Re: Experimental design

Aniko wrote:
On Apr 19, 4:08 am, Tim De Meyer <Tim.DeMe...@xxxxxxxx> wrote:
Hello,

I have a small question about an experimental design.
Suppose I have a set of samples, there are three subsets of samples (control, treatment 1, treatment 2), each subset consists of an equal number of samples (suppose 10). I want to measure a certain characteristic of these samples, but the measurements have to be done succesively and drift is possible. What (and why?) is the best design (order) to measure the samples?
A. Totally randomize the samples
B. Alternate the treatment (control, treatment1, treatment2, control, treatment 1, treatment 2, ...), and randomize the samples within each treatment.

I think the latter possibility is the better one to take into account the possible drift but I'm not sure.

Thanks a lot,
Tim


The B design is certainly _not_ good as stated: imagine that the drift
adds a value 'c' to each subsequent measurement. Then the observed
mean of Trt2 will always be 2c higher than the observed mean of the
control even if the the true means are equal. However you can fix this
design: within each block of 3, randomize the order of the three
groups. So it will be something like C, T1, T2, T2, C, T1, T1,C, T2,
etc. Since there are 6 possible orders for the three groups, if the
number of samples is a multiple of 6, you can even design a balanced
block design, using each of the 6 orderings the same number of times
(in a random order though). An important note: during the analysis you
have to take into account the design by adding a block effect.

If there is drift, then it would make sense to include it in the analysis as a time effect. This is more powerful than just blocking. In that case, repeating would be OK, although blocking might still be preferable (I can't see whether there is a good reason why one is better than the other).

That said, I don't think the first idea of just randomizing everything
is bad at all, especially if you are able to adjust for the drift in
the analysis by including a model for the drift. I'll leave it to
others to figure out the relative efficiency. It might depend on how
much you know about the drift, eg. whether you can assume it is
linear.

The advantage of some form of blocking is that you don't end up with lots of controls at the start, and lots of T1s at the end (for example). The estimate of the drift is therefore better.

I would certainly block: whether I would have a regular pattern or randomise I'm not sure. It may be that there will be practical reasons why one is better than the other (e.g. a regular pattern is less confusing to do!).

Bob

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Bob O'Hara
Department of Mathematics and Statistics
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FIN-00014 University of Helsinki
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