91Ó°ÊÓ

Judging sampling design \(\quad\) In each of the following situations, summarize negative aspects of the sample design. a. A newspaper asks readers to vote at its Internet site to determine whether they believe government expenditures should be reduced by cutting social programs. Based on 1434 votes, the newspaper reports that \(93 \%\) of the city's residents believe that social programs should be reduced. b. A congresswoman reports that letters to her office are running 3 to 1 in opposition to the passage of stricter gun control laws. She concludes that approximately \(75 \%\) of her constituents oppose stricter gun control laws. c. An anthropology professor wants to compare attitudes toward premarital sex of physical science majors and social science majors. She administers a questionnaire to her Anthropology 437, Comparative Human Sexuality class. She finds no appreciable difference in attitudes between the two majors, so she concludes that the two student groups are about the same in their views about premarital sex. d. A questionnaire is mailed to a simple random sample of 500 household addresses in a city. Ten are returned as bad addresses, 63 are returned completed, and the rest are not returned. The researcher analyzes the 63 cases and reports that they represent a "simple random sample of city households."

Step by step solution

01

Situation a - Identify the Polling Method

The newspaper is using an Internet poll, which is a type of voluntary response sample. This inherently attracts only those readers who feel strongly about the issue and choose to participate, leading to biased results that do not accurately represent the entire population of the city's residents.

02

Situation a - Evaluate the Conclusion

The conclusion drawn that 93% of the city's residents support reducing social programs based on the Internet votes lacks validity. The sample is not representative of the whole population because it includes only individuals who decided to participate in the online poll.

03

Situation b - Analyze the Source of Data

The congresswoman is using letters received in her office as the data source. This data reflects those constituents who are motivated to write, typically those with stronger opinions. This method of sampling leads to overrepresentation of these views and cannot reliably infer the opinions of all constituents.

04

Situation b - Critique the Conclusion

Concluding that 75% of constituents oppose stricter gun control laws based on the letters received is misleading. This approach is biased as it does not include the opinions of those who did not write, who might have different views.

05

Situation c - Review the Sampling Frame

The professor surveyed students in her Anthropology 437 class, which is a convenience sample. This approach is limited because the class does not represent the full range of majors at the institution, leading to skewed results based on a non-representative sample.

06

Situation c - Assess the Generalization

Concluding no appreciable difference between the two majors in terms of views on premarital sex is flawed because the sample is not randomly selected across the university. The views of these students may not be representative of their entire peer groups in physical and social sciences.

07

Situation d - Describe the Sampling Method

The researcher mailed questionnaires to a simple random sample of 500 addresses. However, with only 63 responses, the return rate is very low, leading to nonresponse bias. This means the results may not reflect the views of all households in the city.

08

Situation d - Examine the Representation

The conclusion that the 63 completed cases represent a simple random sample is incorrect. Due to low response rate and potential nonresponse bias, these results should not be generalized to reflect the views of the entire city.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Voluntary Response Sampling

Voluntary response sampling is a method where individuals choose whether to participate in a study. This generally leads to a self-selected group that does not represent the entire population. People with strong opinions are more likely to respond.
- For example, when a newspaper asks its readers to vote on an issue at their website, it is relying on voluntary response sampling. This means that the survey results are likely to be skewed towards those who feel strongly about the topic and are motivated to respond, such as in situation (a) from the exercise.
- The problem lies in the fact that those who are indifferent or less motivated to respond won’t participate, leading to biased outcomes. This skew can make it appear as though a majority supports or opposes an issue when that may not be the case.

Nonresponse Bias

Nonresponse bias occurs when a significant portion of the individuals selected for a survey do not respond, which can make the results unrepresentative of the entire population. This type of bias affects the validity of the study's conclusions.
- In situation (d) from the exercise, where a questionnaire was sent out to households, only a small number of replies were received. As a result, the sample is not fully reflective of the population since many households did not provide their input.
- The opinions of non-responders could be systematically different from those who responded, skewing the results. Addressing nonresponse bias is crucial to ensure that survey findings are genuinely indicative of the population's views.

Convenience Sampling

Convenience sampling involves choosing individuals who are easiest to reach or sample. This approach, although simple, can lead to biased results because the selected sample is not random.
- When an anthropology professor surveys students from her own class to draw conclusions about the views of physical science and social science majors, she utilizes convenience sampling, as described in situation (c) from the exercise.
- The problem with convenience sampling is that those easily accessible (such as a professor's class) do not necessarily reflect the larger group the study aims to understand. This approach risks over- or under-representing certain opinions, making it unreliable for making generalizations.

Representative Sample

A representative sample accurately reflects the population as a whole, capturing all significant diversity within it – be that age, gender, income, or behavior traits.
- Ensuring that a sample is representative is crucial since only then can we confidently generalize the study's results to the entire population.
- Without a representative sample, conclusions drawn from the study can be misleading or incorrect because certain segments of the population are over- or under-represented. For instance, if conclusions are drawn from a biased or non-representative set of responses, as mentioned in several examples from the exercise, the study cannot be used to accurately portray public opinion.
- Ensuring random, extensive, and inclusive sampling techniques and addressing potential biases are essential to achieve a representative sample.