Design of the Month

Injecting rabbits

The following quotation is taken from `The biological assay of testicular diffusing factor' by A. L. Bacharach, M. R. A. Chance and T. R. Middleton, published on pages 1464-1471 of volume 34 of Biochemical Journal in 1940.

It was considered necessary to attempt further to measure the influence, if any, on bleb size of the position of the injection on the back of the animal and of the order (in time) of injection, as well as to estimate the contribution made by animal variation to the error of the method. ... It was decided to carry out an experiment with six rabbits and six positions for injection on the back of each rabbit and to base the experiment on a Latin square design.

A 6 x 6 Latin square was therefore selected by the procedure described by Fisher & Yates [1938]. ... Arabic numerals (1 to 6) refer to the animals, letters (a to f) to the position on the backs of the animals and Roman numerals (i to vi) to the order of injection. Thus each animal was injected once and once only in each position and each position was the rth to be injected (r=i, ii, ..., vi) in only one animal. Also, the sites (a to f) were so arranged that three of them (a, c and e) lay near the animals' vertebrae, while the other three (b, d and f) occupied more lateral positions. In Table 1 are also shown the actual bleb sizes (in square centimetres) 20 min. after the injection.

  1. What were the experimental units and how many of them were there?
  2. What were the treatments and how many of them were there?
  3. How should the design have been randomized?
  4. Exactly what was measured?
  5. Draw the Hasse diagram for the factors on the experimental units before treatments were applied.
  6. Write down the skeleton analysis-of-variance table, show stratum, source and degrees of freedom.

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