| Stat 251: Statistical Methods I | Last updated 09/12/2008 |
Complete the following exercises from your text: pages 86-90, #17, 20, 23, and practice problem 1.3.4 (page 32).
These exercises are reproduced below.
#17) Suppose that Dr. Fisher teaches an 8 A.M. statistic class and Dr. Newton teaches an 11 A.M. calculus class. During lunch one day they begin comparing notes on their students' attitudes in class, and they quickly agree that the calculus students are much more engaged and enthusiastic than the statistics students. Consider the students' subject (statistics or calculus) as the explanatory variable and a measure of their engagement as the response variable.
(a) Identify two confounding variables, and explain how they prevent you from concluding that the students' subject is the cause of the difference in their engagement and enthusiasm levels. (Be sure to state them clearly as variables.)
(b) Suppose that next semester Dr. Fisher will teach his statistics class at 11 A.M. and Dr. Newton will teach his calculus class at 8 A.M.. Then they will compare all of the data gathered on their students' levels of engagement and enthusiasm from both semesters. Does this plan eliminate all potentially confounding variables? Explain.
#20) A recent study (Milberger et
al., 1997) found that children whose mothers smoked during pregnancy were
more likely to be diagnosed with attention deficit hyperactivity disorder
than children of nonsmoking mothers.
(a) Is this an observational
study or an experiment? Explain briefly.
(b) Identify the explanatory
variable and the response variable in this study.
(c) Is it valid to
conclude from this study that a mother's smoking causes this disorder in her
children? Explain briefly.
(d) Explain why it would not be reasonable to conduct a randomized,
comparative experiment to investigate whether a mother's smoking causes this
disorder in her children.
#23) Zadnik et al. (2000) conducted a study of children's lightning conditions and myopia. They studied 1220 children who were seen by various optometrists in schools across the United States. The researchers found that of 417 children who had slept with not light on, 20% became myopic (near-sighted); 0f 758 children who slept with a night light on 17% became myopic; and of 45 children who slept in a fully lit room, 22% became myopic.
(a) Create a segmented bar graph to compare the conditional distributions of myopia across the three lighting categories.
(b) Does this graph reveal much of an association between lighting condition and myopia? How would your findings from this study compare to those of the study in Investigation 1.3.1?
(c) These researchers points out that their subjects came from schools across the country, while the subjects in the Quinn et al. study had come to one specialty clinic. Does this raise the issue of cause-and-effect or the issue of generalizability-of-results? Explain.
Practice Problem 1.3.4: Construct a Simpson's Paradox
Construct your own hypothetical data to illustrate Simpson's paradox in the following context. Show that it is possible for one softball player (Alex) to have a higher proportion of hits than another (Bob) in July and in August, and yet Alex can have a lower proportion of hits for the two months combined. [Hints: You might want give each player the same number of at-bats (maybe 200) for the two months combined, and you may want to use Excel to help you automatically update the calculations as you try different numbers. Try to make the differences in the players' proportions of hits (number of hits divided by the number of at-bats) as larger as you can (don't worry about these proportions being realistic).] Also briefly explain the apparent paradox as if to a baseball fan with limited knowledge of statistics, for the example that you construct.