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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