An experiment was performed to determine the effect of nutritionally inadequate diets on the quality of sheep’s wool. The experiment consisted of a 21-day preexperimental period (ending on 22 October 1997), a 12-week restricted-intake 246 Two case studies period (ending on 14 January 1998) and a 6-week recovery period (ending on 25 February). Three experimental treatments were defined: • Treatment 1. A control dietary regime. • Treatment 2. An energy-deficient/protein-deficient nutritional regime. • Treatment 3. An energy-deficient/protein-adequate nutritional regime. Animals in the control group were fed at 1.3× the level required for maintenance (1.3 M) throughout the experiment. The energy-deficient/protein-deficient group were fed at 0.75 M during the restricted-intake period, then ad libitum up to 2 M during the recovery period. The energy-deficient/protein-adequate group received the same diet as the energy-deficient/protein-deficient group except that they received a supplement of 3.3 g/day of active methionine throughout the experimental period. Twenty-one Merino wether hoggets were used in the experiment. Following the 21-day adjustment period the animals were divided into seven groups on the basis of live weight, and one randomly chosen animal from each group was allocated to each treatment. Measurements of the live weight and the fibre diameter of the wool of each animal were taken at the end of the pre-experimental period, and measurements of fibre diameter were also taken during the recovery period. The results are presented in Table 7.13. (Data reproduced by kind permission of Rachel Kirby.) The experimental design includes a block factor which is not shown explicitly in Table 7.13.

(a) Assign an appropriate block number to each row of the data.

(b) Analysing measurements made on each occasion separately, and using the block factor and the treatment factor as model terms, perform analyses of variance on the measurements of fibre diameter made during the restricted-intake period and the recovery period. Interpret the results.

(c) Stack the measurements made on these three occasions into a single variate, and perform a new analysis by mixed modelling. Include the following variables in your initial model: (i) the time at which the measurement was made; (ii) the fibre diameter from the same sheep during the pre-experimental period; (iii) the live weight of the sheep during the pre-experimental period. Determine whether any terms can reasonably be dropped from the model. If so, make the appropriate changes and re-fit the model.

(d) Interpret the results of your analysis. In particular, consider the following points: (i) Is the fibre diameter influenced by the sheep’s pre-experiment live weight? (ii) Is the fibre diameter during the experiment related to the fibre diameter in the pre-experimental period? (iii) Is the fibre diameter influenced by the treatment, the date (i.e. the time elapsed since the restricted-intake period) and the treatment × date interaction? If so, what is the direction or nature of these effects? Exercises 247 Table 7.13 Live weight and fibre diameter of sheep on a range of nutritional regimes Tag Treatment Live weight (kg), Fibre diameter (microns) 20 October 1997 22 October 1997 07 January 1998 28 January 1998 18 February 1998 100 3 36.5 20.44 13.92 15.43 19.90 170 2 33.5 16.62 16.38 17.09 16.68 1519 1 34.0 18.12 16.30 16.74 19.22 162 1 35.0 18.55 15.74 15.25 18.02 1582 3 32.0 19.33 15.77 16.41 19.22 175 2 35.0 18.26 16.85 17.47 18.08 124 1 35.0 20.35 19.39 18.94 21.68 95 1 33.0 18.27 16.30 16.95 19.70 1497 2 35.0 17.95 18.55 19.78 20.01 1337 3 34.0 19.12 14.78 16.52 19.27 62 1 31.5 20.88 17.58 18.52 21.22 1420 3 33.5 17.05 13.18 14.35 17.12 171 2 33.0 18.21 17.77 18.44 19.14 1556 2 33.5 18.05 16.59 17.55 17.93 167 1 35.5 18.16 14.67 17.61 20.87 1048 1 33.0 20.63 14.93 15.58 19.40 1083 3 35.0 17.97 13.64 14.86 18.66 1422 2 35.5 17.70 16.69 17.74 18.64 1042 2 31.5 18.41 16.90 17.96 19.18 1065 3 32.5 18.57 14.64 15.86 19.09 142 3 34.0 20.08 16.20 18.48 21.71

(e) Obtain predicted values of fibre diameter for each treatment at representative times, and make a graphical display of the relationship between these variables.