Perbedaan ANOVA dengan MANOVA ( What is your ccomment ? )
Perbedaan ANOVA dengan MANOVA
( What is your ccomment ? )
ANOVA
Jenis
kelamin
MANOVA
Jenis
kelamin
IPK
mahasisw
a
Tempat
tinggal
Lama
studi
mahasisw
a
IPK
mahasisw
a
Tempat
tinggal
Make your own model !
ANOVA
MANOVA
t-test vs. ANOVA vs.
MANOVA
Test
# of IVs
# of DVs
t-test
One
One
ANOVA
Multiple
One
MANOVA
Multiple
Multiple
Kinds of research questions (1)
Main efects of IVs
Holding all else constant, are mean diferences
in the composite DV among groups at
diferent leveels of an IV larger than expected by
chance?
Interaction among IVs
Holding all else constant, does change in the DV
oveer leveels of one IV depend on the leveel of
another IV?
Importance of DVs
Which of the DVs are changed and which are
unafected by the IVs?
Kinds of research questions (2)
Parameter estimates
After removeal of the efects of coveariate(s), what are
the means adjusted for particular DV(s)?
Specifc comparisons and trend analysis
If an interaction or main efect for an IV with more
than 2 leveels is signifcant, which leveels of main efect
or cells of interaction are diferent from which others?
Strength of association
If an interaction or main efect for an IV is signifcant,
what proportion of veariance of the linear combination
of DV scores is explained by the IV?
Efects of Coveariates
To what degree does a coveariate adjust the composite
DV?
MANOVA/ MANCOVA
SPSS Example
IVs
DVs
Covariate
Analyze GLM Multivariate
IVs
DVs
Covariate
Example of MANOVA (1)
Efect of training ( V) on satisfaction with
the system and performance (DVs)
Group means
Training
Satisfaction
Performance
Control
4.2
4.9
Face-to-face
training
7.9
7.0
Online training
6.0
6.9
1 IV
2 DVs
MANOVA test statistics
Between-Subjects Factors
N
Training 1.0
Group 2.0
3.0
25
22
23
Multivariate Tests c
Effect
Intercept
Value
Pillai's Trace
Hypothesis df
Error df
Sig.
.872
223.996 a
2.000
66.000
.000
.128
223.996 a
2.000
66.000
.000
Hotelling's Trace
6.788
223.996 a
2.000
66.000
.000
Roy's Largest Root
6.788
223.996 a
2.000
66.000
.000
Wilks' Lambda
Training
Group
F
Pillai's Trace
.183
3.376
4.000
134.000
.011
Wilks' Lambda
.820
3.434 a
4.000
132.000
.010
Hotelling's Trace
.215
3.489
4.000
130.000
.010
.193
6.458 b
2.000
67.000
.003
Roy's Largest Root
a. Exact statistic
b. The statistic is an upper bound on F that yields a lower bound on the significance level.
c. Design: Intercept+RACE
All four multivariate statistics indicate that training is
significantly related to the interrelationship between
satisfaction and performance.
ANOVAs on the efect of training
on satisfaction and performance
Tests of Between-Subjects Effects
Source
Dependent Variable
Corrected Model SATISFACTION
PERFORMANCE
Intercept
SATISFACTION
PERFORMANCE
Training
SATISFACTION
Group
PERFORMANCE
Error
SATISFACTION
PERFORMANCE
Total
SATISFACTION
PERFORMANCE
Corrected Total SATISFACTION
PERFORMANCE
Type III Sum
of Squares
157.537a
66.382b
2542.512
2713.380
157.537
66.382
1535.335
422.203
4177.000
3167.000
1692.871
488.586
df
2
2
1
1
2
2
67
67
70
70
69
69
Mean Square
78.768
33.191
2542.512
2713.380
78.768
33.191
22.915
6.302
F
3.437
5.267
110.952
430.590
3.437
5.267
Sig.
.038
.008
.000
.000
.038
.008
a. R Squared = .093 (Adjusted R Squared = .066)
b. R Squared = .136 (Adjusted R Squared = .110)
There are significant differences between training groups in both mean
satisfaction and mean performance.
Example of MANOVA (2)
Efect of training and job ( Vs) on satisfaction
with the system and performance (DVs)
Group means
Control
Face-to-face
training
Online
training
Satisfaction
5.9
8.2
6.9
Performance
6.0
6.9
8.0
Satisfaction
3.6
7.6
4.3
Performance
4.4
7.0
4.8
IT
Non-IT
MANOVA test statistics
c
Multivariate Tests
Effect
Intercept
Training
Group
Job
Training Group *
Gender
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Value
.878
.122
7.170
7.170
.124
.877
.139
.128
.109
.891
.122
.122
.077
.923
.084
.083
F
Hypothesis df
225.868a
2.000
a
225.868
2.000
a
225.868
2.000
a
225.868
2.000
2.116
4.000
a
2.134
4.000
2.150
4.000
b
4.100
2.000
a
3.853
2.000
a
3.853
2.000
a
3.853
2.000
a
3.853
2.000
1.287
4.000
a
1.292
4.000
1.296
4.000
b
2.643
2.000
Error df
63.000
63.000
63.000
63.000
128.000
126.000
124.000
64.000
63.000
63.000
63.000
63.000
128.000
126.000
124.000
64.000
Sig.
.000
.000
.000
.000
.083
.080
.079
.021
.026
.026
.026
.026
.279
.277
.275
.079
a. Exact statistic
b. The statistic is an upper bound on F that yields a lower bound on the significance level.
c. Design: Intercept+RACE+GENDER+RACE * GENDER
Are there significant multivariate relationships? How do we interpret this?
ANOVAs on the efect of training
and job on satisfaction and
performance
Tests of Between-Subjects Effects
Source
Corrected Model
Intercept
Training
Group
Job
Training Group *
Job
Error
Total
Corrected Total
Dependent Variable
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
Type III Sum
of Squares
220.589a
133.718b
2278.580
2383.114
109.195
32.250
51.586
38.677
12.162
29.151
1472.283
354.868
4177.000
3167.000
1692.871
488.586
a.
R Squared = .130 (Adjusted R Squared = .062)
b.
R Squared = .274 (Adjusted R Squared = .217)
df
5
5
1
1
2
2
1
1
2
2
64
64
70
70
69
69
Mean Square
44.118
26.744
2278.580
2383.114
54.598
16.125
51.586
F
1.918
4.823
99.050
429.792
2.373
2.908
2.242
Sig.
.104
.001
.000
.000
.101
.062
.139
38.677
6.081
14.576
23.004
5.545
6.975
.264
2.629
.010
.769
.080
Are there significant univariate relationships? How do we interpret this?
Example of MANCOVA
Efect of training on satisfaction and performance,
controlling for computer self-efcacy and computer
anxiety
Training group means
Control
Face-to-face
training
Online
training
Satisfaction
4.2
7.9
6.0
Performance
4.9
7.0
6.9
Computer
self-efficacy
3.5
4.5
3.6
Computer
anxiety
16.6
15.7
17.0
MANCOVA test statistics
c
Multivariate Tests
Effect
Intercept
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Computer
Pillai's Trace
Self-efficacy Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Computer
Pillai's Trace
Anxiety
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Training
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Value
.188
.812
.232
.232
.468
.532
.881
.881
.068
.932
.073
.073
.157
.844
.184
.178
F
Hypothesis df
7.409a
2.000
a
7.409
2.000
7.409a
2.000
a
7.409
2.000
28.195a
2.000
a
28.195
2.000
a
28.195
2.000
a
28.195
2.000
a
2.333
2.000
2.333a
2.000
a
2.333
2.000
2.333a
2.000
2.774
4.000
a
2.840
4.000
2.903
4.000
b
5.797
2.000
Error df
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
130.000
128.000
126.000
65.000
a. Exact statistic
b.
The statistic is an upper bound on F that yields a lower bound on the significance level.
c.Design: Intercept+Computer Self-efficacy +Computer anxiety+training
Sig.
.001
.001
.001
.001
.000
.000
.000
.000
.105
.105
.105
.105
.030
.027
.024
.005
?
?
nterpretation
Coveariates
Computer
self-eficacy
is
multiveariate
signifcant, but computer anxiety is not. (There
was an adjustment in the group means on the
DVs due to diferences in computer selfeficacy but no signifcant adjustment of group
means due to diferences in computer anxiety).
Main efect of training
Training is signifcantly multiveariate related to
the interrelationship between satisfaction
and performance.
ANOVAs output
Tests of Between-Subjects Effects
Source
Dependent Variable
Corrected Model SATISFACTION
PERFORMANCE
Intercept
SATISFACTION
PERFORMANCE
Computer
SATISFACTION
Self-efficacy
PERFORMANCE
Computer
SATISFACTION
Anxiety
PERFORMANCE
Training
SATISFACTION
PERFORMANCE
Error
SATISFACTION
PERFORMANCE
Total
SATISFACTION
PERFORMANCE
Corrected Total SATISFACTION
PERFORMANCE
Type III Sum
of Squares
995.326a
117.825b
4.920
85.587
614.328
6.631
8.738
24.577
44.072
51.832
697.545
370.761
4177.000
3167.000
1692.871
488.586
a. R Squared = .588 (Adjusted R Squared = .563)
b. R Squared = .241 (Adjusted R Squared = .194)
df
4
4
1
1
1
1
1
1
2
2
65
65
70
70
69
69
Mean Square
248.832
29.456
4.920
85.587
614.328
6.631
8.738
24.577
22.036
25.916
10.731
5.704
F
23.187
5.164
.459
15.005
57.246
1.163
.814
4.309
2.053
4.543
Sig.
.000
.001
.501
.000
.000
.285
.370
.042
.137
.014
?
?
?
nterpretation
Coveariates
If a coveariate is signifcantly related to a DV, it
means that the training group means on the DV
were signifcantly adjusted due to diferences
on the coveariates.
Main efect of IV
No signifcant diferences in satisfaction are
found.
There are signifcant diferences in mean
performance.
( What is your ccomment ? )
ANOVA
Jenis
kelamin
MANOVA
Jenis
kelamin
IPK
mahasisw
a
Tempat
tinggal
Lama
studi
mahasisw
a
IPK
mahasisw
a
Tempat
tinggal
Make your own model !
ANOVA
MANOVA
t-test vs. ANOVA vs.
MANOVA
Test
# of IVs
# of DVs
t-test
One
One
ANOVA
Multiple
One
MANOVA
Multiple
Multiple
Kinds of research questions (1)
Main efects of IVs
Holding all else constant, are mean diferences
in the composite DV among groups at
diferent leveels of an IV larger than expected by
chance?
Interaction among IVs
Holding all else constant, does change in the DV
oveer leveels of one IV depend on the leveel of
another IV?
Importance of DVs
Which of the DVs are changed and which are
unafected by the IVs?
Kinds of research questions (2)
Parameter estimates
After removeal of the efects of coveariate(s), what are
the means adjusted for particular DV(s)?
Specifc comparisons and trend analysis
If an interaction or main efect for an IV with more
than 2 leveels is signifcant, which leveels of main efect
or cells of interaction are diferent from which others?
Strength of association
If an interaction or main efect for an IV is signifcant,
what proportion of veariance of the linear combination
of DV scores is explained by the IV?
Efects of Coveariates
To what degree does a coveariate adjust the composite
DV?
MANOVA/ MANCOVA
SPSS Example
IVs
DVs
Covariate
Analyze GLM Multivariate
IVs
DVs
Covariate
Example of MANOVA (1)
Efect of training ( V) on satisfaction with
the system and performance (DVs)
Group means
Training
Satisfaction
Performance
Control
4.2
4.9
Face-to-face
training
7.9
7.0
Online training
6.0
6.9
1 IV
2 DVs
MANOVA test statistics
Between-Subjects Factors
N
Training 1.0
Group 2.0
3.0
25
22
23
Multivariate Tests c
Effect
Intercept
Value
Pillai's Trace
Hypothesis df
Error df
Sig.
.872
223.996 a
2.000
66.000
.000
.128
223.996 a
2.000
66.000
.000
Hotelling's Trace
6.788
223.996 a
2.000
66.000
.000
Roy's Largest Root
6.788
223.996 a
2.000
66.000
.000
Wilks' Lambda
Training
Group
F
Pillai's Trace
.183
3.376
4.000
134.000
.011
Wilks' Lambda
.820
3.434 a
4.000
132.000
.010
Hotelling's Trace
.215
3.489
4.000
130.000
.010
.193
6.458 b
2.000
67.000
.003
Roy's Largest Root
a. Exact statistic
b. The statistic is an upper bound on F that yields a lower bound on the significance level.
c. Design: Intercept+RACE
All four multivariate statistics indicate that training is
significantly related to the interrelationship between
satisfaction and performance.
ANOVAs on the efect of training
on satisfaction and performance
Tests of Between-Subjects Effects
Source
Dependent Variable
Corrected Model SATISFACTION
PERFORMANCE
Intercept
SATISFACTION
PERFORMANCE
Training
SATISFACTION
Group
PERFORMANCE
Error
SATISFACTION
PERFORMANCE
Total
SATISFACTION
PERFORMANCE
Corrected Total SATISFACTION
PERFORMANCE
Type III Sum
of Squares
157.537a
66.382b
2542.512
2713.380
157.537
66.382
1535.335
422.203
4177.000
3167.000
1692.871
488.586
df
2
2
1
1
2
2
67
67
70
70
69
69
Mean Square
78.768
33.191
2542.512
2713.380
78.768
33.191
22.915
6.302
F
3.437
5.267
110.952
430.590
3.437
5.267
Sig.
.038
.008
.000
.000
.038
.008
a. R Squared = .093 (Adjusted R Squared = .066)
b. R Squared = .136 (Adjusted R Squared = .110)
There are significant differences between training groups in both mean
satisfaction and mean performance.
Example of MANOVA (2)
Efect of training and job ( Vs) on satisfaction
with the system and performance (DVs)
Group means
Control
Face-to-face
training
Online
training
Satisfaction
5.9
8.2
6.9
Performance
6.0
6.9
8.0
Satisfaction
3.6
7.6
4.3
Performance
4.4
7.0
4.8
IT
Non-IT
MANOVA test statistics
c
Multivariate Tests
Effect
Intercept
Training
Group
Job
Training Group *
Gender
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Value
.878
.122
7.170
7.170
.124
.877
.139
.128
.109
.891
.122
.122
.077
.923
.084
.083
F
Hypothesis df
225.868a
2.000
a
225.868
2.000
a
225.868
2.000
a
225.868
2.000
2.116
4.000
a
2.134
4.000
2.150
4.000
b
4.100
2.000
a
3.853
2.000
a
3.853
2.000
a
3.853
2.000
a
3.853
2.000
1.287
4.000
a
1.292
4.000
1.296
4.000
b
2.643
2.000
Error df
63.000
63.000
63.000
63.000
128.000
126.000
124.000
64.000
63.000
63.000
63.000
63.000
128.000
126.000
124.000
64.000
Sig.
.000
.000
.000
.000
.083
.080
.079
.021
.026
.026
.026
.026
.279
.277
.275
.079
a. Exact statistic
b. The statistic is an upper bound on F that yields a lower bound on the significance level.
c. Design: Intercept+RACE+GENDER+RACE * GENDER
Are there significant multivariate relationships? How do we interpret this?
ANOVAs on the efect of training
and job on satisfaction and
performance
Tests of Between-Subjects Effects
Source
Corrected Model
Intercept
Training
Group
Job
Training Group *
Job
Error
Total
Corrected Total
Dependent Variable
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
SATISFACTION
PERFORMANCE
Type III Sum
of Squares
220.589a
133.718b
2278.580
2383.114
109.195
32.250
51.586
38.677
12.162
29.151
1472.283
354.868
4177.000
3167.000
1692.871
488.586
a.
R Squared = .130 (Adjusted R Squared = .062)
b.
R Squared = .274 (Adjusted R Squared = .217)
df
5
5
1
1
2
2
1
1
2
2
64
64
70
70
69
69
Mean Square
44.118
26.744
2278.580
2383.114
54.598
16.125
51.586
F
1.918
4.823
99.050
429.792
2.373
2.908
2.242
Sig.
.104
.001
.000
.000
.101
.062
.139
38.677
6.081
14.576
23.004
5.545
6.975
.264
2.629
.010
.769
.080
Are there significant univariate relationships? How do we interpret this?
Example of MANCOVA
Efect of training on satisfaction and performance,
controlling for computer self-efcacy and computer
anxiety
Training group means
Control
Face-to-face
training
Online
training
Satisfaction
4.2
7.9
6.0
Performance
4.9
7.0
6.9
Computer
self-efficacy
3.5
4.5
3.6
Computer
anxiety
16.6
15.7
17.0
MANCOVA test statistics
c
Multivariate Tests
Effect
Intercept
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Computer
Pillai's Trace
Self-efficacy Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Computer
Pillai's Trace
Anxiety
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Training
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Value
.188
.812
.232
.232
.468
.532
.881
.881
.068
.932
.073
.073
.157
.844
.184
.178
F
Hypothesis df
7.409a
2.000
a
7.409
2.000
7.409a
2.000
a
7.409
2.000
28.195a
2.000
a
28.195
2.000
a
28.195
2.000
a
28.195
2.000
a
2.333
2.000
2.333a
2.000
a
2.333
2.000
2.333a
2.000
2.774
4.000
a
2.840
4.000
2.903
4.000
b
5.797
2.000
Error df
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
64.000
130.000
128.000
126.000
65.000
a. Exact statistic
b.
The statistic is an upper bound on F that yields a lower bound on the significance level.
c.Design: Intercept+Computer Self-efficacy +Computer anxiety+training
Sig.
.001
.001
.001
.001
.000
.000
.000
.000
.105
.105
.105
.105
.030
.027
.024
.005
?
?
nterpretation
Coveariates
Computer
self-eficacy
is
multiveariate
signifcant, but computer anxiety is not. (There
was an adjustment in the group means on the
DVs due to diferences in computer selfeficacy but no signifcant adjustment of group
means due to diferences in computer anxiety).
Main efect of training
Training is signifcantly multiveariate related to
the interrelationship between satisfaction
and performance.
ANOVAs output
Tests of Between-Subjects Effects
Source
Dependent Variable
Corrected Model SATISFACTION
PERFORMANCE
Intercept
SATISFACTION
PERFORMANCE
Computer
SATISFACTION
Self-efficacy
PERFORMANCE
Computer
SATISFACTION
Anxiety
PERFORMANCE
Training
SATISFACTION
PERFORMANCE
Error
SATISFACTION
PERFORMANCE
Total
SATISFACTION
PERFORMANCE
Corrected Total SATISFACTION
PERFORMANCE
Type III Sum
of Squares
995.326a
117.825b
4.920
85.587
614.328
6.631
8.738
24.577
44.072
51.832
697.545
370.761
4177.000
3167.000
1692.871
488.586
a. R Squared = .588 (Adjusted R Squared = .563)
b. R Squared = .241 (Adjusted R Squared = .194)
df
4
4
1
1
1
1
1
1
2
2
65
65
70
70
69
69
Mean Square
248.832
29.456
4.920
85.587
614.328
6.631
8.738
24.577
22.036
25.916
10.731
5.704
F
23.187
5.164
.459
15.005
57.246
1.163
.814
4.309
2.053
4.543
Sig.
.000
.001
.501
.000
.000
.285
.370
.042
.137
.014
?
?
?
nterpretation
Coveariates
If a coveariate is signifcantly related to a DV, it
means that the training group means on the DV
were signifcantly adjusted due to diferences
on the coveariates.
Main efect of IV
No signifcant diferences in satisfaction are
found.
There are signifcant diferences in mean
performance.