August 2013
Intermediate to advanced
195 pages
5h 45m
English
Content preview from Nonparametric Methods in Statistics with SAS Applications
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26 HYPOTHESES TESTING FOR TWO SAMPLES
generality, the five observations can be taken as 1, 2, 3, 4, and 5. The total number of
distinct permutations is
5
2
= 10.
The Kolmogorov-Smirnov two-sided test statistic D = max |
ˆ
F
1
−
ˆ
F
2
| is computed for
each permutation. The procedure is summarized below.
Sample 1 Sample 2 Obs
ˆ
F
1
ˆ
F
2
|
ˆ
F
1
−
ˆ
F
2
| D
1 2 3 4 5
1 1/2 0 1/2
1
2 1 0 1
3 1 1/3 2/3
4 1 2/3 1/3
5 1 1 0
1 3 2 4 5
1 1/2 0 1/2
2/3
2 1/2 1/3 1/6
3 1 1/3 2/3
4 1 2/3 1/3
5 1 1 0
1 4 2 3 5
1 1/2 0 1/2
1/2
2 1/2 1/3 1/6
3 1/2 2/3 1/6
4 1 2/3 1/3
5 1 1 0
1 5 2 3 4
1 1/2 0 1/2
1/2
2 1/2 1/3 1/6
3 1/2 2/3 1/6
4 1/2 1 1/2
5 1 1 0
2 3 1 4 5
1 0 1/3 1/3
2/3
2 1/2 1/3 1/6
3 1 1/3 2/3
4 1 2/3 1/3
5 1 1
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