Design of a Study: Sampling, Surveys, and Experiments Rapid Review for AP Statistics
Review the following concepts if necessary:
- Samples for AP Statistics
- Sampling Bias for AP Statistics
- Statistical Significance for AP Statistics
- Experiments and Observational Studies for AP Statistics
- You are doing a research project on attitudes toward fast food and decide to use as your sample the first 25 people to enter the door at the local FatBurgers restaurant. Which of the following is (are) true of this sample?
- It is a systematic sample.
- It is a convenience sample.
- It is a random sample.
- It is a simple random sample.
- It is a self-selected sample.
- How does an experiment differ from an observational study?
- What are the three key components of an experiment? Explain each.
- Your local pro football team has just suffered a humiliating defeat at the hands of its arch rival. A local radio sports talk show conducts a call-in poll on whether or not the coach should be fired. What is the poll likely to find?
- It is known that exercise and diet both influence weight loss. Your task is to conduct a study of the effects of diet on weight loss. Explain the concept of blocking as it relates to this study.
- Explain the concept of a double-blind study and why it is important.
- You are interested in studying the effects of preparation programs on SAT performance. Briefly describe a matched-pairs design and a completely randomized design for this study.
Answer: Only (b) is correct. (a), (c), and (d) are all probability samples, which rely on some random process to select the sample, and there is nothing random about the selection process in this situation. (e) is incorrect because, although the sample members voluntarily entered Fat Burgers, they haven't volunteered to respond to a survey.
Answer: In an experiment, the researcher imposes some treatment on the subjects (or experimental units) in order to observe a response. In an observational study, the researcher simply observes, compares, and measures, but does not impose a treatment.
Answer: The three components are randomization, control, and replication. You randomize to be sure that the response does not systematically favor one outcome over another. The idea is to equalize groups as much as possible so that differences in response are attributable to the treatment variable alone. Control is designed to hold confounding variables constant (such as the placebo effect). Replication ensures that the experiment is conducted on sufficient numbers of subjects to minimize the effects of chance variation.
Answer: The poll is likely to find that, overwhelmingly, respondents think the coach should be fired. This is a voluntary response poll, and we know that such a poll is most likely to draw a response from those who feel most strongly about the issue being polled. Fans who bother to vote in a call-in poll such as this are most likely upset at their team's loss and are looking for someone to blame—this gives them the opportunity. There is, of course, a chance that the coach may be very popular and draw support, but the point to remember is that this is a self-selecting nonrandom sample, and will probably exhibit response bias.
Answer: If you did a completely randomized design for this study using diet at the treatment variable, it's very possible that your results would be confounded by the effects of exercise. Because you are aware of this, you would like to control for the effects of exercise. Hence, you block by exercise level. You might define, say, three blocks by level of exercise (very active, active, not very active) and do a completely randomized study within each of the blocks. Because exercise level is held constant, you can be confident that differences between treatment and control groups within each block are attributable to diet, not exercise.
Answer: A study is double-blind if neither the subject of the study nor the researchers are aware of who is in the treatment group and who is in the control group. This is to control for the well-known effect of people to (subconsciously) attempt to respond in the way they think they should.
Answer: Matched pairs: Choose, say, 100 students who have not participated in an SAT prep course. Have them take the SAT. Then have these students take a preparation course and retake the SAT. Do a statistical analysis of the difference between the pre- and postpreparation scores for each student. (Note that this design doesn't deal with the influence of retaking the SAT independent of any preparation course, which could be a confounding variable.)
Completely randomized design: Select 100 students and randomly assign them to two groups, one of which takes the SAT with no preparation course and one of which has a preparation course before taking the SAT. Statistically, compare the average performance of each group.
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