4c. In the absence of random assignment, arguments addressing confounding often have to be made some other way. What are two arguments that one might be able to make to support results obtained from a quasi-design like the one in Question 2?
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An area of research in biomechanics and gerontology concerns falls and fall-related injuries, especially for elderly people. Recent studies have focused on how individuals respond to large postural disturbances (e.g., tripping, induced slips). One question is whether subjects can be instructed to improve their recovery from such disturbances. Suppose researchers want to compare two such recovery strategies, lowering (quickly stepping down with front leg and then raising back leg over the object) and elevating (lifting front leg over the object). Subjects will have first been trained on one of these two recovery strategies, and they will be asked to apply it after they feel themselves tripping. The researchers will then induce the subject to trip while walking (but harnessed for safety) using a concealed mechanical obstacle. Suppose the following 24 subjects have agreed to participate in such a study: Females: Alisha, Alice, Betty, Martha, Audrey, Mary, Barbie, Anna Males: Matt, Peter, Shawn, Brad, Michael, Kyle, Russ, Patrick, Bob, Kevin, Mitch, Marvin, Paul, Pedro, Roger, Sam 1a. One way to design this study would be to assign the 8 females to use the elevating strategy and the 16 males to use the lowering strategy. Would this be a reasonable strategy? Why not? 1b. One way to deal with this issue is to assign 4 females and 8 males to each group. Show how the proportion of males in each group is the same. 1c. Now, if you saw a difference in the proportion of trips in the two groups, could it be because of the sex of the subject? Why or why not? Could it be due to other variables, distinct from the recovery strategy? Why or why not? 1d. Because there will always be more potential confounding variables which could be distributed unevenly between the groups being compared, identify a better method for deciding who uses which strategy. 1e. Let's explore the process of random assignment to determine whether it does "work." First, let's focus on the sex (male vs. female) variable. Suppose we put each person's name on a slip, put those slips in a hat and mix them up thoroughly, and then randomly draw out 12 slips for names of people to assign to the elevating strategy. What proportion of this group do you expect will be male? What proportion of the lowering strategy do you expect will be male? Do you think we will always get an 8/8 split (8 males in each treatment group)? 1f. To repeat this random assignment a large number of times to observe the long-run behavior, we will use the Randomizing Subjects applet. Open the applet and press the Randomize button. What proportion of subjects assigned to Group 1 are men? Of Group 2? What is the difference in these two proportions? 1g. Press the Randomize button again. Was the difference in proportions of men the same this time? 1h. Change the number of replications from 1 to 198 (for 200 total), uncheck the Animate option, and press the Randomize button. The dotplot will display the difference between the two proportions of men for each of the 200 repetitions of the random assignment process. Where are these values centered? 1i. Does random assignment always equally distribute/balance the men and women between the two groups? Is there a tendency for there to be a similar proportion of men in the two groups? Explain. 1j. Prior research has also shown that the likelihood of falling is related to variables such as walking speed, stride rate, and height, so we would like the random assignment to distribute these variables equally between the groups as well. In the applet, use the pull-down menu to switch from the sex-of-participant variable to the height variable. The dotplot now displays the differences in average height between Group 1 and Group 2 for these 200 repetitions. In the long run, does random assignment tend to equally distribute the height variable between the two groups? Explain how you are deciding. 1k. Suppose there is a "balance gene" that is related to people's ability to recover from a trip. We didn't know about this gene ahead of time, but if you select the Reveal gene? button and then select gene from the pull-down menu, the applet shows you this gene information for each subject and also how the proportions with the gene differ in the two groups. Does this variable tend to equalize between the two groups in the long run? Explain. 1l. Suppose there were other "x-variables" that we could not measure such as stride rate or walking speed. Select the Reveal both? button and use the pull-down menu to display the results for the x-variable (X-var). Does random assignment generally succeed in equalizing this variable between the two groups or is there a tendency for one group to always have higher results for the x-variable? Explain. 1m. Suppose this study finds a statistically significant difference between the two groups. What conclusion would you draw? For what population? What additional information would you need to know? 1n. As in #1m, if you obtain a statistically significant result, what does that suggest about the potential for a cause-and-effect relationship? Why?
Patha S.
Using the following three variables (where i indexes individuals), write out the reduced form and first stage regression equations that you would run in order to calculate the IV estimate of the effect of the treatment on the outcome. Write the formula for the IV estimate in terms of parameters from these two equations. Outcome: L Instrument: D Treatment: T You are trying to estimate the causal effect of a college education on later life earnings. Why might the difference between the mean earnings of college graduates and the mean earnings of non-college graduates not be a good estimate of the causal effect of college education on earnings? You are trying to estimate the effect of a college education on later life earnings. In the context of this research question, state the three IV assumptions needed for a variable to be a valid instrument for education. Based on the KIPP charter school lottery example in the text, describe the type of person that would fall under each of the following: Compliers, Always-Takers, Never-Takers, Defiers. Which type are the LATE estimates based on? Which type is assumed not to exist? State the two main assumptions of RD and give an example of how a researcher could provide evidence that each assumption is valid in their study. Using the following three variables (where i indexes individuals and t indexes time periods), write out the regression equation that you would run in order to calculate the differences-in-differences effect of treatment on the outcome. Which parameter in your equation corresponds to the DD estimate? Outcome: K Treatment: TREAT (dummy indicating treated individuals) Time Period: POST (dummy indicating post-treatment periods)
Dominador T.
Here is a variable: Some people support a government-backed health insurance plan that would cover all citizens, whereas others oppose such a plan. This variable has two values: "support government plan" and "oppose government plan." Let's say that one explanation, the "income explanation," suggests this hypothesis: In a comparison of individuals, those who have low incomes will be more likely to support a government plan than will those who have high incomes. A rival explanation, the "age explanation," suggests this hypothesis: In a comparison of individuals, those who are older will be more likely to support a government health plan than will those who are younger. For the purposes of this exercise, income will be X, age will be Z, and support for government-backed health insurance will be Y. A. Suppose that after controlling for age (Z), the relationship between income (X) and health insurance opinions (Y) turned out to be spurious. (i) Using this chapter's discussion of spuriousness as a guide, write 4-5 sentences explaining how the Z-Y relationship and the Z-X relationship would produce a spurious relationship between X and Y. (ii) Sketch a line graph depicting a spurious relationship between X and Y, controlling for Z. The vertical axis will show the percentage supporting a government plan. Invent plausible percentages for the values of Y. The horizontal axis will show the two values of income. There will be two lines inside the graph: one for younger people and one for older people. B. Suppose that after controlling for age (Z), the relationship between X, Z, and Y turned out to be additive. (i) Using this chapter's discussion of additive relationships as a guide, write 4-5 sentences explaining how this set of relationships would fit an additive pattern. (ii) Sketch a line graph depicting the additive relationships between X, Z, and Y. The vertical axis will show the percentage supporting a government plan. Just as you did in part A, invent plausible percentages for the values of Y. The horizontal axis will show the two values of income. There will be two lines inside the graph: one for younger people and one for older people. C. Suppose that a set of interaction relationships exists between X, Y, and Z. Suppose further that the interaction takes this form. Among younger people, income has no effect on the dependent variable; among older people, those with lower incomes are more likely to support a government plan than those with high incomes. Sketch a line graph depicting this set of interaction relationships. Remember that the vertical axis shows the percentage supporting a government plan. As before, invent plausible percentages for the values of Y. The horizontal axis will show the two values of income. There will be two lines inside the graph: one for younger people and one for older people.
Sri K.
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