Statistical Package for the Social Sciences Program - Assignment Example

Part I: Fill in the blanks: Of the total of 98 prisoners in this study, 22.4% (22) were female. Mean age of the sample was 36.41 yrs. About half (52) of the prisoners were in medium-level security, about a quarter (28) in high-level security, and just under a fifth (18) in low-level security. 48% (47) were victims of violence within the prison. Overall, 30 (30.61%) of the 98 subjects were determined to be clinically depressed. At the bivariate level of analysis, the prevalence of depression was significantly higher for males (38.2%) than females (4.5%) (Fisher’s exact test, p = 0.002). The prevalence of depression was lower (16.2%) in those detained in low-security environments compared to medium with the highest prevalence of depression (36.5%), or high security (28.6%) environments. However, this difference did not attain statistical significance (Likelihood ratio 22 = 2.7, p = 0.255). Prevalence of depression was significantly higher for prisoners who had experienced violence during their detention. 3.9 percent of those not experiencing violence were determined to be clinically depressed compared with 59.6% of prisoners who had experienced violence (Fisher’s exact test, p < 0.001). Complete the Table: Table 1. Bi-variate relationships between clinically determined depression and demographic and prison environment variables in a sample of 98 prisoners, Brisbane, 2002. Number % Crude ORa Subjects depressed Ageb 98 30.6 1.05 Gender female 22 4.5 .05 referent male 76 38.2 .62 Security low 18 16.7 .20 referent medium 52 36.5 .58 high 28 28.6 .40 Violence no 51 3.9 .04 referent yes 47 59.6 1.47 a OR, odds ratio of depression b Relative odds of depression for each additional year of age (ie relative odds compared to preceding year) Relative to females, the odds of depression in males was 13 times higher. Relative to those with no experience of violence, the odds of depression was over 36-fold higher among those who had experienced violence in the prison. Although the association was statistically significant, the confidence interval was wide, indicating imprecision in this estimate. Part II Question 1: Hypothesis: H0: There is no improvement in the range of movement over time. H1: There is a significant improvement in the range of movement over time. Methodology: Method Used: To test the null hypothesis Analysis of Variance (ANOVA) method is used. Variable Type: For using ANOVA method two variables namely Moves and Range of Movement are used. Moves: It reflects the time period over which the data is collected it takes three values namely MOVE 1, MOVE 2 and MOVE 3. This variable is used as independent variable or factor for analysis. MOVE 1: Baseline MOVE 2: One month after the surgery MOVE 3: 12 months after the surgery Range of movement: For the dependent variable the range of movement data over the time period is used. Method: ANOVA contrast is used to determine that differences exist among the means. Once it is determined post hoc range tests can be used to determine which means differ. Here we have used a conservative post hoc test, The Tukey Test. Results: The tables obtained from the SPSS software is given as follows: Descriptives Range of movement N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Lower Bound Upper Bound MOVE 1 96 44.33 16.147 1.648 41.06 47.61 MOVE 2 96 75.75 16.507 1.685 72.41 79.09 MOVE 3 96 122.78 16.523 1.686 119.43 126.13 Total 288 80.95 36.190 2.133 76.76 85.15 For each dependent variable (Range of movement), the Descriptives table gives the sample size, mean, standard deviation, minimum, maximum, standard error, and confidence interval for each level of the independent variable (Moves). MOVE 1 has a mean value of 44 degree while MOVE 2 has mean value of 75 and MOVE 3 has a mean value of 123 degree. Test of Homogeneity of Variances Range of movement Levene Statistic df1 df2 Sig. .610 2 285 .544 The test of Homogeneity of variance uses null hypothesis: There is no difference in the variance of MOVE 1, MOVE 2 and MOVE 3. Insignificant value of p (.544) suggests that the null hypothesis is true and homogeneity of variance assumption is met. ANOVA Range of movement Sum of Squares df Mean Square F Sig. Between Groups 299296.674 2 149648.337 556.846 .000 Within Groups 76591.740 285 268.743 Total 375888.413 287 The ANOVA table shows the result of F-test (p=.000), which can be interpreted as, between MOVES analysis of variance reveals a significant effect of time on the range of movement. That means over the time the range of movement has changed. Hence we reject the null hypothesis and conclude that there is a significant improvement in the range of movement over time. Multiple Comparisons Range of movement Tukey HSD (I) Moves (J) Moves Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound MOVE 1 MOVE 2 -31.417* 2.366 .000 -36.99 -25.84 MOVE 3 -78.448* 2.366 .000 -84.02 -72.87 MOVE 2 MOVE 1 31.417* 2.366 .000 25.84 36.99 MOVE 3 -47.031* 2.366 .000 -52.61 -41.46 MOVE 3 MOVE 1 78.448* 2.366 .000 72.87 84.02 MOVE 2 47.031* 2.366 .000 41.46 52.61 *. The mean difference is significant at the 0.05 level. Now once we know that there is a significant difference in range of movement we will use post hoc tests for multiple comparisons. The above table shows that the means for all the level of independent variable is significantly different from others. Question 2: Hypothesis: H0: There is no relationship between Range of Movement at baseline and patients’ age. H1: There is a significant relationship between Range of Movement at baseline and patients’ age. Methodology: Method Used: To test the null hypothesis the linear regression method is used. Variable Type: For regression analysis two variables namely Age and Range of movement at baseline are used. Age: Age is taken as independent variable it reflects the patients’ age. Range of movement: Range of movement at baseline is used as dependent variable. Method: For variable selection Enter method is used in which all variables in a block are entered in a single step. For normality test the Normal P Chart is used. The graph below shows that the data is satisfying the normality test and hence the linear regression method is justified in this case. Results: The tables of results obtained from SPSS software are presented below: Descriptive Statistics Mean Std. Deviation N Range of movement Prior to surgery_baseline (Degrees) 44.7660 16.02245 94 Age in completed years 23.2234 4.31839 94 The above table shows that the mean of Range of movement in baseline case is 44.76 while the mean age of the participants is 23.33 years. Correlations Range of movement Prior to surgery_baseline (Degrees) Age in completed years Pearson Correlation Range of movement Prior to surgery_baseline (Degrees) 1.000 .096 Age in completed years .096 1.000 Sig. (1-tailed) Range of movement Prior to surgery_baseline (Degrees) . .179 Age in completed years .179 . N Range of movement Prior to surgery_baseline (Degrees) 94 94 Age in completed years 94 94 The Correlation table shows that there is a very minimal correlation (.096) between the dependent and independent variables taken in the case. At 5% significance level, we accept the null hypothesis that there is no correlation between range of movement in baseline case and the age of the participants. Model Summaryb Model R R Square Adjusted R Square Std. Error of the Estimate 1 .096a .009 -.002 16.03509 a. Predictors: (Constant), Age in completed years b. Dependent Variable: Range of movement Prior to surgery_baseline (Degrees) By looking at the Model Summary table, we can analyze that only 9% of the variance in the Change in Movement is explained by age. This analysis is explained by R square measure, which shows how much percentage of variance in dependent variable is explained by independent variable. ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 219.444 1 219.444 .853 .358a Residual 23655.407 92 257.124 Total 23874.851 93 a. Predictors: (Constant), Age in completed years b. Dependent Variable: Range of movement Prior to surgery_baseline (Degrees) The ANOVA table also justifies the above result. In ANOVA the null hypothesis that is considered is “The value of R Square measure is zero”. Looking at the F value for the analysis we accept the null hypothesis and hence we conclude that age does not explain the variance in the Change in Movement in baseline case for the participants. Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta (Constant) 36.505 9.094 4.014 .000 Age in completed years .356 .385 .096 .924 .358 a. Dependent Variable: Range of movement Prior to surgery_baseline (Degrees) The coefficients table analyzes the significance of coefficients of regression. The coefficient of regression shows the extent of relationship between dependent and independent variables. That means it shows, what is the change in dependent variable for a unit change in independent variable? The un-standardized coefficient is .356 and standardized value is .096. The standardized value is calculated considering the standardized conditions i.e. the regression line passes through origin. The t-test suggests the non-significance of the regression coefficient in this case. In this case also we will accept the null hypothesis that is “the value of regression coefficient is zero”. Question 3: Hypothesis: For Multiple Logistic Regression: H0: At baseline, Severity of Injury does not depend on Gender and Dominant Side. H1: At baseline, Severity of Injury does significantly depend on Gender and Dominant Side. For Simple Logistic Regression: H0: At baseline, Severity of Injury does not depend on Gender. H1: At baseline, Severity of Injury does significantly depend on Gender. Methodology: Method Used: In this case for analyzing the data logistic regression method is used. It is similar to a linear regression model but is suited to models where the dependent variable is dichotomous. Logistic regression coefficients can be used to estimate odds ratios for each of the independent variables in the model. Variable Type: Three variables namely severity of injury, gender and domside are used for the logistic regression. Severity of Injury: It is used as dependent variable which reflects the severity of injury at baseline. Gender and Domside: These two variables are used as categorical independent variables. Domside reflects the dominant side of the patients. In the first case both are used as independent variable while in the second case only Gender is used as independent variable. Method: For variable entry the Enter method is used. For testing the goodness of fit Hosmer-Lemeshow method, which uses chi square test, is followed. Results: Multiple Logistic Regression Analysis: The tables obtained from the SPSS software are displayed below, followed by their analysis: Omnibus Tests of Model Coefficients Chi-square df Sig. Step 1 Step 13.191 2 .001 Block 13.191 2 .001 Model 13.191 2 .001 Since we chose the Method Enter, SPSS starts by inserting only a constant in the model initially. On Step 1, SPSS enters all the variables in the model (see table Omnibus Tests of Model Coefficients). The coefficients here give us a measure of how well the model fits. We must look mostly at the Model coefficient. It is analogous to the multivariate F test for linear regression. The null hypothesis states that information about the independent variables does not allow us to make better prediction of the dependent variable. Therefore we would want that this chi-squared value is significant (as in this case). Model Summary Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square 1 73.317a .128 .216 a. Estimation terminated at iteration number 6 because parameter estimates changed by less than .001. Hosmer and Lemeshow Test Step Chi-square df Sig. 1 3.361 2 .186 Contingency Table for Hosmer and Lemeshow Test Indicator variable for severe severity = Not severe Indicator variable for severe severity = Severe severity Total Observed Expected Observed Expected Step 1 1 20 21.150 2 .850 22 2 28 26.850 0 1.150 28 3 18 16.850 6 7.150 24 4 14 15.150 8 6.850 22 The goodness of fit test can be analyzed using the tables Model Summary and Hosmer and Lemenshow Test. The Goodness-of-Fit Chi-Square is the log likelihood multiplied by –2. Because the log-likelihood is negative, the Goodness-of-Fit Chi Square is positive, and larger values indicate worse prediction of the dependent variable. Therefore we are after a non-significant p value (=0.186). Since Goodness-of-Fit Chi square (73.317) is NOT significant, no heterogeneity factor is used in the calculation of confidence limits. Variables in the Equation B S.E. Wald df Sig. Exp(B) Step 1a gender(1) -2.357 .791 8.868 1 .003 .095 domside(1) -.064 .587 .012 1 .914 .938 Constant -.794 .441 3.242 1 .072 .452 a. Variable(s) entered on step 1: gender, domside. The previous table Variables in the Equation produced by SPSS is the one containing the variable coefficients. The Wald Chi-square test in non significant for domside (p=.914) while it is significant for gender (p=.003) thus signifying that, gender is a good predictor of the dependent variable Severity of Injury. The estimated logistic regression coefficient for gender is -2.357 and the exponential of this value is .0947. This indicates that for a change in gender, the odds in favor of severity of injury are estimated to be increased by a multiplicative factor of .0947. Classification Tablea Observed Predicted Indicator variable for severe severity Percentage Correct Not severe Severe severity Step 1 Indicator variable for severe severity Not severe 80 0 100.0 Severe severity 16 0 .0 Overall Percentage 83.3 a. The cut value is .500 To aid in interpretation, a classification table can be constructed by predicting the severity of injury of each participant based on whether or not the odds for survival are greater or less than 1.0, and comparing these predictions to the actual outcome for each participant. As shown in Classification Table the percents of correct decisions are 100 for participants whose injury is not severe, 0 for participants who have severe severity, and 83 overall. Simple Logistic Regression between Severity of Injury and Gender: In this case only one independent variable is used for analysis. The whole analysis part goes same as in the previous case except that here only one independent variable is considered and that is Gender. However, the results are no very much different. The last table summarizes that Wald Chi-square value for gender is significant at p=.003. And its value is -2.351 which is very close to the value that we got in previous case. Hence, we reject the null hypothesis and conclude that the severity of injury depend on gender of patient. Omnibus Tests of Model Coefficients Chi-square df Sig. Step 1 Step 13.179 1 .000 Block 13.179 1 .000 Model 13.179 1 .000 Model Summary Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square 1 73.329a .128 .216 a. Estimation terminated at iteration number 6 because parameter estimates changed by less than .001. Classification Tablea Observed Predicted Indicator variable for severe severity Percentage Correct Not severe Severe severity Step 1 Indicator variable for severe severity Not severe 80 0 100.0 Severe severity 16 0 .0 Overall Percentage 83.3 a. The cut value is .500 Variables in the Equation B S.E. Wald df Sig. Exp(B) Step 1a gender(1) -2.351 .790 8.867 1 .003 .095 Constant -.827 .320 6.656 1 .010 .437 a. Variable(s) entered on step 1: gender. On comparing both the case it is evident that domside (Dominant side) does not affect the severity of injury and there is no confounding of the severity of injury and gender relationship by the variable domiside. Summary: From the first question it is clear that the range of movement has changed significantly over the time and the descriptive analysis shows that the range of movement has increased from 44 degree to 122 degree over the time period. And significant improvement of range of movement suggests that surgery is an effective way to treat the injuries. The results of question 2 show that the range of movement in baseline case does not depend upon the age of the patients. Finally the results from the question 3 show that severity of injury depends upon the gender, however it does not depend upon the dominant side. Part III: Question 1: Hypothesis: H0: There is no difference in premature born infants group and full term born infants group in terms of their mother’s education, income, marital status and depression level. H1: There is a significant difference in premature born infants group and full term born infants group in terms of their mother’s education, income, marital status and depression level. Methodology: Method Used: For analysis the Independent Sample for t-test is used. Variables Used: Mother’s education, income, marital status and depression level are considered as testing variables while infants born preterm and full term are used as grouping variable. Significance level: The test is done at 5% significance level. Results: The results and tables obtained from the SPSS software is as follows: Group Statistics Id N Mean Std. Deviation Std. Error Mean Marital status preterm infants 74 1.1892 .39433 .04584 full-term infants 74 1.2432 .43197 .05022 Mother's education level preterm infants 74 2.3784 .91715 .10662 full-term infants 74 2.8919 1.02793 .11949 Family income per annual preterm infants 74 1.6486 .69109 .08034 full-term infants 74 2.4595 .68625 .07977 Depression level preterm infants 74 1.2838 .45391 .05277 full-term infants 74 1.8919 .31264 .03634 Independent Samples Test     Levene's Test for Equality of Variances t-test for Equality of Means     F Sig. t df Sig. (2-tailed)     Marital status Equal variances assumed 2.549 0.113 -0.795 146 0.428 Equal variances not assumed     -0.795 144.803 0.428 Mother's education level Equal variances assumed 3.446 0.065 -3.207 146 0.002 Equal variances not assumed     -3.207 144.142 0.002 Family income per annual Equal variances assumed 0 1 -7.162 146 0 Equal variances not assumed     -7.162 145.993 0 Depression level Equal variances assumed 34.271 0 -9.491 146 0 Equal variances not assumed     -9.491 129.538 0 The first table presents the groups statistics for each test variable. While the second table presents the independent sample test for each test variable. Looking at the second table its clear that for Marital status the t value is not significant while for Mother’s education level, family income pa and Depression level the t- values are significant for equality of means for both the groups categorized by whether the infant was born preterm or full term. Thus we can say that there is no difference in the means of marital status of the infant whether they are preterm or full term born. In both the cases the marital status is close to married. The demography of mother’s who gave preterm birth is different in terms of their education level, family income and depression level. The depression and income factors are the most discriminating factors between both the groups. Almost 50% (35) mothers belonged to the less than 30k income level who gave preterm birth while in other case only 7 belonged to this income level. Out of 74 preterm born infant’s mother 53 were suffering from depression while only 9 in other case where infants were born full term. Question 2: Hypothesis: H0: There is no difference between premature born children and full-term infants in motor and mental scores H1: There is a significant difference between premature born children and full-term infants in motor and mental scores Methodology: This question checks whether there is any difference between the premature born children and full-term infants in motor and mental scores. For analysis the Independent sample for t- test is used as in the previous case. Variables Used: Infant’s motor and mental scores are considered as testing variables while infants born preterm and full term are used as grouping variable. Significance level: The test is done at 5% significance level. Results: The results and tables obtained from the SPSS software is as follows: Group Statistics id N Mean Std. Deviation Std. Error Mean Motor score of Development Quotient preterm infants 74 93.7973 10.85645 1.26204 full-term infants 74 1.0001E2 10.02257 1.16510 Mental IQ score of Development Quotient preterm infants 74 93.4730 9.39283 1.09189 full-term infants 74 1.1159E2 6.48902 .75433 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Motor score of Development Quotient Equal variances assumed .002 .962 -3.619 146 .000 Equal variances not assumed -3.619 145.077 .000 Mental IQ score of Development Quotient Equal variances assumed 9.053 .003 -13.655 146 .000 Equal variances not assumed -13.655 129.754 .000 The first table shows the group statistics about the test variables. It shows that the mean Motor score of Development Quotient is less in preterm infants (93.79) as comparison to full-term infants (100.01). Similarly mean of the Mental IQ score of Development Quotient is less in preterm infants (93.47) as comparison to full term infants (111.59). The test to check the significance of the difference in motor and mental score in preterm and full term infants is shown in second table. It shows that there is a significant difference in the mean of the motor score and mental score for preterm and full term infants (p=.000). Summary: From the results that we obtained it is clear that premature born infants are different from the full term infants in terms of mother’s education, income and depression level. However, there is no difference in the marital status of mothers of both the groups. The premature born infants are also different in terms of motor and mental scores. They score less in both the cases as comparison to full term infants. Hence we conclude that these above factors might play a role in learning and behaviour of the prematurely born infants when they reach to the schools. 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