The Mann-Whitney U Test Is Equivalent to the Wilcoxon Rank-Sum

Essay

The Mann-Whitney U test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense
that they both apply to the same situations and always lead to the same conclusions. In the Mann-Whitney U
test we calculate $$\mathrm { z } = \frac { \mathrm { U } - \frac { \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } } { 2 } } { \sqrt { \frac { \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \left( \mathrm { n } _ { 1 } + \mathrm { n } _ { 2 } + 1 \right) } { 12 } } } , \text { where } \mathrm { U } = \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } + \frac { \mathrm { n } _ { 1 } \left( \mathrm { n } _ { 1 } + 1 \right) } { 2 } - \mathrm { R }$$ For the sample data below, use the Mann-Whitney U test to test the null hypothesis that the two independent
samples come from populations with the same median. State the hypotheses, the value of the test statistic, the
critical values, and your conclusion. Test scores (men): $\quad 70,96,77,90,81,45,55,68,74,99,88$
Test scores (women): $89,92,60,78,84,96,51,67,85,94$