Wilcoxon Matched-Pairs Signed Ranks Test
© 1998 by Dr. Thomas W. MacFarland -- All Rights Reserved
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wilcoxon.doc
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Background: The Wilcoxon Matched-Pairs Ranks test is a non-
parametric test that is often regarded as being
similar to a matched pairs t-test. The Wilcoxon
Matched-Pairs Ranks test is used to determine
differences between groups of paired data when
the data do not meet the rigor associated with
a parametric test.
Unlike less robust nonparametric tests such as the
sign test:
-- The Wilcoxon test is used to determine the
magnitude of difference between matched groups.
-- The Wilcoxon test is used to determine more than
only the direction of difference.
Scenario: This file examines if separating students who
previously worked on programming assignments
as a pair has any impact on project quality
when:
-- One member of the pair is required to
work on their own,
-- And the other member of the pair is assigned
a new programming partner.
Dr. Kieta teaches Cobol I and Cobol II at a
local community college. There are 60 students in
Cobol I, with instruction offered in a laboratory-
type classroom setting with only 30 computers.
Logically, Dr. Kieta used random assignment to
segregate the 60 students into 30 sets of paired
students.
During the 10-day break between Cobol I and Cobol
II, more computers are brought into the classroom.
Further, many of the students who enrolled in
Cobol I immediately enrolled for Dr. Kieta's
class in Cobol II.
Seeing an opportunity for a research project on
group vs. individual work with the introduction of
these new computers, Dr. Kieta makes new assignments:
-- 20 students who were enrolled in Cobol I, working
with an assigned partner, now have the chance to
work on their own in Cobol II
-- their counterparts from Cobol I are now assigned
a new partner for Cobol II
This test will determine if there are differences
in the Cobol II final examination among these 40
Cobol I and Cobol II students.
A summary of the study is presented in Table 1.
Table 1
Final Exam Scores in Cobol II of Students Who Were
Previously Paired Together in Cobol I
===================================================
Exam Score for Previously
Paired Students
----------------------------------------
Pair Member: Pair Member:
Worked on Own Worked With a New
Pair in Cobol II Partner in Cobol II
---------------------------------------------------
01 090 083
02 084 089
03 078 058
04 079 093
05 065 049
06 049 082
07 092 093
08 071 100
09 085 083
10 076 055
11 068 065
12 071 083
13 088 081
14 089 088
15 076 083
16 061 078
17 088 088
18 058 080
19 073 070
20 082 083
_______________________________________________________
Ho: Null Hypothesis: There is no difference in final
examination test scores in Cobol II between students
who were previously paired together in Cobol I, with
the pairs now redesigned so that one student in Cobol
II now works on their own and their matched counterpart
now works with another student in Cobol II (p <= .05).
Files: 1. wilcoxon.doc
2. wilcoxon.dat
3. wilcoxon.r01
4. wilcoxon.o01
5. wilcoxon.con
6. wilcoxon.lis
Command: At the Unix prompt (%), key:
%spss -m < wilcoxon.r01 > wilcoxon.o01
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wilcoxon.dat
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01 090 083
02 084 089
03 078 058
04 079 093
05 065 049
06 049 082
07 092 093
08 071 100
09 085 083
10 076 055
11 068 065
12 071 083
13 088 081
14 089 088
15 076 083
16 061 078
17 088 088
18 058 080
19 073 070
20 082 083
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wilcoxon.r01
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SET WIDTH = 80
SET LENGTH = NONE
SET CASE = UPLOW
SET HEADER = NO
TITLE = Wilcoxon Matched Pairs Signed Ranks Test
COMMENT = This file examines if separating students who
previously worked on programming assignments
as a pair has any impact on project quality
when: one member of the pair is required to
work on their own and the other member of the
pair is assigned a new programming partner.
Dr. Kieta teaches Cobol I and Cobol II at a
local community college. There are 60 students in
Cobol I, with instruction offered in a laboratory-
type classroom setting with only 30 computers.
Logically, Dr. Kieta used random assignment to
segregate the 60 students into 30 sets of paired
students.
During the 10-day break between Cobol I and Cobol
II more computers are brought into the classroom.
Further, many of the students who enrolled in
Cobol I immediately enrolled for Dr. Kieta's
class in Cobol II.
Seeing an opportunity for a research project on
group vs. individual work with the introduction of
these new computers, Dr. Kieta makes new assignments:
-- 20 students who were enrolled in Cobol I, working
with an assigned partner, now have the chance to
work on their own in Cobol II
-- their counterparts from Cobol I are now assigned
a new partner for Cobol II
This test will determine if there are differences
in the Cobol II final examination among these 40
Cobol I and Cobol II students.
DATA LIST FILE = 'wilcoxon.dat' FIXED
/ Pair 20-21
Wk_Own 34-36
Wk_New 49-51
Variable Labels
Pair "Pair Number"
/ Wk_Own "Exam Score: Student Who Worked on Their Own"
/ Wk_New "Exam Score: Student Assigned a New Partner"
NPAR TESTS WILCOXON = Wk_Own WITH Wk_New
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wilcoxon.o01
************
1 SET WIDTH = 80
2 SET LENGTH = NONE
3 SET CASE = UPLOW
4 SET HEADER = NO
5 TITLE = Wilcoxon Matched Pairs Signed Ranks Test
6 COMMENT = This file examines if separating students who
7 previously worked on programming assignments
8 as a pair has any impact on project quality
9 when: one member of the pair is required to
10 work on their own and the other member of the
11 pair is assigned a new programming partner.
12
13 Dr. Kieta teaches Cobol I and Cobol II at a
14 local community college. There are 60 students in
15 Cobol I, with instruction offered in a laboratory-
16 type classroom setting with only 30 computers.
17 Logically, Dr. Kieta used random assignment to
18 segregate the 60 students into 30 sets of paired
19 students.
20
21 During the 10-day break between Cobol I and Cobol
22 II more computers are brought into the classroom.
23 Further, many of the students who enrolled in
24 Cobol I immediately enrolled for Dr. Kieta's
25 class in Cobol II.
26
27 Seeing an opportunity for a research project on
28 group vs. individual work with the introduction of
29 these new computers, Dr. Kieta makes new assignments:
30
31 -- 20 students who were enrolled in Cobol I, working
32 with an assigned partner, now have the chance to
33 work on their own in Cobol II
34
35 -- their counterparts from Cobol I are now assigned
36 a new partner for Cobol II
37
38 This test will determine if there are differences
39 in the Cobol II final examination among these 40
40 Cobol I and Cobol II students.
41
42 DATA LIST FILE = 'wilcoxon.dat' FIXED
43 / Pair 20-21
44 Wk_Own 34-36
45 Wk_New 49-51
46
This command will read 1 records from wilcoxon.dat
Variable Rec Start End Format
PAIR 1 20 21 F2.0
WK_OWN 1 34 36 F3.0
WK_NEW 1 49 51 F3.0
47 Variable Labels
48 Pair "Pair Number"
49 / Wk_Own "Exam Score: Student Who Worked on Their Own"
50 / Wk_New "Exam Score: Student Assigned a New Partner"
51
52 NPAR TESTS WILCOXON = Wk_Own WITH Wk_New
***** Workspace allows for 18724 cases for NPAR tests *****
- - - - - Wilcoxon Matched-Pairs Signed-Ranks Test
WK_OWN Exam Score: Student Who Worked on Their
with WK_NEW Exam Score: Student Assigned a New Part
Mean Rank Cases
8.78 9 - Ranks (WK_NEW LT WK_OWN)
11.10 10 + Ranks (WK_NEW GT WK_OWN)
1 Ties (WK_NEW EQ WK_OWN)
--
20 Total
Z = -.6439 2-Tailed P = .5197
************
wilcoxon.con
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Outcome: It is certainly possible to determine the status
of the Null Hypothesis by comparing the calculated
z statistic against the criterion z statistic:
z = |-0.644| (p = .520)
z |-0.644| < |-1.960| (criterion z with alpha = .05)
Note. The | and | characters are used to indicate
absolute value.
The null hypothesis is accepted at p <= .05. Any
differences in final examination scores in Cobol II
between students who were previously paired in
Cobol I are due to chance.
Of course, you can also observe that the calculated
p value of .5197 exceeded the declared p value of .05
to determine the probability level of difference.
Conclusion: In further analysis of the output file and the
"practical" significance of p values:
1. There were nine cases where students who were
assigned to a new partner had lower final exam
scores in Cobol II than their original partner
in Cobol I.
8.78 9 - Ranks (WK_NEW LT WK_OWN)
11.10 10 + Ranks (WK_NEW GT WK_OWN)
1 Ties (WK_NEW EQ WK_OWN)
2. There were ten cases where students who were
assigned to a new partner had higher final exam
scores in Cobol II than their original partner
in Cobol I.
3. There was one case where scores between the two
original partners from Cobol I were the same in
Cobol II.
With final examination scores all over the range,
such as what you see here, it would be surprising
if differences between the two groups were due to
anything but chance.
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wilcoxon.lis
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% minitab
MTB > outfile 'wilcoxon.lis'
Collecting Minitab session in file: wilcoxon.lis
MTB > # MINITAB addendum for wilcoxon.dat
MTB > read 'wilcoxon.dat' c1 c2 c3
Entering data from file: wilcoxon.dat
20 rows read.
MTB > print c1 c2 c3
ROW C1 C2 C3
1 1 90 83
2 2 84 89
3 3 78 58
4 4 79 93
5 5 65 49
6 6 49 82
7 7 92 93
8 8 71 100
9 9 85 83
10 10 76 55
11 11 68 65
12 12 71 83
13 13 88 81
14 14 89 88
15 15 76 83
16 16 61 78
17 17 88 88
18 18 58 80
Continue? y
19 19 73 70
20 20 82 83
MTB > describe c2 c3
N MEAN MEDIAN TRMEAN STDEV SEMEAN
C2 20 76.15 77.00 76.78 11.75 2.63
C3 20 79.20 83.00 79.72 13.34 2.98
MIN MAX Q1 Q3
C2 49.00 92.00 68.75 87.25
C3 49.00 100.00 72.00 88.00
MTB > winterval c2 c3
ESTIMATED ACHIEVED
N MEDIAN CONFIDENCE CONFIDENCE INTERVAL
C2 20 76.7 95.0 ( 70.5, 82.0)
C3 20 81.5 95.0 ( 73.0, 85.5)
MTB > mann-whitney c2 c3
Mann-Whitney Confidence Interval and Test
C2 N = 20 Median = 77.00
C3 N = 20 Median = 83.00
Point estimate for ETA1-ETA2 is -4.00
95.0 pct c.i. for ETA1-ETA2 is (-12.00,5.00)
W = 377.0
Test of ETA1 = ETA2 vs. ETA1 n.e. ETA2 is significant at 0.3793
The test is significant at 0.3785 (adjusted for ties)
Cannot reject at alpha = 0.05
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Disclaimer: All care was used to prepare the information in this
tutorial. Even so, the author does not and cannot guarantee the
accuracy of this information. The author disclaims any and all
injury that may come about from the use of this tutorial. As
always, students and all others should check with their advisor(s)
and/or other appropriate professionals for any and all assistance
on research design, analysis, selected levels of significance, and
interpretation of output file(s).
The author is entitled to exclusive distribution of this tutorial.
Readers have permission to print this tutorial for individual use,
provided that the copyright statement appears and that there is no
redistribution of this tutorial without permission.
Prepared 980316
Revised 980914
end-of-file 'wilcoxon.ssi'