Answers (Chapter 6) - Discovering Statistics Using SPSS:...

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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 Chi-square 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 Chi-square 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 (self-control, measured out of 9, indicates the degree of self-control 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 Self-control, 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 chi-square). 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 Chi-square 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 goodness-of-fit 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 non-significant 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 real-world data fairly well. Hosmer and Lemeshow Test Step 1 Chi-square 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 16 ô ô ó ó ó ó F ó ó R 12 ô C ô E ó C C ó Q ó C C ó U ó C C ó E 8 ô C C ô N ó C C C ó C ó U C C C C ó Y ó UC U U U C C C C ó 4 ô UU U U U U C U C C ô ó U UU C U U C C U U U U C C ó óUUUUU UU C U U U U U U U U C C C C ó óUUUUU UU U U U U U CU U CU U U U UC CCC UCCUC ó 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, self-control 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 log-likelihood to 87.971 (a reduction of 48.69 from the original model as shown in the model chi-square 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 Chi-square 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 Chi-square 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 self-control (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 self-control 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 16 ô ô ó ó ó ó F ó ó R 12 ô ô E ó ó Q ó ó U ó U ó E 8 ô U ô N ó U ó C ó U ó Y ó U C ó 4 ô U U CC ô ó U U UU U UU U C C C C C C ó óUUUUUUU CU UU U U CC C U C C C CC CCCC ó óUUUUUUU CCUUUU U UUUUCUU CUUCUU C CUUUUCCCU C CCCCCUUCCCCCó 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. 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 cut-off 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 cross-products 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 cross-products matrix is said to be ill-conditioned, 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 Self-Control 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 9.728E-02 5.170 .632 .460 .303 .235 .135 6.510E-02 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 Self-Control 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 5-10% 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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