# Design of the Month

## Fivefold replication

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.

1. Draw the Hasse diagram for the factors on the experimental units before treatments were applied.
2. Describe how to construct the design, and how to randomize it.
3. Write down the skeleton analysis-of-variance table, show stratum, source and degrees of freedom.

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