Use STATA for any of the test questions requiring software applications. Show your work for partial credit. Discuss and support any assumptions that you make, be sure to answer the questions completely in the form requested, and please type your answers directly below the questions in this document. You should be able to paste any necessary Stata output in with your answers as well. For each problem, report your calculations and state your conclusions.
Part I. Choosing Statistical Tests
An important skill necessary for conducting applied social science research is to be able to translate a research question into the correct choice of a statistical test. For each of the following research questions below, a) identify the EV, b) identify the RV, c) state a hypothesis about the expected association between the EV and the RV and d) choose the statistical test that will appropriately test whether or not the EV and RV are associated in the population.
1. Does viewing TV/movie violence lead to displays of aggression in children? Viewing TV/movie violence is measured by whether or not each child viewed any programs with PG-13 ratings due to violent content in the last month. Aggression is measured as the number of incidents of fighting, bullying, taunting or verbal arguments observed in each child outside the classroom by school staff.
2. Does mentoring help to reduce criminal activity among gang members? Mentoring is measured by whether or not each gang member who participated as a research subject received support from a mentor in a mentoring program. Criminal activity is measured by whether or not each gang member was detained or arrested in the following year for either a felony or misdemeanor.
Part II. Evaluating cause-and-effect conclusions
Another important skill necessary for conducting social science research is to decide whether or not a causal inference is appropriate to make about the nature of an EV/RV association that is found in a research study. Oftentimes research findings are reported in the media about the association between an EV and a RV as though the association is a cause-and-effect association. But these cause-and-effect conclusions are sometimes not appropriate. Consider the media report in the exercise below:
3. In 1972, the Los Angeles Times reported that women who take birth control pills are more intelligent than women who do not take birth control pills. The authors of the article claimed that this beneficial side effect of birth control pills had not been noted before.
This claim was based on a research study conducted in several states in the nation in which intelligence tests were administered to research participants. Several other variables were measured in this study as well, including whether or not the female participants were taking birth control pills. So all variables in the study were measured at the same time.
Clearly implied by the authors is a cause-and-effect association between taking birth control pills (the EV) and intelligence (the RV):
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EV - birth control pills
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RV - intelligence
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Taking birth control pills
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High intelligence
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Not taking birth control pills
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Lower intelligence
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The study found a statistically significant difference in mean intelligence levels between the sample of women taking birth control pills and the sample not taking birth control pills from a two-sample t-test, where women taking birth control pills showed significant higher intelligence means than women not taking birth control pills.
Is the conclusion that the authors drew stating that taking birth control pills causes increased intelligence among women justified in light of what you know about criteria for causal inference? Explain how each of the three criteria for causal inference is met (or not met) when formulating your answer (NOTE: if you decide that the no confounding criterion is not met, then give an example of a possible CV that is likely associated with both the EV and RV and might represent a possible cause of the difference between groups in intelligence levels that were observed).
Part III. Statistical inference: Confidence intervals and hypothesis testing procedures.
The next several problems require that you calculate 95% confidence intervals for the value of a population parameter or conduct null/alternative hypothesis tests with one of the hypothesis testing procedures we covered during the first half of SOC 113.
4. In a simple random sample of 625 female army officers obtained from VA records, 125 reported having experienced at least one incident of sexual harassment in the past year. Construct, report and interpret a 95% CI for the true proportion of all female army officers experiencing sexual harassment in the past year.
5. The following data correspond to the number of alcoholic drinks per week reported by 30 adolescents before and after an alcohol reduction intervention (Before, After). Conduct a one-sample t-test on the difference scores (# of alcoholic drinks consumed after the intervention minus # of alcoholic drinks consumed before the intervention), in order to evaluate the effectiveness of the program. The before/after values of the RV (number of alcoholic drinks consumed) are presented below for each of the 30 subjects. Each ordered pair displays the number of alcoholic drinks per week before the intervention, followed by the number of drinks per week after the intervention.
(0,0) ; (0,0); (0,0); (0,0); (0,0)
(0,1); (0,1); (0,1)
(1,0); (1,0); (1,0)
(1,1); (2,0); (2,1); (2,3)
(3,2); (3,0); (3,3)
(4,5); (4,3)
(5,4); (5,0)
(6,2)
(7,4)
(8,10)
(9,12)
(10,8)
(11,3)
(12,8)
(14,12)
Enter the raw data into a Stata spreadsheet using the EDIT command. Your data file should have two columns of numbers: drinks consumed before the intervention and drinks consumed after the intervention. You will also have to create a new variable in which you create a difference score variable (after drinks minus before drinks).
You completed a similar problem on HW2. Answer the following questions:
a. State the null and alternative hypotheses in words and statistical symbols.
b. Run the one-sample t-test in STATA and display your output below:
c. Also run a SUMMARIZE (SUM) program in Stata on the before-drinks and after-drinks variables and display your output below. The means on each of these variables will help you to interpret your results because the mean change-in-alcoholic drinks consumed in your one-sample t-test output from Part b will be equal to the after-drinks mean from Part c minus the before-drinks mean in Part c.
d. Did the mean number of alcoholic drinks consumed per week change significantly from before the intervention to after? Support your answer by reporting the sample mean change-in-alcoholic drink count, its t-statistic and its applicable p-value. Is your decision to reject or retain the null hypothesis on the basis of these results?
e. State your conclusion conceptually. What do you conclude about the nature of the association (or lack of association) between receiving the intervention and changes in overall levels of alcohol consumption among adolescents? What do you conclude about the impact of the program?
6. The October 3, 1986 issue of Science reported the early termination of a clinical trial testing the impact of AZT on mortality reduction among individuals with AIDS who had recently been diagnosed with Pneumocystis carinii pneumonia (PCP). PCP is one of the deadliest diseases that people get who have late-stage AIDS, and at the time of the study, was the most common cause of AIDS-related death. At the time of the Science article, the results of the trial for mortality reduction were so encouraging, it was decided that continuing to withhold AZT from placebo-control recipients from a potentially life-saving treatment would be unethical. And the trial was subsequently terminated.
The observed-frequency raw data from the trial were reported in the Science article, and are displayed in the crosstab table below:
| mortality
arm | 1=survive 2=died | Total
-----------+----------------------+----------
1=AZT | 144 1 | 145
2=placebo | 121 16 | 137
-----------+----------------------+----------
Total | 265 17 | 282
You will conduct a chi-square test of independence on the frequency data.
a) State the null and alternative hypotheses in words and symbols. The symbols should show expected differences in population mortality rates between the trial arms (note the term "trial arm" means trial group (AZT group and placebo control group). This is a common terminology in randomized clinical trials (RCTs) that test the impacts of drugs).
b) Enter the cell frequencies above into a small spreadsheet in Stata and use TAB2 in Stata to generate the crosstab table above. In your TAB2 program, specify the options for the chi-square statistic, row percentages, and expected frequencies (we didn't generate expected frequencies in lab, so I'll tell you how to get expected frequencies. Just type the word EXPECTED after you specify the options for the chi-square statistic and the row percentages).
c) Do the data satisfy the minimum expected frequency per cell assumption? Explain.
d) Interpret the results of the chi-square test. Be sure to comment on the chi-square, its associated p-value, and whether the mortality rates in the AZT and placebo arms differ/do not differ significantly. If significant, describe the magnitude of the difference.
e) Calculate and interpret the relative risk as the mortality risk for AZT recipients relative to the mortality risk for non-recipients. Does this suggest a strong or weak impact of AZT on mortality reduction?
f) At the time of the Science article, there were 11,170 people diagnosed with AIDS nationwide who were still living, and 60% of these (approximately 6700) had PCP. These are the people who would be targeted for AZT treatment.
The 95% confidence interval for the difference between proportions (obtained from ?AZT - ?placebo) is:
-.17
Use the existing population data from the time of the article to translate this CI into an interval estimate of the number of lives of AIDS patients with PCP that could be prolonged nationwide with AZT.