Statistics That Lends Credibility to the Arguments - Essay Example

Running Head: STATISTICS PAPER STATISTICS PAPER Karen Butler,M.D. Northcentral Prof. McNellie September 12, 2008 Statistics Paper Each part of a research study has its own significance in the completion of a scholarly paper. While King and Wincup (2008) argues that the chosen research design determines whether the study stands or falls, Lane (2003) contends that it is statistics which lends credibility to the arguments being presented. Hence, the choice of appropriate statistical measures complement the research design. Original research journal articles from the annotated bibliography of the concept paper entitled “The Effects of Mind Altering Drugs on Juvenile Recidivism” were chosen for discussion in this statistics paper from the works of Bennett (2004), Greenblatt (2002), Hiller, Knight, Rao and Simpson (2000), Makkai and Payne (2003), Niazi, Pervaiz, Minhas and Najam (2005), Wei, Makkai and McGregor (2003), and Young, Dembo and Henderson (2007). The Bennett (2004) study The Bennett (2004) study began in 1996 to ascertain the prevalence of drug usage among offenders in the United Kingdom, and to trace whatever links there are between drugs and crime in relation to arrestees. This study was patterned after the Drug Use Forecasting (DUF) program of the United States Department of Justice. Like the DUF program, the Bennett (2004) research is being carried out using interviews and drug tests as the key methodology. The following substances are being tested as part of the large-scale drug research : amphetamines (including ecstasy), benzodiazepines, cannabinoid metabolite, cocaine metabolite (including ‘crack’), LSD, methadone, opiates (including heroin) and alcohol. The Bennett (2004) research used both descriptive and inferential statistics. Measures of central tendency including the range, median, proportion, frequency, percentage were used to describe the prevalence of drug use among the arrestees. The range was used to describe the length of the interval which contains all the data. The range also indicates dispersion of the data. Arrestees who tested for cannabis, for example, ranged from 36 per cent to 58 percent across the five survey area (p. 17). The proportion states the relationship of one part of a measure compared to a whole. In this study, proportion was oftentimes used to depict the picture of the size of the populations of arrestees testing positive for any of the eight substances in the aforementioned paragraph, such as “ … three out of four arrestees tested positive for at least one drug (including alcohol)” (p. 18). The median in this study describes the midpoint of the range where half of the data contained in the range falls below the median and the other half falls above the median. For example, “… the proportion testing positive for any of the drug types tested ranged from 72 per cent and 82 per cent, with a median value of 74 percent…” (p. 18). With the median for this particular data at 74 percent, it means that half of the data falls below 74 per cent with the lowest at 72 per cent; while the other half of the data falls above 74 per cent with the lowest at 82 per cent. Frequency is the number of times a particular data occurred in a given study. In Table E.1 (p. 104), in the self-report, there were only 7 occurrences of arrests with a drug supply offense only and this accounts for a frequency of 7. Percentage is an expression a frequency as a fraction of 100. A frequency of 7 from a total frequency of 123 in Table E.1 means a percentage of 5.7 or 6 per cent. The chi-squared test was the inferential statistics used in the Bennett (2004) study to measure the assumption that the distribution characteristics namely gender, age, ethnic group and suspected offense of the arrestees considered in the study. The chi-square test is believed to be the most appropriate statistical test for the inferential part of the study since it compares the observed frequencies in one specific categories to frequencies which the researcher may expect to fall in these categories by chance. Further, the assumptions of normality which are usually required when using the t-test or the analysis of variance, is not required in using the chi-square test (Field, 2005). The Greenblatt (2002) study The Greenblatt (2002) research studied the relationship between adolescent behaviors and marijuana. It utilized a methodology developed using a combination of household interviews and compiled historical data. Respondents for the household interview were sourced from non-institutional group accommodations such as shelters and dormitories. Aside from measures of central tendency using frequency and the percentage [the definition of which were already both discussed in the Bennett (2004) study], the rest of the statistical treatment in the Greenblatt (2004) study was carried out using correlation analysis. Cohen, Cohen, West and Aiken (2003) maintained that correlation analysis is a very general and flexible method of data analysis and may be used to study the dependent variable(s) as a function of the independent variable(s). The following variables were described in this study using frequency and percentage: percentage distribution of marijuana usage by age, frequency distribution of marijuana usage by age, race, gender, population density, region, family income, moves in past year and family structure. On the other hand, correlation analysis was used to confirm association between self-reported behaviors (such as withdrawal, somatic complaints, anxiety or depression, social problems, thought, problems, attention problems, delinquent behavior, aggressive behaviour and criminal behavior) and marijuana usage. The Hiller, Knight, Rao and Simpson (2000) study The objective of the study was to describe the baseline and during treatment evaluation of the probationer – subjects in a “real world” treatment environment provided in conjunction with the National Institute of Justice funded grant called the Process Assessment of Correctional Treatment project. The study locale is the Dallas County Judicial Center in Wilmer, Texas. The treatment model consists of three phases: orientation, treatment and re-entry. Treatment data were analyzed for 417 cases. The variables considered in the study are social history, classification of drug problems, psychological problems, abuse history, behavioural risk for HIV/AIDS, criminality and criminal history, psychological functioning, social functioning, treatment motivation and treatment drop-out. Descriptive statistics in the form of indices were used to quantify the upon treatment entry variables social history, drug dependence, psychological problems, abuse history, behavioral risks for HIV/AIDS, as well as criminality and criminal history. These are the same variables considered under the needs analysis. An index in statistics is a number or a ratio or at times a value on a scale of measurement, which is derived from a series of observations or data. One of the important functions of a statistical index is to show comparative changes over time (Vogt & Barta, 1997). Reactions of the probationer – subjects to the treatment given as part of the project (and research) were assessed using a series of growth curve models to describe psychosocial functioning and treatment motivation. In theory, a growth curve model is generally applied in the examination of longitudinal data where measurements are taken on a particular response variable during a number of points in time (Hwang and Takane, 2005). Correlation analysis was used to determine the relationship between treatment discharge status and the variables involved in the needs analysis. Finally, one of the most powerful statistical procedures, regression analysis, by way of the stepwise logistic regression model was used in the analysis. Regression analysis facilitated the determination of which among the so-called baseline characteristics can predict probationers who will drop out early in the treatment. Regression analysis makes it possible to understand the conditional distribution of the dependent variable across a number of subpopulations, as determined by the possible predictors (Berk, ). The Makkai and Payne (2003) study This objective of this study conducted under the auspices of the Australian Institute of Criminology, is to report on the drug usage and criminal careers of male offenders imprisoned in the Northern Territory, Queensland, Tasmania and Western Australia during the middle of year 2001. Some 2,135 male offenders were included in the study, while a separate study was conducted for female prisoners by the same researchers. Description of the offender – participants in the study was accomplished using the frequency distribution presented in tabulation form or in bar graph form. Demographic characteristics in the study included age, indigenous status, and educational attainment. The mean and the median were extensively used in describing the offending history of the respondents. Data were presented in terms of the following categories: regular property offenders, regular violent offenders, regular multiple offenders, regular fraud offenders, regular drug sellers, regular drug buyers, homicide offenders and non-regular offenders. Another variable, drug market activity, was presented in terms of frequency and percentage distribution and using bar chart. The last variable considered in the study, risk factors used frequency and percentage distribution, bar graph, and line graph. On the whole, it was evident that the study was a simple survey which involved only descriptive statistics. The Niazi, Pervaiz, Minhas and Najam (2005) study This study from an Asian perspective assessed and compared the personality traits and the external locus of control among 100 male abusers and non-users of addictive substances in a retrospective study. Personality traits were described in terms of openness to change, self reliance, perfectionism and tension. Both descriptive and inferential statistics were used to analyzed the data gathered. The frequency distribution in tabular and graphical forms was extensively used to describe the demographic profile of the study participants. Personality characteristics and external locus of control were described using the mean and the standard deviation. The t-test was utilized to compare the personality and external locus control of substance abusers and non-users, based on the p-value and the hypothesized level of significance. The standard deviation measures the spread of the data from the average or mean (Fink & Kosecoff, 2006). The t-test, which is used to test differences between two groups, evaluated whether or not there are significant differences in the personality characteristics, as well as in the locus of control, between the abusers and non-users. The Wei, Makkai and McGregor (2003) study This study ascertained the drug-use patterns of 493 juvenile detainees who have been interviewed in connection with the project dubbed as Drug Use Monitoring Australia (DUMA). The research participants voluntarily presented their urine sample for analysis, which generally looked for six classes of drugs. The percentage distribution and the mean were the main statistical measures used in the study. These two statistics were used to describe the profile of the research participants in terms of age, gender, schooling, housing status, as well as the age of first initiation to drugs. Percentage bar charts were utilized to describe self-reported lifetime drug usage usage for the past 30 days, results of the urinalysis and offending patterns. Like the Makkai and Payne (2003) work which is a survey research, this study also involved simple descriptive statistical measures. The Young, Dembo and Henderson (2007) study The Young, Dembo and Henderson (2007) study was undertaken to gain knowledge of the prevalence and availability of treatment facilities for substance abuse among delinquent youth owing to a dearth of information on the area. The document showcased the findings from a nationwide survey of directors of some 141 juvenile institutions and community correctional facilities. The percentage and the median were used to describe the prevalence of correctional services and programs, as well as substance abuse services. Meanwhile, quartile values were used to present the prevalence of youth provided with various services. Quartiles are used in statistics to represent a sequential quarter of a group in an ordered distribution. The quartile is one way of measuring dispersion (Bird, 2005). It was observed that only descriptive statistics were used in this study, but the nature of the study justifies the use of only descriptive statistics. Statistics for Proposed Dissertation The insights from the Optimal Designs Paper, which compared the pros and cons of an experimental design, a quasi-experimental design and a descriptive correlational design points the proposed dissertation for the adoption of a descriptive correlational research. As the impositions of control to the variables considered in the proposed study will definitely be met with ethical implications, the most optimal design is the descriptive correlational research. The concept paper written for the proposed dissertation indicated the use of the following statistical techniques for the analysis of research date : (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. A frequency distribution is a tabulation resulting from a tally of the number of occurrences of the variable being measured. Meanwhile, a percentage distribution or a relative frequency distribution is a tabulation in which each class frequency has a corresponding percentage of the total frequency, where the total frequency is equated to 100 (Salkind, 2006). The t-test, which is used for variables with two categories, is used to ascertain whether the mean of one group is higher than the other group. On the other hand, analysis of variance is used to determine whether the mean of a class of one variable is higher than one or more of the other classes of the same variable. 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 rates of recidivism of the juvenile offenders when they are grouped according to their gender, history of drug use [whether or with previous criminal/arrest record(s)] and results of the urinalysis [positive or negative] will be verified using the t-test. In this study, the t-test will be used to determine whether the rate of recidivism of the : (1) male detainees are higher than those of the female detainees; (2) detainees with previous criminal or arrest record are higher than those which do not have previous criminal/arrest records; (3) detainees who tested positive in the urinalysis are higher than those who tested negative; and (4) detainees who used drugs are higher than those who do not use drugs. Significant differences in the rates of recidivism of the juvenile offenders when they are grouped according to their age, ethnicity, religion, past and present offenses and frequency of commission of offenses will be confirmed using a bi-directional one-way analysis of variance. For example, using analysis of variance, it will be observed whether the mean of the rate of recidivism of a particular age group is higher than one or more age groups. With the results of the analysis of variance it can be determined whether the mean of the rate of recidivism of one particular race group is higher than one or more of the other race groups. 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. Significant relationships between the rates of recidivism of the juvenile offenders and the drug(s) they are taking will be ascertained using analysis of variance. 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 rates of recidivism. Corollary to the use of the t-test and the analysis of variance, a hypothesized level of significance of 0.05 (α = 0.05) will be used. A level of significance of 0.05 means that the probability of making a decision to reject the null hypothesis during hypothesis testing is when the null hypothesis, is in fact true is only 0.05 or 5%. This level of significance is usually compared with the the probability value (p-value) or the observe level of significance based on the actual data analyzed. If the computed p-value is less than or equal to α (0.05), then the null hypothesis must be rejected since there are significant differences in the means of the variables being compared. Conversely, if the computed p-value is greater than the hypothesized level of significance α (0.05), the null hypothesis is accepted, since there are no significant differences in the means of the variables being compared. In correlation analysis, two statistical parameter are observed. These are the Pearson coefficient of correlation and the p-value. The coefficient of correlation is the measure of the strength of relationship between two set of variables. A direct or positive relationship is observed if one variable assumes a high value when the other variable has a high value or when one variable exhibits a low value when the other variable has a low value. However, the relationship is negative when one variable get higher as the other variable gets lower,or vice versa. A description of the strenght of the relationships is given in the following interpretation scale of the Pearson coefficient of correlation in Table 1. Table 1. Interpretation of the coefficient of correlation (Monzon-Ybañez, 1993). Range of Coefficient of Pearson Correlation Qualitative Interpretation 0.00 to ± 0.20 Slight correlation; almost negligible relationship ± 0.20 to ± 0.40 Low correlation; small relationship ± 0.40 to ± 0.70 Moderate correlation; relationship substantial ± 0.70 to ± 0.90 High correlation; marked relationship ± 0.90 to ± 1.00 Very high correlation; very dependable relationship It should, however, be borne in mind that the strength of the relationship in a correlation analysis as interpreted in Table 1 is not significant unless the p-value of the data analyzed is less than α (0.05). References Bennett, T. (2004). Drugs and Crime: The Results of Research on Drug Testing and Interviewing Arrestees. London, UK: Home Office. Berk, R. A. (2004). Regression Analysis: A Constructive Critique. Thousand Oaks: Sage Publishing. Bird, J. (2005). Basic Engineering Mathematics (4th Ed). Burlington, MA: Newnes. Cohen, C., Cohen , P., West, S. G. & Aiken, L. S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd Ed). Philadelphia: Lawrence Erlbaum Associates. Field, A. (2005). Discovering Statistics Using SPSS (2nd Ed). Thousand Oaks: Sage Publications. Fink, A. & Kosecoff, J. B. (2006). How to Conduct Surveys: A Step-by-step Guide. Thousand Oaks: Sage Publishing. Greenblatt, J. (2002). Adolescent Self-Reported Behaviors and Their Association with Marijuana Use. Retrieved 23 May 2008, from: http://www.oas.samhsa.gov/NHSDA/ Treatan/ treana17.htm Hiller, M. L., Knight, K., Rao, S. R., & Simpson, D. D. (2000). Process Assessment of Correctional Treatment. United States: Department of Justice. Hwang, H. & Takane, Y. (). Estimation of growth curve models with structured error covariances by generalized estimating equations. Retrieved September 11, 2008 from http://takane.brinkster.net/Yoshio/p067.pdf. King, R. D. & Wincup, E. (2008). Doing Research on Crime and Justice. Oxford, UK: Oxford University Press. Lane, D. (2003). Importance of Statistics. Retrieved September 11, 2008 from http://cnx.org/content/m10182/latest/ Makkai, T. & Payne, J. (2003). Drugs and crime: A study of incarcerated male offenders. Research and Public Policy Series, 52. Canberra: Australian Institute of Criminology. Monzon-Ybañez, L. (1993). Basic Statistics. Phoenix Publishing House. Salkind, N. J. (2006). Statistics for People who (think They) Hate Statistics: The Excel Edition. Thousand Oaks: Sage Publishing. Vogt, A. & Barta, J. (1997). The Making of Tests for Index Numbers: Mathematical Methods for Descriptive Statistics. New York: Springer Publishing Company. Wei, Z., Makkai, T. & McGregor, K. (2003). Drug Use Among a Sample of Juvenile Detainees. Canberra, Australia: Australian Institute of Criminology. Young, D. W., Dembo, R. & Henderson, C. E. (2007). A national survey of substance abuse treatment for juvenile offenders. Journal of Substance Abuse Treatment, 32(3), 255-266. Read More