UNISTAT statistical package extends Excel with Kruskal-Wallis One-Way ANOVA support.
Sample output
Here we provide annotated example report output from the UNISTAT Excel add-in for data analysis.
Kruskal-Wallis One-Way ANOVA
Cases
Rank Sum
Mean Rank
North
12
270.5000
22.5417
East
12
197.0000
16.4167
South
12
421.5000
35.1250
West
12
287.0000
23.9167
Total
48
1176.0000
24.5000
Correction for Ties
0.0030
Chi-Square Statistic
11.2012
Degrees of Freedom
3
Right-Tail Probability
0.0107
Multiple Comparisons with Rank Sums (Tukey-HSD)
Method: 95% Tukey-HSD interval.
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Rank Sum
East
North
West
South
East
12
197.0000
**
|
North
12
270.5000
||
West
12
287.0000
||
South
12
421.5000
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - East
224.5000
48.4974
4.6291
3.6332
0.0059
48.3011
400.6989
**
West - East
90.0000
48.4974
1.8558
3.6332
0.5551
-86.1989
266.1989
North - East
73.5000
48.4974
1.5155
3.6332
0.7069
-102.6989
249.6989
South - North
151.0000
48.4974
3.1136
3.6332
0.1227
-25.1989
327.1989
West - North
16.5000
48.4974
0.3402
3.6332
0.9951
-159.6989
192.6989
South - West
134.5000
48.4974
2.7733
3.6332
0.2029
-41.6989
310.6989
Homogeneous Subsets:
Group 1: East North West
Group 2: North West South
Multiple Comparisons with Mean Ranks (Tukey-HSD)
Method: 95% Tukey-HSD interval.
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Mean Rank
East
North
West
South
East
12
16.4167
**
|
North
12
22.5417
||
West
12
23.9167
||
South
12
35.1250
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - East
18.7083
4.0415
4.6291
3.6332
0.0059
4.0251
33.3916
**
West - East
7.5000
4.0415
1.8558
3.6332
0.5551
-7.1832
22.1832
North - East
6.1250
4.0415
1.5155
3.6332
0.7069
-8.5582
20.8082
South - North
12.5833
4.0415
3.1136
3.6332
0.1227
-2.0999
27.2666
West - North
1.3750
4.0415
0.3402
3.6332
0.9951
-13.3082
16.0582
South - West
11.2083
4.0415
2.7733
3.6332
0.2029
-3.4749
25.8916
Homogeneous Subsets:
Group 1: East North West
Group 2: North West South
Multiple Comparisons with Rank Sums (S-N-K)
Method: 95% Student-Newman-Keuls interval.
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Rank Sum
East
North
West
South
East
12
197.0000
**
|
North
12
270.5000
||
West
12
287.0000
**
||
South
12
421.5000
**
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - East
224.5000
48.4974
4.6291
3.6332
0.0059
*
*
**
West - East
90.0000
48.4974
1.8558
3.3145
0.3883
*
*
North - East
73.5000
48.4974
1.5155
2.7718
0.2839
*
*
South - North
151.0000
48.4974
3.1136
3.3145
0.0709
*
*
West - North
16.5000
48.4974
0.3402
2.7718
0.8099
*
*
South - West
134.5000
48.4974
2.7733
2.7718
0.0499
*
*
**
Homogeneous Subsets:
Group 1: East North West
Group 2: North West South
Multiple Comparisons with Mean Ranks (S-N-K)
Method: 95% Student-Newman-Keuls interval.
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Mean Rank
East
North
West
South
East
12
16.4167
**
|
North
12
22.5417
||
West
12
23.9167
**
||
South
12
35.1250
**
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - East
18.7083
4.0415
4.6291
3.6332
0.0059
*
*
**
West - East
7.5000
4.0415
1.8558
3.3145
0.3883
*
*
North - East
6.1250
4.0415
1.5155
2.7718
0.2839
*
*
South - North
12.5833
4.0415
3.1136
3.3145
0.0709
*
*
West - North
1.3750
4.0415
0.3402
2.7718
0.8099
*
*
South - West
11.2083
4.0415
2.7733
2.7718
0.0499
*
*
**
Homogeneous Subsets:
Group 1: East North West
Group 2: North West South
Multiple Comparisons with t Distribution
Method: 95% t interval.
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Mean
East
North
West
South
East
12
16.4167
**
|
North
12
22.5417
**
|
West
12
23.9167
**
|
South
12
35.1250
**
**
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - East
18.7083
5.1477
3.6343
2.0154
0.0007
8.3339
29.0828
**
West - East
7.5000
5.1477
1.4570
2.0154
0.1522
-2.8745
17.8745
North - East
6.1250
5.1477
1.1899
2.0154
0.2405
-4.2495
16.4995
South - North
12.5833
5.1477
2.4445
2.0154
0.0186
2.2089
22.9578
**
West - North
1.3750
5.1477
0.2671
2.0154
0.7906
-8.9995
11.7495
South - West
11.2083
5.1477
2.1774
2.0154
0.0349
0.8339
21.5828
**
Homogeneous Subsets:
Group 1: East North West
Group 2: South
Multiple Comparisons (Dunn)
Method: 95% Dunn interval.
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Mean Rank
East
North
West
South
East
12
16.4167
**
|
North
12
22.5417
||
West
12
23.9167
||
South
12
35.1250
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - East
18.7083
5.7069
3.2782
2.6383
0.0063
3.6520
33.7647
**
West - East
7.5000
5.7069
1.3142
2.6383
1.0000
-7.5564
22.5564
North - East
6.1250
5.7069
1.0733
2.6383
1.0000
-8.9314
21.1814
South - North
12.5833
5.7069
2.2049
2.6383
0.1648
-2.4730
27.6397
West - North
1.3750
5.7069
0.2409
2.6383
1.0000
-13.6814
16.4314
South - West
11.2083
5.7069
1.9640
2.6383
0.2972
-3.8480
26.2647
Homogeneous Subsets:
Group 1: East North West
Group 2: North West South
Comparisons against a Control Group (Dunnett)
Method: 95% Dunnett interval.
Control Group: North, Two-Tailed Test
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.
Group
Cases
Rank Sum
North
East
12
197.0000
|
North
12
270.5000
||
West
12
287.0000
|
South
12
421.5000
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
South - North
151.0000
68.5857
2.2016
2.3491
0.0722
-10.1137
312.1137
West - North
16.5000
68.5857
0.2406
2.3491
0.9904
-144.6137
177.6137
East - North
-73.5000
68.5857
1.0717
2.3491
0.5739
-234.6137
87.6137
Homogeneous Subsets:
Group 1: East North
Group 2: North West South
Comparisons against a Control Group (Dunn)
Method: 95% Dunn interval.
Control Group: North, Two-Tailed Test
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.