Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 either to the left or to the right of distribution 2, based on samples of sizes = 7 and = 9.
a. Should you use or as the test statistic?
b. What is the rejection region for the test if
c. What is the rejection region for the test if

Question

Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 either to the left or to the right of distribution 2, based on samples of sizes  = 7 and  = 9. 
a. Should you use  or  as the test statistic? 
b. What is the rejection region for the test if  
c. What is the rejection region for the test if

Quizplus · Accepted Answer

The Answer is a. If the test is two-tailed, you should use the smaller of

That is, the test statistic is T = min (

).
b. Since the test is two-tailed with

= 0.05, half of this probability should be placed in each of the two tails. From the table of critical values for the Wilcoxon rank sum test (2.5% points),

will be rejected if T = min

40.
c. From the table of critical values for the Wilcoxon rank sum test (0.5% points),

will be rejected if T = min

35.

Suppose You Want to Use the Wilcoxon Rank Sum Test