Unistat Statistics Software | Friedman Two-Way ANOVA in Excel

Friedman Two-Way ANOVA in Excel with UNISTAT

The UNISTAT statistics add-in extends Excel with Friedman Two-Way ANOVA capabilities.

For further information visit UNISTAT User's Guide section 6.5.4. Friedman Two-Way ANOVA.

Here we provide a sample output from the UNISTAT Excel statistics 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 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	Probability	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	Probability	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.

Group	Cases	Rank Sum	Treatment 1
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	Probability	Lower 95%	Upper 95%	Result
Treatment 4 - Treatment 1	18.5000	5.1640	3.5825	2.3491	0.0010	6.3694	30.6306	**
Treatment 3 - Treatment 1	12.5000	5.1640	2.4206	2.3491	0.0415	0.3694	24.6306	**
Treatment 2 - Treatment 1	5.0000	5.1640	0.9682	2.3491	0.6468	-7.1306	17.1306

Homogeneous Subsets:
Group 1: Treatment 1 Treatment 2
Group 2: Treatment 3
Group 3: Treatment 4