Procedure: Multiple Comparisons

UNISTAT statistical package extends Excel with Multiple Comparisons support.

Sample output

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

Multiple Comparisons

Student-Newman-Keuls

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000****
|
C 5-2.6000**
||
E 5 1.0000
|||
A 5 3.6000**
 ||
D 5 4.8000****
  |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 5.1610 4.2319 0.0123****
A - B 8.4000 2.6306 4.5159 3.9583 0.0218****
E - B 5.8000 2.6306 3.1181 3.5779 0.0947**
C - B 2.2000 2.6306 1.1827 2.9500 0.4129**
D - C 7.4000 2.6306 3.9783 3.9583 0.0486****
A - C 6.2000 2.6306 3.3331 3.5779 0.0707**
E - C 3.6000 2.6306 1.9354 2.9500 0.1863**
D - E 3.8000 2.6306 2.0429 3.5779 0.3380**
A - E 2.6000 2.6306 1.3978 2.9500 0.3348**
D - A 1.2000 2.6306 0.6451 2.9500 0.6532**

Homogeneous Subsets:
Group 1: B C E
Pooled mean-2.1333
95% Confidence Interval-4.3735 <> 0.1069
Group 2: C E A
Pooled mean 0.6667
95% Confidence Interval-1.5735 <> 2.9069
Group 3: E A D
Pooled mean 3.1333
95% Confidence Interval 0.8931 <> 5.3735
Between Homogeneous subsets:
Group 2 - Group 1
Difference 2.8000
95% Confidence Interval-0.3681 <> 5.9681
Group 3 - Group 2
Difference 2.4667
95% Confidence Interval-0.7014 <> 5.6348

Tukey-HSD

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000****
|
C 5-2.6000
||
E 5 1.0000
||
A 5 3.6000**
 |
D 5 4.8000**
 |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 5.1610 4.2319 0.0123 1.7283 17.4717**
A - B 8.4000 2.6306 4.5159 4.2319 0.0329 0.5283 16.2717**
E - B 5.8000 2.6306 3.1181 4.2319 0.2182-2.0717 13.6717
C - B 2.2000 2.6306 1.1827 4.2319 0.9161-5.6717 10.0717
D - C 7.4000 2.6306 3.9783 4.2319 0.0717-0.4717 15.2717
A - C 6.2000 2.6306 3.3331 4.2319 0.1685-1.6717 14.0717
E - C 3.6000 2.6306 1.9354 4.2319 0.6536-4.2717 11.4717
D - E 3.8000 2.6306 2.0429 4.2319 0.6077-4.0717 11.6717
A - E 2.6000 2.6306 1.3978 4.2319 0.8574-5.2717 10.4717
D - A 1.2000 2.6306 0.6451 4.2319 0.9904-6.6717 9.0717

Homogeneous Subsets:
Group 1: B C E
Pooled mean-2.1333
95% Confidence Interval-4.3735 <> 0.1069
Group 2: C E A D
Pooled mean 1.7000
95% Confidence Interval-0.2401 <> 3.6401
Between Homogeneous subsets:
Group 2 - Group 1
Difference 3.8333
95% Confidence Interval-0.4179 <> 8.0845

Tukey-B

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000****
|
C 5-2.6000
||
E 5 1.0000
||
A 5 3.6000**
 |
D 5 4.8000**
 |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 5.1610 4.2319 0.0123 1.7283 17.4717**
A - B 8.4000 2.6306 4.5159 4.0951 0.0218 0.5283 16.2717**
E - B 5.8000 2.6306 3.1181 3.9049 0.0947-2.0717 13.6717
C - B 2.2000 2.6306 1.1827 3.5909 0.4129-5.6717 10.0717
D - C 7.4000 2.6306 3.9783 4.0951 0.0486-0.4717 15.2717
A - C 6.2000 2.6306 3.3331 3.9049 0.0707-1.6717 14.0717
E - C 3.6000 2.6306 1.9354 3.5909 0.1863-4.2717 11.4717
D - E 3.8000 2.6306 2.0429 3.9049 0.3380-4.0717 11.6717
A - E 2.6000 2.6306 1.3978 3.5909 0.3348-5.2717 10.4717
D - A 1.2000 2.6306 0.6451 3.5909 0.6532-6.6717 9.0717

Homogeneous Subsets:
Group 1: B C E
Pooled mean-2.1333
95% Confidence Interval-4.3735 <> 0.1069
Group 2: C E A D
Pooled mean 1.7000
95% Confidence Interval-0.2401 <> 3.6401
Between Homogeneous subsets:
Group 2 - Group 1
Difference 3.8333
95% Confidence Interval 0.2260 <> 7.4407

Duncan

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000******
|
C 5-2.6000****
||
E 5 1.0000**
 ||
A 5 3.6000****
  |
D 5 4.8000****
  |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 5.1610 3.2558*****
A - B 8.4000 2.6306 4.5159 3.1960*****
E - B 5.8000 2.6306 3.1181 3.0938*****
C - B 2.2000 2.6306 1.1827 2.9453***
D - C 7.4000 2.6306 3.9783 3.1960*****
A - C 6.2000 2.6306 3.3331 3.0938*****
E - C 3.6000 2.6306 1.9354 2.9453***
D - E 3.8000 2.6306 2.0429 3.0938***
A - E 2.6000 2.6306 1.3978 2.9453***
D - A 1.2000 2.6306 0.6451 2.9453***

Homogeneous Subsets:
Group 1: B C
Pooled mean-3.7000
95% Confidence Interval-6.4437 <>-0.9563
Group 2: C E
Pooled mean-0.8000
95% Confidence Interval-3.5437 <> 1.9437
Group 3: E A D
Pooled mean 3.1333
95% Confidence Interval 0.8931 <> 5.3735

Scheffe

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000**
|
C 5-2.6000
||
E 5 1.0000
||
A 5 3.6000
||
D 5 4.8000**
 |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 3.6494 3.3859 0.0304 0.6931 18.5069**
A - B 8.4000 2.6306 3.1932 3.3859 0.0711-0.5069 17.3069
E - B 5.8000 2.6306 2.2048 3.3859 0.3355-3.1069 14.7069
C - B 2.2000 2.6306 0.8363 3.3859 0.9487-6.7069 11.1069
D - C 7.4000 2.6306 2.8131 3.3859 0.1368-1.5069 16.3069
A - C 6.2000 2.6306 2.3569 3.3859 0.2736-2.7069 15.1069
E - C 3.6000 2.6306 1.3685 3.3859 0.7584-5.3069 12.5069
D - E 3.8000 2.6306 1.4445 3.3859 0.7209-5.1069 12.7069
A - E 2.6000 2.6306 0.9884 3.3859 0.9098-6.3069 11.5069
D - A 1.2000 2.6306 0.4562 3.3859 0.9945-7.7069 10.1069

Homogeneous Subsets:
Group 1: B C E A
Pooled mean-0.7000
95% Confidence Interval-2.6401 <> 1.2401
Group 2: C E A D
Pooled mean 1.7000
95% Confidence Interval-0.2401 <> 3.6401
Between Homogeneous subsets:
Group 2 - Group 1
Difference 2.4000
95% Confidence Interval-2.0535 <> 6.8535

Least Significant Difference (LSD)

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000******
|
C 5-2.6000****
||
E 5 1.0000**
 ||
A 5 3.6000****
  |
D 5 4.8000****
  |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 3.6494 2.0860 0.0016 4.1127 15.0873**
A - B 8.4000 2.6306 3.1932 2.0860 0.0046 2.9127 13.8873**
E - B 5.8000 2.6306 2.2048 2.0860 0.0393 0.3127 11.2873**
C - B 2.2000 2.6306 0.8363 2.0860 0.4129-3.2873 7.6873
D - C 7.4000 2.6306 2.8131 2.0860 0.0107 1.9127 12.8873**
A - C 6.2000 2.6306 2.3569 2.0860 0.0287 0.7127 11.6873**
E - C 3.6000 2.6306 1.3685 2.0860 0.1863-1.8873 9.0873
D - E 3.8000 2.6306 1.4445 2.0860 0.1641-1.6873 9.2873
A - E 2.6000 2.6306 0.9884 2.0860 0.3348-2.8873 8.0873
D - A 1.2000 2.6306 0.4562 2.0860 0.6532-4.2873 6.6873

Homogeneous Subsets:
Group 1: B C
Pooled mean-3.7000
95% Confidence Interval-6.4437 <>-0.9563
Group 2: C E
Pooled mean-0.8000
95% Confidence Interval-3.5437 <> 1.9437
Group 3: E A D
Pooled mean 3.1333
95% Confidence Interval 0.8931 <> 5.3735

Bonferroni (Modified LSD)

For Coded Data, classified by Formulation
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanBCEAD
B 5-4.8000****
|
C 5-2.6000
||
E 5 1.0000
||
A 5 3.6000**
 |
D 5 4.8000**
 |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - B 9.6000 2.6306 3.6494 3.1534 0.0159 1.3047 17.8953**
A - B 8.4000 2.6306 3.1932 3.1534 0.0457 0.1047 16.6953**
E - B 5.8000 2.6306 2.2048 3.1534 0.3934-2.4953 14.0953
C - B 2.2000 2.6306 0.8363 3.1534 1.0000-6.0953 10.4953
D - C 7.4000 2.6306 2.8131 3.1534 0.1074-0.8953 15.6953
A - C 6.2000 2.6306 2.3569 3.1534 0.2873-2.0953 14.4953
E - C 3.6000 2.6306 1.3685 3.1534 1.0000-4.6953 11.8953
D - E 3.8000 2.6306 1.4445 3.1534 1.0000-4.4953 12.0953
A - E 2.6000 2.6306 0.9884 3.1534 1.0000-5.6953 10.8953
D - A 1.2000 2.6306 0.4562 3.1534 1.0000-7.0953 9.4953

Homogeneous Subsets:
Group 1: B C E
Pooled mean-2.1333
95% Confidence Interval-4.3735 <> 0.1069
Group 2: C E A D
Pooled mean 1.7000
95% Confidence Interval-0.2401 <> 3.6401

Dunnett

For Coded Data, classified by Formulation
Control Group: A, Two-Tailed Test
Mean Square Error: 17.3, Degrees of Freedom: 20
** 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.

GroupCasesMeanA
B 5-4.8000**
|
C 5-2.6000
 |
E 5 1.0000
 |
A 5 3.6000
 ||
D 5 4.8000
  |

ComparisonDifferenceStandard Errorq StatTable qSignificanceLower 95%Upper 95%Result
D - A 1.2000 2.6306 0.4562 2.6510 0.9732-5.7738 8.1738
E - A-2.6000 2.6306 0.9884 2.6510 0.7226-9.5738 4.3738
C - A-6.2000 2.6306 2.3569 2.6510 0.0902-13.1738 0.7738
B - A-8.4000 2.6306 3.1932 2.6510 0.0157-15.3738-1.4262**

Homogeneous Subsets:
Group 1: B
Pooled mean-4.8000
95% Confidence Interval-8.6801 <>-0.9199
Group 2: C E A
Pooled mean 0.6667
95% Confidence Interval-1.5735 <> 2.9069
Group 3: A D
Pooled mean 4.2000
95% Confidence Interval 1.4563 <> 6.9437
Between Homogeneous subsets:
Group 2 - Group 1
Difference 5.4667
95% Confidence Interval-0.2274 <> 11.1607
Group 3 - Group 2
Difference 3.5333
95% Confidence Interval-0.9682 <> 8.0349