10.42 Permuting therapies Refer to Exercise 10.38, which compared two therapies for depression patients. Suppose that in a different experiment, only four patients took part; two were randomly assigned to the group that received therapy 1 and the remaining two to the group that received therapy 2.

The following table shows the improvement scores for these 4 patients.

Patient: 1 2 3 4 Therapy: 1 1 2 2 Score: 30 60 20 30

a. List all six possible ways these four patients could have been assigned to the two therapies. That is, give all six possible ways of dividing the four patients into two groups of two patients each.

b. Using the observed improvement scores shown in the table, find the sample means in each group and their difference under each possible assignment.