[R] Incomplete, unbalanced design, and pseudoreplication?
Jennifer Mollon
jennifer.mollon at kcl.ac.uk
Mon Nov 9 10:57:45 CET 2009
Hello,
I am trying to help someone who has carried out an experiment and I'm
finding it quite difficult to understand the appropriate model to use
& code it.
The response is a measurement - the amount of DNA extracted during the
experiment. There were 2 factors to be tested - one is the condition
under which the experiment took place and the other is the type of DNA
to be extracted. Each set of factors was replicated, so condition A
and DNA type A were tested twice using the same input material.
Finally, the whole experiment was repeated twice, but in one of the
experiments there was not enough input material and one of the DNA
types (call it type D) was not tested at all, but all other levels of
that factor and the condition factor were tested. From this, I think:
1. The replicates within each experiment are pseudoreplicates - there
are pairs of measures with the same input material, and both factor
levels are the same.
2. The 2 experiments can be treated as blocks, but they are not
balanced or complete.
There are 2 questions of interest to the experimenter:
1. Does the amount of DNA extracted differ for the different DNA types
under the different conditions?
2. One of the conditions is new, and of particular interest. Under
this condition, are there significantly different amounts of DNA
extracted depending on DNA type? There are 2 particular contrasts of
interest here, call them DNA types B&C vs A, and B&C vs D. DNA type D
is only tested in the second experiment.
I would be very grateful for comments about the analysis of this
complicated data set. Are my beliefs above correct, regarding the
design? If so, which R packages and methods can help me with this
analysis? In particular, how should the error term be structured for
this design? And finally, are the 2 research questions best answered
by 2 separate analyses (e.g. the second one looking at only the one
condition in isolation), or can a single analysis of a full model
answer both of these questions?
Many thanks for your consideration and time,
Jen
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