These exercises all propose causal links. Your job is to design experiments illustrating each of our three types - randomized, prospective, and retrospective - for the proposed causal link. If it seems practically impossible or unethical to carry out one of these types of experiments in the case at hand, explain why. As you go about designing each experimental test, try to criticize your own work. In particular, make sure you are satisfied with the answers to the following questions:

1. Do you have a good sense, statistically speaking, of the level of effect required to indicate a causal link?

2. Have you controlled for other causal factors that might effect the outcome of your experiment?

3. Does your experimental design rule out the possibility of experimenter bias?

4. Does it rule out effects due to experimental subject expectations?

[At this time do only the first problem below.]

1. Of all people who see chiropractors for lower back problems, 70% report some improvement within 90 days. Is chiropractic manipulation of the spine more effective at treating lower back problems than the methods of treatment employed by mainstream medical doctors? For lower back problems, medical doctors typically prescribe drugs - anti-inflammatories and muscle relaxers - and, in many cases, surgery.

2. Maybe class attendance by itself doesn't have much effect on test performance; a student might attend every class but fail to pay attention to what is going on. And students who pay careful attention to my lectures generally take extensive notes. Thus it seems to me that one factor contributing to high test scores is note-taking. Students who take extensive notes will do better on tests than those who do not.

3. Have you ever had a powerful urge while watching a movie at a theater to purchase popcorn, candy, soft drinks, or the like? No matter how exciting the film, it seems all you can think of is food, food, food. The urge seems to arise even when you are not particularly hungry or thirsty. Though you may not realize it, you may be the victim of subliminal advertising. Here's how it works. When we see a minute's worth of film we actually see nearly 1000 individual frames. Yet consciously we are not aware of any single frame. What some filmmakers allegedly do is insert a single frame every minute or so that contains pictures of various refreshments and a written message like "buy these things now." Even though you are not consciously aware of this message, your subconscious mind may pick it up with the result that you feel a vague urge to purchase the pictured refreshments. The more times you "see" the message, the stronger the urge becomes. Is it any wonder, then, that we so frequently leave an interesting, compelling film to buy junk food we probably don't even want?