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_Homework_wilcoxongehan

# _Homework_wilcoxongehan - How to carry out a Wilcoxon...

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How to carry out a Wilcoxon test (Gehan) The uncensored case Suppose we have two samples with observations X 1 , . . . , X m ; Y 1 , . . . , Y n . Order the combined sample and find the ranks of each observation within the combined sample. We will assume for now that there are no ties. Let R i be the rank of X i within the combined sample and let R + = m i =1 R i . We would reject the null hypothesis that the two samples are drawn from an identical underlying distribution in favor of the alternative that one distribution is “shifted” up or down if R is either too large or too small. It can be shown that R is asymptotically normally distributed under the null hypothesis with E 0 ( R ) = m ( m + n + 1) 2 and V 0 ( R ) = mn ( m + n + 1) 12 . Thus we could construct a test based on the standardized value of R , Z = R - E 0 ( R ) V 0 ( R ) . The Mann-Whitney version of the Wilcoxon is useful. Consider all m × n possible pairs of observations, ( X i , Y j , and define U ij = +1 if X i > Y j ; 0 if X i = Y j ; - 1 if X i < Y j .

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_Homework_wilcoxongehan - How to carry out a Wilcoxon...

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