January 18 2002
Dear Colleagues
The Australian group is meeting shortly to discuss the form of the questionnaire for our third
survey. Attached you will find a rather scrappy document that provides some statistics, derived
from the Survey #2 data, on the performance of individual items. Any comments or advice will
be appreciated.
Discussion document in preparation for Survey #3
Bob Cummins and Julie Pallant
Draft #3: 18/1/02
Table of Contents
1.
Factor analysis from Survey #2
1.1 All personal well-being items (N=9)
1.2 All national well-being items (N=12)
1.3 Personal and National items together (N=21)
1.3.1 Three-factor solution
1.3.2 Two-factor solution
1.4 Conclusions and recommendations
2.
Exploratory factor analyses for gender and event – Looking for a third factor
3.
Varimax vs. Oblimin
4.
All national items regressed against ‘How satisfied are you with life in Australia?’
4.1 Standard regression
4.2 Stepwise regression
4.3 Hierarchical regression
4.4 Hierarchical x Gender
5.
Index item intercorrelations
5.1 Personal index
5.2 National index
6.
Personal Index item validation (from Survey #1)
6.1 Prediction of other variables by the index domains
7.
Inter-item correlations
1.
Factor analyses: Survey #2 (N = 3,000)
1.1 All personal well-being items (N=9)
All items inter-correlated .19 (relationships vs. safety) to .63 (standard of living
vs. life as a whole). All variables correlated >.3 with at least one other variable.
KMO = .892
Bartlett chi-square = 6333.76, df = 36, p=.000
Two-factor solution (Principle Component Analysis; Oblimin with Kaiser
normalisation, Pattern matrix).
Factor 1
‘Personal’
Happiness
Life as a whole
Relationships
Achievements
Standard of living
Health
.86
.82
.82
.71
.66
.37
Safe you feel
Future security
Comm. connectedness
Eigenvalue
Variance explained
Total variance explained = 57.84
Note:
Factor 2
‘Social Capital’
.93
.58
.56
4.19
46.53
1.02
11.30
Here and throughout the document, items forming the ‘Index of Personal Wellbeing’ are
in bold. The other non-bolded items are additional personal items included in Survey #2.
Correlation between the factors = .455
Comment:
The equivalent analysis from Survey #1 produced a single factor.
The emergence of a separate ‘Security/Social Capital’ factor is
new. However, The 7 items of the P-Index hang together as a
single factor if left to their own devices, and the second factor is
weak. There are further analyses pertaining to this putative new
factor in 1.3.
2
1.2 National Well-Being (all items, N=12)
All items inter-correlated .31 (health sciences vs. life in Australia) to .57 (family
support vs. health services).
KMO = .930
Bartlett chi-square = 9214.15, df = 66, p = .000
One-factor solution (Component matrix)
Economic stability
Business
Economic situation
How Australia is governed
Wealth/income distribution
Family support
Social conditions
State of environment
Health services
National security
Life in Australia
Trust in people
Factor
.75
.73
.73
.72
.72
.70
.70
.68
.66
.62
.60
.45
_________________________________________________
Eigen value
Variance explained
5.50
45.81%
_________________________________________________
Note:
The ‘Index of National Wellbeing’ items are in bold.
Comment:
The analysis is failing to distinguish between ‘Index’, other
national items, and social capital (Trust). While the six N-Index
items do form a single factor by themselves, the above analysis
does indicate the possibility that some items, (eg National
security), could be replaced by others (eg Economic stability).
3
1.3 Personal and National items together (N=21)
KMO = .933
Bartlett chi-square = 16,403.11, df = 210, p = .000
1.3.1
Three factor solution
Factor 1
National WB
How Australia is governed
Family support
Economic stability
Wealth/income distribution
Business
Economic situation
Health services
Social conditions
State of the environment
Life in Australia
National security
Happiness
Life as a whole
Relationships
Standard of living
Achievements
Future security
Health
How safe you feel
Trust in people
Comm. connectedness
.73
.71
.71
.70
.69
.69
.68
.68
.67
.55
.53
Eigen values
7.11
Variance explained
33.85
Total variance explained = 51.85%
Comment:
Factor 2
Personal WB
Factor 3
Social Capital
.46
.83
.82
.73
.71
.70
.51
.47
.47
.43
.77
.60
.48
2.69
12.79
1.09
5.21
The third factor ‘social capital’ has captured National,
Personal, and Social Capital items. However, it just fails
to form an acceptable factor due to complex loadings,
which only leaves two clean items.
Could the addition of more items pertaining to ‘social capital’ yield a
coherent third factor? Possibly not, because the three cross-loaded items
had approximately equal degrees of shared variance with both factors, and
in 2/3 cases the loading was higher on the National or Personal factor.
4
1.3.2
Personal and National items together (N=21)
Two-factor solution
Factor 1
National WB
Economic stability
How Australia is governed
Business
Wealth/income distribution
Family support
Economic situation
Social conditions
Health services
State of environment
National security
Life in Australia
Trust in people
Life as a whole
Happiness
Standard of living
Personal relationships
Achievements in life
Future security
Comm. connectedness
Health
How safe you feel
Eigen values
Variance explained
Total variance explained = 46.64%
Comments:
Factor 2
Personal WB
.73
.71
.71
.70
.70
.69
.68
.67
.66
.61
.56
.39
.82
.81
.72
.71
.68
.63
.56
.51
.44
7.11
33.85
2.69
12.79
The five items comprising Factor 3 ‘social capital’ in the
three-factor solution have been generally, if in some cases
marginally, incorporated into the two major factors.
Notably, however, Social Capital (Trust) actually fails to
load on National Well-Being using a criterion of >.4.
Note: Varimax produced an inferior solution, where health and trust both
failed to load >.4.
5
1.4 Conclusions and Recommendations
(a)
The two indices have been generally confirmed.
(b)
In terms of the Personal Index, the factor strongly includes both ‘Life as a
whole’ and ‘Happiness’
Recommendation 1: ‘Happiness’ be omitted from Survey #3.
(c)
In terms of the National Index, the factor clearly includes ‘Life in Australia’,
but very marginally includes Social capital. The factor also fails to
discriminate between the six ‘Index’ items and the four ‘specific’ items.
Recommendation 2: That additional Social Capital item(s) be included in
Survey #3 to replace 4 items in Factor 1.
6
2.
Exploratory factor analyses for gender and event
Due to the almost-emergence of a third factor of ‘ Social capital’ when all the items
were combined (see 1.3.1), we ran a series of sub-sample analyses where the group was
divided based on the impact of the USA attacks. Our rationale is that the emergence of
this potential factor could be dependent on the extent to which people felt their sense of
social capital needed to be drawn-on as a consequence of feeling threatened. We also
explored whether the data factor differently between the genders.
2.1 Analyses based on event impact groupings
The factor loadings (oblimin only) for the four items in question (Pattern matrix),
N=3,000. Only the items loading onto the third factor are reported.
Impact Group
Not made sadder
N=
Item
A.
B.
C.
D.
E.
National security
How safe you feel
Future security
Trust in people
Connection to comm.
Eigen values (whole factor)
% variance explained
Total variance explained
Impact 4 or less
N = 303
A.
B.
C.
D.
E.
National security
How safe you feel
Future security
Trust in people
Connection to comm.
Eigen values (whole factor)
% variance explained
Total variance explained
Impact 5,6
N = 281
A.
B.
C.
D.
E.
National security
How safe you feel
Future security
Trust in people
Connection to comm.
Eigen values (whole factor)
% variance explained
Total variance explained
Factor 1
National
Factor 2
Personal
.46
Factor 3
Social
Capital
.53
.56
.50
.49
.52
6.87
32.70
53.04%
3.17
15.09
1.10
5.25
.48
.58
.76
.36
.44
.63
2.43
11.56
1.31
6.26
.40
7.12
33.92
51.74%
.70
.50
.56
7.81
37.18
54.98%
.58
.58
-.32
2.65
12.63
1.09
5.17
7
Impact 7
N = 247
A.
B.
C.
D.
E.
National security
How safe you feel
Future security
Trust in people
Connection to comm.
Eigen values (whole factor)
% variance explained
Total variance explained
Impact 8
N = 293
A.
B.
C.
D.
E.
National security
How safe you feel
Future security
Trust in people
Connection to comm.
Eigen values (whole factor)
% variance explained
Total variance explained
Impact 9
N = 245
A. National security
B. How safe you feel
C. Future security
D. Trust in people
E. Connection to comm.
(social conditions)
(standard of living)
(health)
Eigen values (whole factor)
% variance explained
Total variance explained
Impact 10
N = 455
A.
B.
C.
D.
E.
National security
How safe you feel
Future security
Trust in people
Connection to comm.
Eigen values (whole factor)
% variance explained
Total variance explained
Conclusion:
.47
.37
.40
.80
.34
.64
.33
2.86
13.60
1.20
5.73
.35
.86
.64
.60
.36
2.79
13.27
1.32
6.29
.35
.74
.50
.43
6.49
30.89
50.21%
.68
6.97
33.20
52.56%
.61
.30
.48
6.62
31.51
50.62
2.72
12.94
.45
.59
.35
.35
.31
1.29
6.16
.50
.66
.58
7.38
35.12
53.20%
.50
.69
.42
2.71
12.90
1.09
5.18
(a) Only two groups (Impact 4 or less, and 8) produced a clean
3-item third factor.
(b) Impact group 9 produced a quite different third factor that
omitted ‘Trust’.
(c) It is notable that ‘safety’ and ‘security’ items also comprise
this putative third factor. This offers an alternative factor name
as ‘security’.
8
2.2 Analyses based on gender groupings
No additional factor patterns emerged using gender groupings. For both genders,
the 3-factor solution failed to produce a distinct third factor, and the oblimin 2factor solution produced two distinct factors. The ordering of items within each
factor also differed very little between the genders as shown below.
Item
Economic stability
How Australia is governed
Business
Wealth/income distribution
Family support
Social conditions
Health services
Economic situation
National security
State of environment
Life in Australia
Trust in people
Factor 1
Rank (loading)
Male
Female
1 (.76)
2 (.75)
3 (.72)
4 (.71)
5 (.70)
6 (.67)
7 (.67)
8 (.67)
9 (.64)
10 (.61)
11 (.46)
12 (.41)
1 (.74)
2 (.73)
4 (.73)
7 (.71)
3 (.73)
6 (.72)
5 (.72)
9 (.71)
10 (.62)
8 (.71)
11 (.61)
12 (.32)
Happiness
Life as a whole
Standard of living
Personal relationships
Achievements
Future security
Comm. connectedness
Health
How safe you feel
Eigen values
Variance explained
Total variance explained
7.09
33.75
46.21%
Factor 2
Rank (loading)
Male
Female
7.18
34.17
47.14%
1 (.85)
2 (.84)
3 (.78)
4 (.78)
5 (.68)
6 (.60)
7 (.54)
8 (.52)
9 (.42)
2 (.86)
1 (.86)
4 (.69)
3 (.74)
5 (.69)
6 (.61)
7 (.54)
8 (.50)
9 (.43)
2.62
12.46
2.73
12.98
9
3.
A comparison of Varimax vs. Oblimin on 2-factor solutions based on
USA attacks impact
Impact Group
Variable
Varimax
Oblimin
Not made sadder
F1 Eigen
Variance
F2 Eigen
Variance
Total variance
Clear factors¹
6.87
32.70
3.17
15.09
47.79
No
6.87
32.70
3.17
15.09
47.79
Yes
Impact = 10
F1 Eigen
Variance
F2 Eigen
Variance
Total variance
Clear factors¹
7.38
35.12
2.71
12.90
48.03
No
Yes
F1 Eigen
Variance
F2 Eigen
Variance
Total variance
Clear factors¹
7.12
33.92
2.43
11.56
45.48
No
Yes
Impact = 4 or less
¹ Loading criterion >.3
Conclusion:
The oblimin rotation provides the best solution. This is also the preferred
form of rotation as the two factors are significantly correlated with one
another.
10
4.
National items regressed against ‘How satisfied are you with life in
Australia?’
This analysis was undertaken to determine the extent to which each Index item
contributed to the prediction of the global item.
4.1 Standard regression (N = 2,004)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Economic situation
State of environment
Social conditions
How Australia is governed
Business
National security
Wealth/income distribution
Health services
Family support
Economic stability

p
Zero
order
Unique
%¹
.29
.05
.18
.02
.08
.07
.00
.03
.06
-.04
.000
.026
.000
.456
.002
.001
.941
.204
.014
.128
.485
.368
.425
.364
.396
.326
.333
.311
.340
.358
4.45
.17
1.99
.02
.34
.37
.00
.01
.20
.01
¹ Part ²
R = .562
R² = .316
Adjusted R² = .313
Unique variance = 7.56%
Shared variance = 23.74%
Conclusion:
(a) The Index items generally performed better than the non-index items
(b) The exceptions are ‘How Australia is governed’ and ‘Family support’
(c) The overall level of prediction is weak
4.2 Stepwise regression
STEP
1. Economic situation
(plus)
2. Social conditions
(plus)
3. Business
(plus)
4. Family support
(plus)
5. National security
(plus)
6. State of environment
Adjusted R²
R² change
p
.235
.236
.000
.293
.058
.000
.302
.010
.000
.307
.005
.000
.311
.004
.001
.313
.002
.016
11
Variables not appearing
How Australia is governed
Wealth/income distribution
Health services
Economic stability
Conclusion: This confirms the greater predictive value of Family Support over
How Australia is governed.
Recommendation: That ‘Family support’ replace ‘How Australia is Governed’ in
the National Index.
4.3 Hierarchical regression
Step 1
National security
State of environment
Australia governed
Economic situation
Social conditions
Business
Step 2
Health services
Wealth/income distribution
Family support
Economic stability
Adjusted R²
R² change
p
.310
.312
.000
.313
.004
.015
12
4.4 Hierarchical x Gender
Adjusted R²
R² change
p
Males
Step 1
Step 2
.242
.244
.248
.006
.000
.255
Females
Step 1
Step 2
.355
.356
.358
.003
.000
.148
Zero order
Step 1
1. Economic situation
2. State of environment
3. Social conditions
4. Australia governed
5. Business
6. National security
Step 2
1.
2.
3.
4.
5.
6.
7. Wealth distribution
8. Health services
9. Family support
10. Economic stability
Unique (Part²)
Male
Female
Male
Female
.42
.30
.40
.33
.34
.23
.52
.41
.44
.39
.44
.39
4.37
.23
3.57
.00
.26
.00
4.80
.30
1.88
.10
.45
.94
.36
.34
.36
.40
3.92
.13
2.53
.02
.26
.00
.00
.00
.38
.02
4.62
.20
1.64
.07
.40
.86
.00
.12
.08
.07
.30
.26
.31
.31
Conclusion: A great deal of similarity.
13
5.
Index item intercorrelations
5.1
Personal Index item intercorrelations
Domain
1
2
3
4
5
6
7
1. Life as a whole
2. Standard of living
.62
3. Health
.38
.38
4. Achievements in life
.51
.48
.31
5. Personal relationships
.51
.41
.26
.39
6. How safe you feel
.28
.30
.24
.21
.20
7. Community connectedness
.38
.35
.24
.33
.33
.33
8. Future security
.44
.45
.29
.40
.33
.41
.40
B

sr2
.36***
.34
.072
.08***
.09
.006
.19***
.18
.022
.21***
.23
.039
.02
.02
.000
.06***
.07
.004
.07***
.08
.004
***p<.001
R = .720 R² = .519
Unique explained variance = 14.7 percent
Shared explained variance = 37.2 percent
5.2
National Index domain intercorrelations
Domain
1.
2.
3.
4.
5.
6.
Economic
Environment
Social
Governed
Business
National Security
1
.41
.43
.51
.55
.40
2
.51
.43
.41
.32
3
.45
.42
.34
4
.51
.36
5
.44
14
6.
Personal Index item validation from Survey #1
Multiple regression was used to validate the domains of each Index. The seven domains
of the Personal Index and the three domains of the National Index were regressed
against the other variables. The results are presented in Table 2.
6.1
Prediction of other variables by the index domains
Personal Index
A
ß
sr²
Dependent Variable
B
C
D
ß
sr²
ß
sr²
ß
sr²
E
ß
sr²
Standard of living
.32*** 6.4
.15*** 1.4
.06* 0.2
.13*** 1.0
.12*** 0.9
Health
.14*** 1.5
.08** 0.5
.08*** 0.5
.10*** 0.7
.07** 0.3
Productivity
.20*** 2.7
-.02 0.0
-.00 0.0
.04 0.0
.02 0.0
Relationships
.19*** 2.9
-.01 0.0
-.01 0.0
.02 0.0
-.02 0.0
.02 0.0
.08** 0.5
.12*** 1.1
.06* 0.3
.06* 0.3
Community
.08*** 0.5
.11*** 0.9
.15*** 1.6
-.02 0.0
.10*** 0.7
Future security
.10*** 0.5
.11*** 0.6
.14*** 1.0
.16*** 1.5
.14*** 1.1
Safety
R
.73***
.38***
.40***
.46***
.32***
.52
.14
.16
.21
.10
Unique variability
14.5%
3.9%
4.4%
4.6%
3.5%
Shared variability
37.7%
10.1%
11.6%
16.4%
6.5%
Adjusted R²
Key
A = Life as a whole; B = Life in Australia; C = Social capital; D = Own life changing;
E = Australia changing
sr² = Percentage of unique variance
Within the personal index, standard of living makes by far the largest unique
contribution to the prediction of life as a whole. All other domains made a significant
contribution of unique variance with the exception of safety. This domain also
exhibited the lowest set of bi-variate correlates with the other domains (Table 5.1) and
the weakest loading (.51) within the Personal Well-Being factor.
On these grounds an argument could be mounted to exclude the domain of safety from
the Personal Well-Being Index. This domain does, however, exhibit more relevance
when used to predict other variables, while the contribution of other domains
approaches zero.
This changing pattern can be seen in columns B to E in Table 6.1. Here, for example,
safety contributes 1.1% unique variance to the prediction of social capital (one quarter
of the total unique variance), while the other domains of achievements and relationships
15
make no unique contribution to this prediction. A summary of these analyses, based on
the Personal Index, domains, is as follows:
1.
All of the variables (A to E) are significantly predicted by the combined domains.
2.
The two domains that make no unique contribution to the prediction of variables
B to E are achievement and relationships. Both of these, however, made a
significant unique contribution to the prediction of ‘Life as a whole’ (Variable A).
3.
The domains that provide the most consistent unique contribution to the prediction
of variables A to E are Future Security, Health, and Standard of Living. Each
made a significant unique contribution to the prediction of all six dependent
variables.
7. Inter-item correlations
Correlations
N = 2,004
Future
security
Personal
well-being
index
Life in
Australia
Economic
situation
State of
environment
.353**
.464**
.730**
.270**
.302**
.241**
.267**
.248**
.26
.239**
.290**
.589**
.186**
.204**
.178**
.172**
.151**
.21
.208**
.334**
.402**
.665**
.222**
.289**
.208**
.177**
.231**
.22
1.000
.191**
.329**
.328**
.641**
.146**
.142**
.146**
.138**
.113**
.13
.208**
.191**
1.000
.346**
.418**
.588**
.217**
.215**
.172**
.201**
.149**
.21
.239**
.334**
.329**
.346**
1.000
.403**
.661**
.206**
.213**
.266**
.250**
.220**
.21
.464**
.290**
.402**
.328**
.418**
.403**
1.000
.721**
.265**
.315**
.251**
.266**
.249**
.30
.730**
.589**
.665**
.641**
.588**
.661**
.721**
1.000
.328**
.363**
.318**
.319**
.294**
.33
Life in Australia
.270**
.186**
.222**
.146**
.217**
.206**
.265**
.328**
1.000
.485**
.368**
.425**
.364**
.39
Economic situation
.302**
.204**
.289**
.142**
.215**
.213**
.315**
.363**
.485**
1.000
.434**
.425**
.520**
.55
State of the
environment
.241**
.178**
.208**
.146**
.172**
.266**
.251**
.318**
.368**
.434**
1.000
.536**
.451**
.43
Social conditions
.267**
.172**
.177**
.138**
.201**
.250**
.266**
.319**
.425**
.425**
.536**
1.000
.456**
.41
How Australia is
governed
.248**
.151**
.231**
.113**
.149**
.220**
.249**
.294**
.364**
.520**
.451**
.456**
1.000
.52
Business
.261**
.213**
.220**
.137**
.210**
.217**
.307**
.339**
.396**
.554**
.434**
.414**
.526**
1.0
National security
.200**
.179**
.159**
.095**
.251**
.228**
.260**
.298**
.329**
.409**
.343**
.349**
.371**
.44
Wealth/ income
distribution
.317**
.174**
.227**
.148**
.201**
.238**
.320**
.351**
.333**
.432**
.431**
.455**
.500**
.47
Health services
.223**
.114**
.130**
.096**
.147**
.145**
.223**
.234**
.311**
.343**
.404**
.414**
.404**
.40
Family support
.264**
.161**
.199**
.123**
.166**
.194**
.248**
.293**
.340**
.388**
.435**
.449**
.425**
.39
Economic stability
.264**
.175**
.237**
.110**
.213**
.225**
.317**
.333**
.358**
.589**
.409**
.424**
.495**
.52
National well-being
index (new)
.344**
.247**
.292**
.174**
.270**
.316**
.373**
.437**
.535**
.755**
.721**
.711**
.777**
.76
Standard of
living
Health
AchievePersonal How safe Comm.
ments in life relationships you feel Connect.
Standard of living
1.000
.395**
.467**
.421**
.301**
Health
.395**
1.000
.308**
.242**
.236**
Achievements in
life
.467**
.308**
1.000
.385**
Personal
relationships
.421**
.242**
.385**
How safe you feel
.301**
.236**
Community
connectedness
.353**
Future security
Personal wellbeing index
How
Social
Australia is Busin
conditions
governed
** Correlation is significant at the 0.01 level (2-tailed).
16
17