Solved: The ranking procedure described in Exercise 35 is somewhatasymmetric, because

Chapter 15, Problem 36

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The ranking procedure described in Exercise 35 is somewhatasymmetric, because the smallest observation receives rank1, whereas the largest receives rank 2, and so on. Supposeboth the smallest and the largest receive rank 1, the secondsmallest and second largest receive rank 2, and so on, and letbe the sum of the X ranks. The null distribution of isnot identical to the null distribution of W, so different tablesare needed. Consider the case List all 35possible orderings of the three X values among the sevenobservations (e.g., 1, 3, 7 or 4, 5, 6), assign ranks in themanner described, compute the value of for each possibility,and then tabulate the null distribution of . For thetest that rejects if , what value of c prescribes approximatelya level .10 test? This is the Ansari-Bradley test; foradditional information, see the book by Hollander and Wolfein the chapter bibliography.

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