Question

How do you expect the rank sum for sample A to compare to the rank sum for sample B if the median of distribution A is to the right of the median of distribution B? Explain your answer.

Answer 1

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Suppose that H1 : A>B is true:

This results in sample A containing more of the larger ranks. i.e. Rank sums of sample A will be higher than that of sample B

Evidence against H0 which confirms H1 : A>B is thus provided by an observed rank sum wA which is unusually large according to the distribution of rank sums when H0 is true.

Thus the P-value for the test is (H1 : A>B)

P-value = pr(WA ≥ wA), where the probability is calculated using the distribution that WA would have if H0 was true