Victoria University of Wellington
School of Psychology
PSYC325
ADVANCED RESEARCH METHODS IN PSYCHOLOGY
MONDAY August 29th, 2003
SAMPLE TEST 1
Time allowed: 45 minutes
This test is worth 20% of your course mark.
Write your answers in the booklet provided.
There are two sections, and you must answer BOTH.
Both sections are worth 50%.
SECTION ONE: ANSWER ONE OF THE FOLLOWING TWO QUESTIONS
QUESTION 1 (50%):
There follow the results of four factor analyses of a set of items which asked 104
people to indicate how much they liked different types of foods. All questions were
rated on a 1 (don’t like at all) to 7 (Like very much) scale. The variable labels are selfexplanatory, and the food types are: Thai, French, Malaysian, BBQ (barbecue), Indian,
Fast food, Chinese, Trad_NZ (traditional NZ food), Japanese, Mexican, Turkish, Greek,
and Vegetarian.
The following four pages include SPSS printout of four factor analyses of these data.
The first represents factors extracted under a latent root criterion. The remainder
present three, two, and one-factor solutions of the same data.
Summarise these analyses, selecting a solution that seems most appropriate,
describing your rationale, and labelling (interpreting) your factor(s). If appropriate,
comment on any problems with the data or solutions, and make suggestions on how to
address your concerns.
KMO a nd Bartlett's Te st
Kaiser-Mey er-Olkin Measure of Sampling
Adequacy.
Bartlet t's Test of
Sphericity
Approx . Chi-Square
df
Sig.
.745
630.672
91
.000
Correlations
THAI
THAI
Pearson Correlation
Sig. (2-tailed)
N
FRENCH
Pearson Correlation
Sig. (2-tailed)
N
MALAYSN
Pearson Correlation
Sig. (2-tailed)
N
BBQ
Pearson Correlation
Sig. (2-tailed)
N
INDIAN
Pearson Correlation
Sig. (2-tailed)
N
ITALIAN
Pearson Correlation
Sig. (2-tailed)
N
FASFOOD
Pearson Correlation
Sig. (2-tailed)
N
CHINESE
Pearson Correlation
Sig. (2-tailed)
N
TRAD_NZ
Pearson Correlation
Sig. (2-tailed)
N
JAPANESE Pearson Correlation
Sig. (2-tailed)
N
MEXICAN
Pearson Correlation
Sig. (2-tailed)
N
TURKISH
Pearson Correlation
Sig. (2-tailed)
N
GREEK
Pearson Correlation
Sig. (2-tailed)
N
VEGETARN Pearson Correlation
Sig. (2-tailed)
N
1
.
106
.149
.128
106
.735**
.000
106
.082
.405
106
.627**
.000
106
.261**
.007
106
-.073
.459
106
.115
.239
106
.144
.140
106
.283**
.003
106
.359**
.000
106
.285**
.003
106
.244*
.012
106
.221*
.023
106
FRENCH MALAYSN
.149
.735**
.128
.000
106
106
1
.157
.
.108
106
106
.157
1
.108
.
106
106
-.023
.201*
.813
.039
106
106
.060
.597**
.538
.000
106
106
.271**
.369**
.005
.000
106
106
-.133
.026
.173
.795
106
106
.253**
.296**
.009
.002
106
106
.077
.176
.432
.072
106
106
.229*
.304**
.018
.002
106
106
.142
.357**
.148
.000
106
106
.290**
.359**
.003
.000
106
106
.323**
.272**
.001
.005
106
106
.035
.186
.724
.057
106
106
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
BBQ
INDIAN
ITALIAN FASFOOD CHINESE TRAD_NZ JAPANESE MEXICAN TURKISH
GREEK VEGETARN
.082
.627**
.261**
-.073
.115
.144
.283**
.359**
.285**
.244*
.221*
.405
.000
.007
.459
.239
.140
.003
.000
.003
.012
.023
106
106
106
106
106
106
106
106
106
106
106
-.023
.060
.271**
-.133
.253**
.077
.229*
.142
.290**
.323**
.035
.813
.538
.005
.173
.009
.432
.018
.148
.003
.001
.724
106
106
106
106
106
106
106
106
106
106
106
.201*
.597**
.369**
.026
.296**
.176
.304**
.357**
.359**
.272**
.186
.039
.000
.000
.795
.002
.072
.002
.000
.000
.005
.057
106
106
106
106
106
106
106
106
106
106
106
1
.120
.496**
.561**
.141
.458**
.079
.266**
.103
.209*
-.439**
.
.219
.000
.000
.150
.000
.420
.006
.293
.031
.000
106
106
106
106
106
106
106
106
106
106
106
.120
1
.390**
.003
.082
.209*
.241*
.570**
.538**
.356**
.139
.219
.
.000
.979
.406
.031
.013
.000
.000
.000
.155
106
106
106
106
106
106
106
106
106
106
106
.496**
.390**
1
.225*
.332**
.244*
.236*
.543**
.351**
.471**
.020
.000
.000
.
.020
.001
.012
.015
.000
.000
.000
.842
106
106
106
106
106
106
106
106
106
106
106
.561**
.003
.225*
1
.055
.239*
-.164
.126
.054
-.034
-.388**
.000
.979
.020
.
.573
.014
.094
.199
.580
.729
.000
106
106
106
106
106
106
106
106
106
106
106
.141
.082
.332**
.055
1
.254**
.224*
.319**
.199*
.177
.113
.150
.406
.001
.573
.
.009
.021
.001
.041
.069
.249
106
106
106
106
106
106
106
106
106
106
106
.458**
.209*
.244*
.239*
.254**
1
.211*
.264**
.235*
.247*
-.265**
.000
.031
.012
.014
.009
.
.030
.006
.015
.011
.006
106
106
106
106
106
106
106
106
106
106
106
.079
.241*
.236*
-.164
.224*
.211*
1
.417**
.418**
.494**
.372**
.420
.013
.015
.094
.021
.030
.
.000
.000
.000
.000
106
106
106
106
106
106
106
106
106
106
106
.266**
.570**
.543**
.126
.319**
.264**
.417**
1
.598**
.597**
.176
.006
.000
.000
.199
.001
.006
.000
.
.000
.000
.071
106
106
106
106
106
106
106
106
106
106
106
.103
.538**
.351**
.054
.199*
.235*
.418**
.598**
1
.674**
.177
.293
.000
.000
.580
.041
.015
.000
.000
.
.000
.069
106
106
106
106
106
106
106
106
106
106
106
.209*
.356**
.471**
-.034
.177
.247*
.494**
.597**
.674**
1
.210*
.031
.000
.000
.729
.069
.011
.000
.000
.000
.
.031
106
106
106
106
106
106
106
106
106
106
106
-.439**
.139
.020
-.388**
.113
-.265**
.372**
.176
.177
.210*
1
.000
.155
.842
.000
.249
.006
.000
.071
.069
.031
.
106
106
106
106
106
106
106
106
106
106
106
Default: All Eigenvalues greater than one
Total Variance Explained
Component
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total
4.544
2.317
1.412
1.062
.881
.838
.674
.561
.403
.385
.318
.220
.198
.187
Initial Eigenvalues
% of Variance
Cumulative %
32.458
32.458
16.553
49.011
10.089
59.100
7.588
66.688
6.292
72.980
5.986
78.966
4.817
83.783
4.004
87.786
2.876
90.663
2.747
93.410
2.268
95.678
1.570
97.248
1.416
98.665
1.335
100.000
Extraction Sums of Squared Loadings
Total
% of Variance
Cumulative %
4.544
32.458
32.458
2.317
16.553
49.011
1.412
10.089
59.100
1.062
7.588
66.688
Rotation Sums of Squared Loadings
Total
% of Variance
Cumulative %
3.015
21.536
21.536
2.420
17.285
38.821
2.408
17.200
56.020
1.493
10.667
66.688
Extraction Method: Principal Component Analysis.
Rotated Component Matrixa
Scree Plot
5
4
3
Eigenvalue
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Component Number
1
.866
.811
.745
.614
.459
GREEK
TURKISH
MEXICAN
JAPANESE
ITALIAN
THAI
MALAYSN
INDIAN
BBQ
FASFOOD
VEGETARN
TRAD_NZ
CHINESE
FRENCH
.445
Component
2
3
.318
.416
.852
.774
-.695
.561
.303
.781
.693
Component Transformation Matrix
1
.733
-.139
.404
-.529
2
.566
-.156
-.775
.234
.331
.889
.866
.742
Extraction Method: Principal Component Analys is.
Rotation Method: Varimax with Kaiser Normalization.
a. Rotation converged in 6 iterations .
Component
1
2
3
4
4
3
.205
.977
-.051
-.013
Extraction Method: Principal Component Analys is.
Rotation Method: Varimax with Kaiser Normalization.
4
.316
-.030
.484
.816
Forced three-factor extraction
Total Variance Explained
Component
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total
4.544
2.317
1.412
1.062
.881
.838
.674
.561
.403
.385
.318
.220
.198
.187
Initial Eigenvalues
% of Variance
Cumulative %
32.458
32.458
16.553
49.011
10.089
59.100
7.588
66.688
6.292
72.980
5.986
78.966
4.817
83.783
4.004
87.786
2.876
90.663
2.747
93.410
2.268
95.678
1.570
97.248
1.416
98.665
1.335
100.000
Extraction Sums of Squared Loadings
Total
% of Variance
Cumulative %
4.544
32.458
32.458
2.317
16.553
49.011
1.412
10.089
59.100
Rotation Sums of Squared Loadings
Total
% of Variance
Cumulative %
3.113
22.234
22.234
2.754
19.674
41.908
2.407
17.192
59.100
Extraction Method: Principal Component Analysis.
Rotated Component Matrixa
Scree Plot
GREEK
TURKISH
JAPANESE
MEXICAN
FRENCH
ITALIAN
CHINESE
THAI
MALAYSN
INDIAN
BBQ
FASFOOD
VEGETARN
TRAD_NZ
5
4
3
Eigenvalue
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Component Number
1
.801
.684
.657
.635
.579
.540
.490
Component
2
3
.356
.444
.307
.416
.878
.835
.830
.310
.852
.772
-.696
.562
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
a. Rotation converged in 4 iterations.
Compone nt Transformation Matrix
Component
1
2
3
1
.734
-.120
.668
2
.648
-.170
-.742
3
.203
.978
-.047
Ex trac tion Met hod: Principal Component Analy sis.
Rotation Method: Varimax with Kaiser Normaliz ation.
Forced two-factor extraction
Total Variance Explained
Component
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Initial Eigenvalues
% of Variance
Cumulative %
32.458
32.458
16.553
49.011
10.089
59.100
7.588
66.688
6.292
72.980
5.986
78.966
4.817
83.783
4.004
87.786
2.876
90.663
2.747
93.410
2.268
95.678
1.570
97.248
1.416
98.665
1.335
100.000
Total
4.544
2.317
1.412
1.062
.881
.838
.674
.561
.403
.385
.318
.220
.198
.187
Extraction Sums of Squared Loadings
Total
% of Variance
Cumulative %
4.544
32.458
32.458
2.317
16.553
49.011
Rotation Sums of Squared Loadings
Total
% of Variance
Cumulative %
4.426
31.613
31.613
2.436
17.398
49.011
Extraction Method: Principal Component Analysis.
Rotated Component Matrixa
Scree Plot
5
4
3
Eigenvalue
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Component Number
MEXICAN
TURKISH
GREEK
INDIAN
MALAYSN
THAI
JAPANESE
ITALIAN
CHINESE
FRENCH
BBQ
FASFOOD
VEGETARN
TRAD_NZ
Component
1
2
.764
.745
.730
.720
.691
.656
.637
.595
.439
.394
.377
.857
.766
.385
-.684
.575
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
a. Rotation converged in 3 iterations.
Component Transformation Matrix
Component
1
2
1
.973
-.231
2
.231
.973
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
Forced two-factor extraction
Total Variance Explained
Component
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Initial Eigenvalues
% of Variance
Cumulative %
32.458
32.458
16.553
49.011
10.089
59.100
7.588
66.688
6.292
72.980
5.986
78.966
4.817
83.783
4.004
87.786
2.876
90.663
2.747
93.410
2.268
95.678
1.570
97.248
1.416
98.665
1.335
100.000
Total
4.544
2.317
1.412
1.062
.881
.838
.674
.561
.403
.385
.318
.220
.198
.187
Extraction Sums of Squared Loadings
Total
% of Variance
Cumulative %
4.544
32.458
32.458
Extraction Method: Principal Component Analys is.
Component Matrixa
Scree Plot
5
4
3
Eigenvalue
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Component Number
MEXICAN
TURKISH
GREEK
INDIAN
MALAYSN
ITALIAN
THAI
JAPANESE
CHINESE
TRAD_NZ
BBQ
FRENCH
VEGETARN
FASFOOD
Compone
nt
1
.792
.740
.729
.714
.685
.680
.621
.585
.422
.418
.367
.352
Extraction Method: Principal Component Analysis.
a. 1 components extracted.
a
Rotate d Component Matrix
a. Only one c omponent was extracted.
The solution c annot be rot ated.
Cronbach’s Alphas for the three solutions are:
Factor One
Factor Two
Factor Three
Factor Four
Four factor soln
.82
.85
-.08
.40
Three factor soln
.74
.85
-.08
Two factor soln
.84
-.08
One factor soln
.80
QUESTION 2 (50%):
There follows SPSS output of a two-block regression analysis.
The data set is the same one you’ve seen used in lectures, containing social dominance (high
scores mean people favour social hierarchies), Authoritarianism (high scores mean people think we
should do as we’re told by those in charge), and political conservatism (high scores mean people
are increasingly politically conservative, e.g., they favour free-market economics, lower taxes, are
pro-life, and against gay marriage, etc).
The variables in the data set were:
SDO:
RWA:
CON:
SDOBYRWA:
Social Dominance
Authoritarianism
Conservatism
The interaction term describing the multiplication of SDO and RWA scores for
each participant.
In the regression, the predicted variable is conservatism (CON), the first block of predictors
includes Social Dominance (SDO) and Authoritarianism (RWA), and the second block includes only
the interaction between SDO and RWA (SDOBYRWA).
Questions:
(a) Summarise the relevant output. Be sure to provide (at least) an indication of the amount of
variance accounted for by the predictors, whether the regression is significant, and the
relative importance (and direction of association) of predictors in the resulting regression
equations(s).
(b) Is there any evidence of a moderating relationship between SDO and RWA in predicting
conservatism? (justify your answer). What adjustments should be made to the data before
analysis, in what circumstances might one conduct such an analysis, and how would one go
about interpreting a moderation when there’s one to be found?
Variables Entered/Removedb
Model
1
2
Variables
Entered
Variables
Removed
Method
Right-Wing
Authoritari
anism,
Social
Dominanc
a
e
.
Enter
SDOBYRW
a
A
.
Enter
a. All requested variables entered.
b. Dependent Variable: Conservatis m Scale
Model Summary
Change Statistics
Model
1
2
R
.638a
.646b
R Square
.407
.418
Adjusted
R Square
.403
.411
Std. Error of
the Estimate
.37265
.37009
R Square
Change
.407
.010
F Change
88.696
4.583
df1
2
1
df2
258
257
Sig. F Change
.000
.033
a. Predictors: (Constant), Right-Wing Authoritarianism, Social Dominance
b. Predictors: (Constant), Right-Wing Authoritarianism, Social Dominance, SDOBYRWA
ANOVAc
Model
1
2
Regres sion
Residual
Total
Regres sion
Residual
Total
Sum of
Squares
24.634
35.828
60.461
25.262
35.200
60.461
df
2
258
260
3
257
260
Mean Square
12.317
.139
F
88.696
Sig.
.000a
8.421
.137
61.480
.000b
a. Predictors: (Constant), Right-Wing Authoritarianism, Social Dominance
b. Predictors: (Constant), Right-Wing Authoritarianism, Social Dominance,
SDOBYRWA
c. Dependent Variable: Conservatism Scale
Coefficientsa
Model
1
2
(Constant)
Social Dominance
Right-Wing
Authoritarianism
(Constant)
Social Dominance
Right-Wing
Authoritarianism
SDOBYRWA
Unstandardized
Coefficients
B
Std. Error
2.139
.099
.263
.028
Standardized
Coefficients
Beta
.473
t
21.591
9.494
Sig.
.000
.000
.318
6.391
Collinearity Statistics
Tolerance
VIF
.925
1.081
.000
.925
1.081
.000
.000
.087
11.494
.180
.028
1.678
.447
.236
.090
.802
7.098
4.969
.345
.082
.610
4.208
.000
.108
9.284
-.064
.030
-.506
-2.141
.033
.041
24.670
a. Dependent Variable: Conservatis m Scale
b
Ex cluded Variabl es
Model
1
SDOBYRW A
Beta In
-.506a
t
-2. 141
Sig.
.033
Partial
Correlation
-.132
Collinearity Statistics
Minimum
Tolerance
VIF
Tolerance
.041
24.670
.041
a. Predic tors in the Model: (Const ant), Right-W ing Aut horitarianism, Social Dominance
b. Dependent Variable: Conservat ism Scale
a
Collineari ty Diagnostics
Model
1
2
Dimension
1
2
3
1
2
3
4
Eigenvalue
2.902
.062
.036
3.845
.094
.059
.002
Condit ion
Index
1.000
6.842
9.028
1.000
6.393
8.087
42.418
(Const ant)
.01
.02
.97
.00
.05
.01
.94
Variance Proportions
Right-W ing
Social
Authoritaria
Dominance
nis m
.01
.01
.83
.42
.16
.57
.00
.00
.00
.00
.06
.07
.93
.93
SDOBYRW A
.00
.03
.00
.96
a. Dependent Variable: Conservatism Scale
SECTION TWO:
QUESTION 3 (5% for each part): Terms
Define and discuss ten (each worth 5%) of the following terms. Where appropriate, give brief
examples, or describe where these would be appropriate:
a) Oblique rotation.
b) Multiple-R.
c) Scree plot.
d) Response set.
e) Latent root criterion.
f) Mediation.
g) Unstandardised regression coefficient.
h) Bartlett’s test of sphericity.
i) Nocebo effects.
j) Factor loading.
k) Self-deceptive positivity.
l) Exploratory factor analysis.
m) Cronbach’s Alpha.
n) Extreme Response bias.
o) Cramèr’s phi.