Exploration 4.2

Have a nice trip

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 (lift ing 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

1. 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?

2. 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.

3. Now, if you saw a diff erence 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?

4. 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. Note our change in terminology: We now will sometimes call the individuals in the study experimental units instead of observational units, because they are in an experiment instead of an observational study.

5. 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)?

6. 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 diff erence in these two proportions?

You will notice that the diff erence in proportions of males is shown in the dotplot in the bottom graph. In this graph, each dot represents one repetition of the random assignment process where we are recording the diff erence in proportions of men between the two groups.

7. Press the Randomize button again. Was the diff erence in proportions of men the same this time?

8. Change the number of replications from 1 to 198 (for 200 total), uncheck the Animate option, and press the Randomize button. Th e dotplot will display the diff erence between the two proportions of men for each of the 200 repetitions of the random assignment process. Where are these values centered?

9. 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.

10. 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.

11. 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 diff er in the two groups. Does this variable tend to equalize between the two groups in the long run? Explain.

12. 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.

13. 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?

14. As in #13, if you obtain a statistically signifi cant result, what does that suggest about the potential for a cause-and-eff ect relationship? Why?

An article about handwriting appeared in the October 11, 2006, issue of the Washington Post. Th e article mentioned that among students who took the essay portion of the SAT exam in 2005-2006, those who wrote in cursive style scored signifi cantly higher on the essay, on average, than students who used printed block letters.

15. Identify the observational units in this study as well as the explanatory and response variables. Also classify each variable as categorical or quantitative.

Observational units:

Explanatory variable: Type:

Response variable: Type:

16. Explain how you know that this was an observational study.

17. Is it reasonable to conclude that using a cursive writing style caused higher scores on the essay, or can you think of an alternative explanation for why students who wrote in cursive style scored higher on average than students who write with block letters? In other words, can you think of other ways in which the cursive and block letter groups might have systematically diff ered and identify a potential confounding variable?

The same Washington Post article also mentioned a diff erent study in which the identical essay was shown to many graders, but some graders were randomly chosen to see a cursive version of the essay and the other graders were shown a version with printed block letters. Th e average score assigned to the essay with the cursive style was signifi cantly higher than the average score assigned to the essay with the printed block letters.

18. How does this study diff er from the original one? Explain.

19. Would you be willing to draw a cause-and-eff ect conclusion from this study, as opposed to the original study? Explain why.

See the Section summary for a helpful table (Figure 4.5) which summarizes the types of conclusions you can draw with and without random sampling and with and without random assignment.

The "placebo eff ect" has been found in numerous studies: When subjects are told something good is going to happen, they oft en have a positive response even if nothing is actually done to them. For this reason, subjects are oft en kept "blind" as to which treatment group they are placed in, for example by giving one group the actual treatment and the other group a "fake" treatment, like a placebo (an inert pill). Placebo treatments have even been used in studies about knee surgery!

20. Discuss why it was important in this second study for the scorers of the essays to not know that there was no diff erence in the essays given to diff erent individuals other than the writing style.

21. Discuss how this study also reveals that those evaluating the response variable in a study, if it requires any subjective judgment, should be "blind" to which treatment group individuals are in.