Applied Statistics and Probability for Engineers

Alloy Number Axial Stress Rank

2 3187 psi 1

1 3190 2

1 3195 3

1 3204 4

2 3209 5

2 3212 6

2 3215 7

1 3217 8

1 3225 9

2 3226 10

1 3229 11

2 3234 12

1 3238 13

2 3240 14

1 3241 15

1 3246 16

2 3248 17

1 3254 18

2 3258 19

2 3261 20

15-4 WILCOXON RANK-SUM TEST 587

7. Computations: The data from Table 15-3 are analyzed in ascending order and ranked
   as follows:

The sum of the ranks for alloy 1 is

and for alloy 2

8. Conclusions: Since neither w 1 nor w 2 is less than or equal to w0.0578, we cannot
   reject the null hypothesis that both alloys exhibit the same mean axial stress.

15-4.2 Large-Sample Approximation

When both n 1 and n 2 are moderately large, say, greater than 8, the distribution of w 1 can be

well approximated by the normal distribution with mean

and variance

^2 W 1 

n 1 n 21 n 1 n 2  12

12

W 1 

n 11 n 1 n 2  12

2

w 2 

1 n 1 n 221 n 1 n 2  12

2

w 1 

110  102110  10  12

2

 99  111

w 1  2  3  4  8  9  11  13  15  16  18  99

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