UNISTAT - the ultimate Excel statistics add-in

Kruskal-Wallis One-Way ANOVA in Excel with Unistat

The Unistat statistics add-in extends Excel with Kruskal-Wallis One-Way ANOVA capabilities.

Further documentation is available at section 6.5.1 of the manual, Nonparametric Tests > Kruskal-Wallis One-Way ANOVA.

Sample output

Here we provide annotated example report output from the Unistat Excel statistics 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	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)

Group	Cases	Mean Rank	East	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	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)

Group	Cases	Mean Rank	East	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	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
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%
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.

Group	Cases	Mean Rank
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%
South - North	12.5833	5.7069	2.2049	2.3940	0.0824	-1.0790	26.2456
West - North	1.3750	5.7069	0.2409	2.3940	1.0000	-12.2873	15.0373
East - North	-6.1250	5.7069	1.0733	2.3940	0.8495	-19.7873	7.5373

Homogeneous Subsets:
Group 1: East North
Group 2: North West South

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