Statistical analysis software is a valuable tool that helps researchers perform the complex calculations. However, to use such a tool effectively, the study must be well designed. The social worker must understand all the relationships involved in the study. He or she must understand the study’s purpose and select the most appropriate design. The social worker must correctly represent the relationship being examined and the variables involved. Finally, he or she must enter those variables correctly into the software package. This assignment will allow you to analyze in detail the decisions made in the “Social Work Research: Chi Square” case study and the relationship between study design and statistical analysis. Assume that the data has been entered into SPSS and you’ve been given the output of the chi-square results. (See Week 4 Handout: Chi-Square findings).
To prepare for this Assignment, review the Handout: Chi-Square Findings and follow the instructions.
Submit a 1-page paper of the following:
An analysis of the relationship between study design and statistical analysis used in the case study that includes:
An explanation of why you think that the agency created a plan to evaluate the program
An explanation of why the social work agency in the case study chose to use a chi square statistic to evaluate whether there is a difference between those who participated in the program and those who did not (Hint:       Think about the level of measurement of the variables)
A description of the research design in terms of observations (O) and interventions (X) for each group.
Interpret  the chi-square output data. What do the data say about the program?
Chi Square case study
Molly, an administrator with a regional organization that advocates for alternatives to long-term prison sentences for nonviolent offenders, asked a team of researchers to conduct an outcome evaluation of a new vocational rehabilitation program for recently paroled prison inmates. The primary goal of the program is to promote full-time employment among its participants. To evaluate the program, the evaluators decided to use a quasi-experimental research design. The program enrolled 30 individuals to participate in the new program. Additionally, there was a waiting list of 30 other participants who planned to enroll after the first group completed the program. After the first group of 30 participants completed the vocational program (the “intervention” group), the researchers compared those participants’ levels of employment with the 30 on the waiting list (the “comparison” group). In order to collect data on employment levels, the probation officers for each of the 60 people in the sample (those in both the intervention and comparison groups) completed a short survey on the status of each client in the sample. The survey contained demographic questions that included an item that inquired about the employment level of the client. This was measured through variables identified as none, part-time, or full-time. A hard copy of the survey was mailed to each probation officer and a stamped, self-addressed envelope was provided for return of the survey to the researchers. After the surveys were returned, the researchers entered the data into an SPSS program for statistical analysis. Because both the independent variable (participation in the vocational rehabilitation program) and dependent variable (employment outcome) used nominal/categorical measurement, the bivariate statistic selected to compare the outcome of the two groups was the Pearson chi-square. After all of the information was entered into the SPSS program, the following output charts were generated: 
TABLE 1. CASE PROCESSING SUMMARY   Cases Valid Missing Total N Percent N Percent N Percent Program Participation *Employment 59 98.3% 1 1.7% 60 100.0% TABLE 2. PROGRAM PARTICIPATION *EMPLOYMENT CROSS TABULATION   Employment Total None Part-Time Full-Time Program Participation Intervention Group Count % within Program Participation  5 16.7%  7 23.3% 18 60.0%  30 100.0%   Comparison Group Count % within Program Participation 16 55.2%  7 24.1%  6 20.7%  29 100.0% Total   Count % within Program Participation 21 35.6% 14 23.7% 24 40.7%  59 100.0% TABLE 3. CHI-SQUARE TESTS   Value df Asymp. Sig. (2-sided) Pearson Chi-Square 11.748a 2 .003 Likelihood Ratio 12.321 2 .002 Linear-by-Linear Association 11.548 1 .001 N of Valid Cases     59 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.88. The first table, titled Case Processing Summary, provided the sample size (N = 59). Information for one of the 60 participants was not available, while the information was collected for all of the other 59 participants. The second table, Program Participation Employment Cross Tabulation, provided the frequency table, which showed that among participants in the intervention group, 18 or 60% were found to be employed full time, while 7 or 23% were found to be employed part time, and 5 or 17% were unemployed. The corresponding numbers for the comparison group (parolees who had not yet enrolled in the program but were on the waiting list for admission) showed that only 6 or 21% were employed full-time, while 7 or 24% were employed part time, and 16 or 55% were unemployed. The third table, which provided the outcome of the Pearson chi-square test, found that the difference between the intervention and comparison groups were highly significant, with a p value of .003, which is significantly beyond the usual alpha-level of .05 that most researchers use to establish significance. These results indicate that the vocational rehabilitation intervention program may be effective at promoting full-time employment among recently paroled inmates. However, there are multiple limitations to this study, including that 1) no random assignment was used, and 2) it is possible that differences between the groups were due to preexisting differences among the participants (such as selection bias). Potential future studies could include a matched comparison group or, if possible, a control group. In addition, future studies should assess not only whether or not a recently paroled individual obtains employment but also the degree to which he or she is able to maintain employment, earn a living wage, and satisfy other conditions of probation.
Handout: Chi-Square Findings
The chi square test for independence is used to determine whether there is a relationship between the two variables that are categorical in the level of measurement. In this case, the variables are:
employment level and treatment condition. It tests whether there is a difference between groups.
The research question for the study is: Is there a relationship between the independent variable,treatment, and the dependent variable, employment level? In other words, is there a difference in the number of participants who are not employed, employed part-time and employed full-time in the program and the control group (i.e., waitlist group)?
The hypotheses are:
H0 (The null hypothesis): There is no difference in the proportions of individuals in the three employment categories between the treatment group and the waitlist group. In other words, the frequency distribution for variable 2 (employment) has the same proportions for both categories of variable 1 (program participation).
** It is the null hypothesis that is actually tested by the statistic. A chi square statistic that is found to be statistically significant, (e.g. p< .05) indicates that we can reject the null hypothesis (understanding that there is less than a 5% chance that the relationship between the variables is due to chance).
H1 (The alternative hypothesis): There is a difference in the proportions of individuals in the three employment categories between the treatment group and the waitlist group.
** The alternative hypothesis states that there is a difference. It would allow us to say that it appears that the treatment (voc rehab program) is effective in increasing the employment status of participants.
Assume that the data has been collected to answer the above research question. Someone has entered the data into SPSS. A chi-square test was conducted, and you were given the following SPSS output:  

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