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NPR Facebook Survey. In 2010, National Public Radio (NPR) conducted a survey of preferences and habits of its Facebook fans by recruiting respondents through messages posted on its Facebook page. The survey was conducted online and deployed July \(12-19\). A total of 40,043 respondents began the survey, with 33,304 completing all questions. It was found that people accessed NPR on the radio, at the website NPR_org, through iPhone apps, and several other platforms. Asked about time spent with NPR, about \(20 \%\) of respondents indicated that they spent more than three hours per day, including radio listening. (a) Here is what NPR says about the survey methodology: "Respondents were self-selected and the resulting sample is non-random-therefore a margin of error cannot be calculated, and the survey results cannot be projected to any population other than the sample itself."18 Why can't inference about any population be made? (b) Suppose that people who spent more time with NPR were more likely to respond to the survey. Do you think the true percentage of NPR's Facebook fans who spend more than three hours with NPR is higher or lower than the \(20 \%\) found from the survey? Explain why.

Step by step solution

01

Understanding the Survey Methodology

The survey conducted by NPR was based on self-selection. This means that respondents decided themselves whether or not to participate in the survey. As a result, the sample was non-random, meaning that not all members of the intended population had an equal chance of being selected.

02

Explaining Non-random Sampling

Since the sample is non-random, it's biased. This bias can occur because the people who chose to participate in the survey might have different characteristics than those who did not participate. As NPR noted, this means that the survey results cannot be generalized beyond the respondent pool, and a margin of error cannot be calculated.

03

Considering Respondent Bias in Time Spent

If individuals who spent more time with NPR were more inclined to participate in the survey, then it is likely that their responses are overrepresented. This can skew the results, showing a higher percentage of people spending more than three hours compared to the true average if the whole population took part.

04

Making a Conclusion about the Survey Results

Given the possibility of respondent bias, where enthusiastic NPR fans might have been more likely to participate, the true percentage of NPR's Facebook fans who spend more than three hours with NPR might be lower than the 20% reported in the survey.

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Key Concepts

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

Non-random Sampling

Non-random sampling is when participants in a survey or study are not selected at random from the entire population. It means that not everyone has an equal chance of being included in the survey. In the NPR Facebook Survey, respondents chose to participate on their own, leading to a non-random sample. This type of sampling can introduce biases, as individuals who opt-in may share certain characteristics that aren't representative of the entire population. For example, people who have a strong opinion or greater interest in a topic are more likely to volunteer to participate in a survey about that topic.
This results in a sample that might not reflect the true diversity and variation of the larger population. Because of this, the survey results can't be generalized beyond the sample itself. That means you can't say the survey results are true for everyone, just for those who participated.

Self-selection Bias

Self-selection bias occurs when the participants of a study or survey have the power to decide whether they join or not. This bias can heavily impact the accuracy of the survey findings. In the NPR survey, because respondents self-selected to participate, those who did might differ in significant ways from those who did not. For instance, if people who feel positively about NPR decide to take the survey, while those who aren't as enthusiastic choose not to, the results will likely skew positively towards NPR.
This form of bias suggests that the survey results might reflect the views of only the most engaged or interested people, not the average opinion of all NPR Facebook fans. This can lead to skewed results that do not accurately portray the entire group's preferences and behaviors.

Margin of Error

The margin of error is a statistic that reflects the amount of random sampling error in a survey's results. It expresses the range within which the true value in the general population is expected to fall, with a certain level of confidence. However, it's important to note that the margin of error assumes a random sample. Since the NPR Facebook Survey used a non-random sampling method through self-selection, a margin of error cannot be accurately calculated.
This absence of a margin of error means there is no reliable way to estimate how much the survey results might deviate from the entire population. Without knowing this potential deviation, researchers cannot confidently project the survey results to a broader population. This limitation confines the reliability of conclusions drawn from the survey to the surveyed group only.

Respondent Bias

Respondent bias refers to the influences that sway survey participants' responses. It occurs when survey respondents have characteristics that lead to consistently biased answers. In the case of the NPR survey, if people who spend more than three hours with NPR each day were more likely to take the survey, this group is overrepresented. These individuals may have reported higher levels of engagement due to their personal preference or habit, rather than accurately reflecting the habits of all NPR Facebook fans.
Such bias impacts the overall results, potentially exaggerating the reported time spent with NPR. This means the true percentage of NPR's Facebook fans who spend over three hours a day may actually be lower than the 20% the survey suggests. Understanding respondent bias helps illustrate why results may not always fully capture the reality of the broader population's behavior or preferences.