Exercises 409Exercises
12.1 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 treat-
ment 3 animals were food deprived, in treatment 4 they were water deprived, and in treat-
ment 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.Ad Lib Two per Food Water Food and
Control Day Control Deprived Deprived Water Deprived
18 20 6 15 12
20 25 9 10 11
21 23 8 9 8
16 27 6 12 13
15 25 11 14 11
90 120 40 60 55a. 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.
12.2 Using the data from Exercise 11.1, compute the linear contrasts for 5 versus (20 and 35)
days and 20 versus 35 days, using a5.05 for each contrast. (Note that this and subsequent
exercises refer to exercises in Chapter 11, not this chapter.)
12.3 What would be the per comparison and familywise error rates in Exercise 12.2? (Hint: Are
the contrasts orthogonal?)
12.4 Compute Ffor the linear contrast on the two groups in Exercise 11.2. Is this a waste of
time? Why or why not?
12.5 Compute the Studentized range statistic for the two groups in Exercise 11.2, and show that
it is equal to (where t is taken from Exercise 11.2b).
12.6 Compute the Fs for the following linear contrasts in Exercise 11.3. Save the results for use
in Chapter 13.
a. 1 and 2 versus 3 and 4
b. 1 and 3 versus 2 and 4
c. 1 and 4 versus 2 and 3
d. What questions do the contrasts in (a), (b), and (c) address?
12.7 Run the Bonferroni t test on the data for Exercise 11.1, using the contrasts supplied in
Exercise 12.2. Set the maximum FWat .05.
12.8 Repeat Exercise 12.7, using Holm’s multistage test. What differences do you find between
these answers and the answers to Exercise 12.7?
12.9 Apply Holm’s multistage test to Exercise 12.1.
12.10 Run a REGWQ test on the example given in Table 11.2 (p. 324) and interpret the results.t 12SStreat