Factors Influencing Inadequate Finances Among Elderly Rural Women
Submitted as Project Two for CHS 627
Spring 2000
1
Logistic Regression
Logistic regression will be used to analyze the probability of a woman having inadequate
(INADEQ$) finances, given the state of her health (NEWHLTH) and the number of years she was
employed outside the home (YRSEMPLY). Because the logistic procedure makes none of the
customary assumptions regarding equal variance and normal distribution, there is no need to
review here the distribution of YRSEMPLY.
Inadequate finances by Number of Years Employed
If the logistic regression model uses only years of employment to predict inadequate
finances, the results are not significant, as is shown below:
Total number of cases:
228 (Unweighted)
Number of selected cases:
228
Number of unselected cases: 0
Number of selected cases:
228
Number rejected because of missing data: 15
Number of cases included in the analysis: 213
Dependent Variable Encoding:
Original
Internal
Value
Value
0
0
1
1
_
Dependent Variable..
INADEQ$
Inadequate finances?
Beginning Block Number 0. Initial Log Likelihood Function
-2 Log Likelihood
262.06528
* Constant is included in the model.
Beginning Block Number
1.
Method: Enter
Variable(s) Entered on Step Number
1..
YRSEMPLY # Yrs employed
Estimation terminated at iteration number 3 because
parameter estimates changed by less than .001
-2 Log Likelihood
Goodness of Fit
Cox & Snell - R^2
Nagelkerke - R^2
261.920
213.027
.001
.001
2
Chi-Square
Model
Block
Step
df Significance
.145
.145
.145
1
1
1
.7029
.7029
.7029
The model is
not significant.
How well does the model fit the data? Ho: Model is a good fit.
---------- Hosmer and Lemeshow Goodness-of-Fit Test----------INADEQ$
= no, adequate fin INADEQ$
= yes, inadequate
Group
Observed
Expected
Observed
Expected
Total
1
2
3
4
5
6
7
8
9
10
14.000
15.000
13.000
14.000
15.000
17.000
16.000
15.000
4.000
25.000
15.043
14.158
13.379
14.016
14.645
16.661
14.491
13.691
4.766
27.152
7.000
5.000
6.000
6.000
6.000
7.000
5.000
5.000
3.000
15.000
5.957
5.842
5.621
5.984
6.355
7.339
6.509
6.309
2.234
12.848
21.000
20.000
19.000
20.000
21.000
24.000
21.000
20.000
7.000
40.000
The null hypothesis cannot be
rejected, indicating that the
Goodness-of-fit test
2.3344
8
.9690
model fits the data. There is not
----------------------------------------------------much difference between the
expected and observed values.
Chi-Square
df Significance
Classification Table for INADEQ$
The Cut Value is .50
Observed
no, adequate fin
n
yes, inadequate
y
Predicted
no, adequate finyes, inadequate
Percent Correct
n
I
y
+---------------+---------------+
I
148
I
0
I 100.00%
+---------------+---------------+
I
65
I
0
I
.00%
+---------------+---------------+
Overall 69.48%
The classification table shows that this model correctly predicts only 69.48% of the cases.
It fails to correctly predict any of the women with inadequate finances.
----------------- Variables in the Equation -----------------Variable
B
S.E.
Wald
df
Sig
R
YRSEMPLY
Constant
-.0035
-.7482
.0091
.2447
.1450
9.3457
1
1
.7034
.0022
.0000
3
Given the significance level of .7034, the null hypothesis that the slope of the predictor
(INADEQ$) is equal to zero cannot be rejected. The model is not significant; years of employment
is not a significant predictor of inadequate finances. The equation for predicting inadequate
finances using this model is:
P(INADEQ$yes) = e-.7482-(.0035*YRSEMPLY) / 1 + e-.7482-(.0035*YRSEMPLY)
Below is a plot of this equation.
.33
.32
.31
.30
.29
.28
.27
.26
-20
0
20
40
60
80
# Yrs employed
The relationship revealed by the plot would probably be better explained using simple
linear regression, but that will be ignored for this project. The negative coefficients indicate an
inverse relationship between the number of years a woman worked outside the home and the
probability of her currently having inadequate finances; as the number of years employed
increases, the probability of inadequate finances decreases.
Variable
Exp(B)
YRSEMPLY
.9965
95% CI for Exp(B)
Lower
Upper
.9790
1.0144
4
The odds ratio is .9965; for every year a woman was employed, the probability that she
has inadequate finances decreases by a measly 1.0035 (1/.9965). We know from above that the
relationship is not significant; the 95% C.I. of (.99, 1.02) supports the finding. To illustrate,
compared to woman who was employed for 10 years, a woman who was never employed has a
4% increased risk of having inadequate finances (e-.0035*(10-0), O.R.=1.04). When compared to a
woman with a 20 year employment history, she is at 7% increased risk, and compared to the two
women who were employed 70 years, she is 1.28 times more likely to have inadequate finances.
Observed Groups and Predicted Probabilities
160 +
+
I
I
I
I
F
I
I
R
120 +
+
E
I
I
Q
I
I
U
I
I
E
80 +
y
+
N
I
yy
I
C
I
yn
I
Y
I
nny
I
40 +
nny
+
I
nnn
I
I
nnn
I
I
nnnn
I
Predicted --------------+--------------+--------------+--------------Prob:
0
.25
.5
.75
1
Group: nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Predicted Probability is of Membership for yes, inadequate finances
The Cut Value is .50
Symbols: n - no, adequate finances
y - yes, inadequate finances
Each Symbol Represents 10 Cases.
This chart shows no real difference between the predicted probabilities of the groups, as
might be expected, given the nonsignificance of the model. As with the classification table, no
cases are predicted to have inadequate finances.
5
In summary, according to this model (which was not significant), unless a woman had
been employed for a really long time, her chances of having inadequate finances are not much
worse than a woman who was never employed. No one is predicted to have inadequate finances.
Inadequate Finances by Health Status
If we use the categorical variable NEWHLTH (1 = poor, 2 = fair, 3 = good) to predict
INADEQ$
in a logistic regression model, we find it to be a significant predictor, as is shown
below:
Total number of cases:
228 (Unweighted)
Number of selected cases:
228
Number of unselected cases: 0
Number of selected cases:
228
Number rejected because of missing data: 9
Number of cases included in the analysis: 219
Dependent Variable Encoding:
Original
Value
0
1
Internal
Value
0
1
Dependent Variable..
INADEQ$
Inadequate finances?
Beginning Block Number 0. Initial Log Likelihood Function
-2 Log Likelihood
268.06499
* Constant is included in the model.
Beginning Block Number
1.
Method: Enter
Variable(s) Entered on Step Number
1..
NEWHLTH
Health recoded
Estimation terminated at iteration number 3 because
Log Likelihood decreased by less than .01 percent.
-2 Log Likelihood
Goodness of Fit
Cox & Snell - R^2
Nagelkerke - R^2
Model
Block
Step
257.409
217.867
.047
.067
Chi-Square
10.656
10.656
10.656
df Significance
1
.0011
1
.0011
1
.0011
6
The model is significant (p = .0011). Health status is a significant predictor of financial
inadequacy.
---------- Hosmer and Lemeshow Goodness-of-Fit Test----------INADEQ$
= no, adequate fin INADEQ$
= yes, inadequate
Group
Observed
Expected
Observed
Expected
Total
1
2
3
76.000
70.000
7.000
74.724
72.551
5.725
17.000
43.000
6.000
18.276
40.449
7.275
93.000
113.000
13.000
Goodness-of-fit test
Chi-Square
.8692
df Significance
1
.3512
>Warning # 18585
>The Hosmer-Lemeshow statistic is calculated from fewer than 6 groups.
>Sensitivity to departures from model fit is substantially reduced.
--------------------------------------------------------------
The predicted values are close to the observed ones, and the .3512 significance value of
the Hosmer-Lemeshow statistic indicates that the model is a good fit for the data.
Classification Table for INADEQ$
The Cut Value is .50
Observed
no, adequate fin
Predicted
no, adequate finyes, inadequate
Percent Correct
n
I
y
+---------------+---------------+
I
146
I
7
I
95.42%
+---------------+---------------+
I
60
I
6
I
9.09%
+---------------+---------------+
Overall 69.41%
n
yes, inadequate
y
However, the model correctly predicts only 69.41% of the cases and only 9.1% of the
cases with inadequate finances.
----------------- Variables in the Equation -----------------Variable
B
S.E.
Wald
df
Sig
R
NEWHLTH
Constant
-.8240
1.0637
.2592
.6054
10.1048
3.0872
1
1
.0015
.0789
-.1739
The results show that health status is a significant (p = .0015) predictor of inadequate
finances and allow us to construct the prediction equation:
7
P(INADEQ$yes) = e 1.0637-(.8240*NEWHLTH) / 1 + e 1.0637-(.8240*NEWHLTH)
Variable
NEWHLTH
Exp(B)
95% CI for Exp(B)
Lower
Upper
.4387
.2639
.7291
The odds ratio is not helpful because of the categorical nature of this variable. To better
understand the predictive relationship of health status on inadequate finances, it is necessary to
create dummy variable to represent the different categories of health status in the logistic
regression.
Total number of cases:
228 (Unweighted)
Number of selected cases:
228
Number of unselected cases: 0
Number of selected cases:
228
Number rejected because of missing data: 9
Number of cases included in the analysis: 219
Dependent Variable Encoding:
Original
Value
0
1
_
Internal
Value
0
1
NEWHLTH
poor
fair
good/excellent
Value
Freq
1
2
3
13
110
89
Parameter
Coding
(1)
(2)
.000
1.000
.000
.000
.000
1.000
“Poor” health status was designated as the indicator category for this analysis.
Dependent Variable..
INADEQ$
Inadequate finances?
Beginning Block Number 0. Initial Log Likelihood Function
-2 Log Likelihood
268.06499
* Constant is included in the model.
Beginning Block Number 1. Method: Enter
Variable(s) Entered on Step Number
1..
NEWHLTH
Health recoded
Estimation terminated at iteration number 3 because
Log Likelihood decreased by less than .01 percent.
-2 Log Likelihood
256.545
8
Goodness of Fit
Cox & Snell - R^2
Nagelkerke - R^2
218.996
.051
.073
Chi-Square
Model
Block
Step
df Significance
11.520
11.520
11.520
2
2
2
.0032
.0032
.0032
The model is significant at the .0032 level.
---------- Hosmer and Lemeshow Goodness-of-Fit Test----------INADEQ$
= no, adequate fin INADEQ$
= yes, inadequate
Group
Observed
Expected
Observed
Expected
Total
1
2
3
76.000
70.000
7.000
75.999
70.000
7.000
17.000
43.000
6.000
17.001
43.000
6.000
93.000
113.000
13.000
Chi-Square
Goodness-of-fit test
.0000
df Significance
1
1.000
>Warning # 18585
>The Hosmer-Lemeshow statistic is calculated from fewer than 6 groups.
>Sensitivity to departures from model fit is substantially reduced.
Despite the warning, the model appears to be an excellent fit for the data; observed and
expected values are nearly identical. Based on the significance level of 1.000 on the Hosmer and
Lemeshow Goodness-of-Fit test, the null hypothesis that the model fits the data cannot be
rejected.
Classification Table for INADEQ$
The Cut Value is .50
Observed
no, adequate fin
yes, inadequate
n
y
Predicted
no, adequate finyes, inadequate
Percent Correct
n
I
y
+---------------+---------------+
I
153
I
0
I 100.00%
+---------------+---------------+
I
66
I
0
I
.00%
+---------------+---------------+
Overall 69.86%
9
Using the criteria in the Classification Table, only 69.86% of cases are correctly
predicted by the model, which is almost identical to that predicted by YRSEMPLY. This model
also fails to correctly predict any cases with inadequate finances.
------------------ Variables in the Equation ------------------Variable
NEWHLTH
NEWHLTH(1)
NEWHLTH(2)
Constant
B
S.E.
Wald
df
Sig
R
-.3331
-1.3433
-.1542
.5891
.6177
.5563
10.6984
.3198
4.7299
.0768
2
1
1
1
.0048
.5717
.0296
.7817
.1581
.0000
-.1009
The significance level of .0048 indicates that the variable NEWHLTH is a significant
predictor of inadequate finances. Using the dummy variables NEWHLTH1 and NEWHLTH2, the
prediction equation can be written as:
P(INADEQ$yes) = e-.1542 - (.3331*NEWHLTH1) - (1.3433*NEWHLTH2) / 1 + e-.1542 - (.3331*NEWHLTH1) - (1.3433*NEWHLTH2)
Variable
NEWHLTH(1)
NEWHLTH(2)
Exp(B)
.7167
.2610
95% CI for Exp(B)
Lower
Upper
.2259
.0778
2.2739
.8757
The odds ratios show that women in poor health are 1.4 (1/.7167) times as likely as
women fair health to have inadequate finances, but the 95% C.I. (.81, 1.99) means there is no
difference in the probability of inadequate finances between the women in poor health and those
whose health is fair. However, when compared to women in good health, those in poor health are
3.8 times more likely (95% C.I. (2.62, 5.04)) to have inadequate finances.
Observed Groups and Predicted Probabilities
F
R
E
Q
U
E
N
160 +
I
I
I
120 +
I
I
I
80 +
I
y
n
n
+
I
I
I
+
I
I
I
+
I
y
y
y
y
n
10
C
Y
I
n
n
I
I
n
n
I
40 +
n
n
+
I
n
n
I
I
n
n
I
I
n
n
n
I
Predicted --------------+--------------+--------------+--------------Prob:
0
.25
.5
.75
1
Group: nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Predicted Probability is of Membership for yes, inadequate finances
The Cut Value is .50
Symbols: n - no, adequate finances
y - yes, inadequate finances
Each Symbol Represents 10 Cases.
The plot shows that no cases are predicted to have inadequate finances.
Inadequate Finances by Health Status and Years Employed
Although years of employment was not a significant predictor by itself, we will add it to
the model with health status to see if it achieves significance when combines with health status,
or if it improves the health status model.
Total number of cases:
228 (Unweighted)
Number of selected cases:
228
Number of unselected cases: 0
Number of selected cases:
228
Number rejected because of missing data: 16
Number of cases included in the analysis: 212
Dependent Variable Encoding:
Original
Value
0
1
NEWHLTH
poor
fair
good/excellent
Internal
Value
0
1
Value
Freq
1
2
3
13
110
89
Parameter
Coding
(1)
(2)
.000
1.000
.000
.000
.000
1.000
Dependent Variable..
INADEQ$
Inadequate finances?
Beginning Block Number 0. Initial Log Likelihood Function
-2 Log Likelihood
261.33505
* Constant is included in the model.
11
Beginning Block Number
1.
Method: Enter
Variable(s) Entered on Step Number
1..
NEWHLTH
Health recoded
YRSEMPLY # Yrs employed
Estimation terminated at iteration number 3 because
Log Likelihood decreased by less than .01 percent.
-2 Log Likelihood
Goodness of Fit
Cox & Snell - R^2
Nagelkerke - R^2
251.028
212.106
.047
.067
Chi-Square
Model
Block
Step
df Significance
10.307
10.307
10.307
3
3
3
.0161
.0161
.0161
The model is significant at the .0161 level.
---------- Hosmer and Lemeshow Goodness-of-Fit Test----------INADEQ$
= no, adequate fin INADEQ$
= yes, inadequate
Group
Observed
Expected
Observed
Expected
Total
1
2
3
4
5
6
7
8
9
10
16.000
15.000
18.000
23.000
14.000
11.000
13.000
15.000
15.000
7.000
17.055
15.393
16.987
22.565
13.121
11.176
13.604
13.549
16.550
7.000
5.000
4.000
3.000
5.000
7.000
7.000
9.000
7.000
12.000
6.000
3.945
3.607
4.013
5.435
7.879
6.824
8.396
8.451
10.450
6.000
21.000
19.000
21.000
28.000
21.000
18.000
22.000
22.000
27.000
13.000
Chi-Square
Goodness-of-fit test
1.7741
df Significance
8
.9872
The model appears to be an excellent fit for the data, with not much difference between
observed and expected values. Based on the significance level of .9872 on the Hosmer and
Lemeshow Goodness-of-Fit test, the null hypothesis that the model fits the data cannot be
rejected.
Classification Table for INADEQ$
The Cut Value is .50
Predicted
12
Observed
no, adequate fin
n
yes, inadequate
y
no, adequate finyes, inadequate
Percent Correct
n
I
y
+---------------+---------------+
I
147
I
0
I 100.00%
+---------------+---------------+
I
65
I
0
I
.00%
+---------------+---------------+
Overall 69.34%
As in the previous models, only about 69% of cases are correctly predicted by the model.
This model also fails to correctly predict any cases with inadequate finances.
------------------ Variables in the Equation ------------------Variable
NEWHLTH
NEWHLTH(1)
NEWHLTH(2)
YRSEMPLY
Constant
B
S.E.
Wald
df
Sig
R
-.3218
-1.2811
-.0011
-.1374
.5922
.6222
.0092
.5749
9.4763
.2953
4.2393
.0134
.0571
2
1
1
1
1
.0088
.5869
.0395
.9080
.8111
.1448
.0000
-.0926
.0000
When controlled for YRSEMPLY, NEWHLTH is significant in the model (.0088), but
controlling for health status does not change the lack of significance (.9080) of YRSEMPLY as a
predictor. The negative values of the coefficients are also as expected: As the number of years a
woman was employed outside the home decreases, the probability of her having inadequate
finances increases; similarly, as the state of heath improves, the probability of having inadequate
finances decreases. The small coefficient for YRSEMPLY (-.0011) demonstrates how little it adds
to the equation.
The equation for predicting inadequate finances using this model is:
P(INADEQ$yes) =
e-.1374 - (.3218*NEWHLTH1 - 1.2811*NEWHLTH2-.0011*YRSEMPLY) / 1 + e-.1374 - (.3218*NEWHLTH1 - 1.2811*NEWHLTH2-.0011*YRSEMPLY)
Variable
NEWHLTH(1)
NEWHLTH(2)
YRSEMPLY
Exp(B)
.7249
.2777
.9989
95% CI for Exp(B)
Lower
Upper
.2271
.0820
.9810
2.3137
.9403
1.0172
13
The odds ratios are also very close to those of the model with health status alone. Women
in poor health are equally as likely (95% C.I. (.23, 2.3)) as women fair health to have inadequate
finances. They are 3.6 (95% C.I. (2.3, 4.8)) times more likely than women in good health to have
inadequate finances.
Observed Groups and Predicted Probabilities
160 +
+
I
I
I
I
F
I
I
R
120 +
+
E
I
I
Q
I
I
U
I
y
I
E
80 +
y
+
N
I
n
I
C
I
n
y
I
Y
I
n
yy
I
40 +
n
ny
+
I
n
nn
I
I
n
nn
I
I
n
nn
n
I
Predicted --------------+--------------+--------------+--------------Prob:
0
.25
.5
.75
1
Group: nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Predicted Probability is of Membership for yes, inadequate finances
The Cut Value is .50
Symbols: n - no, adequate finances
y - yes, inadequate finances
Each Symbol Represents 10 Cases.
This plot also shows that the failure of the model to correctly predict cases of inadequate
finances.
Multicollinearity
Because relationships among predictor variables can influence outcome, one-way
analysis of variance is used to investigate multicollinearity between the two predictor variables.
Testing the assumptions of a normal distribution shows that values for YRSEMPLY ranged from a
minimum of zero (which was also the mode) to a maximum of 70 years. The median number of
14
years employed was 20, and the mean was 21.63, with a variance of 267.05. Skewnness of .37
and kurtosis of -.412 indicate a relatively normal distribution, and the histogram is reasonably
normal, although a large number (n = 41) of women were never employed.
Statistics
YRSEMPLY # Yrs employed
N
Valid
Missing
Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtosis
Std. Error of Kurtosis
Range
Minimum
Maximum
Frequency
221
7
21.63
20.00
0
16.34
267.05
.370
.164
-.412
.326
70
0
70
# Yrs employed
50
40
30
20
10
Std. Dev = 16.34
Mean = 21.6
N = 221.00
0
0.0
10.0
5.0
20.0
15.0
30.0
25.0
40.0
35.0
50.0
45.0
55.0
60.0
70.0
65.0
# Yrs employed
Test of Homogeneity of Variances
YRSEMPLY # Yrs employed
Levene
Statistic
.622
df1
2
df2
216
Sig.
.538
We cannot reject the null
hypothesis of equal variance.
Based on the significance level of .538, the null hypothesis that the mean number of years
employed is equal across the 3 categories of health status cannot be rejected.
ANOVA
YRSEMPLY # Yrs employed
Between Groups
Within Groups
Total
Sum of
Squares
836.344
57307.136
58143.479
df
2
216
218
Mean
Square
418.172
265.311
15
F
1.576
Sig.
.209
Descriptives
YRSEMPLY # Yrs employed
N
1 poor
2 fair
3 good/excellent
Total
13
116
90
219
Mean
15.69
21.06
23.59
21.78
Std.
Deviation
17.08
16.81
15.48
16.33
Std. Error
4.74
1.56
1.63
1.10
95% Confidence Interval
for Mean
Lower
Upper
Bound
Bound
5.37
26.01
17.97
24.15
20.35
26.83
19.61
23.96
Minimum
0
0
0
0
Although the mean number of years employed increases as the health status improves, the
differences are not significant, perhaps a consequence of the small (n = 13) number of women in
the “poor” health category.
Log-Linear Analysis
The number of years a woman was employed has not been shown to have a significant
effect on her current financial status, perhaps because so many of the women were never
employed. The following analysis will substitute the categorical variable EVEREMPL, which has a
value of “1” if a woman was ever employed and “2” if she was not. The Log-Linear method will
be used to examine the relationships, including possible interactions, among inadequate finances,
health status, and whether or not a woman was ever employed.
* * * * * * * *
DATA
H I E R A R C H I C A L
L O G
L I N E A R
* * * * * * * *
Information
219 unweighted cases accepted.
0 cases rejected because of out-of-range factor values.
9 cases rejected because of missing data.
219 weighted cases will be used in the analysis.
FACTOR Information
Factor Level
NEWHLTH
3
INADEQ$
2
EVEREMPL
2
Label
Health recoded
Inadequate finances?
Ever employed?
16
Maximum
45
70
70
70
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * * * * * * * *
H I E R A R C H I C A L
L O G
L I N E A R
* * * * * * * *
DESIGN 1 has generating class
NEWHLTH*INADEQ$*EVEREMPL
Note: For saturated models
.500 has been added to all observed cells.
This value may be changed by using the CRITERIA = DELTA subcommand.
The Iterative Proportional Fit algorithm converged at iteration 1.
The maximum difference between observed and fitted marginal totals is
and the convergence criterion is
.250
.000
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Observed, Expected Frequencies and Residuals.
Factor
Code
NEWHLTH
INADEQ$
EVEREMPL
EVEREMPL
INADEQ$
EVEREMPL
EVEREMPL
poor
no, adeq
yes
no
yes, ina
yes
no
NEWHLTH
INADEQ$
EVEREMPL
EVEREMPL
INADEQ$
EVEREMPL
EVEREMPL
fair
no, adeq
yes
no
yes, ina
yes
no
NEWHLTH
INADEQ$
EVEREMPL
EVEREMPL
INADEQ$
EVEREMPL
EVEREMPL
good/exc
no, adeq
yes
no
yes, ina
yes
no
OBS count
EXP count
Residual
Std Resid
5.5
2.5
5.5
2.5
.00
.00
.00
.00
4.5
2.5
4.5
2.5
.00
.00
.00
.00
58.5
12.5
58.5
12.5
.00
.00
.00
.00
33.5
10.5
33.5
10.5
.00
.00
.00
.00
65.5
11.5
65.5
11.5
.00
.00
.00
.00
14.5
3.5
14.5
3.5
.00
.00
.00
.00
The Frequency Table shows that some of the cells have a small n, but none are empty.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Goodness-of-fit test statistics
Likelihood ratio chi square =
.00000
DF = 0 P = 1.000
Pearson chi square =
.00000
DF = 0 P = 1.000
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tests that K-way and higher order effects are zero.
K
DF
L.R. Chisq
Prob
Pearson Chisq
17
Prob
Iteration
3
2
1
2
.037
.9818
.037
7
14.252
.0469
14.756
11
244.085
.0000
290.425
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
.9819
.0393
.0000
- - - - - - - -
3
2
0
- - - -
Tests that K-way effects are zero.
K
DF
L.R. Chisq
Prob
Pearson Chisq
Prob
Iteration
1
2
3
4
5
2
229.834
14.215
.037
.0000
.0143
.9818
275.669
14.719
.037
.0000
.0116
.9819
0
0
0
The interaction of inadequate finances, health status, and employed is not significant
(.9819).
* * * * * * * *
H I E R A R C H I C A L
L O G
L I N E A R
* * * * * * * *
Tests of PARTIAL associations.
Effect Name
DF
NEWHLTH*INADEQ$
NEWHLTH*EVEREMPL
INADEQ$*EVEREMPL
NEWHLTH
INADEQ$
EVEREMPL
- - - - - - - - - - - - - - - - - - - - - - - - -
Partial Chisq
2
2
1
2
1
1
- - - - -
Prob
Iter
11.027
.0040
2
1.473
.4788
2
.729
.3933
2
98.921
.0000
2
35.534
.0000
2
95.380
.0000
2
- - - - - - - - - -
Although the 3-way interaction was not significant, we look at the 2-way interactions and
find that health status has a significant effect of inadequate finances (p = .004), but employment
does not (p = .3933).
These 2-way interactions could also have been examined with the results that are
summarized below.
Chi-Square
12.249
12.249
12.249
Model
Block
Step
df Significance
3
.0066
3
.0066
3
.0066
The model is significant.
---------- Hosmer and Lemeshow Goodness-of-Fit Test----------INADEQ$
Group
= no, adequate fin INADEQ$
Observed
Expected
= yes, inadequate
Observed
Expected
18
Total
1
2
3
4
65.000
11.000
58.000
19.000
65.175
10.824
57.754
19.246
14.000
3.000
33.000
16.000
Chi-Square
Goodness-of-fit test
13.825
3.176
33.246
15.754
79.000
14.000
91.000
35.000
df Significance
.0253
2
.9875
>Warning # 18585
>The Hosmer-Lemeshow statistic is calculated from fewer than 6 groups.
>Sensitivity to departures from model fit is substantially reduced.
--------------------------------------------------------------
The model is a good fit for the data.
Classification Table for INADEQ$
The Cut Value is .50
Observed
no, adequate fin
n
yes, inadequate
y
Predicted
no, adequate finyes, inadequate
Percent Correct
n
I
y
+---------------+---------------+
I
151
I
2
I
98.69%
+---------------+---------------+
I
64
I
2
I
3.03%
+---------------+---------------+
Overall 69.86%
The model correctly classified 70% of cases but only 1% of those with inadequate
finances.
Variable
NEWHLTH
NEWHLTH(1)
NEWHLTH(2)
EVEREMPL
Constant
B
S.E.
Wald
df
Sig
R
-.2976
-1.2960
.3247
-.5794
.5921
.6213
.3772
.7455
10.2634
.2526
4.3515
.7407
.6039
2
1
1
1
1
.0059
.6153
.0370
.3894
.4371
.1529
.0000
-.0937
.0000
When controlled for whether or not a women was ever employed, health status was
shown to be a significant predicator of inadequate finances (p = .0059). EVEREMPL, controlled
for NEWHLTH was not.
Variable
Exp(B)
NEWHLTH(1)
NEWHLTH(2)
EVEREMPL
.7426
.2736
1.3836
95% CI for Exp(B)
Lower
Upper
.2327
.0810
.6605
2.3700
.9247
2.8980
19
The 95% C.I. for the odds ratio of comparing ever-employed to never-employed includes
1, so the O.R. value of 1.4 cannot be interpreted as meaning women who have never been
employed are 1.4 times more likely to have inadequate finances when health status is controlled.
When controlled for whether or not they were ever employed, women in poor health are 1.35
(O.R. = 1/.7426) times more likely than women in fair health and 3.65 times more likely than
women in good health to have inadequate finances. These figures are not much different from
those in the logistic regression with health status alone.
When the odds ratios of inadequate to adequate finances are calculated, controlling
NEWHLTH
for EVEREMPL and vice versa, the following results are obtained:
Ever employed?
Health Status
yes
no
O.R.
95% C.I.
O.R.
95% C.I.
Poor – Fair
1.4
-.54, 3.35
1.2
-1.36, 3.76
Poor - Good
3.7
-1.62, 9.05
3.7
-4.91, 12.24
Fair - Good
2.6
.74, 4.54
3.1
-1.61, 7.72
Employment appears to have the greatest effect on inadequate finances when the when
those in fair health are compared to those in good health. Among women who never were
employed, the odds for women in fair health having inadequate finances are 3.1 times those for
women in good health. but the odds are only 2.6 for those women who were employed. Women
in poor health are 3.7 times as likely as women in good health to have inadequate finances,
regardless of whether they were employed or not. However, if the confidence intervals are
correct, none of these odds ratios can be considered with 95% confidence.
20
The graph below, comparing health status of the employed and never-employed women
who have inadequate finances, shows higher percentages of inadequate finances for women who
were never employed, regardless of health status. Although the lines are not parallel, they are
nearly so on both segments, as might be expected given the lack of significance of the
interaction.
Inadequate Finances by Health
Status and Employed
60%
50%
employed
40%
never
employed
30%
20%
10%
0%
poor
fair
good
Health Status
Inadequate Finances by Employment
40%
37.5%
35%
30%
25%
28.5%
20%
15%
10%
5%
0%
yes
no
Ever Employed?
21
The graph of EVEREMPL and INADEQ$ shows that a higher percentage of women who
were never employed have inadequate finances, although this 2-way interaction was not
significant.
Inadequate Finances by Health Status
50%
45%
40%
46.2%
38.1%
35%
30%
25%
20%
18.3%
15%
10%
5%
0%
poor
fair
good
Health Status
The graph of the significant effect of health status on inadequate finances shows that as
the state of health improves, the percentage of women with inadequate finances decreases.
22
MANOVA (2 outcomes, 1 predictor)
As discussed in the previous paper, this study used measures of personal control score
and autonomy as outcome variables. These measures were described in more detail previously,
but to summarize them briefly:
Personal control was measured using an 8-item instrument that was a modified version of
an existing instrument. Items were measured using a four-point Likert-type scale with responses
ranging from “strongly disagree” to “strongly agree,” with values of one to four, respectively.
Items were summed to produce an overall score ranging from 8 to 32; higher scores indicate
greater sense of personal control.
Autonomy was measured using a existing 14-item inventory with a reported internal
consistency of .83. Items were measured using a six-point Likert-type scale with responses
ranging from “strongly disagree” to “strongly agree,” with value of one to six, respectively.
Items were summed to produce an overall score that could range from 14 to 84; higher scores
indicate greater sense of autonomy.
Personal control scores were obtained for 227 women and ranged from a low score of 12
to a high score of 32. The median score was 23, and the mean score was 23.20, with a variance
of 14.86. Autonomy scores, obtained for 226 women, ranged from 25 to 84, with a median score
of 57, a mean of 58.17, and a variance of 157.46. Skewness and kurtosis statistics, as well as
histograms of the frequency distributions for both variables indicated reasonably normal
distributions of scores.
Statistics
N
Mean
Median
Valid
Missing
PCSCORE
227
1
23.1982
23.0000
AUTSCORE
226
2
58.1726
57.0000
23
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtosis
Std. Error of Kurtosis
Range
Minimum
Maximum
24.00
3.8547
14.8588
-.095
.162
.186
.322
20.00
12.00
32.00
49.00
12.5483
157.4590
.183
.162
-.502
.322
59.00
25.00
84.00
PCSCORE
AUTSCORE
70
50
60
40
50
30
40
20
20
Std. Dev = 3.85
10
Mean = 23.2
N = 227.00
0
12.0
16.0
14.0
20.0
18.0
24.0
22.0
28.0
26.0
Frequency
Frequency
30
32.0
30.0
PCSCORE
10
Std. Dev = 12.55
Mean = 58.2
N = 226.00
0
25.0
35.0
30.0
45.0
40.0
55.0
50.0
65.0
60.0
75.0
70.0
85.0
80.0
A UTSCORE
To examine the effect of inadequate finances on these scores simultaneously requires a
multivariate analysis of variance (MANOVA).
b
j
l
u
N
b
I
0
N
n
I
n
2
a
f
f i
1
y
6
i
n
f
24
e
t
I
d
N
e
ia
N
f
a
i
P
0
2
0
2
1
2
2
6
f
i
T
5
9
8
A
0
6
2
2
1
3
7
6
f
i
T
7
6
8
a
o
B
F
d
d
S
T
o
a
D
The significance level of .749 means that the null hypothesis of equal covariance
structures in both groups cannot be rejected, and the assumption of equal variance has not been
violated. In other words, although differences in the covariances are seen in the following
Correlations table, they are not significant (PCSCORE covariances: poor = 13.590, fair = 12.931,
good = 15.615; AUTSCORE covariances: poor = 87.526, fair = 170.491, good = 138.765).
The table also shows moderate correlations between PCSCORE and AUTSCORE for all
levels of health; for those in fair and good health, the correlations are significant at p < .001.
25
r
e l
a t i
o
A U
N
T
E
S
W
C
C
S
H
R
C
e
E
O
a l
.
P
P
C
e
a
S
0
0
0
0
0
0
*
*
S
ig .
.
.
S u m
0
0
0
0
0
0
C
r o
C
o v
0
0
0
0
0
0
N
2
2
A
P
U
e
a
T
0
0
0
0
0
0
*
*
S
ig .
.
.
S u m
0
5
0
0
0
0
C
r o
C
o v
0
5
0
0
0
0
N
2
2
1
P
P
C
e
p
a
S
o
0
4
0
9
0
7
S
ig .
0 8
4
.
S u m
0
8
7
4
7
6
C
r o
C
o v
5
1
9
5
0
4
N
1
1
3
3
A
P
U
e a
T
4
0
9
0
7
0
S
ig .
0 8 4
.
S u m
8
3
4
0
6
8
C
r o
C
o v
1
5
5
2
4
6
N
1
1
3
3
2
P
P
C
e
f
a
a
S
0
5
0
5
0
2
*
*
S
i
g
.
0 0 0
.
S u m
8
0
4
5
9
0
C
r o
C
o v
9
9
3
3
1
3
N
1
1
1
1
9
9
A
P
U
e
a
T
5
0
5
0
2
0
*
*
S
ig .
0 0 0
.
S u m
0
9
5
8
0
3
C
r o
C
o v
9
4
3
9
3
1
N
1
1
1
1
9
9
3
P
P
C
e
g
a
S
o
0
5
0
8
0
4
*
*
S
ig .
0 0
0
.
S u m
5
6
8
7
1
4
C
r o
C
o v
6
4
1
0
5
3
N
9
9
3
2
A
P
U
e
a
T
5
0
8
0
4
0
*
*
S
ig .
0 0 0
.
S u m
6
6
7
0
4
9
C
r o
C
o v
4
7
0
6
3
5
N
9
9
2
2
*
*o
.
C
r r
26
Continuing discussion of the MANOVA below, using an alpha level of .06 allows us to
reject the null hypothesis of no difference between the mean vectors of the two groups:
Ho: pc1 = pc2
aut1 = aut1
and accept the model as significant.
i
b
a
o
t
h
S
a
d
F
o
E
l
i
u
g
f
a
I
P
n
0
8
0
0
0
a
W
0
8
0
0
0
a
H
4
8
0
0
0
a
R
4
8
0
0
0
a
I
P
N
6
7
0
0
7
a
W
4
7
0
0
7
a
H
7
7
0
0
7
a
R
7
7
0
0
7
a
E
b
D
We investigate the significance by first examining the univariate results.
a
a
l
F
f
f
i
g
1
2
P
7
1
6
0
A
1
1
6
8
T
v
a
D
There is no problem with variance at the univariate level, even before applying the
Bonferroni correction.
27
n
-
p
e
M
u
m
e
a
q
u
S
d
S
u
D
a
F
i
f
a
g
o
a
C
P
7
3
2
9
1
9
4
0
b
A
4
9
7
0
1
0
7
3
I
P
n
6
9
0
9
1
9
6
0
A
7
9
0
3
1
3
3
0
I
P
N
7
3
2
9
1
9
4
0
A
4
9
7
0
1
0
7
3
E
P
r
8
7
6
8
A
1
9
6
6
T
P
o
0
8
A
0
8
C
P
6
7
A
9
7
a
.
R
b
.
R
The means from the Descriptive Statistics table showed that women with inadequate
finances had lower scores in both personal control and autonomy than did women with adequate
finances. The Between-Subjects Effects table shows that when personal control scores and
autonomy scores are considered simultaneously, those differences are significantly lower on
personal control scores (p = .02), but there is no significant difference in autonomy scores (p =
.373). Even after controlling for  using the Bonferroni-corrected value of .025 (.05/2), personal
control scores for women with inadequate finances are significantly lower. The following
pairwise comparisons show the same thing and are not necessary since there are only two groups,
they are included for example only.
m
d
e
p
w
p
o
o
e
D
u
u
I
E
a
n
P
0
8
9
0
7
1
8
9
5
2
f
i
A
0
2
0
2
1
1
7
7
8
7
f
i
28
C o
m
d
e
a
f
f
e
e
a
e
o
p
r
w
e
p
a
S
o
o
.
I
D
(
(
u
i
u
E
J
I
g
J
P
0
1
1
2
0
1
0
4
6
*
f
i
1
0
2
1
0
1
0
6
4
*
f
i
n
A
0
1
U
9
0
4
3
3
8
7
f
i
1
0
0
9
4
3
3
7
8
f
i
n
B
i
*.
T
h
a
.
A
d
a
o
t
h
S
a
d
F
o
l
i u
g
f
a
P
6
7
0
0
7
a
W
4
7
0
0
7
a
H
7
7
0
0
7
a
R
7
7
0
0
7
E
o
m
a
E
This table also shows, at  = .06, the significance of the multivariate model.
a
t
m
e
a
S
u
d
u
F
D
a
i
g
f
P
C
9
1
9
4
0
E
7
6
8
A
C
0
1
0
7
3
E
9
6
6
T
p
This table also shows again the significance levels of the univariate tests.
29
Estimated Marginal Means of PCSCORE
23.8
23.6
Estimated Marginal Means
23.4
23.2
23.0
22.8
22.6
22.4
22.2
no, adequate finance
yes, inadequate fina
Inadequate finances?
This plot shows that the lower personal control scores for women with inadequate
finances when personal control and autonomy scores are considered simultaneously.
Estimated Marginal Means of AUTSCORE
59.0
Estimated Marginal Means
58.5
58.0
57.5
57.0
no, adequate finance
yes, inadequate fina
Inadequate finances?
Similarly, this plot shows that the lower autonomy scores for women with inadequate
finances when personal control and autonomy scores are considered simultaneously.
30
Discriminant Function Analysis
Discriminant Function Analysis analyzes the relationships among these variables
(INADEQ$, PCSCORE, AUTSCORE) in a different way and allows the construction of an equation,
using PCSCORE and AUTSCORE, that best discriminates between those with inadequate and
adequate finances.
o
c
r
N
U
c
V
8
6
E
M
8
5
g
A
2
9
d
B
o
0
0
a
d
T
0
4
T
8
0
S
t
(
l
I
e
g
f
i
g
0
P
2
0
A
2
0
1
P
6
0
f
A
6
0
T
P
8
0
A
8
0
a
G
C
C
C
P
8
4
A
4
6
C
P
0
7
A
7
0
a
T
31
Because we learned form the MANOVA that the Box’s test was not significant, we can
pool the within-groups covariance matrices. The variables PCSCORE and AUTSCORE are
moderately correlated at .567.
Box's Test of Equality of Covariance Matrices
e
r
o
I
a
m
f
n
0
2
7
1
2
7
f
P
2
8
T
t
h
R
2
6
3
8
9
e
B
F
A
d
d
S
T
The Box’s Test is not significant, allowing us to pool the variance.
Summary of Canonical Discriminant Functions
v
o
u
o
n
e
n
%
a
F
l
v
a
1
0
0
2
a
F
a
32
L
l
k
m
d
i
q
T
g
1
7
i
c
1
P
A
The Standardized Canonical Discriminant Function Coefficients allows comparison of
the amounts each variable contributes to the differentiation between the INADEQ$ groups. The
PCSCORE
coefficient (1.128) is four times larger than that of AUTSCORE (-.269), reflecting its
greater importance in differentiating between the groups; it is also in a different direction from
the AUTSCORE coefficient. These coefficients can be used to calculate a new variable, x, that uses
standardized scores for personal control and autonomy to give the best separation of women with
and without adequate finances. The equation for calculating the variable is:
x = (1.128*PCSCOREstd) – (.269*AUTSCOREstd)
r
c
I
N
1
f
i
0
8
1
8
f
i
U
g
33
r
e
c
1
P
A
P
v
V
Classification Statistics
c
P
E
M
g
A
d
U
t
i
d
I
N
g
f
i
i
o
g
0
0
2
0
1
0
6
0
f
T
8
0
c
I
n
c
y
n
e
q
q
u
n
n
c
c
P
A
(
C
F
34
i
a
o
e
d
b
e
y
n
e
e
q
I
q
N
u
a
o
n
n
f
i
t
O
C
0
6
6
2
1
9
7
6
f
i
U
5
3
8
%
0
6
4
0
1
9
1
0
f
i
U
5
5
0
a
5
Only 56.4% of cases were correctly classified, which is little better than chance.
MANOVA (2 outcomes, 2 predictors)
Perhaps ethnicity, combined with inadequate finances, has an effect on the outcomes.
NEWETH
is a categorical variable with the value of 1 for Caucasian and 2 for African American.
Adding NEWETH into the analysis gives the following results:
b
j
N
I
0
n
2
I
f
f
1
y
2
f
N
1
3
C
E
2
1
A
The descriptive statistics that follow reveal higher mean personal control scores and
autonomy scores for African American women when compared to Caucasian women, regardless
of financial status. All cells have a reasonable number of cases.
35
v
e
S
I
N
N
td
M
v
e
f
i
r
N
i
a
e
n
a
P
0
1
C
0
2
2
8
7
2
5
2
0
1
5
T
2
5
2
0
2
1
1
0
4
1
2
6
f
i
n
2
9
1
0
1
6
T
9
6
7
9
2
T
1
o
7
7
2
4
3
2
4
4
9
9
1
T
4
1
1
4
4
A
0
1
U
9
2
2
7
7
2
2
2
0
0
5
T
2
5
6
2
2
1
1
6
4
3
9
6
f
i
n
2
0
1
5
1
6
T
6
6
9
5
2
T
1
o
4
7
3
0
3
2
0
4
4
6
1
T
6
1
9
2
4
a
o
B
F
d
d
S
T
o
a
D
N
Box’s Test of the null hypothesis of equal covariance matrices cannot be rejected.
36
r
b
ia
o
th
r
a
S
r
E
d
F
o
l
i
u
f
g
f
a
I
P
n
t
0
0
9
5
0
0
0
a
W
0
0
1
5
0
0
0
a
H
0
0
1
5
0
0
0
a
R
0
0
1
5
0
0
0
a
I
P
N
0
5
8
6
0
0
1
a
W
0
5
2
6
0
0
1
a
H
0
5
8
6
0
0
1
a
R
0
5
8
6
0
0
1
a
N
P
E
0
8
4
4
0
0
3
a
W
0
8
6
4
0
0
3
a
H
0
8
4
4
0
0
3
a
R
0
8
4
4
0
0
3
a
I
P
N
0
7
4
9
0
0
8
a
W
0
7
6
9
0
0
8
a
H
0
7
4
9
0
0
8
a
R
0
7
4
9
0
0
8
a
.
E
b
.
D
All tests have the identical significance value of .678, indicating that the interaction of
inadequate finances and ethnicity does not have a significant effect on personal control and
autonomy scores when they are considered simultaneously. Nonetheless, let’s consider what a
significant interaction would have meant.
Had the interaction been significant for PSCORE, it would have indicated that finances and
ethnicity, when considered together, have a significant effect on PSCORE when it is considered
simultaneously with AUTSCORE. Similarly, a significant interaction for AUTSCORE would have
indicated that finances and ethnicity, when considered together, have a significant effect on
AUTSCORE
when it is considered simultaneously with PCSCORE. This is discussed in more detail
later.
Since the interaction is not significant, we look at the significance values of the main
effects and find that neither achives significance.
37
a
a
F
f
f
i
g
1
2
P
6
3
0
0
A
8
3
0
4
T
v
a
D
N
The null hypothesis of equal error variance cannot be rejected.
n
-S
p
e
M
u
m
e
a
q
u
S
d
S
u
D
a
F
i
f
a
g
o
a
C
P
9
9
3
9
3
0
5
1
b
A
5
0
6
6
3
2
0
1
I
P
n
t
6
3
0
2
1
2
2
0
A
2
0
0
4
1
4
3
0
I
P
N
5
2
5
4
1
4
4
2
A
6
8
0
5
1
5
2
0
N
P
E
5
3
8
1
1
1
0
9
A
1
1
2
8
1
8
4
6
I
P
N
9
7
9
7
1
7
0
2
A
8
1
9
5
1
5
6
8
E
P
r
9
1
0
3
A
6
2
0
9
To
P
0
4
A
0
4
C
P
0
3
A
8
3
a
.
R
b
.
R
When INADEQ$ is controlled for ETHNICITY, autonomy scores are not significant (p =
.300), but personal control scores are significant in the table at .052, indicating a significant
effect if  is set at .10. Even after applying the Bonferroni correction, rounding, and comparing
.05 to the corrected  value of .05 (.10/2), personal control scores are significant. Personal
control scores are not significantly affected by the ethnicity variable (p = .289) when it is
38
controlled for financial status, but autonomy scores are significant in the table (p = .026) and
remain so after applying the Bonferroni correction with  = .10 (.026 < .05). As discussed
previously, the interaction of ethnicity and inadequate finances was not significant, which
indicates that the combined effect of NEWETH and INADEQ$ is not significant when personal
control and autonomy scores are considered simultaneously.
We look at marginal means to learn more about these differences.
Estimated Marginal Means
1. Inadequate finances?
m
d
e
p
w
p
o
o
e
D
u
u
I
E
a
n
P
0
4
4
9
9
1
1
9
9
2
f
i
A
0
0
4
1
9
1
1
6
0
1
f
i
o
m
d
e
a
f f a
e
e
e
o
p
r
w
p
e
a
S
o
.
o
I
D
(
(
i
u
E
u
J
I
g
J
P
0
1
9
4
7
2
2
8
f i
1
0
0
4
7
2
8
2
f
i
n
A
0
1
7
9
9
0
5
3
f i
1
0
9
9
9
0
3
5
f
i
n
B
a
.
A
39
Estimated Marginal Means of PCSCORE
24.2
24.0
23.8
Estimated Marginal Means
23.6
23.4
23.2
23.0
22.8
22.6
22.4
no, adequate finance
yes, inadequate fina
Inadequate finances?
Estimated Marginal Means of AUTSCORE
61.5
61.0
Estimated Marginal Means
60.5
60.0
59.5
59.0
58.5
no, adequate finance
yes, inadequate fina
Inadequate finances?
When adjusted for ethnicity, women with inadequate finances had significantly lower
personal control scores than did women with adequate finances. As discussed above, although
their autonomy scores were also lower, the difference was not significant. Pairwise comparisons
(following) are not really necessary, since INADEQ$ has only two categories.
2. Ethnicity recoded
40
m
e
p
w
p
e
u
D
u
E
E
a
P
1
7
5
6
8
2
7
5
4
1
A
1
2
5
3
1
2
9
1
3
4
o
d
e
a
f
f
e
e
a
e
o
p
r
w
e
p
a
S
o
o
.
I
D
(
(
i
u
u
E
J
I
g
J
P
1
2
0
7
9
5
4
2
1
0
7
9
4
5
A
1
2
6
9
6
0
3
*
2
1
6
9
6
3
0
*
B
*
.
T
a
A
Estimated Marginal Means of PCSCORE
23.8
Estimated Marginal Means
23.6
23.4
23.2
23.0
22.8
Cauc asian
Afric an-Americ an
Ethnicity recoded
41
Estimated Marginal Means of AUTSCORE
63
62
Estimated Marginal Means
61
60
59
58
57
Cauc asian
Afric an-Americ an
Ethnicity recoded
When adjusted for financial situation, both personal control and autonomy scores of
African-American women were higher than those of Caucasians. As discussed above, the
difference was significant for autonomy but not for personal control. Pairwise comparisons are
not really necessary, since ethnicity has only two categories.
e
s
d
e
o
p
w
p
o
o
.
e
D
I
u
E
u
E
n
a
P
0
1
8
5
7
0
2
0
6
9
1
1
1
6
7
7
5
f
i
2
5
5
2
8
A
0
1
0
8
5
5
2
0
5
1
9
1
1
4
5
7
2
f
i
2
7
4
8
7
interaction
Profile Plots
PCSCORE
42
Estimated Marginal Means of PCSCORE
25.0
24.5
Estimated Marginal Means
24.0
23.5
Inadequate finances?
23.0
no, adequate finance
s
22.5
yes, inadequate fina
22.0
nces
Cauc asian
Afric an-Americ an
Ethnicity recoded
The lines in both graphs (above and below) are almost parallel, as is expected, given the
lack of a significant interaction. African-American women have higher personal control scores
than do Caucasian women, more so for women with adequate finances than for those without.
Estimated Marginal Means of PCSCORE
25.0
24.5
Estimated Marginal Means
24.0
23.5
23.0
Ethnicity recoded
22.5
Cauc asian
22.0
Afric an-Americ an
no, adequate finance
yes, inadequate fina
Inadequate finances?
Seen another way, women with inadequate finances have lower personal control scores,
but this difference is greater for African-Americans.
43
AUTSCORE
Estimated Marginal Means of AUTSCORE
66
Estimated Marginal Means
64
62
Inadequate finances?
60
no, adequate finance
s
58
yes, inadequate fina
56
nces
Cauc asian
Afric an-Americ an
Ethnicity recoded
This graph shows more evidence of an interaction, although it is not significant. For both
ethnic groups, the scores of women with inadequate finances are lower than those of women
whose financial situation is adequate, but this difference is much smaller for Caucasian women
than for are African-Americans.
Estimated Marginal Means of AUTSCORE
66
Estimated Marginal Means
64
62
60
Ethnicity recoded
58
Cauc asian
56
Afric an-Americ an
no, adequate finance
yes, inadequate fina
Inadequate finances?
44
This graph also shows that, for Caucasian women, financial status has little effect on
autonomy scores, but the scores for African-American women are lower for those whose
financial situation is inadequate than are those of women with adequate finances.
The table below shows not much difference in the covariances (excluding the missing
values), which helps understand why the Box’s test was not significant. The correlations of
personal control and autonomy scores from the table on the following page are summarized
below:
Adequate finances
Caucasian
n
r
p
127
.529
.000
26
.536
.006
46
.671
.000
16
.5786
.019
African-American
Inadequate finances Caucasian
African-American
Personal control and autonomy scores are moderately and significantly correlated within
all groups.
45
o
r
r
e
l
a
t
i
o
n
s
I
N
N
A
E
D
W
E
Q
E
T
$
H
A
P
C
U
S
T
C
S
C
O
O
R
R
E
f
i
n
r
a
e
n
c
c
o
e
d
s
e
?
d
.
1
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P
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a
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a
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o
1
.
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8
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2
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f
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r
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s
s
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o
v
a
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4
8
.
2
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8
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3
N
4
4
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s
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ic
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v
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5
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2
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.
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r
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s
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o
v
a
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6
5
2
.
8
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3
3
3
3
3
N
4
4
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1
n
P
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e
,
a
a
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d
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1
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ra
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2
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y
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4
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1
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1
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4
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6
6
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1
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4
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5
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1
1
6
6
.
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o
1
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3
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6
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o
v
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2
1
8
2
.
0
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0
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4
4
A
P
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s
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1
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ig
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1
1
2
3
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6
0
6
0
7
N
4
4
*
*
C
*
.
C
.
o
o
r
r
r
r
46
e
e
la
la
t
io
t
io
Summary
We have investigated variables hypothesized to have an effect on whether or not a
woman has inadequate finances. Using logistic regression, we found that employment history
was not a good predictor of inadequate finances. The number of years a woman was employed
was not a significant predictor, either alone or in a model with health status. Similarly, the
interaction of whether or not a woman had ever been employed with health status was not
significant in a loglinear analysis, and EVEREMPL was not a significant predictor in a logistic
regression model with health status.
Health status, however, was found to be a significant predictor of inadequate finances,
and neither of the employment variables had much effect on the relationship when they were
added separately to different logistic regressions. The effect of health status was also found to be
significant in the loglinear analysis. Women on poor health were found to be about 1.4 times
more likely than women in fair health and 3.6 times more likely than women in good health to
have inadequate finances, regardless of whether or not either of the employment variables was
included in the model.
Multivariate analysis of variance was used to investigate the effect of inadequate finances
on personal control and autonomy scores considered simultaneously. Financial status was
significant predictor if  = .06. Discriminant function analysis showed that personal control
scores were more important than autonomy scores in discriminating between women with and
without adequate finances. With the addition of ethnicity to the MANOVA model, financial
situation could no longer be considered a significant predictor of the scores considered
simultaneously. The interaction was not significant, although plots of marginal means suggested
47
that the autonomy scores of African American women were more strongly influenced by
financial status than were those of Caucasian women.
Of the variables and methods used with regard to inadequate finances, a simple bivariate
logistic regression using health status with dummy variables seems the most desirable.
48