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A newspaper designs a survey to estimate the proportion of the population willing to invest in the stock market. It takes a list of the 1000 people who have subscribed to the paper the longest and sends each of them a questionnaire that asks, "Given the extremely volatile performance of the stock market as of late, are you willing to invest in stocks to save for retirement?" After analyzing result from the 50 people who reply, they report that only \(10 \%\) of the local citizens are willing to invest in stocks for retirement. Identify the bias that results from the following: a. Sampling bias due to undercoverage b. Sampling bias due to the sampling design c. Nonresponse bias d. Response bias due to the way the question was asked

Step by step solution

01

Identifying Sampling Bias - Undercoverage

Undercoverage occurs when some members of the population are inadequately represented in the sample. In this case, the survey only includes individuals who have subscribed to the newspaper the longest. This does not represent a fair cross-section of the entire population, as it excludes non-subscribers and others who might be willing to invest in stocks.

02

Analyzing Sampling Bias - Sampling Design

The sampling design can introduce bias if it systematically favors certain outcomes. Here, using only subscribers to the newspaper might bias the results because these individuals may not reflect the broader population's investing habits or intentions, as subscribers may have different financial behaviors compared to non-subscribers.

03

Examining Nonresponse Bias

Nonresponse bias occurs when individuals who do not respond differ in meaningful ways from those who do respond. With only 50 out of 1000 people responding, there is a high chance that those who did not respond have different views about investing in stocks, leading to misleading results.

04

Assessing Response Bias - Question Framing

Response bias can result from the way questions are asked. In this survey, the question references the 'extremely volatile performance of the stock market,' which could influence respondents to answer negatively due to the negative framing, regardless of their actual intentions.

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Key Concepts

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

Sampling Bias

Sampling bias occurs when the sample chosen for the survey does not accurately reflect the overall population. Imagine you are conducting a survey, and you only ask your closest friends what they think. Even if you gather honest answers, it might not represent wider opinions. In the case of the newspaper survey, the sample consisted only of long-term subscribers. This is potentially problematic because:

• It excludes non-subscribers, who might have different views or investment behaviors.
• Long-term subscribers may share certain characteristics or traits, like being more traditional, which can skew the results.

Thus, this biased sampling design can lead to results that do not accurately represent the whole population’s willingness to invest in the stock market.

Nonresponse Bias

Nonresponse bias occurs when there is a significant difference between those who respond to the survey and those who do not. In any survey, you might find that not every person selects to reply. This is a normal thing, but it becomes an issue when the nonrespondents and respondents have differing characteristics.

• In our newspaper example, out of 1000 individuals contacted, only 50 responded. The vast majority, 950 people, didn’t reply.
• Those who did not respond might feel more positively or negatively about investing in stocks than those who did respond. Their silence can lead to skewed results since their opinions aren't captured.

To mitigate this, surveyors could follow up with nonrespondents through reminders or additional questions, aiming to improve the representation of the sample.

Response Bias

Response bias is often introduced through the design of the questions themselves. It happens when the way a question is phrased influences the participant's answer. In this case, the question "Given the extremely volatile performance of the stock market as of late..." might sway people to focus on recent instability rather than their personal investment strategies.

• Such framing can lead people to think about recent turmoil, nudging them towards a negative response even if they were inclined to invest.
• To avoid response bias, questions should be neutral and objective. For instance, asking "Are you willing to invest in stocks for retirement?" without mentioning market performance would yield a more balanced response.

Neutral phrasing ensures that answers reflect true opinions rather than the influence of the question’s wording.

Question Framing

Question framing refers to how the way a question is posed can shape the respondent’s answers. It’s a subtle yet powerful tool that can impact survey results: the same topic can seem different based on its context.

• In the newspaper survey, emphasizing the 'extremely volatile performance' can cause concern and potentially shape responses to reflect apprehension about stock investments.
• A well-framed question should be careful to avoid introducing any presumptions or emotions, ensuring that the focus remains on understanding genuine sentiments.

Proper question framing helps ensure the reliability and validity of survey results by allowing respondents to answer based on their beliefs instead of reacting to the wording alone.