Refer to Exercise 16.10.

a. Write a model that allows a second-order relationship between y and D.

b. How would you test for parallelism of the second-order model? Include the research hypothesis in terms of the model parameters and the form of the F test.

c. What are the degrees of freedom of the F test for parallelism?

d. Indicate how you would perform a test for the effects of treatments adjusted for the covariate.

Exercise 16.10

In a study of allergic reactions to genetically engineered foods (GEFs), a nutritionist designed a study in which 20 subjects were exposed to five different GEFs. The order in which the subjects were exposed to the five GEFs was randomized, and there was an appropriate washout time between exposures. Let y be a measure of the allergic reaction to the exposures. The nutritionist was concerned that the subjects had very different diets in their normal habits. Thus, she devised an index, D, that measured the diversity in a subject’s diet, with large values of D indicating a widely diverse diet. After running the experhnent, the nutritionist plotted the data, and the scatterplot indicated a straight-line relationship between y and D.

a. Write a model for this experiment that allows a different slope for each of the five GEFs. Make sure to identify all variables and parameters in your model.

b. Indicate how you would test for parallelism among the five lines. What are the degrees of freedom of the F test for parallelisn?

c. Indicate how you would perform a test for differences in the mean allergic reactions to the five GEFs after adjusting for the relationship between the allergic reactions and the difference in diet diversity as measured by D.