Question

A local TV station conducted a "PulsePoll" about the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the latenight news. Based on the phone calls, the station predicted that Amabo would win the election with \(52 \%\) of the vote. They were wrong: Amabo lost, getting only \(46 \%\) of the vote. Do you think the station's faulty prediction is more likely to be a result of bias or sampling error? Explain.

Short answer

The faulty prediction was likely due to bias from voluntary response sampling.

Step-by-step solution

Understanding the Problem

The local TV station conducted a poll by asking evening news viewers to phone in their votes for the upcoming mayoral election. The station predicted that Amabo would win with 52% of the votes, but in reality, Amabo received only 46%. We need to determine if the inaccurate prediction was due to bias or sampling error.

Define Bias and Sampling Error

Bias refers to systematic errors introduced into sampling or testing by selecting or encouraging one outcome over others. Sampling error, on the other hand, refers to the variation in the sample estimate from the true population parameter purely due to chance.

Analyzing the Sampling Method

The poll relied on viewers who voluntarily called in. This sampling method is voluntary response sampling, which is likely to introduce bias because it might not represent the entire eligible voting population properly. Evening news viewers who call are a self-selected group and may not reflect the broader electorate's opinions.

Evaluate the Potential for Sampling Error

While sampling error is always a possibility whenever a sample is taken, a 6% difference (52% predicted vs. 46% actual) is quite large for typical sampling error associated with random sampling unless the sample size was very small. However, given the self-selection method, bias is the more plausible cause.

Conclusion

Since the poll allowed a specific group (evening viewers) to voluntarily participate, it likely led to a non-representative sample (bias). The significant difference between the predicted 52% and the actual 46% suggests that bias rather than random sampling error is responsible for the inaccurate prediction.

Key concepts

Voluntary Response Sampling

Voluntary response sampling is a particular method of gathering data where individuals choose to participate entirely on their own. This approach often leads to a skewed dataset, primarily because it captures responses from people who feel strongly about the subject, leading to overrepresentation of those opinions.
For instance, in the TV station's "PulsePoll," only those viewers who were motivated enough to call in would have their votes counted. This means:

• The sample is not randomly selected from the population.
• There is a high potential for bias, as it doesn't accurately reflect the broader population's opinions.

This method is often used for polling because it's cost-effective and easy to implement. However, it seldom provides an accurate picture of the public's broader opinion.

Sampling Error

Sampling error refers to the natural variation that can occur when a sample is used to estimate a parameter of a population. This error occurs strictly due to chance and is not influenced by any bias in the sampling method.
In our example, if the local TV station had used random sampling and still ended up with the 6% discrepancy between their prediction and the actual results, it could have been attributed to sampling error.
Let's consider the characteristics of sampling error:

• It reduces with an increase in sample size. A larger sample generally provides a more accurate reflection of the population because there are more data points over which chance variations average out.
• It is an expected aspect of data collection and usually smaller than the observed discrepancy when bias like that from voluntary response sampling is present.

This concept highlights the importance of choosing the right sampling methods to avoid surprising discrepancies.

Non-representative Sample

A non-representative sample occurs when the individuals in your data collection do not faithfully reflect the larger population. This can happen through several routes, such as voluntary participation, time-based constraints, or geographic limitations.
In the exercise case, the TV station's poll ended up with a non-representative sample because:

• The viewers who call in are likely an unrepresentative subset of the general population, since perhaps only certain demographics are watching TV at that time and have the inclination to call.
• Non-representative samples often lead to bias, as the surveyed group does not match the diversity and viewpoints of the whole set of voters.

It's crucial to design surveys or polls with methodologies that consider the full spectrum of the population to avoid non-representation issues.