Hi all,
I've spent quite a lot of time searching through the help lists and reading
about how best to run perform a 2-way ANOVA with unbalanced data. I realize
this has been covered a great deal so I was trying to avoid adding yet
another entry to the long list considering the use of different SS, etc.
Unfortunately, I have come to the point where I feel I have to wade in and
see if someone can help me out. Hopefully I'll phrase this properly given
and hopefully it will end up only requiring a simple response.
I have an experiment where I have measured a response variable (such as
water content) following exposure to two treatments ("oxygen content" and
"medium"). Oxygen content has three levels (5, 20, 35) and medium has two
levels (Air, Water). I am interested if water content is different under
the two treatments and whether the effect of oxygen content depends upon
the medium in which the experiment was conducted (Air or Water).
Unfortunately, the design is unbalanced as some experimental subjects had
to be removed from the experiment.
I realize that if I just use aov() to perform a two-way ANOVA the order in
which the terms ("oxygen content" and "medium") are entered will give
different results because of the sequential SS.
What I have done in the past is utilize drop1() in conjunction with aov()
drop1(aov(WaterContent~Oxygen*Medium, data), test="F")
to see if the interaction term was significant (F, p-value) and if its
inclusion improved model fit (AIC). If from this I determine that the
interaction term can be removed and the model can be rerun without it, I am
able to test for main-effects and get F and p-values that I can report in a
manuscript.
However, if the interaction term is significant and its inclusion is
warranted, drop1() only provide me with SS, F, and p-value for the
interaction term. Now this is fine, because I do not wish to interpret the
main-effects with a significant interaction, but in a manuscript reviewers
will request an "ANOVA table" where l will be asked to report SS, F and
p-values for the other terms. I don't have those because I used drop1()
which only provides these for the highest order term in the model.
How best should I calculate the values that I know I will be asked to
provide in a manuscript?
I don't wish to come across as a scientist who is simply a slave to the F
and p-values with little regard for the data, the hypotheses, and the
actual statistical interpretation. I am interested in doing this "right",
but I also know that practically in the current status of our field, while
I focus on doing statistics that address my hypotheses of interest and can
choose to not discuss the main effects in isolation when an interaction
exists, I will be asked to provide the "ANOVA table" with all the degrees
of freedom, SS, F-values, p-values etc...for the entire model, not just the
highest order term.
Can anyone provide advice here? Should I just use the car package and Type
III SS with an appropriate contrast and not use the drop1() function, even
though I'm really not interested in using the Type III SS and I kinda like
the drop1()? I am not opposed to Type II SS, but clearly if the interaction
is important then using Type II SS, which do not consider interactions, are
not appropriate.
Hopefully this is somewhat clear and doesn't simply sound like a rehashing
of the same old "ANOVA and SS" story. Maybe I should be doing something
completely different
I greatly appreciate constructive comments.
Thanks,
Nate
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