Perbedaan ANOVA dengan MANOVA
( What is your ccomment ? )
ANOVA
MANOVA
Jenis
kelamin
Tempat
tinggal
IPK
mahasisw
a
Jenis
kelamin
Tempat
tinggal
IPK
mahasisw
a
Lama
studi
mahasisw
Make your own model !
t-test vs. ANOVA vs.
MANOVA
Test
# of IVs
# of DVs
t-test
One
One
ANOVA
Multiple
One
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
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
MANOVA/ MANCOVA
SPSS Example
IVs
DVs
Analyze
GLM
Multivariate
DVs
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
MANOVA test statistics
Between-Subjects Factors 25 22 23 1.0 2.0 3.0 Training Group NAll four multivariate statistics indicate that training is
significantly related to the interrelationship between
satisfaction and performance.
Multivariate Testsc
.872 223.996a 2.000 66.000 .000
.128 223.996a 2.000 66.000 .000 6.788 223.996a 2.000 66.000 .000 6.788 223.996a 2.000 66.000 .000 .183 3.376 4.000 134.000 .011 .820 3.434a 4.000 132.000 .010 .215 3.489 4.000 130.000 .010 .193 6.458b 2.000 67.000 .003 Pillai's Trace
Wilks' Lambda Hotelling's Trace Roy's Largest Root Pillai's Trace Wilks' Lambda Hotelling's Trace Roy's Largest Root Effect
Intercept
Training Group
Value F Hypothesis df Error df Sig.
Exact statistic a.
The statistic is an upper bound on F that yields a lower bound on the significance level. b.
ANOVAs on the efect of training
on satisfaction and performance
Tests of Between-Subjects Effects
157.537a 2 78.768 3.437 .038
66.382b 2 33.191 5.267 .008
2542.512 1 2542.512 110.952 .000
2713.380 1 2713.380 430.590 .000
157.537 2 78.768 3.437 .038
66.382 2 33.191 5.267 .008
1535.335 67 22.915
422.203 67 6.302
4177.000 70 3167.000 70 1692.871 69 488.586 69 Dependent Variable SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE Source Corrected Model Intercept Training Group Error Total Corrected Total
Type III Sum
of Squares df Mean Square F Sig.
R Squared = .093 (Adjusted R Squared = .066) a.
R Squared = .136 (Adjusted R Squared = .110) b.
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
training
Online
IT
Satisfaction
5.9
8.2
6.9
Performance
6.0
6.9
8.0
Non-IT
MANOVA test statistics
Multivariate Testsc
.878 225.868a 2.000 63.000 .000
.122 225.868a 2.000 63.000 .000
7.170 225.868a 2.000 63.000 .000
7.170 225.868a 2.000 63.000 .000
.124 2.116 4.000 128.000 .083
.877 2.134a 4.000 126.000 .080
.139 2.150 4.000 124.000 .079
.128 4.100b 2.000 64.000 .021
.109 3.853a 2.000 63.000 .026
.891 3.853a 2.000 63.000 .026
.122 3.853a 2.000 63.000 .026
.122 3.853a 2.000 63.000 .026
.077 1.287 4.000 128.000 .279
.923 1.292a 4.000 126.000 .277
.084 1.296 4.000 124.000 .275
.083 2.643b 2.000 64.000 .079
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 Effect
Intercept
Training Group
Job
Training Group * Gender
Value F Hypothesis df Error df Sig.
Exact statistic a.
The statistic is an upper bound on F that yields a lower bound on the significance level. b.
Design: Intercept+RACE+GENDER+RACE * GENDER c.
ANOVAs on the efect of training
and job on satisfaction and
performance
Tests of Between-Subjects Effects
220.589a 5 44.118 1.918 .104 133.718b 5 26.744 4.823 .001 2278.580 1 2278.580 99.050 .000 2383.114 1 2383.114 429.792 .000 109.195 2 54.598 2.373 .101 32.250 2 16.125 2.908 .062 51.586 1 51.586 2.242 .139 38.677 1 38.677 6.975 .010 12.162 2 6.081 .264 .769 29.151 2 14.576 2.629 .080 1472.283 64 23.004
354.868 64 5.545 4177.000 70 3167.000 70 1692.871 69 488.586 69 Dependent Variable SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE Source Corrected Model Intercept Training Group Job
Training Group * Job
Error Total
Corrected Total
Type III Sum
of Squares df Mean Square F Sig.
R Squared = .130 (Adjusted R Squared = .062) a.
R Squared = .274 (Adjusted R Squared = .217) b.
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
MANCOVA test statistics
Multivariate Testsc
.188 7.409a 2.000 64.000 .001
.812 7.409a 2.000 64.000 .001
.232 7.409a 2.000 64.000 .001
.232 7.409a 2.000 64.000 .001
.468 28.195a 2.000 64.000 .000
.532 28.195a 2.000 64.000 .000
.881 28.195a 2.000 64.000 .000
.881 28.195a 2.000 64.000 .000
.068 2.333a 2.000 64.000 .105
.932 2.333a 2.000 64.000 .105
.073 2.333a 2.000 64.000 .105
.073 2.333a 2.000 64.000 .105
.157 2.774 4.000 130.000 .030
.844 2.840a 4.000 128.000 .027
.184 2.903 4.000 126.000 .024
.178 5.797b 2.000 65.000 .005
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 Effect Intercept Computer Self-efficacy Computer Anxiety Training
Value F Hypothesis df Error df Sig.
Exact statistic a.
The statistic is an upper bound on F that yields a lower bound on the significance level. b.
Design: Intercept+Computer Self-efficacy +Computer anxiety+training c.
?
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
self-eficacy but no signifcant adjustment of group
means due to diferences in computer anxiety).
Main efect of training
Training is signifcantly multiveariate related to
ANOVAs output
Tests of Between-Subjects Effects
995.326a 4 248.832 23.187 .000
117.825b 4 29.456 5.164 .001
4.920 1 4.920 .459 .501
85.587 1 85.587 15.005 .000
614.328 1 614.328 57.246 .000
6.631 1 6.631 1.163 .285
8.738 1 8.738 .814 .370
24.577 1 24.577 4.309 .042
44.072 2 22.036 2.053 .137
51.832 2 25.916 4.543 .014
697.545 65 10.731
370.761 65 5.704
4177.000 70 3167.000 70 1692.871 69 488.586 69 Dependent Variable SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE SATISFACTION PERFORMANCE Source Corrected Model Intercept Computer Self-efficacy Computer Anxiety Training Error Total Corrected Total
Type III Sum
of Squares df Mean Square F Sig.
R Squared = .588 (Adjusted R Squared = .563) a.
R Squared = .241 (Adjusted R Squared = .194) b.
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
