Analysis of Statistical Methods - Case Study Example

RUNNING HEAD: Statistics Simulation STATISTICAL ANALYSIS SIMULATION PAPER Karen Butler,M.D. Northcentral Prof. McNellie September 20, 2008 Statistical Analysis Simulation Paper Summary of Proposed Statistical Methods The following statistical methods are being suggested in the concept paper (Butler, 2008a) written for the proposed dissertation : (1) descriptive statistics in the form of frequency (and percentage) distributions, mean and standard deviation; and (2) inferential statistics in the form of the t-test, one way analysis of variance and correlation analysis. Frequency and percentage distributions will be used to describe the following set of data : (1) profile of juvenile offenders in terms of the variables age, gender, ethnicity, religion, past and present offenses, frequency of commission of offenses, history of drug use and results of the urinalysis; (2) comparison of the rate of recidivism among juvenile offenders who use drugs and those who do not use drugs (3) prevalence of usage of mind altering drugs, as well as the methods by which these drugs are administered and (4) rates of recidivism among juvenile recidivists based on the drugs they are using/abusing. The mean and standard deviation of the age of the research participants will also be calculated to see how close the ages are to the center of the distribution, and also the length of scatter from the center. Significant differences in the levels of recidivism of the juvenile offenders when they are grouped according to their gender, drug use profile [whether with or without drug use experience] and results of the urinalysis [positive or negative] will be verified using the t-test. Significant differences in the rates of recidivism of the juvenile offenders when they are grouped according to their other profile characteristics – age, ethnicity and religion will be confirmed using a bi-directional one-way analysis of variance. Applicable post hoc analysis or multiple comparisons test(s) like the Bonferroni test or the least significant difference (LSD) test will be utilized to discover which sub-groups among the aforementioned variables exhibited significant differences. Correlation analysis, specifically bivariate analysis will be adopted to ascertain whether the use and/or abuse of mind altering drugs have an effect on the level of recidivism. Corollary to the use of the t-test and the analysis of variance (ANOVA) and Levene’s test of normality which is built in for the t-test and ANOVA in SPSS , a hypothesized level of significance of 0.05 (α = 0.05) will be used (Butler, 2008b). Simulation Data The data matrix used in the statistical simulation is shown in Figure 1. This data matrix, which measures 17 columns by 50 rows, is prepared by making use of coded data following the parameters specified in the coding guide. Simulation data were produced using the random number generator function of Microsoft Excel XP. The syntax command of the random number generator in Excel used was “=randbetween(bottom,top)”. The coding guide is exhibited in Appendix A. The simulation consist of 50 sets of data (n = 50). The 17 columns contains most of the variables considered in the study, namely : column 1 – gender; column 2 – age; column 3 - age level (grouped); column 4 – ethnicity; column 5 – religion; column 6 - Factor 1 (time elapsed between release from prison and commission of the next crime); column 7 - Factor 2 (frequency of previous arrests); column 8 - Factor 3 (age at first arrest); column 9 - Factor 4 (criminal versatility); column 10 - level of recidivism; column 11 - Factor A (age of initiation); column 12 - Factor B (use of multiple drugs); column 13 - Factor C (frequency of commission of crime to sustain drug use); column 14 - Factor D (amount spent on drugs per month); column 15 - Factor D (dual abuse risk); column 16 - extent of drug use; and column 17 - drug use profile (whether user or non-user). Figure 1. Data matrix The Statistical Software : SPSS for Windows SPSS for Windows Version 11.0.0 (2001) is the software chosen by this researcher to facilitate statistical analysis of both the simulation data in this paper and the actual data which will be gathered from the proposed study. SPSS is the acronym for Statistical Package for the Social Sciences. It is now regarded as among the most widely used computer programs to aid analysis of statistical data in the social sciences. Aside from descriptive statistics, bivariate statistics, regression analysis and factor analysis, the base SPSS software can also handle data management and data documentation (Boslaugh, 2005). Statistical Analysis and Interpretation Under the statistical analysis section, only the inferential statistics will be analyzed and interpreted. The rationale for this is that the inferential part needs considerable interpretation. Cropped screen-shots of the actual SPSS output tables will be used in the illustration of the statistical analysis. Figure 2 presents the result of the t-test performed on the level of recidivism when the respondents are arranged in terms of their gender. Figure 2. Gender and level of recidivism From the lower table in Figure 2, Levene’s test, which is automatically displayed when the t-test is used in SPSS revealed that the simulation data are normally distributed (Pallant, 2005). Hence, the results of the t-test when equal variances are assumed are applicable for the data set. With a p-value (displayed as Sig. in SPSS) = 0.050, findings revealed that there are significant differences in the levels of recidivism of the detainees when they are arranged according to gender. The significant differences were observed by virtue of the p-value (0.05) being equal to the significance level of the test (α = 0.05). The basic rule in this case is that, when the p-value is greater than α (0.05), there are no significant differences between the means of the variables being compared. However, when the p-value is equal or less than α (0.05), there are significant differences between the means of the variables. The findings from Figure 2 imply that the mean of the level of recidivism of the male detainees (4.041 ± 0.9645) is significantly higher than those of the female detainees (3.530 ± 0.8048). Presented in Figure 3 is the result of the t-test performed on the level of recidivism when the respondents are arranged in terms of their history of drug use (whether or not they have experience on use of illegal drugs). Figure 3. Drug use profile and level of recidivism As indicated in the lower table in Figure 3, the p-value of 0.125 (which is higher than 0.05) in Levene’s test showed that the simulation data are normally distributed. Results of the t-test with equal variances assumed are applicable for the data set. With a p-value (displayed as Sig. in SPSS) equal to 0.333, which is greater than α = 0.05, findings revealed that there are no significant differences in the levels of recidivism of the detainees when they are arranged according to their history of drug use. This means that recidivism between detainees who have experienced using drugs and those do not have prior experience in drug use have similar levels. Figures 4 presents the result of the t-test performed on the level of recidivism when the respondents are arranged in terms of the urinalysis results. Figure 4. Result of urinalysis and level of recidivism It may be gleaned in the lower table in Figure 4, the p-value of 0.179 (which is higher than 0.05) in Levene’s test showed that the simulation data are normally distributed. Results of the t-test with equal variances assumed are applicable for the data set. With a p-value (displayed as Sig. in SPSS) of 0.730 which is greater than α = 0.05, findings revealed that there are no significant differences in the levels of recidivism of the detainees when they are arranged according to the results of their urinalysis. The result indicates that the level of recidivism between those who have tested positive in the urinalysis are fairly the same as those who tested negative. Figures 5, 6 and 7 present the results of the ANOVA performed on the level of recidivism when the respondents are arranged in terms of age, ethnicity and religion. Figure 5. Age and level of recidivism As may be observed from the second table in Figure 5, the p-value of 0.516 (which is higher than 0.05) in Levene’s test means that the simulation data are normally distributed. Results of the ANOVA with an F-statistic of 0.475 and a p-value (displayed as Sig. in SPSS) of 0.823 (which is greater than α = 0.05), revealed that there are no significant differences in the levels of recidivism of the detainees when they are arranged according to their ages. These result signify that no specific age level had higher levels of recidivism that the other age levels. Figure 6. Ethnicity and level of recidivism As presented in the second table in Figure 6, the p-value of 0.526 (which is higher than 0.05) in Levene’s test indicates that the simulation data are normally distributed. Results of the ANOVA with an F-statistic of 0.844 and a p-value (displayed as Sig. in SPSS) of 0.477 (which is greater than α = 0.05), revealed that there are no significant differences in the levels of recidivism of the detainees when they are arranged according to their ethnicity. These findings point out that no specific group of detainees clustered by ethnicity had higher levels of recidivism that the other groups. Figure 7. Religion and level of recidivism Shown in the second table in Figure 7,is the p-value of 0.526 (which is higher than 0.05) in Levene’s test indicating that the simulation data are normally distributed. Results of the ANOVA with an F-statistic of 0.655 and a p-value (displayed as Sig. in SPSS) of 0.584 (which is greater than α = 0.05), disclosed that there are no significant differences in the levels of recidivism of the detainees when they are arranged according to their ethnicity. These findings point out that no specific group of detainees clustered by religion had higher levels of recidivism that the other groups. Figure 8 presents the results of the correlation analysis carried out to ascertain whether there are significant associations between the extent of drug use of the detainees and their level of recidivism. Figure 7. Correlation between extent of drug use and level of recidivism It may be noted from the above figure that the Pearson coefficient of correlation was computed as -0.115, which connotes indirect or negative and almost negligible relationship which is not even statistically significant, between the extent of drug use and the level of recidivism. These findings imply that the lesser the extent of the drug usage the higher the detainees tend to recidivate, and conversely, the higher the extent of drug use, the lesser is the propensity of the detainees to recidivate. References Boslaugh, S. (2005). An Intermediate Guide to SPSS Programming: Using Syntax for Data Management. Thousand Oaks, CA: Sage Publications. Butler, K. (2008a). The Effects of Mind Altering Drugs on Juvenile Recidivism: A Concept Paper. Unpublished Manuscript. Butler, K. (2008b). Statistics Paper. Unpublished Manuscript. Butler, K. (2008c). Instrumentation Paper. Unpublished Manuscript. Pallant, J. F. (2007). SPSS Survival Manual: A Step by Step Guide to Data Analysis Using SPSS (3rd Ed). St. Leonards, NSW: Allen & Unwin. SPSS for Windows. (2001). Statistical Package for the Social Sciences (Version 11.0.0) [Software]. Chicago, IL: SPSS Inc. Appendix A: Coding Guide The following codes were used in the heading of the Data Matrix : Gen = Gender FacA = Factor A Age = Age FacB = Factor B Lev = Age Level FacC = Factor C Eth = Ethnicity FacD = Factor D Rel = Religion FacE = Factor E Fac1 = Factor 1 Ext = Extent of Drug Use Fac2 = Factor 2 Dep = Drug Use Profile Fac3 = Factor 3 Fac4 = Factor 4 Rec = Level of Recidivism The following codes were used in coding survey data into the Data Matrix For Gender : 1 = Male 2 = Female For Age : As is For Age Level : Same as Factor A scale from Table 5 (Butler, 2008c) For Ethnicity : 1 = Asian 2 = Black 3 = White 4 = Others For Religion : 1 = Protestant 2 = Catholic 3 = Born Again Christian 4 = Other Religions For Factor 1 : Factor 1 scale from Table 1 (Butler, 2008c) For Factor 2 : Factor 2 scale from Table 2 (Butler, 2008c) For Factor 3 : Factor 3 scale from Table 3 (Butler, 2008c) For Factor 4 : Factor 4 scale from Table 4 (Butler, 2008c) For Level of Recidivism : Table 10 (Butler, 2008c) For Factor A : Factor A scale from Table 5 (Butler, 2008c) For Factor B : Factor Bscale from Table 6 (Butler, 2008c) For Factor C : Factor C scale from Table 7 (Butler, 2008c) For Factor D : Factor D scale from Table 8 (Butler, 2008c) For Factor E : Factor E scale from Table 9 (Butler, 2008c) For Extent of Drug Use : Table 11 (Butler, 2008c) For Drug Use Profile : 1 = Drug user 2 = Non user Read More