The rank-sum test is sometimes thought of as a test for population medians. Under the
Chapter 6, Problem 17(choose chapter or problem)
Exercises 16 and 17 illustrate that distribution-free methods can produce misleading results when their assumptions are seriously violated.
The rank-sum test is sometimes thought of as a test for population medians. Under the assumptions of equal spread and shape, the means of two populations will differ if and only if the medians differ; therefore tests for equality of population means are also tests for equality of population medians. This exercise illustrates that when these assumptions are seriously violated, the rank-sum test can give misleading results concerning the equality of population medians. Consider the following two samples:
X: 1 2 3 4 5 6 7
20 40 50 60 70 80 90 100
Y: −10 −9 −8 −7 −6 −5 −4
20 21 22 23 24 25 26 27
a. Show that both samples have the same median.
b. Compute the P-value for a two-tailed rank-sum test. If small P-values provide evidence against the null hypothesis that the population medians are equal, would you conclude that the population medians are different?
c. Do the assumptions of the rank-sum test appear to be satisfied? Explain why or why not.
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