Instructions for Doing Some Ch. 8 Tests Using StatXact
One can start by stacking the two samples on top of one another in the first column (Var1) of the CaseData
editor. Since there are 15 x values and 10 y values, in the second column (Var2) put 15 1s
followed by 10 2s.
Normal Scores Test (van der Waerden version)
Use
Nonparametrics > Two Independent Samples > Normal Scores...
Click Var1 into the Response Box and Var2 into the Population box. Then, click the exact button under
Compute, and finally click OK. The exact p-value for a two-sided test rounds to 0.0012.
(Note: The 12th and 13th values in the ordered combined sample are equal. To deal with this tie, StatXact
computes the normal scores assuming there are 25 values with no ties, averages the 12th and 13th normal scores,
and assigns this average to the 12th and 13th observations in the ordered combined sample (as opposed to taking
the inverse cdf of 12.5/26 and assigning this value to the two tied observations). I think this is the proper way
to do deal with the tied values.)
Savage Scores Test
Same as above, only use
Nonparametrics > Two Independent Samples > Savage Scores...
The exact p-value for a two-sided test rounds to 0.00079.
Pitman Permutation Test
Same as above, only use
Nonparametrics > Two Independent Samples > Permutation...
The exact p-value for a two-sided test rounds to 0.00086.
Percentile Modified Rank Test
First one needs to create the scores. Go to the CaseData editor and then select
DataEditor > Compute Scores...
Type Var3 in the Target Variable box, select/highlight Var1 (the column of data values) and click it into the
Response box, click the button to choose Wilcoxon (Mid-Rank) in the Score area, and then click OK. This puts
the ranks into Var3, and these values can be used as you enter the scores for the percentile modified rank test (for
location differences) into the next column (Var4). If you want to assign nonzero scores to the smallest 10 (40%)
values and the largest 10 (40%) values in the ordered combined sample, you type -10 in the Var 4 column beside the
Wilcoxon rank of 1 in Var 3, type -9 in the Var4 column beside the Wilcoxon rank of 2, ..., and type -1 in the Var4
column beside the Wilcoxon rank of 10. Then
type 10 in the Var 4 column beside the
Wilcoxon rank of 25 in Var 3, type 9 in the Var4 column beside the Wilcoxon rank of 24, ..., and type 1 in the Var4
column beside the Wilcoxon rank of 16. Finally, enter 0 as the score for the remaining positions in Var4 (corresponding
to ranks/midranks ranging from 11 to 15).
Now use
Nonparametrics > Two Independent Samples > Permutation...
Click Var4 (the percentile modified rank test scores)
into the Response Box and Var2 into the Population box. Then, click the exact button under
Compute, and finally click OK. The exact p-value for a two-sided test rounds to 0.0028.
(As a check that you entered the scores correctly, in the Summary of the Test Statistic near the top of the output,
the values for Minimum, Maximum, and Mean should be -55, 55, and 0 (respectively).)
"Sutton Scores Test"
The Wilcoxon ranks in Var3 can again be used as you enter the "Sutton scores"
into the next column (Var5). If you want to assign nonzero scores to the smallest 6 (24%)
values and the largest 6 (24%) values in the ordered combined sample, you type -1 in the Var 5 column beside the
Wilcoxon ranks of 1 through 6 in Var 3.
Then
type 1 in the Var 5 column beside the
Wilcoxon ranks of 20 through 25.
Finally, enter 0 as the score for the remaining positions in Var5 (corresponding
to ranks/midranks ranging from 7 to 19).
Now use
Nonparametrics > Two Independent Samples > Permutation...
Click Var5 (the "Sutton scores")
into the Response Box and Var2 into the Population box. Then, click the exact button under
Compute, and finally click OK. The exact p-value for a two-sided test rounds to 0.0062.
(As a check that you entered the scores correctly, in the Summary of the Test Statistic near the top of the output,
the values for Minimum, Maximum, and Mean should be -6, 6, and 0 (respectively).)