A study by Heffner, Drawbaugh, and Zigmond (1974) investigated the effects of an amphetamine on the behavior of rats. Before the study began, 24 "thirsty" rats were trained to press a lever to obtain water. The rats were categorized into three groups (slow, medium, and fast) of equal size according to their initial press rates. Each rat received three doses of the drug (i.e., the amphetamine under study), as well as a placebo, on separate occasions and in random order. One hour after the drug injection, an experimental session began in which the rat received water after pressing the lever a prespecified number of times. Half of the rats received water after two presses of the lever, whereas the other half received water after five presses.
The response measured was the lever press rate (i.e., LPR, the total number of lever presses divided by elapsed time in seconds) used by a thirsty rat to press the lever and receive water. The primary research question was whether the drug affected the LPR. Also of interest was the question of whether there was an effect on the response (LPR) of the number of presses (PRS) required to obtain water (two versus five) and/or the initial press rate (IPR) (slow, medium, or fast) and whether there were any interaction effects. The data are given below.
a. Which of the factors Drug, IPR, and PRS should be treated as fixed factors and which as random factors? Explain.
b. Consider an analysis of these data that focuses only on the effect of the factor Drug (i.e., ignore the factors IPR and PRS in the analysis). Thus, for each of the 24 rats, we have four responses corresponding to the administration of each of the four levels of the factor Drug. State a subject-specific scalar model for analyzing these data, making sure to state the assumptions typically made about the random effects (including the error term) in the model.
c. State the subject-specific matrix model that corresponds to the subject-specific scalar model stated in part (b).
d. Based on a comparison of sample means, does there appear to be a meaningful effect of the factor Drug? Explain.
e. Use the computer output provided below to test for the significance of the factor Drug. Make sure to describe the null hypothesis being tested, the F statistic used, its degrees of freedom, and the resulting P-value for this test. What do you conclude?
f. Use the computer output below to test for the significance of the subject (i.e., Rat) factor. Why might you expect the results for this test to be significant?
g. Explain why it is not possible to test whether there is a significant interaction between Drug and Rat.

IPR = initial press rate; PRS = number of presses