Design of the Month
On pages 244-245 of his book Statistical Methods in Medical Research,
which was published by Blackwell Scientific Publications in 1971,
P. Armitage describes the experiment on rabbits given in the previous
design of the month. Then he discusses ways of
replicating that fivefold, as follows. (His text has been abbreviated.)
Consider three different ways in which the experiment could be replicated
five-fold to give a total of 180 (=5×36) observations.
- If the animals in [the previous experiment] were all from the same
litter a total of five litters could be used. A separately randomized Latin
square would be used for each of the five replicates.
- If 30 animals were available, not separable into litters or other
rational sub-groups, they could be divided randomly into six equal sub-groups
each of which would be allotted to a column of the [previous Latin square.]
- If the experiment described [previously] could be repeated with
the same animals on five different occasions, a separate randomization
could be performed on each occasion.
For each of the three possibilities, do the following.
- Draw the Hasse diagram for the factors on the experimental units
before treatments were applied.
- Describe how to construct the design, and how to randomize it.
- Write down the skeleton analysis-of-variance table, show stratum,
source and degrees of freedom.
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