Due on Canvas on November 14
Please remember that this is an exam, so you are to do your own work and not communicate with other students about the exam
1. A restaurant owner is trying new broths for their ramen soup. They have
four different recipes (the ingredients are secret), and they recruit
eight subjects to try different broths. Each subject can only taste three
of the four broths before getting fatigued, so each was given three
broths, with the order randomized for each subject. The data are in this file . Here is some code to help read
in all of the data sets.
Remember to show your work (or code) and comment on your results for each
problem and sub-problem.
a. Name the design and write the model equation.
b. Use a boxplot to visualize the potential effect of the type of broth. What do the plots suggest about group differences and model assumptions?
c. Use a fixed-effects approach to do an appropriate test for the effect of broths. Conduct an analysis of variance to test the null hypotheses of equality of taste by broth type (show the ANOVA table, including sums of squares, mean squares, F statistic, and P value). If there is a significant effect of broths, use Tukey multiple comparison tests to perform pairwise tests of the broth types.
d. Examine a residual by predicted plot and a normal plot of the residuals to assess model assumptions of equal variance and normality.
e. Summarize your conclusions about the effects of the different broths.
f. In your own words, explain the potential benefits of performing a mixed-model analysis to test for the effect of broths. (You do not have to perform another analysis)2. Medical researchers are studying the effect of different diets and types of exercise on pulse rates. They are considering five types of diets. They recruit ten subjects and randomize them to the diets so that two subjects get each diet. Then after a week on the diet, the subjects are each tested on a treadmill. Their pulse rate is measured first at rest, then after a light exercise, then after an intensive exercise. Each subject does the exercises in the same order (rest, light, intensive), with a break between each exercise. The data are in this file . Code to read in the data is listed above with the first problem. Remember to show your work and comment on your results for each problem and sub-problem.
a. Name the design and write the model equation.
b. Use boxplots and an interaction plot to examine potential effects of diet, exercise, and their interaction. What do the plots suggest about group differences and model assumptions?
c. Perform a split-plot analysis to test for the effects of diet, exercise, and their interaction. If no interaction exists use Tukey's method to do pairwise tests for any significant main effects. If an interaction exists, use interaction plots and simple main effect tests to understand the interaction.
d. Examine a residual by predicted plot (or a similar plot) and a normal plot of the residuals to assess model assumptions.
e. Summarize your conclusions in a few sentences on what the effects of diet and exercise type have on the pulse rate.
f. Perform the Mauchley sphericity test. Briefly explain what is being tested along with the result. If using SAS, you will need the data in multivariate format.