Multiple Means Comparison (MMC) 1
------------------------------------
Example #1 -- CR design
------------------------------------
The ANOVA Procedure
Class Level Information
Class Levels Values
COTTON 5 15 20 25 30 35
Number of observations 25
Multiple Means Comparison (MMC) 2
------------------------------------
Example #1 -- CR design
------------------------------------
The ANOVA Procedure
Dependent Variable: STRENGTH
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 4 475.7600000 118.9400000 14.76 <.0001
Error 20 161.2000000 8.0600000
Corrected Total 24 636.9600000
R-Square Coeff Var Root MSE STRENGTH Mean
0.746923 18.87642 2.839014 15.04000
Source DF Anova SS Mean Square F Value Pr > F
COTTON 4 475.7600000 118.9400000 14.76 <.0001
Multiple Means Comparison (MMC) 3
------------------------------------
Example #1 -- CR design
------------------------------------
The ANOVA Procedure
Duncan's Multiple Range Test for STRENGTH
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 8.06
Number of Means 2 3 4 5
Critical Range 3.745 3.931 4.050 4.132
Means with the same letter are not significantly different.
Duncan Grouping Mean N COTTON
A 21.600 5 30
B 17.600 5 25
B
B 15.400 5 20
C 10.800 5 35
C
C 9.800 5 15
Multiple Means Comparison (MMC) 4
------------------------------------
Example #2 -- RCB design
------------------------------------
The ANOVA Procedure
Class Level Information
Class Levels Values
DAYS 4 1 2 3 4
SOLUTION 3 1 2 3
Number of observations 12
Multiple Means Comparison (MMC) 5
------------------------------------
Example #2 -- RCB design
------------------------------------
The ANOVA Procedure
Dependent Variable: EFFECTNS
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 5 1810.416667 362.083333 41.91 0.0001
Error 6 51.833333 8.638889
Corrected Total 11 1862.250000
R-Square Coeff Var Root MSE EFFECTNS Mean
0.972166 15.67573 2.939199 18.75000
Source DF Anova SS Mean Square F Value Pr > F
DAYS 3 1106.916667 368.972222 42.71 0.0002
SOLUTION 2 703.500000 351.750000 40.72 0.0003
Multiple Means Comparison (MMC) 6
------------------------------------
Example #2 -- RCB design
------------------------------------
The ANOVA Procedure
Duncan's Multiple Range Test for EFFECTNS
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 6
Error Mean Square 8.638889
Number of Means 2 3 4
Critical Range 5.872 6.086 6.192
Means with the same letter are not significantly different.
Duncan Grouping Mean N DAYS
A 35.000 3 4
B 16.667 3 2
B
B 12.000 3 3
B
B 11.333 3 1
Multiple Means Comparison (MMC) 7
------------------------------------
Example #2 -- RCB design
------------------------------------
The ANOVA Procedure
Duncan's Multiple Range Test for EFFECTNS
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 6
Error Mean Square 8.638889
Number of Means 2 3
Critical Range 5.085 5.271
Means with the same letter are not significantly different.
Duncan Grouping Mean N SOLUTION
A 25.250 4 2
A
A 23.000 4 1
B 8.000 4 3
Multiple Means Comparison (MMC) 8
------------------------------------
Example #3 -- Latin Square Design
------------------------------------
The ANOVA Procedure
Class Level Information
Class Levels Values
BATCH 5 1 2 3 4 5
DAY 5 1 2 3 4 5
CATALYST 5 A B C D E
Number of observations 25
Multiple Means Comparison (MMC) 9
------------------------------------
Example #3 -- Latin Square Design
------------------------------------
The ANOVA Procedure
Dependent Variable: REACTIME
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 12 169.1200000 14.0933333 4.51 0.0072
Error 12 37.5200000 3.1266667
Corrected Total 24 206.6400000
R-Square Coeff Var Root MSE REACTIME Mean
0.818428 30.07208 1.768238 5.880000
Source DF Anova SS Mean Square F Value Pr > F
BATCH 4 15.4400000 3.8600000 1.23 0.3476
DAY 4 12.2400000 3.0600000 0.98 0.4550
CATALYST 4 141.4400000 35.3600000 11.31 0.0005
Multiple Means Comparison (MMC) 10
------------------------------------
Example #3 -- Latin Square Design
------------------------------------
The ANOVA Procedure
Duncan's Multiple Range Test for REACTIME
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 12
Error Mean Square 3.126667
Number of Means 2 3 4 5
Critical Range 2.437 2.550 2.619 2.665
Means with the same letter are not significantly different.
Duncan Grouping Mean N BATCH
A 7.200 5 4
A
A 6.200 5 2
A
A 5.800 5 3
A
A 5.200 5 1
A
A 5.000 5 5
Multiple Means Comparison (MMC) 11
------------------------------------
Example #3 -- Latin Square Design
------------------------------------
The ANOVA Procedure
Duncan's Multiple Range Test for REACTIME
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 12
Error Mean Square 3.126667
Number of Means 2 3 4 5
Critical Range 2.437 2.550 2.619 2.665
Means with the same letter are not significantly different.
Duncan Grouping Mean N DAY
A 6.800 5 5
A
A 6.600 5 1
A
A 5.600 5 2
A
A 5.400 5 3
A
A 5.000 5 4
Multiple Means Comparison (MMC) 12
------------------------------------
Example #3 -- Latin Square Design
------------------------------------
The ANOVA Procedure
Duncan's Multiple Range Test for REACTIME
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 12
Error Mean Square 3.126667
Number of Means 2 3 4 5
Critical Range 2.437 2.550 2.619 2.665
Means with the same letter are not significantly different.
Duncan Grouping Mean N CATALYST
A 8.800 5 C
A
A 8.400 5 A
B 5.600 5 B
B
B 3.400 5 D
B
B 3.200 5 E
Multiple Means Comparison (MMC) 13
------------------------------------
Example #4 -- Factorial Design - a
------------------------------------
The GLM Procedure
Class Level Information
Class Levels Values
PRESS 3 200 215 230
TEMP 3 HIGH LOW MEDIUM
Number of observations 18
Multiple Means Comparison (MMC) 14
------------------------------------
Example #4 -- Factorial Design - a
------------------------------------
The GLM Procedure
Dependent Variable: YIELD
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 8 1.13777778 0.14222222 8.00 0.0026
Error 9 0.16000000 0.01777778
Corrected Total 17 1.29777778
R-Square Coeff Var Root MSE YIELD Mean
0.876712 0.147474 0.133333 90.41111
Source DF Type I SS Mean Square F Value Pr > F
PRESS 2 0.76777778 0.38388889 21.59 0.0004
TEMP 2 0.30111111 0.15055556 8.47 0.0085
PRESS*TEMP 4 0.06888889 0.01722222 0.97 0.4700
Source DF Type III SS Mean Square F Value Pr > F
PRESS 2 0.76777778 0.38388889 21.59 0.0004
TEMP 2 0.30111111 0.15055556 8.47 0.0085
PRESS*TEMP 4 0.06888889 0.01722222 0.97 0.4700
Multiple Means Comparison (MMC) 15
------------------------------------
Example #4 -- Factorial Design - a
------------------------------------
The GLM Procedure
Duncan's Multiple Range Test for YIELD
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 9
Error Mean Square 0.017778
Number of Means 2 3
Critical Range .1741 .1818
Means with the same letter are not significantly different.
Duncan Grouping Mean N PRESS
A 90.68333 6 215
B 90.36667 6 200
C 90.18333 6 230
Multiple Means Comparison (MMC) 16
------------------------------------
Example #4 -- Factorial Design - a
------------------------------------
The GLM Procedure
Duncan's Multiple Range Test for YIELD
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 9
Error Mean Square 0.017778
Number of Means 2 3
Critical Range .1741 .1818
Means with the same letter are not significantly different.
Duncan Grouping Mean N TEMP
A 90.56667 6 HIGH
A
B A 90.41667 6 LOW
B
B 90.25000 6 MEDIUM
Multiple Means Comparison (MMC) 17
------------------------------------
Example #4 -- Factorial Design - a
------------------------------------
The GLM Procedure
Level of Level of ------------YIELD------------
PRESS TEMP N Mean Std Dev
200 HIGH 2 90.6000000 0.14142136
200 LOW 2 90.3000000 0.14142136
200 MEDIUM 2 90.2000000 0.14142136
215 HIGH 2 90.8500000 0.07071068
215 LOW 2 90.6500000 0.07071068
215 MEDIUM 2 90.5500000 0.07071068
230 HIGH 2 90.2500000 0.21213203
230 LOW 2 90.3000000 0.14142136
230 MEDIUM 2 90.0000000 0.14142136
Multiple Means Comparison (MMC) 18
------------------------------------
Example #5 -- Factorial Design - b
------------------------------------
The GLM Procedure
Class Level Information
Class Levels Values
DEPTH 4 0.15 0.18 0.2 0.25
FEED 3 0.2 0.25 0.3
FSYM 3 O P Q
Number of observations 36
Multiple Means Comparison (MMC) 19
------------------------------------
Example #5 -- Factorial Design - b
------------------------------------
The GLM Procedure
Dependent Variable: FINISH
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 11 5842.666667 531.151515 18.49 <.0001
Error 24 689.333333 28.722222
Corrected Total 35 6532.000000
R-Square Coeff Var Root MSE FINISH Mean
0.894468 5.681249 5.359312 94.33333
Source DF Type I SS Mean Square F Value Pr > F
DEPTH 3 2125.111111 708.370370 24.66 <.0001
FEED 2 3160.500000 1580.250000 55.02 <.0001
DEPTH*FEED 6 557.055556 92.842593 3.23 0.0180
Source DF Type III SS Mean Square F Value Pr > F
DEPTH 3 2125.111111 708.370370 24.66 <.0001
FEED 2 3160.500000 1580.250000 55.02 <.0001
DEPTH*FEED 6 557.055556 92.842593 3.23 0.0180
Multiple Means Comparison (MMC) 20
------------------------------------
Example #5 -- Factorial Design - b
------------------------------------
The GLM Procedure
Duncan's Multiple Range Test for FINISH
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 24
Error Mean Square 28.72222
Number of Means 2 3 4
Critical Range 5.214 5.477 5.645
Means with the same letter are not significantly different.
Duncan Grouping Mean N DEPTH
A 104.889 9 0.25
B 97.889 9 0.2
C 89.778 9 0.18
C
C 84.778 9 0.15
Multiple Means Comparison (MMC) 21
------------------------------------
Example #5 -- Factorial Design - b
------------------------------------
The GLM Procedure
Duncan's Multiple Range Test for FINISH
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 24
Error Mean Square 28.72222
Number of Means 2 3
Critical Range 4.516 4.743
Means with the same letter are not significantly different.
Duncan Grouping Mean N FEED
A 103.833 12 0.3
B 97.583 12 0.25
C 81.583 12 0.2
Multiple Means Comparison (MMC) 22
------------------------------------
Example #5 -- Factorial Design - b
------------------------------------
The GLM Procedure
Level of Level of ------------FINISH-----------
DEPTH FEED N Mean Std Dev
0.15 0.2 3 66.000000 7.21110255
0.15 0.25 3 88.666667 3.05505046
0.15 0.3 3 99.666667 2.08166600
0.18 0.2 3 73.333333 5.50757055
0.18 0.25 3 96.666667 8.08290377
0.18 0.3 3 99.333333 4.50924975
0.2 0.2 3 87.333333 5.03322296
0.2 0.25 3 100.666667 6.65832812
0.2 0.3 3 105.666667 5.85946528
0.25 0.2 3 99.666667 4.04145188
0.25 0.25 3 104.333333 5.50757055
0.25 0.3 3 110.666667 3.51188458