Consider a different (fictitious) study to compare two treatments for the relief of heartburn. This new study involves a two-period "cross-over" design in which each subject is given two symptom-provoking meals and receives (with random assignment) an active treatment (A) after one meal and a placebo (P) after the other meal. In other words, each subject receives both treatments in this study; in contrast, for the previously described study (see Problem 5), each subject received either the active treatment or the placebo after both meals. The data set is given below.

Edited computer output from SAS's MIXED procedure is provided below.
a. Specify the subject-specific scalar model form used for this analysis.
b. What do you conclude about whether or not there is a significant difference between the effects of the two treatments on the amount of discomfort experienced by study subjects? Explain briefly.
c. Why are the Den DF equal to 29 in this analysis, whereas the Den DF were equal ro 28 in the analysis used for the data of Problem 5? Suppose that the investigator wished to consider the possibility that the sequence used€”that is, (A:P) versus (P:A)€”had an effect on the response in addition to a possible treatment effect. To carry out such an analysis, he/she modified the model by adding a dichotomous variable, denoted as "seq," to the model. Edited output for this latter model is provided below:
d. Specify the subject-specific scalar model form used that includes both "trt" and "seq."
e. What do you conclude about whether or not there is a significant difference between the effects of the two treatments on the amount of discomfort experienced by study subjects, controlling for the variable "seq"? Explain briefly.
f. How would you evaluate whether or not it was necessary to control for the "seq" variable in order to determine whether or not there was a significant difference between the two treatments?

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