Trauma and Metabolic Expenditure. For the data in Exercise 18 in Chapter 3: (a) Determine the rank transformations for the data. (b) Calculate the rank-sum statistic by hand (taking the trauma...

Trauma and Metabolic Expenditure. For the data in Exercise 18 in Chapter 3: (a) Determine the rank transformations for the data. (b) Calculate the rank-sum statistic by hand (taking the trauma

Exercise

Exercise 18

Suppose that six persons have an illness. Three are randomly chosen to receive an experimental treatment, and the remaining three serve as a control group. After treatment, a physician examines all subjects and assigns ranks to the severity of their symptoms. The patient with the most severe condition has rank 1, the next most severe has rank 2, and so on up to 6. It turns out that the patients in the treatment group have ranks 3, 5, and 6. The patients in the control group have ranks 1, 2, and 4. Is there any evidence that the treatment has an effect on the severity of symptoms? Use the randomization distribution of the sum of ranks in the treatment group to obtain a p-value. (First find the sum of ranks in the treatment group. Then write down all 20 groupings of the 6 ranks; calculate the sum of ranks in the treatment group for each. What proportion of these give a rank-sum as large as or larger than the observed one?)