degrees of freedom allocation should clue you in that
something is amiss, which would be your model specification. In R, nesting
works top-down, so your model should be
aov(catchrate ~ gear/site/habitat, data = pat)

BTW, 186 df for residual? Do you have nine observations in each habitat? Are
the data balanced within habitat (i.e., no missing data)?  Your ANOVA should
look like

Gears                          1
Gears/Sites                 4
Gears/Sites/Habitat    18

if your description is correct. According to your ANOVA, you have 210
observations. If you had nine observations per habitat, there would be 216
observations total, so is it reasonable to conclude you either have missing
responses or unbalanced data within habitat? If so, how severe is the
imbalance?

Thirdly, as far as multiple comparisons go, you need to be very careful to
use the correct variance estimate at each level. However, it seems to me
that comparisons would only make sense within level (assuming they make
sense at all); e.g., comparing the four habitats in a particular site, and
repeating the comparison for each site.

I'd consider investing some time deriving the means and variances of each
set of level means in the hierarchy. That should help sort out some of your
questions. For example, there is only one comparison of gears, and the two
gear means are obtained by averaging the 105 or so observations they each
contain. This averages out site and habitat effects, so asking which gear
works better in each site is an impossible question to answer since each
site is associated with exactly one gear (by the definition of nested
factors). You can compare the three sites within a particular gear, but you
can't compare sites across both gears, because each site is associated with
only one gear. Similarly, each habitat is associated with exactly one site,
and hence one gear. This is what I mean when suggesting that you sit down
and work out the algebra, to understand which effects can be compared and
which can't, along with an understanding of how the variances of the means
at each level of the hierarchy are derived and how they differ.

HTH,
Dennis

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