Assume that the data that follow represent the effects of food and/or water deprivation on behavior in a learning task. Treatments 1 and 2 represent control conditions in which the animal received ad...

Assume that the data that follow represent the effects of food and/or water deprivation on behavior in a learning task. Treatments 1 and 2 represent control conditions in which the animal received ad lib food and water (1) or else food and water twice per day (2). In treatment 3 animals were food deprived, in treatment 4 they were water deprived, and in treatment 5 they were deprived of both food and water. The dependent variable is the number of trials to reach a predetermined criterion. Assume that before running our experiment we decided that we wanted to compare the combined control groups (treatments 1 and 2) with the combined experimental groups, the control groups with each other, the singly deprived treatments with the doubly deprived treatment, and the singly deprived treatments with each other.

a. Analyze the data using linear contrasts. (Note: I am not asking for linear polynomials (trend) here, just standard contrasts.)

b. Show that the contrasts are orthogonal.

c. Show that the sums of squares for the contrasts sum to .