Unistat Statistics Software | Kruskal-Wallis One-Way ANOVA in Excel

Kruskal-Wallis One-Way ANOVA in Excel with UNISTAT

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

For further information visit UNISTAT User's Guide section 6.5.1. Kruskal-Wallis One-Way ANOVA.

Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.

Kruskal-Wallis One-Way ANOVA

Data variable: Coded Data
Subsample selected by: Formulation

Formulation	Cases	Rank Sum	Mean Rank
A	5	88.5000	17.7000
B	5	25.0000	5.0000
C	5	43.0000	8.6000
D	5	94.5000	18.9000
E	5	74.0000	14.8000
Total	25	325.0000	13.0000

Correction for Ties	0.0073
Chi-Square Statistic	13.3437
Degrees of Freedom	4
Right-Tail Probability	0.0097

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	B	A	D
B	5	25.0000		**	**	\|
C	5	43.0000				\|\|
E	5	74.0000				\|\|
A	5	88.5000	**			\|
D	5	94.5000	**			\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - B	69.5000	16.4570	4.2231	3.8577	0.0236	6.0145	132.9855	**
A - B	63.5000	16.4570	3.8585	3.8577	0.0499	0.0145	126.9855	**
E - B	49.0000	16.4570	2.9775	3.8577	0.2176	-14.4855	112.4855
C - B	18.0000	16.4570	1.0938	3.8577	0.9383	-45.4855	81.4855
D - C	51.5000	16.4570	3.1294	3.8577	0.1748	-11.9855	114.9855
A - C	45.5000	16.4570	2.7648	3.8577	0.2883	-17.9855	108.9855
E - C	31.0000	16.4570	1.8837	3.8577	0.6712	-32.4855	94.4855
D - E	20.5000	16.4570	1.2457	3.8577	0.9041	-42.9855	83.9855
A - E	14.5000	16.4570	0.8811	3.8577	0.9714	-48.9855	77.9855
D - A	6.0000	16.4570	0.3646	3.8577	0.9990	-57.4855	69.4855

Homogeneous Subsets:
Group 1: B, C, E
Group 2: C, E, A, D

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	B	A	D
B	5	5.0000		**	**	\|
C	5	8.6000				\|\|
E	5	14.8000				\|\|
A	5	17.7000	**			\|
D	5	18.9000	**			\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - B	13.9000	3.2914	4.2231	3.8577	0.0236	1.2029	26.5971	**
A - B	12.7000	3.2914	3.8585	3.8577	0.0499	0.0029	25.3971	**
E - B	9.8000	3.2914	2.9775	3.8577	0.2176	-2.8971	22.4971
C - B	3.6000	3.2914	1.0938	3.8577	0.9383	-9.0971	16.2971
D - C	10.3000	3.2914	3.1294	3.8577	0.1748	-2.3971	22.9971
A - C	9.1000	3.2914	2.7648	3.8577	0.2883	-3.5971	21.7971
E - C	6.2000	3.2914	1.8837	3.8577	0.6712	-6.4971	18.8971
D - E	4.1000	3.2914	1.2457	3.8577	0.9041	-8.5971	16.7971
A - E	2.9000	3.2914	0.8811	3.8577	0.9714	-9.7971	15.5971
D - A	1.2000	3.2914	0.3646	3.8577	0.9990	-11.4971	13.8971

Homogeneous Subsets:
Group 1: B, C, E
Group 2: C, E, A, D

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	B	A	D
B	5	25.0000		**	**	\|
C	5	43.0000				\|\|
E	5	74.0000				\|\|
A	5	88.5000	**			\|
D	5	94.5000	**			\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - B	69.5000	16.4570	4.2231	3.8577	0.0236	*	*	**
A - B	63.5000	16.4570	3.8585	3.6332	0.0323	*	*	**
E - B	49.0000	16.4570	2.9775	3.3145	0.0887	*	*
C - B	18.0000	16.4570	1.0938	2.7718	0.4393	*	*
D - C	51.5000	16.4570	3.1294	3.6332	0.1197	*	*
A - C	45.5000	16.4570	2.7648	3.3145	0.1236	*	*
E - C	31.0000	16.4570	1.8837	2.7718	0.1829	*	*
D - E	20.5000	16.4570	1.2457	3.3145	0.6524	*	*
A - E	14.5000	16.4570	0.8811	2.7718	0.5333	*	*
D - A	6.0000	16.4570	0.3646	2.7718	0.7966	*	*

Homogeneous Subsets:
Group 1: B, C, E
Group 2: C, E, A, D

Multiple Comparisons with Mean Ranks (S-N-K)

Group	Cases	Mean Rank	B	A	D
B	5	5.0000		**	**	\|
C	5	8.6000				\|\|
E	5	14.8000				\|\|
A	5	17.7000	**			\|
D	5	18.9000	**			\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - B	13.9000	3.2914	4.2231	3.8577	0.0236	*	*	**
A - B	12.7000	3.2914	3.8585	3.6332	0.0323	*	*	**
E - B	9.8000	3.2914	2.9775	3.3145	0.0887	*	*
C - B	3.6000	3.2914	1.0938	2.7718	0.4393	*	*
D - C	10.3000	3.2914	3.1294	3.6332	0.1197	*	*
A - C	9.1000	3.2914	2.7648	3.3145	0.1236	*	*
E - C	6.2000	3.2914	1.8837	2.7718	0.1829	*	*
D - E	4.1000	3.2914	1.2457	3.3145	0.6524	*	*
A - E	2.9000	3.2914	0.8811	2.7718	0.5333	*	*
D - A	1.2000	3.2914	0.3646	2.7718	0.7966	*	*

Homogeneous Subsets:
Group 1: B, C, E
Group 2: C, E, A, D

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	B	C	E	A	D
B	5	5.0000			**	**	**	\|
C	5	8.6000				**	**	\|\|
E	5	14.8000	**					\|\|
A	5	17.7000	**	**				\|
D	5	18.9000	**	**				\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - B	13.9000	3.3853	4.1060	2.0860	0.0005	6.8385	20.9615	**
A - B	12.7000	3.3853	3.7516	2.0860	0.0013	5.6385	19.7615	**
E - B	9.8000	3.3853	2.8949	2.0860	0.0090	2.7385	16.8615	**
C - B	3.6000	3.3853	1.0634	2.0860	0.3003	-3.4615	10.6615
D - C	10.3000	3.3853	3.0426	2.0860	0.0064	3.2385	17.3615	**
A - C	9.1000	3.3853	2.6881	2.0860	0.0141	2.0385	16.1615	**
E - C	6.2000	3.3853	1.8315	2.0860	0.0820	-0.8615	13.2615
D - E	4.1000	3.3853	1.2111	2.0860	0.2400	-2.9615	11.1615
A - E	2.9000	3.3853	0.8567	2.0860	0.4018	-4.1615	9.9615
D - A	1.2000	3.3853	0.3545	2.0860	0.7267	-5.8615	8.2615

Homogeneous Subsets:
Group 1: B, C
Group 2: C, E
Group 3: E, A, D

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	B	D
B	5	5.0000		**	\|
C	5	8.6000			\|\|
E	5	14.8000			\|\|
A	5	17.7000			\|\|
D	5	18.9000	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - B	13.9000	4.6377	2.9972	2.8070	0.0272	0.8818	26.9182	**
A - B	12.7000	4.6377	2.7384	2.8070	0.0617	-0.3182	25.7182
E - B	9.8000	4.6377	2.1131	2.8070	0.3459	-3.2182	22.8182
C - B	3.6000	4.6377	0.7762	2.8070	1.0000	-9.4182	16.6182
D - C	10.3000	4.6377	2.2209	2.8070	0.2636	-2.7182	23.3182
A - C	9.1000	4.6377	1.9622	2.8070	0.4974	-3.9182	22.1182
E - C	6.2000	4.6377	1.3369	2.8070	1.0000	-6.8182	19.2182
D - E	4.1000	4.6377	0.8841	2.8070	1.0000	-8.9182	17.1182
A - E	2.9000	4.6377	0.6253	2.8070	1.0000	-10.1182	15.9182
D - A	1.2000	4.6377	0.2587	2.8070	1.0000	-11.8182	14.2182

Homogeneous Subsets:
Group 1: B, C, E, A
Group 2: C, E, A, D

Comparisons against a Control Group (Dunnett)

Method: 95% Dunnett interval
Control Group: A, 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	A
B	5	25.0000	**	\|
C	5	43.0000		\|
E	5	74.0000		\|
A	5	88.5000		\|\|
D	5	94.5000		\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - A	6.0000	23.2737	0.2578	2.4419	0.9970	-50.8324	62.8324
E - A	-14.5000	23.2737	0.6230	2.4419	0.9260	-71.3324	42.3324
C - A	-45.5000	23.2737	1.9550	2.4419	0.1575	-102.3324	11.3324
B - A	-63.5000	23.2737	2.7284	2.4419	0.0227	-120.3324	-6.6676	**

Homogeneous Subsets:
Group 1: B
Group 2: C, E, A
Group 3: A, D

Comparisons against a Control Group (Dunn)

Method: 95% Dunn interval
Control Group: A, 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	A
B	5	5.0000	**	\|
C	5	8.6000		\|
E	5	14.8000		\|
A	5	17.7000		\|\|
D	5	18.9000		\|

Comparison	Difference	Standard Error	q Stat	Table q	Probability	Lower 95%	Upper 95%	Result
D - A	1.2000	4.6377	0.2587	2.4977	1.0000	-10.3836	12.7836
E - A	-2.9000	4.6377	0.6253	2.4977	1.0000	-14.4836	8.6836
C - A	-9.1000	4.6377	1.9622	2.4977	0.1990	-20.6836	2.4836
B - A	-12.7000	4.6377	2.7384	2.4977	0.0247	-24.2836	-1.1164	**

Homogeneous Subsets:
Group 1: B
Group 2: C, E, A
Group 3: A, D