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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