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Unformatted text preview: Discovering Statistics Using SPSS: Chapter 6 Chapter 6: Answers
Task 1
Recent research has shown that lecturers are among the most stressed workers. A researcher
wanted to know exactly what it was about being a lecturer that created this stress and
subsequent burnout. She took 467 lecturers and administered several questionnaires to them
that measured: Burnout (burnt out or not), Perceived Control (high score = low perceived
control), Coping Style (high score = low ability to cope with stress), Stress from Teaching
(high score = teaching creates a lot of stress for the person), Stress from Research (high
score = research creates a lot of stress for the person), and Stress from Providing Pastoral
Care (high score = providing pastoral care creates a lot of stress for the person). The outcome
of interest was burnout, and Cooper’s (1988) model of stress indicates that perceived control
and coping style are important predictors of this variable. The remaining predictors were
measured to see the unique contribution of different aspects of a lecturer’s work to their
burnout—can you help her out by conducting a logistic regression to see which factor predict
burnout? The data are in Burnout.sav.
Test
The analysis should be done hierarchically because Cooper’s model indicates that perceived
control and coping style are important predictors of burnout. So, these variables should be
entered in the first block. The second block should contain all other variables and because we
don’t know anything much about their predictive ability, we should enter them in a stepwise
fashion (I chose Forward: LR).
SPSS Output
Step 1:
Omnibus Tests of Model Coefficients
Step 1 Step
Block
Model Chisquare
165.928
165.928
165.928 df
2
2
2 Sig.
.000
.000
.000 Model Summary
Step
1 2 Log
likelihood
364.179 Cox & Snell
R Square
.299 Nagelkerke
R Square
.441 Variables in the Equation Step
a
1 LOC
COPE
Constant B
.061
.083
4.484 S.E.
.011
.009
.379 Wald
31.316
77.950
139.668 df
1
1
1 Sig.
.000
.000
.000 Exp(B)
1.063
1.086
.011 95.0% C.I.for EXP(B)
Lower
Upper
1.040
1.086
1.066
1.106 a. Variable(s) entered on step 1: LOC, COPE. The overall fit of the model is significant both at the first step, χ2(2) = 165.93, p < .001.
Overall, the model accounts for 29.9 – 44.1% of the variance in burnout (depending on which
measure R2 you use).
Step 2:
The overall fit of the model is significant after both at the first new variable (teaching), χ2(3) =
193.34, p < .001, and second new variable (pastoral) have been entered, χ2(4) = 205.40, p <
.001 Dr. Andy Field Page 1 9/5/2003 Discovering Statistics Using SPSS: Chapter 6
Overall, the final model accounts for 35.6 – 52.4% of the variance in burnout (depending on
which measure R2 you use.
Omnibus Tests of Model Coefficients
Step 1 Chisquare
27.409
27.409
193.337
12.060
39.470
205.397 Step
Block
Model
Step
Block
Model Step 2 df
1
1
3
1
2
4 Sig.
.000
.000
.000
.001
.000
.000 Model Summary
Step
1
2 2 Log
likelihood
336.770
324.710 Cox & Snell
R Square
.339
.356 Nagelkerke
R Square
.500
.524 Variables in the Equation Step 1a Step 2b LOC
COPE
TEACHING
Constant
LOC
COPE
TEACHING
PASTORAL
Constant B
.092
.131
.083
1.707
.107
.135
.110
.044
3.023 S.E.
.014
.015
.017
.619
.015
.016
.020
.013
.747 Wald
46.340
76.877
23.962
7.599
52.576
75.054
31.660
11.517
16.379 df
1
1
1
1
1
1
1
1
1 Sig.
.000
.000
.000
.006
.000
.000
.000
.001
.000 Exp(B)
1.097
1.139
.921
.181
1.113
1.145
.896
1.045
.049 95.0% C.I.for EXP(B)
Lower
Upper
1.068
1.126
1.107
1.173
.890
.952
1.081
1.110
.862
1.019 1.145
1.181
.931
1.071 a. Variable(s) entered on step 1: TEACHING.
b. Variable(s) entered on step 2: PASTORAL. In terms of the individual predictors we could report:
B 95% CI for Exp(B) (SE)
Lower Exp(β) Upper Step 1
Constant –4.48**
(0.38) Perceived Control 0.06**
(0.01) 1.04 1.06 1.09 Coping Style 0.08**
(0.01) 1.07 1.09 1.11 Final
Constant –3.02**
(0.75) Perceived Control 0.11**
(0.02) 1.08 1.11 1.15 Coping Style 0.14**
(0.02) 1.11 1.15 1.18 Teaching Stress –0.11**
(0.02) 0.86 0.90 0.93 Pastoral Stress 0.04*
(0.01) 1.02 1.05 1.07 Note. R2 = .36 (Cox & Snell), .52 (Nagelkerke). Model χ2(4) = 205.40, p < .001. * p < .01, ** p < .001. Dr. Andy Field Page 2 9/5/2003 Discovering Statistics Using SPSS: Chapter 6
It seems as though burnout is significantly predicted by perceived control, coping style (as
predicted by Cooper), stress from teaching and stress from giving pastoral care. The Exp(B)
and direction of the beta values tells us that for perceived control, coping ability and pastoral
care the relationships are positive. That is (and look back to the question to see the direction
of these scales, i.e. what a high score represents), poor perceived control, poor ability to cope
with stress and stress from giving pastoral care all predict burnout. However, for teaching, the
relationship if the opposite way around: stress from teaching appears to be a positive thing as
it predicts not becoming burnt out! Task 2
A Health Psychologist interested in research into HIV wanted to know the factors that
influenced condom use with a new partner (relationship less than 1 month old). The outcome
measure was whether a condom was used (Use: condom used = 1, Not used = 0). The
predictor variables were mainly scales from the Condom Attitude Scale (CAS) by Sacco,
Levine, Reed and Thompson (Psychological Assessment: A journal of Consulting and Clinical
Psychology, 1991). Gender (gender of the person); Safety (relationship safety, measured out
of 5, indicates the degree to which the person views this relationship as ‘safe’ from sexually
transmitted disease); Sexexp (sexual experience, measured out of 10, indicates the degree to
which previous experience influences attitudes towards condom use); Previous (a measure
not from the CAS, this variable measures whether or not the couple used a condom in their
previous encounter, 1 = condom used, 0 = not used, 2 = no previous encounter with this
partner); selfcon (selfcontrol, measured out of 9, indicates the degree of selfcontrol that a
subject has when it comes to condom use, i.e., do they get carried away with the heat of the
moment, or do they exert control); Perceive (perceived risk, measured out of 6, indicates the
degree to which the person feels at risk from unprotected sex). Previous Research (Sacco,
Rickman, Thompson, Levine and Reed, in Aids Education and Prevention, 1993) has shown
that gender, relationship safety and perceived risk predict condom use. Carry out an
appropriate analysis to verify these previous findings, and to test whether Selfcontrol,
Previous Usage and Sexual Experience can predict any of the remaining variance in condom
use. (1) Interpret all important parts of the SPSS output; (2) How reliable is the final model?
(3) What are the probabilities that participants 12, 53 and 75 will used a condom?; and (4) a
female, who used a condom in her previous encounter with her new partner, scores 2 on all
variables except perceived risk (for which she scores 6). Use the model to estimate the
probability that she will use a condom in her next encounter.
The correct analysis was to run a hierarchical logistic regression entering perceive, safety
and gender in the first block and previous, selfcon and sexexp in a second. I used forced
entry on both blocks, but you could choose to run a Forward stepwise method on block 2
(either strategy is justified). For the variable previous I used an indicator contrast with ‘No
condom’ as the base category.
Block 0
The output of the logistic regression will be arranged in terms of the blocks that were specified.
In other words, SPSS will produce a regression model for the variables specified in block 1,
and then produce a second model that contains the variables from both blocks 1 and 2. The
results from block 1 are shown below. In this analysis we forced SPSS to enter perceive,
safety and gender into the regression model first. First, the output tells us that 100 cases
have been accepted, that the dependent variable has been coded 0 and 1 (because this
variable was coded as 0 and 1 in the data editor, these codings correspond exactly to the data
in SPSS). Dr. Andy Field Page 3 9/5/2003 Discovering Statistics Using SPSS: Chapter 6 Case Processing Summary
Unweighted Cases
Selected Cases a N
Included in Analysis
Missing Cases
Total 100
0
100
0
100 Unselected Cases
Total Percent
100.0
.0
100.0
.0
100.0 a. If weight is in effect, see classification table for the total
number of cases. Dependent Variable Encoding
Original Value
Unprotected
Condom Used Internal Value
0
1 Categorical Variables Codings Previous
Use with
Partner No Condom
Condom used
First Time with partner Parameter coding
(1)
(2)
.000
.000
1.000
.000
.000
1.000 Frequency
50
47
3 a,b
Classification Table Predicted Step 0 Observed
Condom Use Condom Use
Condom
Used
Unprotected
57
0
43
0 Unprotected
Condom Used Overall Percentage Percentage
Correct
100.0
.0
57.0 a. Constant is included in the model.
b. The cut value is .500 Block 1
The next part of the output tells us about block 1: as such it provides information about the
model after the variables perceive, safety and gender have been added. The first thing to
note is that the −2LL has dropped to 105.77, which is a change of 30.89 (which is the value
given by the model chisquare). This value tells us about the model as a whole whereas the
block tells us how the model has improved since the last block. The change in the amount of
information explained by the model is significant (χ2 (3) = 30.92, p < 0.0001) and so using
perceived risk, relationship safety and gender as predictors significantly improves our ability to
predict condom use. Finally, the classification table shows us that 74% of cases can be
correctly classified using these three predictors.
Omnibus Tests of Model Coefficients
Step 1 Step
Block
Model Chisquare
30.892
30.892
30.892 df
3
3
3 Sig.
.000
.000
.000 Model Summary
Step
1 Dr. Andy Field 2 Log
likelihood
105.770 Cox & Snell
R Square
.266 Page 4 Nagelkerke
R Square
.357 9/5/2003 Discovering Statistics Using SPSS: Chapter 6 a
Classification Table Predicted Step 1 Observed
Condom Use Condom Use
Condom
Unprotected
Used
45
12
14
29 Unprotected
Condom Used Overall Percentage Percentage
Correct
78.9
67.4
74.0 a. The cut value is .500 Hosmer and Lemeshow’s goodnessoffit test statistic tests the hypothesis that the observed
data are significantly different from the predicted values from the model. So, in effect, we
want a nonsignificant value for this test (because this would indicate that the model does not
differ significantly from the observed data). In this case (χ2 (8) = 9.70, p = 0.287) it is nonsignificant which is indicative of a model that is predicting the realworld data fairly well.
Hosmer and Lemeshow Test
Step
1 Chisquare
9.700 df
8 Sig.
.287 The part of the Output labelled Variables in the Equation then tells us the parameters of the
model for the first block. The significance values of the Wald statistics for each predictor
indicate that both perceived risk (Wald = 17.76, p < 0.0001) and relationship safety (Wald =
4.54, p < 0.05) significantly predict condom use. Gender, however, does not (Wald = 0.41, p
> 0.05).
Variables in the Equation Step
a
1 PERCEIVE
SAFETY
GENDER
Constant B
.940
.464
.317
2.476 S.E.
.223
.218
.496
.752 Wald
17.780
4.540
.407
10.851 df
1
1
1
1 Sig.
.000
.033
.523
.001 Exp(B)
2.560
.629
1.373
.084 95.0% C.I.for EXP(B)
Lower
Upper
1.654
3.964
.410
.963
.519
3.631 a. Variable(s) entered on step 1: PERCEIVE, SAFETY, GENDER. The values of exp β for perceived risk (exp β = 2.56, CI0.95 = 1.65, 3.96) indicate that if the
value of perceived risk goes up by one, then the odds of using a condom also increase
(because exp β is greater than 1). The confidence interval for this value ranges from 1.65 to
3.96 so we can be very confident that the value of exp β in the population lies somewhere
between these two values. What’s more, because both values are greater than 1 we can also
be confident that the relationship between perceived risk and condom use found in this sample
is true of the whole population. In short, as perceived risk increase by 1, people are just over
twice as likely to use a condom.
The values of exp β for relationship safety (exp β = 0.63, CI0.95 = 0.41, 0.96) indicate that if
the relationship safety increases by one point, then the odds of using a condom decrease
(because exp β is less than 1). The confidence interval for this value ranges from 0.41 to 0.96
so we can be very confident that the value of exp β in the population lies somewhere between
these two values. In addition, because both values are less than 1 we can be confident that
the relationship between relationship safety and condom use found in this sample would be
found in 95% of samples from the same population. In short, as relationship safety increases
by one unit, subjects are about 1.6 times less likely to use a condom.
The values of exp β for gender (exp β = 1.37, CI0.95 = 0.52, 3.63) indicate that as gender
changes from 0 (male) to 1 (female), then the odds of using a condom increase (because exp
β is greater than 1). However, the confidence interval for this value crosses 1 which limits the
generalizability of our findings because the value exp β in other samples (and hence the
population) could indicate either a positive (exp(B) > 1) or negative (exp(B) < 1) relationship.
Therefore, gender is not a reliable predictor of condom use. Dr. Andy Field Page 5 9/5/2003 Discovering Statistics Using SPSS: Chapter 6 A glance at the classification plot brings not such good news because a lot of cases are
clustered around the middle. This indicates that the model could be performing more
accurately (i.e. the classifications made by the model are not completely reliable).
Step number: 1
Observed Groups and Predicted Probabilities
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Predicted òòòòòòòòòòòòòòôòòòòòòòòòòòòòòôòòòòòòòòòòòòòòôòòòòòòòòòòòòòòò
Prob:
0
.25
.5
.75
1
Group: UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Predicted Probability is of Membership for Condom Used
The Cut Value is .50
Symbols: U  Unprotected
C  Condom Used
Each Symbol Represents 1 Case. Block 2
The output below shows what happens to the model when our new predictors are added
(previous use, selfcontrol and sexual experience). This part of the output describes block 2,
which is just the model described in block 1 but with a new predictors added. So, we begin
with the model that we had in block 1 and we then add previous, selfcon and sexexp to it.
The effect of adding these predictors to the model is to reduce the –2 loglikelihood to 87.971
(a reduction of 48.69 from the original model as shown in the model chisquare and an
additional reduction of 17.799 from the reduction caused by block 1 as shown by the block
statistics). This additional improvement of block 2 is significant (χ2 (4) = 17.80, p < 0.01)
which tells us that including these three new predictors in the model has significantly improved
our ability to predict condom use. The classification table tells us that the model is now
correctly classifying 78% of cases. Remember that in block 1 there were 74% correctly
classified and so an extra 4% of cases are now classified (not a great deal more—in fact,
examining the table shows us that only 4 extra cases have now been correctly classified).
Omnibus Tests of Model Coefficients
Step 1 Step
Block
Model Chisquare
17.799
17.799
48.692 df
4
4
7 Sig.
.001
.001
.000 Model Summary
Step
1 2 Log
likelihood
87.971 Cox & Snell
R Square
.385 Nagelkerke
R Square
.517 Hosmer and Lemeshow Test
Step
1 Dr. Andy Field Chisquare
9.186 df Page 6 8 Sig.
.327 9/5/2003 Discovering Statistics Using SPSS: Chapter 6 a
Classification Table Predicted Step 1 Observed
Condom Use Unprotected
Condom Used Condom Use
Condom
Unprotected
Used
47
10
12
31 Overall Percentage Percentage
Correct
82.5
72.1
78.0 a. The cut value is .500 The section labelled Variables in the Equation now contains all predictors. This part of the
output represents the details of the final model. The significance values of the Wald statistics
for each predictor indicate that both perceived risk (Wald = 16.04, p < 0.001)
and
relationship safety (Wald = 4.17, p < 0.05) still significantly predict condom use and, as in
block 1, Gender does not (Wald = 0.00, p > 0.05). We can now look at the new predictors to
see which of these has some predictive power.
Variables in the Equation Step
a
1 PERCEIVE
SAFETY
GENDER
SEXEXP
PREVIOUS
PREVIOUS(1)
PREVIOUS(2)
SELFCON
Constant B
.949
.482
.003
.180 S.E.
.237
.236
.573
.112 1.087
.017
.348
4.959 .552
1.400
.127
1.146 Wald
16.038
4.176
.000
2.614
4.032
3.879
.000
7.510
18.713 df
1
1
1
1
2
1
1
1
1 Sig.
.000
.041
.996
.106
.133
.049
.990
.006
.000 Exp(B)
2.583
.617
1.003
1.198
2.965
.983
1.416
.007 95.0% C.I.for EXP(B)
Lower
Upper
1.623
4.109
.389
.980
.326
3.081
.962
1.490
1.005
.063
1.104 8.747
15.287
1.815 a. Variable(s) entered on step 1: SEXEXP, PREVIOUS, SELFCON. Previous use has been split into two components (according to whatever contrasts were
specified for this variable). Looking at the very beginning of the output we are told the
parameter codings for Previous(1) and previous(2). You can tell by remembering the rule
from contrast coding in ANOVA which groups are being compared: that is, we compare groups
with zero codes against those with codes of 1. From the output we can see that Previous(1)
compares the condom used group against the other two, and Previous(2) compares the base
category of first time with partner against the other two categories. Therefore we can tell that
previous use is not a significant predictor of condom use when it is the first time with a partner
compared to when it is not the first time (Wald = 0.00, p < 0.05). However, when we compare
the condom used category to the other categories we find that using a condom on the previous
occasion does predict use on the current occasion (Wald = 3.88, p < 0.05).
Of the other new predictors we find that self control predicts condom use (Wald = 7.51, p <
0.01) but sexual experience does not (Wald = 2.61, p > 0.05).
The values of exp β for perceived risk (exp β = 2.58, CI0.95 = 1.62, 4.106) indicate that if the
value of perceived risk goes up by one, then the odds of using a condom also increase. What’s
more, because the confidence interval doesn’t cross 1 we can also be confident that the
relationship between perceived risk and condom use found in this sample is true of the whole
population. As perceived risk increase by 1, people are just over twice as likely to use a
condom.
The values of exp β for relationship safety (exp β = 0.62, CI0.95 = 0.39, 0.98) indicate that if
the relationship safety decreases by one point, then the odds of using a condom increase. The
confidence interval does not cross 1 so we can be confident that the relationship between
relationship safety and condom use found in this sample would be found in 95% of samples
from the same population. As relationship safety increases by one unit, subjects are about 1.6
times less likely to use a condom. Dr. Andy Field Page 7 9/5/2003 Discovering Statistics Using SPSS: Chapter 6
The values of exp β for gender (exp β = 1.00, CI0.95 = 0.33, 3.08) indicate that as gender
changes from 0 (male) to 1 (female), then the odds of using a condom do not change
(because exp β is equal to 1). The confidence interval crosses 1, therefore, gender is not a
reliable predictor of condom use.
The values of exp β for previous use (1) (exp β = 2.97, CI0.95 = 1.01, 8.75) indicate that if the
value of previous usage goes up by one (i.e. changes from not having used one or being the
first time to having used one), then the odds of using a condom also increase. What’s more,
because the confidence interval doesn’t cross 1 we can also be confident that this relationship
is true in the whole population. If someone used a condom on their previous encounter with
this partner (compared to if they didn’t use one, or if it is their first time) then they are three
times more likely to use a condom. For previous use (2) the value of exp β (exp β = 0.98,
CI0.95 = 0.06, 15.29) indicates that if the value of previous usage goes up by one (i.e. changes
from not having used one or having used one to it being their first time with this partner), then
the odds of using a condom do not change (because the value is very nearly equal to 1).
What’s more, because the confidence interval crosses 1 we can tell that this is not a reliable
predictor of condom use.
The value of exp β for selfcontrol (exp β = 1.42, CI0.95 = 1.10, 1.82) indicates that if selfcontrol increases by one point, then the odds of using a condom increase also. The confidence
interval does not cross 1 so we can be confident that the relationship between relationship
safety and condom use found in this sample would be found in 95% of samples from the same
population. As selfcontrol increases by one unit, subjects are about 1.4 times more likely to
use a condom.
The values of exp β for sexual experience (exp β = 1.20, CI0.95 = 0.95, 1.49) indicate that as
sexual experience increases by one unit, then the odds of using a condom increase slightly.
However, the confidence interval crosses 1, therefore, sexual experience is not a reliable
predictor of condom use.
A glance at the classification plot brings good news because a lot of cases that were clustered
in the middle are now spread towards the edges. Therefore, overall this new model is more
accurately classifying cases compared to block 1.
Step number: 1
Observed Groups and Predicted Probabilities
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Prob:
0
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.75
1
Group: UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Predicted Probability is of Membership for Condom Used
The Cut Value is .50
Symbols: U  Unprotected
C  Condom Used
Each Symbol Represents 1 Case. Testing for Multicollinearity
Multicollinearity can affect the parameters of a regression model. Logistic regression is equally
as prone to the biasing effect of collinearity and it is essential to test for collinearity following a Dr. Andy Field Page 8 9/5/2003 Discovering Statistics Using SPSS: Chapter 6
logistic regression analysis (see the main book for details of how to do this). The results of the
analysis are shown below. From the first table we can see that the tolerance values for all
variables are all close to 1 and are much larger than the cutoff point of 0.1 below which
Menard (1995) suggests indicates a serious collinearity problem. Myers (1990) also suggests
that a VIF value greater than 10 is cause for concern and in these data the values are all less
than this criterion.
The output below also shows a table labelled Collinearity Diagnostics. In this table, we are
given the eigenvalues of the scaled, uncentred crossproducts matrix, the condition index and
the variance proportions for each predictor. If any of the eigenvalues in this table are much
larger than others then the uncentred crossproducts matrix is said to be illconditioned, which
means that the solutions of the regression parameters can be greatly affected by small
changes in the predictors or outcome. In plain English, these values give us some idea as to
how accurate our regression model is: if the eigenvalues are fairly similar then the derived
model is likely to be unchanged by small changes in the measured variables. The condition
indexes are another way of expressing these eigenvalues and represent the square root of the
ratio of the largest eigenvalue to the eigenvalue of interest (so, for the dimension with the
largest eigenvalue, the condition index will always be 1). For these data the condition indexes
are all relatively similar showing that a problem is unlikely to exist.
Coefficientsa Model
1 2 Perceived Risk
Relationship Safety
GENDER
Perceived Risk
Relationship Safety
GENDER
Previous Use with Partner
SelfControl
Sexual experience Collinearity Statistics
Tolerance
VIF
.849
1.178
.802
1.247
.910
1.098
.740
1.350
.796
1.256
.885
1.130
.964
1.037
.872
1.147
.929
1.076 a. Dependent Variable: Condom Use a
Collinearity Diagnostics Model
1 2 Dimension
1
2
3
4
1
2
3
4
5
6
7 Eigenvalue
3.137
.593
.173
9.728E02
5.170
.632
.460
.303
.235
.135
6.510E02 Condition
Index
1.000
2.300
4.260
5.679
1.000
2.860
3.352
4.129
4.686
6.198
8.911 (Constant)
.01
.00
.01
.98
.00
.00
.00
.00
.00
.01
.98 Perceived
Risk
.02
.02
.55
.40
.01
.02
.03
.07
.04
.61
.23 Variance Proportions
Previous
Use with
Partner
GENDER
.03
.55
.08
.35
.01
.01
.43
.10
.01
.80
.24
.00
.17
.05
.00
.00
.14
.03 Relationship
Safety
.02
.10
.76
.13
.01
.06
.10
.01
.34
.40
.08 SelfControl Sexual
experience .01
.00
.00
.00
.50
.47
.03 .01
.02
.00
.60
.00
.06
.31 a. Dependent Variable: Condom Use The final step in analysing this table is to look at the variance proportions. The variance of
each regression coefficient can be broken down across the eigenvalues and the variance
proportions tell us the proportion of the variance of each predictor’s regression coefficient that
is attributed to each eigenvalue. These proportions can be converted to percentages by
multiplying them by 100 (to make them more easily understood). In terms of collinearity, we
are looking for predictors that have high proportions on the same small eigenvalue, because
this would indicate that the variances of their regression coefficients are dependent (see Field,
2004). Again, no variables appear to have similarly high variance proportions for the same
dimensions. The result of this analysis is pretty clear cut: there is no problem of collinearity in
these data.
Residuals
Residuals should be checked for influential cases and outliers. As a brief guide, the output lists
cases with standardized residuals greater than 2. In a sample of 100, we would expect around
510% of cases to have standardized residuals with absolute values greater than this. For Dr. Andy Field Page 9 9/5/2003 Discovering Statistics Using SPSS: Chapter 6
these data we have only 4 cases and only 1 of these has an absolute value greater than 3.
Therefore, we can be fairly sure that there are no outliers.
Casewise Listb Case
41
53
58
83 Observed
Condom Use
U**
U**
C**
C** Selected
a
Status
S
S
S
S Predicted
.891
.916
.142
.150 Predicted
Group
C
C
U
U Temporary Variable
Resid
ZResid
.891
2.855
.916
3.294
.858
2.455
.850
2.380 a. S = Selected, U = Unselected cases, and ** = Misclassified cases.
b. Cases with studentized residuals greater than 2.000 are listed. Question 3
The values predicted for these cases will depend on exactly how you ran the analysis (and the
paremeter coding used on the variable ‘previous’). Therefore, your answers might differ
slightly from mine.
Case Summariesa
Case
Number
12
53
75 12
53
75 Predicted
Value
.49437
.88529
.37137 Predicted Group
Unprotected
Condom Used
Unprotected a. Limited to first 100 cases. Question 4
Step 1: Logistic Regression Equation: 1
P(Y ) = 1+ e −Z Where Z = β 0 + β1 X 1 + β 2 X 2 + ... + β n X n
Step 2: Use the values of β from the SPSS output (final model), and the values of X for each
variable (from question) to construct the following table:
Variable βi Xi β i Xi Gender 0.0027 1 0.0027 Safety 0.4823 2 0.9646 Sexexp 0.1804 2 0.3608 Previous (1) 1.0870 1 1.0870 Previous (2) .0167 0 0 Selfcon 0.3476 2 0.6952 Perceive 0.9489 6 5.6934 Step 3: Place the values of βi Xi into the equation for z (remembering to include the constant). Dr. Andy Field Page 10 9/5/2003 Discovering Statistics Using SPSS: Chapter 6 z = −4.6009 + 0.0027 − 0.9646 + 0.3608 + 1.0870 + 0 + 0.6952 + 5.6934
= 2.2736 Step 4: Replace this value of z into the logistic regression equation:
1
P (Y ) = 1+ e − Z = 1+ e −12.2736
1
= 1+ 0.10 = 0.9090
Therefore, there is a 91% chance that she will use a condom on her next encounter. Dr. Andy Field Page 11 9/5/2003 ...
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