The analysis described in Problem 1 for the posture measurement data on Shoulder Flexion (SF) may be criticized because information is lost when the 4 observations for a given subject on a given day are combined into an average score rather than being treated individually in the analysis. The data set shown below allows for an analysis t considers all 12 observations per subject. In analyzing this data set, we assume that the 4 observations for a given subject on a given day are true replicates (i.e., we assume that neither the time of day observed nor the rater used, factors that combine to provide the 4 observations for a given subject, is an important factor for predicting SF response).

a. How should the subject-specific scalar model for Problem 1 be modified to consider the data layout below? (You will need to add a second random effect to the model that reflects the interaction of Day with Subjects.)
b. Use the computer information provided below to test whether there is a significant main effect of the factor Day. (See the ANOVA table provided below.) What do you conclude?
c. Use the computer output provided below to test whether there is a significant interaction effect between Subjects and Day. If such a test is nonsignificant, why might you be concerned regarding the model that has been fit, and how might you redo the analysis?