UNISTAT statistical package extends Excel with Friedman Two-Way ANOVA support.
Sample output
Here we provide annotated example report output from the UNISTAT Excel add-in for data analysis.
Friedman Two-Way ANOVA
Cases
Rank Sum
Mean Rank
Treatment 1
8
11.0000
1.3750
Treatment 2
8
16.0000
2.0000
Treatment 3
8
23.5000
2.9375
Treatment 4
8
29.5000
3.6875
Total
32
80.0000
2.5000
Number of Columns
4
Number of Rows
8
Correction for Ties
0.0125
Chi-Square Statistic
15.1519
Degrees of Freedom
3
Right-Tail Probability
0.0017
F(3,21)
11.9871
Right-Tail Probability
0.0001
Multiple Comparisons (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
Treatment 1
Treatment 2
Treatment 3
Treatment 4
Treatment 1
8
11.0000
**
|
Treatment 2
8
16.0000
**
|
Treatment 3
8
23.5000
||
Treatment 4
8
29.5000
**
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
Treatment 4 - Treatment 1
18.5000
3.6515
5.0664
3.6332
0.0019
5.2336
31.7664
**
Treatment 3 - Treatment 1
12.5000
3.6515
3.4233
3.6332
0.0732
-0.7664
25.7664
Treatment 2 - Treatment 1
5.0000
3.6515
1.3693
3.6332
0.7675
-8.2664
18.2664
Treatment 4 - Treatment 2
13.5000
3.6515
3.6971
3.6332
0.0443
0.2336
26.7664
**
Treatment 3 - Treatment 2
7.5000
3.6515
2.0540
3.6332
0.4666
-5.7664
20.7664
Treatment 4 - Treatment 3
6.0000
3.6515
1.6432
3.6332
0.6510
-7.2664
19.2664
Homogeneous Subsets:
Group 1: Treatment 1 Treatment 2 Treatment 3
Group 2: Treatment 3 Treatment 4
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
Rank Sum
Treatment 1
Treatment 2
Treatment 3
Treatment 4
Treatment 1
8
11.0000
**
**
|
Treatment 2
8
16.0000
**
**
|
Treatment 3
8
23.5000
**
**
|
Treatment 4
8
29.5000
**
**
|
Comparison
Difference
Standard Error
q Stat
Table q
Significance
Lower 95%
Upper 95%
Result
Treatment 4 - Treatment 1
18.5000
3.3310
5.5540
2.0796
0.0000
11.5729
25.4271
**
Treatment 3 - Treatment 1
12.5000
3.3310
3.7527
2.0796
0.0012
5.5729
19.4271
**
Treatment 2 - Treatment 1
5.0000
3.3310
1.5011
2.0796
0.1482
-1.9271
11.9271
Treatment 4 - Treatment 2
13.5000
3.3310
4.0529
2.0796
0.0006
6.5729
20.4271
**
Treatment 3 - Treatment 2
7.5000
3.3310
2.2516
2.0796
0.0352
0.5729
14.4271
**
Treatment 4 - Treatment 3
6.0000
3.3310
1.8013
2.0796
0.0860
-0.9271
12.9271
Homogeneous Subsets:
Group 1: Treatment 1 Treatment 2
Group 2: Treatment 3 Treatment 4
Comparisons against a Control Group (Dunnett)
Method: 95% Dunnett interval.
Control Group: Treatment 1, 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.