[R-sig-ME] Cyclic Block Design

[Brandstätter Christian]

Dear list,

I came upon a question of a linear block design for reviewing an article.
It is less of an R-question, but I basically would not know where else to
ask.

The experimental design looked as follows:
Material of different compostion (9 different combinations) was incubated
in a laboratory under 3x3 different conditions (each 3 different water and
temperature levels).
According to the authors, this would lead to 9 treatments (v), 9 blocks
(b), a block size of 3 (k) and # of treatments appearing in the design as 3
(r) for their cyclic incomplete block design. Then they assume, 27
experimental vessels would have been enough to answer their
question.Failing to apply ordinary multivariate linear models they used
MARS models for predicting some measured time series data.

My question would be, is this a) a valid/ experimental (block) design and
b) based on that, a valid statistical regression approach?

Thanks in advance.
Christian

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