STAT 218: Two Group Categorical Practice _____________________________________________________________________________________________ SCENARIO ONE: Blood donations from volunteers serve a crucial role in the nation's health care system. Are Americans any more or less generous about donating blood in some years than others? To investigate this question, we can analyze data from the General Social Survey, which is a national survey conducted every two years on a nationwide random sample of adult Americans. 1. Did this study make use of random sampling, random assignment, both, or neither? Also explain what your answer means in terms of the scope of conclusions that can be drawn from these data. State the parameter (in terms of the long-run difference). (taking the 2002 proportion minus the 2004 proportion). 2. In symbols and words, write the hypotheses. 3. For each year, calculate the (conditional) proportion of adult Americans sampled who donated blood in the previous 12 months. Use appropriate symbols to represent them. Also calculate the difference between these sample proportions. 4. Use the Two Proportions Applet to conduct a simulation analysis to approximate a p-value for testing the hypotheses that you stated in #3. (Use 1000 replications) a. P-value: STAT 218: Two Group Categorical Practice _____________________________________________________________________________________________ b. Standardized Statistic: 5. Can the Theory based method be used for this scenario? Justify your answer. 6. Use the Theory-Based Inference Applet to find the z-statistic, standard deviation and p-value. 7. Calculate the standardized statistic using Theory-Based approach. Using the formula for comparing two proportions. 8. Compare your standardized statistic from the theory-based and simulation approach. 9. Calculate 95% Confidence Interval using the Theory-based approach STAT 218: Two Group Categorical Practice _____________________________________________________________________________________________ a. Interpret in confidence interval in context. 10. Does the conclusion about the hypotheses from the theory-based standardized statistic and the confidence interval match? (i.e. all reject or all fail to reject?) the publishing of his book, Pauling w SCENARIO TWO: In 1970 Linus Pauling, a wellknown chemist and Nobel Prize winning scientist, published Vitamin C and the Common Cold (1970), creating a great deal of public and scientific interest. In short, Pauling argued that taking Vitamin C would reduce one's risk of the common cold. This book almost singlehandedly made Vitamin C one of the most widely used dietary supplements, a status it retains to this day (Nutritional Supplement Review, 2009). Subsequent to rote a paper that a ppeared in the Proceedings of the National Academy of Sciences in 1971. In this paper he describes a study conducted by a physician in Basel, Switzerland, in the early 1960s. Here is an excerpt from the paper explaining the study design: The study was carried out in a ski resort with 279 skiers during two periods of 5-7 days. The conditions were such that the incidence of colds during these short periods was large enough (about 20%) to permit results with statistical significance to be obtained. The subjects were roughly of the same age and had similar nutrition during the period of study. The investigation was double-blind, with neither the participants nor the physicians having any knowledge about the distribution of the ascorbic-acid tablets (1000 mg) and the placebo tablets. The tablets were distributed every morning and taken by the subjects under observation, so that the possibility of interchange of tablets was eliminated. The subjects were examined daily for symptoms of colds and other infections. The records were largely on the basis of subjective symptoms, partially supported by objective observations (measurement of body temperature, inspection of the respiratory organs, auscultation of the lungs, and so on). Persons who showed cold symptoms on the first day were excluded from the investigation. After the completion of the investigation, a completely independent group of professional people was provided with the identification numbers for the ascorbic-acid tablets and placebo tablets, and this group performed the statistical evaluation of the observations. Although not stated explicitly in the paragraph above, the participants were randomly assigned to take ascorbic-acid tablets or the placebo. Research Question: Are you less likely to get a cold when taking vitamin C? 1. Fill out what this dataset would look like. The first column should contain headings/titles. NOTE: THIS IS NOt THE 2x2 TABLE STAT 218: Two Group Categorical Practice _____________________________________________________________________________________________ 2. Describe the observational/experimental units. 3. Identify the explanatory and response variables, categorical or quantitative? Explanatory: Response: 4. Is this study an experiment or an observational study? How did you decide? 5. Describe the parameter (Vitamin C - Placebo) of interest in words. What symbol would you use? 6. Set up the hypothesis in symbols (Vitamin C - Placebo). Of the 139 skiers assigned to take Vitamin C, 17 developed a cold. Of the 140 skiers assigned to take a placebo, 31 developed a cold. 7. Fill out the 2x2 chart. TOTAL STAT 218: Two Group Categorical Practice _____________________________________________________________________________________________ TOTAL 8. Calculate the conditional proportions for each group. Assign a symbol to each. 9. Calculate the relative risk. 10. Calculate the difference in proportions (Vitamin C - Placebo). 11. Using the Two Proportions Applet, simulate a null distribution and identify the following: Simulated SD: P-value (R or FTR?): 12. Calculate the standardized statistic using the simulated standard deviation. (R or FTR) 13. Using the Theory Based Inference Applet, identify the following: Confidence Interval Given from Applet (R or FTR?): 14. Show how the confidence interval above was calculated. 15. Interpret the confidence interval in context. STAT 218: Two Group Categorical Practice _____________________________________________________________________________________________ 16. Identify the population of interest. 17. Can we generalize our results to the population of interest? Explain. 18. Can we determine a cause and effect relationship? Explain. 19. Draw a conclusion in context