UNISTAT - the ultimate Excel statistics add-in

Friedman Two-Way ANOVA in Excel with Unistat

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

Further documentation is available at section 6.5.4 of the manual, Nonparametric Tests > Friedman Two-Way ANOVA.

Sample output

Here we provide annotated example report output from the Unistat Excel statistics add-in for data analysis.

Friedman Two-Way ANOVA

CasesRank SumMean 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.

GroupCasesRank SumTreatment 1Treatment 2Treatment 3Treatment 4
Treatment 1 8 11.0000**
|
Treatment 2 8 16.0000**
|
Treatment 3 8 23.5000
||
Treatment 4 8 29.5000****
 |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 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.

GroupCasesRank SumTreatment 1Treatment 2Treatment 3Treatment 4
Treatment 1 8 11.0000****
|
Treatment 2 8 16.0000****
|
Treatment 3 8 23.5000****
 |
Treatment 4 8 29.5000****
 |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 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.

GroupCasesRank SumTreatment 1
Treatment 1 8 11.0000
|
Treatment 2 8 16.0000
|
Treatment 3 8 23.5000**
 |
Treatment 4 8 29.5000**
  |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 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


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