Sampling Bias for AP Statistics
Practice problems for these concepts can be found at:
- Design of a Study: Sampling, Surveys, and Experiments Multiple Choice Practice Problems for AP Statistics
- Design of a Study: Sampling, Surveys, and Experiments Free Response Practice Problems for AP Statistics
- Design of a Study: Sampling ,Surveys, and Experiments Review Problems for AP Statistics
- Design of a Study: Sampling, Surveys, and Experiments Rapid Review for AP Statistics
Any sample may contain bias. What we are trying to avoid is systematic bias, which is the tendency for our results to favor, systematically, one outcome over another. This can occur through faulty sampling techniques or through faults in the actual measurement instrument.
One type of bias results from undercoverage. This happens when some part of the population being sampled is somehow excluded. This can happen when the sampling frame (the list from which the sample will be drawn) isn't the same as the target population. It can also occur when part of the sample selected fails to respond for some reason.
- example: A pollster conducts a telephone survey to gather opinions of the general population about welfare. Persons on welfare too poor to be able to afford a telephone are certainly interested in this issue, but will be systematically excluded from the sample. The resulting sample will be biased because of the exclusion of this group.
Voluntary Response Bias
Voluntary response bias occurs with self-selected samples. Persons who feel most strongly about an issue are most likely to respond. Non-response bias, the possible biases of those who choose not to respond, is a related issue.
- example: You decide to find out how your neighbors feel about the neighbor who seems to be running a car repair shop on his front lawn. You place a questionnaire in every mailbox within sight of the offending home and ask the people to fill it out and return it to you. About 1/2 of the neighbors return the survey, and 95% of those who do say that they find the situation intolerable. We have no way of knowing the feelings of the 50% of those who didn't return the survey—they may be perfectly happy with the "bad" neighbor. Those who have the strongest opinions are those most likely to return your survey—and they may not represent the opinions of all. Most likely they do not.
- example: In response to a question once posed in Ann Landers's advice column, some 70% of respondents (almost 10,000 readers) wrote that they would choose not to have children if they had the choice to do it over again. This is most likely representative only of those parents who were having a really bad day with their children when they decided to respond to the question. In fact, a properly designed opinion poll a few months later found that more than 90% of parents said they would have children if they had the chance to do it all over again.
Wording bias occurs when the wording of the question itself influences the response in a systematic way. A number of studies have demonstrated that welfare gathers more support from a random sample of the public when it is described as "helping people until they can better help themselves" that when it is described as "allowing people to stay on the dole."
- example: Compare the probable responses to the following ways of phrasing a question.
- "Do you support a woman's right to make medical decisions concerning her own body?"
- "Do you support a woman's right to kill an unborn child?"
It's likely that (i) is designed to show that people are in favor of a woman's right to choose an abortion and that (ii) is designed to show that people are opposed to that right. The authors of both questions would probably argue that both responses reflect society's attitudes toward abortion.
- example: Two different Gallup Polls were conducted in Dec. 2003. Both involved people's opinion about the U.S. space program. Here is one part of each poll.
- Poll A: Would you favor or oppose a new U.S. space program that would send astronauts to the moon? Favor—53%; oppose—45%.
- Poll B: Would you favor or oppose U.S. government spending billions of dollars to send astronauts to the moon? Favor—31%; oppose—67%.
(source: http://www.stat.ucdavis.edu/~jie/stat13.winter2007/lec18.pdf )
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