Statistics - Applications Projects

The National Evaluation of Welfare-to-Work Strategies (NEWWS) involved randomized experiments at seven

The National Evaluation of Welfare-to-Work Strategies (NEWWS) involved randomized experiments at seven sites around the country in the mid-1990s. In Atlanta, families applying for or receiving Aid to Families with Dependent Children (AFDC) were randomly assigned to the Human Capital Development (HCD) program, the Labor Force Attachment (LFA) program, or a control group. The HCD program provided education and basic skills training; while the LFA program emphasized immediate search for job opportunities. These programs were designed for reducing welfare dependency and promoting self-sufficiency. The control condition made no such requirement for welfare receipt. Critics of the HCD approach believed that mandatory education programs for adult parents might delay people’s labor market entry without guaranteeing that their forgone earnings would be made up by better jobs later. Critics of the LFA approach argued that building welfare recipients’ skills would generate long-term rather than short-term benefits. We will examine these arguments in light of the empirical evidence.

For this assignment, the sample includes welfare mothers with young children between 3~5 years of age.

We will consider the following four variables measured at the baseline:

-‐ age,

-‐ on welfare 36 of the past 60 months,

-‐ no high school diploma or GED certificate,

-‐ extent of work search effort.

The outcomes include

-‐ whether the individual was ever employed during the 5 years after randomization,

-‐ first quarter of employment after randomization,

-‐ total number of quarters employed during the 5 years after randomization,

-‐ earnings in the fifth year.

Part I: The Effects of the HCD and LFA Programs on Employment and Earnings

Select individuals who were assigned to either HCD or the control group. Cross-tabulate treatment assignment and ever being employed and display a clustered bar chart. What proportion of the HCD group members was ever employed during the five years after randomization? What proportion of the control group members was ever employed? In this sample, which group seems to have a higher employment rate?
In the population, did random assignment to HCD rather than to the control condition increase employment rate during the five years after randomization? State your null and alternative hypothesis with regard to the difference in employment rate between HCD and control in the population. Conduct a chi-square test. Report the chi-square statistic and the p -value. Define precisely the meaning of the p -value in this context. What is your decision about the null hypothesis? What is your answer to the research question?
Compare between the HCD group and the control group the mean and median of the total number of quarters employed during the five years after randomization. Display a box-plot. In this sample, were individuals in the HCD group employed more often than those in the control group?
In comparison with the control condition, did the HCD program bring advantage to welfare mothers by increasing their time of employment during the five years after randomization? State your null and alternative hypothesis with regard to the population mean difference in the total number of quarters employed between HCD and control. Conduct a two independent sample t test. What is the standard error of the estimated population mean difference? Report the t statistic and the p -value. Define precisely the meaning of the p -value in this context. Compute the 95% confidence interval for the population mean difference. How do you interpret this confidence interval? What is your decision about the null hypothesis? What is your answer to the research question?
Select individuals who were assigned to either HCD or LFA. Compare between HCD and LFA the mean and median of the first quarter of employment after randomization. Display a box- plot. In this sample, did LFA group members find jobs sooner than the HCD group members on average?
In the population, did the LFA program expedite a welfare mother’s success in the job market when compared with the HCD program? State your null and alternative hypothesis with regard to the population mean difference between HCD and LFA in how soon their members were employed. Report the t statistic and the p -value. Define precisely the meaning of the p -value in this context. What is your decision about the null hypothesis? What is your answer to the research question?
Select the entire sample. How did the HCD, LFA, and control groups compare in the mean and median of earnings during the fifth year after randomization? Display a box-plot. In this sample, which group seems to be most successful and which seems to be least successful in becoming economically self-sufficient?
In the population, did random assignment to HCD or LFA rather than to the control condition increase earnings in the fifth year after randomization? State your null and alternative hypothesis with regard to the population mean difference among the three treatment groups in the fifth-year earnings. Conduct a one-way analysis of variance. Report the F statistic and the p -value. Define precisely the meaning of the p -value in this context. What is your decision about the null hypothesis? What is your answer to the research question?
What conclusion can you draw at this point with regard to the relative effectiveness of the HCD and LFA programs in increasing welfare mother’s employment and earnings?
Part II: Associations between Baseline Characteristics and Economic Success
In this sample, which age group was most likely to be employed? Which age group was least likely to be employed? Was there an association in the population between age and employment rate during the five years after randomization? Present your evidence including the point estimates of proportion differences in the population, chi-square statistic, and p -value.
In this sample, did individuals who had a higher dependence on welfare in the past show more difficulty starting employment? Was there an association in the population between the history of welfare dependence and the first quarter employed after randomization? Present your evidence.
In the fifth year after randomization, did individuals who had a high school diploma or GED before randomization earn more than those who had no such education credentials? Was there an association in the population between baseline education level and fifth-year earnings? Present your evidence.
In this sample, did individuals who reported a higher level of work search efforts at the baseline show more quarters employed during the five years after randomization? Display a scatter-plot and fit a loess line. Is the relationship between these two measures linear? If the relationship is linear, compute the Pearson product-moment correlation coefficient.
To determine whether work search efforts at the baseline is associated with the total number of quarters employed after randomization in the population, state your null and alternative hypothesis. Report the correlation coefficient and the p -value. Define precisely the meaning of the p -value in this context. What is your decision about the null hypothesis? What is your answer to the research question?
Part III. Comparability in Baseline Characteristics Across the Treatment Groups
Even though the treatment assignment was random in this experiment, the treatment groups may differ in some baseline characteristics by chance. Examine whether the HCD group, the LFA group, and the control group differed in age composition. Present your evidence including the point estimates of proportion differences across the three treatment groups in the population, chi-square statistic, and p -value.
Examine whether the HCD group, the LFA group, and the control group differed in the history of welfare dependence. Present your evidence including the point estimates of proportion differences across the three treatment groups in the population, chi-square statistic, and p -value. If there is a statistically significant difference among the treatment groups, which group is relatively advantaged? Which group is relatively disadvantaged?
Examine whether the HCD group, the LFA group, and the control group differed in education at the baseline. Present your evidence including the point estimates of proportion differences across the three treatment groups in the population, chi-square statistic, and p -value. If there is a statistically significant difference among the treatment groups, which group is relatively advantaged? Which group is relatively disadvantaged?
Examine whether the HCD group, the LFA group, and the control group differed in the average level of work search efforts at the baseline. Present your evidence including the mean differences among the three treatment groups in the population, F statistic, and p -value. If there is a statistically significant difference among the treatment groups, which group is relatively advantaged? Which group is relatively disadvantaged?
On the basis of the above evidence, if any treatment group appeared to be disadvantaged at the baseline, the mean outcome of that treatment group (e.g., in employment rate, first quarter being employed, total number of quarters being employed, and fifth-year earnings) might have been under-estimated. Would this become a concern in evaluating the relative effectiveness of the HCD and LFA programs? Please explain why or why not.