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2) It is desired to see what the effect of three diets (A=full grain, B=partial grain, and C=roughage) is on the milk production of cows (in pounds per week). Unfortunately because cows are highly variable in their milk production, if you didn't block on cow the sample size would have to be very large. Similarily, one should account for the change in milk production over time. It was decided to do a latin square design with three randomly selected cows (I, II, III) over a span of 18 weeks (grouped into 1-6, 7-12, and 13-18). Based on the data below, does diet seem to have an effect? Which diet(s) perform significantly better than the others? What is the estimate of the variance of the effect on weekly milk production due to the cows?
Weeks Cow 1-6 7-12 13-18 ------------------------------------- I A 608 B 716 C 845 II B 885 C 1086 A 711 III C 940 A 766 B 832 -------------------------------------(This problem is adapted from an example in Cobb, 1998, and the data originally appered in the Journal of Dairy Science in 1941.)
(For how to use the SAS output to estimate the variances of random effects, see page 263-264.)