Chapter 15, Problem 21CP

Comparing tans Examples 1 and 2 compared two methods of getting a tan. Suppose Allison conducted an expanded experiment in which nine participants were randomly assigned to one of two brands of tanning lotion or to the tanning studio, three participants to each treatment. The nine were ranked on the quality of tan.

1. a. Which nonparametric test could be used to compare the three treatments?
2. b. Give an example of ranks for the three treatments that would have the largest possible test statistic value and the smallest possible P-value for this experiment. (Hint: What allocation of ranks would have the greatest between-groups variation in the mean ranks?)