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734 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS
4. Test statistic. See Equation 13.10.1.
5. Distribution of test statistic. Critical values of the test statistic are
given in Appendix Table P.
6. Decision rule. For the present test we will reject H 0 if the computed
value of r s is less than -.3789.
7. Calculation of test statistic. When the X and Y values are ranked, we
have the results shown in Table 13.10.2. The d and g d 2 i , d i 2 ,
i are shown
in the same table.
Substitution of the data from Table 13.10.2 into Equation 13.10.1
gives
6123402
r s = 1 -
2031202 2 - 14 = -.76
8. Statistical decision. Since our computed r s = -.76 is less than the critical
r* s , we reject the null hypothesis.
9. Conclusion. We conclude that the two variables are inversely related.
10. p value. Since -.76 6-0.6586, we have for this test p 6 .001.
TABLE 13.10.2 Ranks for Data of Example 13.10.1
Subject
Number Rank (X ) Rank (Y )
d i
d 2 i
1 1 18 -17 289
2 2 15 -13 169
3 3 17 -14 196
4 4 20 -16 256
5 5 19 -14 196
6 6 7 -1 1
7 7 6 1 1
8 8 12 -4 16
9 9 16 -7 49
10 10 14 -4 16
11 11 10 1 1
12 12 8 4 16
13 13 13 0 0
14 14 4 10 100
15 15 11 4 16
16 16 2 14 196
17 17 5 12 144
18 18 1 17 289
19 19 9 10 100
20 20 3 17 289
gd 2 i = 2340
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