Consider the same study by Heffner et al. (1974) and the data set described in Problem 4, in which the response measured was the lever press rate (LPR) used by a thirsty rat to press a lever and receive water. The three factors identified as possible predictors were Drug (three doses plus a placebo), IPR (initial press rate, categorized as slow, medium, or fast), and PRS (number of presses required to obtain water: two or five). Another factor of importance is the random factor Rat (with 24 levels). Furthermore, the factors IPR and PRS were combined into a single Factor A with six levels according to the following categorization:

In this problem, we consider both Factor A and Drug together in a repeated measures analysis to evaluate whether there is an effect of either (or both) of the factors and their intetaction on the response.
a. Describe the data layout for this analysis using the format given by Table 25.2 of Chapter 25.
b. Using the data provided in Problem 4 together with the above definition of Factor A, we obtained following table of sample means:
Factor A

Based on this table, describe whether there appears to be a meaningful main effect of Factor A, a main effect of Drug, and/or an interaction effect between Factor A and Drug. Explain.
c. State the formula for a subject-specific scalar model for the analysis of these data, and specify the assumptions typically made about the random effects (and error term) for this model.
d. For the model stated in part (c), use a flow diagram to describe how the variation (sums of squares) is partitioned into contributions from various sources of predictors. {Consider Figure 26.5 in the text.)

IPR PRS Level of Factor A slow slow medium medium fast 2 Average 1,8083 0.8375 23450 10650 2.5575 1.2725 2:722518000 1.6038 0.5325 0.86000.7750 1,0225 1.0000 26000.9083 Average076004 0982520938 1.2025 2.3425 1.5301 Drug 1 (Placebo) 0.8325 2.1350 0350 2.5775 1.2475 3.0225 2 3 0.8375 8575055022175.290 2.3650