"Pork has been associated with an unhealthy image due to it's fat content and relative proportions of polyunsaturated and saturated fatty acids. Flax seed oil contains approximately 72% polyunsaturates and is the richest oilseed source of linolenic acid (58%). Feeding flax, which contains 40 to 45% oil, to finishing pigs will increase the percentage beneficial omega-3 (n-3) fatty acids in carcass fat and produce pork with value added potential."
This question is based on an experiment conducted by the Agriculture and Agri-Food Canada experimental station in Alberta. The numbers have been modified to preserve confidentiality.
An experiment was conducted to investigate the impact of different amounts of flax (5%, 10%, and 15%) in the diets of pigs for different amounts of time (4, 8, or 12 weeks) upon the fatty acid composition of backfat. The amount of one of the fatty acids (Fatty Acid 1) was measured in the backfat just after slaughter. Eight pigs were treated with each combination of amount of flax and feeding time. Two pigs of each treatment combination were housed in separate barns (four barns in total), but each pig is in a separate stall within the barn. Some output is available at the end of exam.
1. Draw a picture of the experimental layout (curly tails on the pigs leads to bonus marks) and describe the treatment, experimental unit, and randomization structures.
2. Use the standard "shorthand syntax" and specify the appropriate model, i.e. what is the response variable and what "effect" terms would be used and why.
3. Output is given at the end of the exam and presents some of the statistical tests conducted. State the hypothesis of interest for the last line of the Fixed Effect Tests, and your conclusion.
4. State the hypothesis of interest for the first line in the Fixed Effect Tests and your conclusion.
5. Using the results, construct a "joined lines" diagram (a.k.a. connected letters report) for the (main) effect of Diet showing the results of the Tukey multiple comparison procedure. What do you conclude from this? Explain any "odd" results.
6. Using the results, construct a profile plot. Carefully explain what features of the plot illustrate the main effects of each factor and their interaction.
7. The results for the Time factor were somewhat surprising to the scientists as they had expected to see an effect. Suppose that a difference of 0.2 in the fatty acid response variable leads to differences that need to be detected. Complete the dialogue box for a power analysis as shown in output at the end of the exam with the appropriate values (don't forget to transfer this to your exam book).
8. The results from a sample size determination are shown in the output at the end of the exam. What sample size is needed for a 80% power to detect the important difference above. Express the sample size in terms of the number of animals needed for each COMBINATION of flax and time factor levels. Are you surprised?
9. The experimental design was somewhat constrained because the fatty acid composition could only be measured after slaughtering the animals. But suppose a non-lethal method was available to measure fatty acid composition.
Outline an alternative experimental plan that does not require a separate animal for each combination of flax and time feeding. What are the potential advantages and disadvantages of this design?