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13.6 THE MANN–WHITNEY TEST 705
TABLE 13.6.2 Original Data and Ranks,
Example 13.6.1
X Rank Y Rank
13.7 1
13.8 2
14.0 3
14.1 4.5
14.1 4.5
14.2 6
14.4 7
15.3 10.5
15.3 10.5
15.6 12
15.7 13
15.9 14
16.5 18
16.6 19
16.7 20
_____
Total 145
15.0 8.5
15.0 8.5
16.0 15
16.2 16
16.3 17
16.8 21
16.9 22
17.1 23
17.4 24
17.5 25
The test statistic is
T = S -
n 1n + 12
2
(13.6.1)
where n is the number of sample X observations and S is the sum of the
ranks assigned to the sample observations from the population of X values.
The choice of which sample’s values we label X is arbitrary.
5. Distribution of test statistic. Critical values from the distribution of the
test statistic are given in Appendix Table L for various levels of a.
6. Decision rule. If the median of the X population is, in fact, smaller than
the median of the Y population, as specified in the alternative hypothesis,
we would expect (for equal sample sizes) the sum of the ranks