The ranking procedure described in Exercise 35 is somewhat asymmetric, because the smallest observation receives rank 1, whereas the largest receives rank 2, and so on. Suppose both the smallest and the largest receive rank 1, the second smallest and second largest receive rank 2, and so on, and let be the sum of the X ranks. The null distribution of W″ is W″ not identical to the null distribution of W, so different tables are needed. Consider the case m = 3, n = 4List all 35 possible orderings of the three X values among the seven observations (e.g., 1, 3, 7 or 4, 5, 6), assign ranks in the manner described, compute the value of W″ for each possibility, and then tabulate the null distribution of W″ . For the test that rejects if W″≥ c, what value of c prescribes approximately a level .10 test? This is the Ansari-Bradley test; for additional information, see the book by Hollander and Wolfe in the chapter bibliography.
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