Selecting the Appropriate Statistical Analysis Approach

Research utilizes sample data to understand the characteristics of a population. Chi-square tests the association between categorical variables by checking the observed against expected variables (Stocks, 2001). The researchers are interested in establishing whether there exists a difference in the proportion of unemployed, part-time employees, and full-time employees in the treatment and waitlist groups. The research results would help understand whether the program's participation depends on the three categories of employment status. The appropriateness of the Chi-square test relies on the nature of the variables (Stocks, 2001). Both employment and program participation are categorized into groups using a nominal scale. The dependent variable is employment status, which is categorized into unemployed, part-time employees, and full-time employees. On the other hand, the independent variable is program participation categorized into intervention and comparison groups. 

The observed data indicates that 55.2%, 24.1%, and 20.7% of the respondents were unemployed, part-time employees, and full-time employees. On the other hand, the proportions of intervention groups were 16.7%, 23.3%, and 60.0% for unemployed, part-time, and full-time employees, respectively. The SPSS software conducts cross-tabulation to calculate a chi-square statistic that explains the relationship between the categorical variables. The SPSS output provides a Pearson Chi-Square value, associated degrees of freedom, and the 2-sided asymptotic significance value. The decision rule rejects the null hypothesis if the Chi-square statistic value is greater than the critical chi-square or the p-value is less than the assumed level of significance, 0.05 (Zikmund et al., 2013). Chi-square statistic, 11.748 > critical value 5.99 at 0.05 level of significance and 2 degrees of freedom. Also, the p-value, 0.003 < the level of significance, is 0.05, implying that there is sufficient statistical evidence to reject the null hypothesis and conclude that there is a difference in the proportions of individuals in the three employment categories between the treatment group and the waitlist group. 

References 

Stocks, J. T. (2001). Statistics for social workers. The handbook of social work research methods. 

Zikmund, W. G., Carr, J. C., & Griffin, M. (2013). Business Research Methods. Cengage Learning.