[R] ANOVA and Pseudoreplication in R

[Bert Gunter]

I can hopefully save bandwidth here by suggesting that this belongs on
the R-sig-mixed-models list.

-- Bert

As an aside, shouldn't you be figuring this out yourself or seeking
local consulting expertise?

On Fri, Feb 25, 2011 at 9:08 AM, Ben Ward <benjamin.ward at bathspa.org> wrote:
> Hi, As part of my dissertation, I'm going to be doing an Anova, comparing
> the "dead zone" diameters on plates of microbial growth with little paper
> disks "loaded" with antimicrobial, a clear zone appears where death occurs,
> the size depending on the strength and succeptibility. So it's basically 4
> different treatments, and I'm comparing the diameters (in mm) of circles.
> I'm concerned however, about Pseudoreplication and how to deal with it in R,
> (I thought of using the Error() term.
>
> I have four levels of one factor(called "Treatment"): NE.Dettol, EV.Dettol,
> NE.Garlic, EV.Garlic.   ("NE.Dettol" is E.coli not evolved to dettol,
> exposed to dettol to get "dead zones". And the same for NE.Garlic, but with
> garlic, not dettol. "EV.Dettol" is E.coli that has been evolved against
> dettol, and then tested afterwards against dettol to get the "dead zones".
> Same applies for "EV.Garlic" but with garlic).  You see from the four levels
> (or treatments) there are two chemicals involved. So my first concern is
> whether they should be analysed using two seperate ANOVA's.
>
> NE.Dettol and NE.Garlic are both the same organism - a lab stock E.coli,
> just exposed to two different chemicals.
> EV.Dettol and EV.Garlic, are in principle, likely to be two different forms
> of the organism after the many experimental doses of their respective
> chemical.
>
> For NE.Garlic and NE.Dettol I have 5, what I've called "Lineages", basically
> seperate bottles of them (10 in total).
> Then I have 5 Bottles (Lineages) of EV.Dettol, and 5 of EV.Garlic. - This
> was done because there was the possiblity that, whilst I'm expecting them
> all to respond in a similar manner, there are many evolutionary paths to the
> same result, and previous research and reading shows that occasionally one
> or two react differently to the rest through random chance.
> The point I observed above ("NE.Dettol and NE.Garlic are both the same
> organism...") is also applicable to the 5 bottles: The 5 bottles each of
> NE.Garlic and NE.Dettol are supposed to be all the same organism - from a
> stock one kept in store in the lab.
> There is potential though for the 5 of EV.Garlic, to be different from one
> another, and potential for the 5 EV.Dettol to be different from one another.
>
> The Lineage (bottle) is also a factor then, with 5 levels (1,2,3,4,5).
> Because they may be different.
>
> To get the measurements of the diamter of the zones. I take out a small
> amount from a tube and spread it on a plate, then take three paper disks,
> soaked in their respective chemical, either Dettol or Garlic. and press them
> and and incubate them.
> Then when the zones have appeared after a day or 2. I take 4 diameter
> measurements from each zone, across the zone at different angles, to take
> account for the fact, that there may be a weird shape, or not quite
> circular.
>
> I'm concerned about pseudoreplication, such as the multiple readings from
> one disk, and the 5 lineages - which might be different from one another in
> each of the Two "EV." treatments, but not with "NE." treatments.
>
> I read that I can remove pseudoreplication from  the multiple readings from
> each disk, by using the 4 readings on each disk, to produce a mean for the
> disks, and analyse those means - Exerciseing caution where there are extreme
> values. I think the 3 disks for each lineage themselves are not
> pseudoreplication, because they are genuinley 3 disks on a plate: the "Disk
> Diffusion Test" replicated 3 times - but the multiple readings from one disk
> if eel, is pseudoreplication. I've also read about including Error() terms
> in a formula.
>
> I'm unsure of the two NE. Treatments comming from the same culture does not
> introduce pseudoreplications at Treatment Factor Level, because of the two
> different antimicrobials used have two different effects.
>
> I was hoping for a more expert opinion on whether I have identified
> pseudoreplication correctly or if there is indeed pseudoreplication in the 5
> Lineages or anywhere else I haven't seen. And how best this is dealt with in
> R. At the minute my solution to the multiple readings from one disk is to
> simply make a new factor, with the means on and do Anova from that, or even
> take the means before I even load the dataset into R. I'm wondering if an
> Error() term would be correct.
>
> Thanks,
> Ben W.
>
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-- 
Bert Gunter
Genentech Nonclinical Biostatistics