Question

Prior to the mayoral election discussed in Exercise 15, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with \(52 \%\) of the vote. The newspaper was wrong: Amabo lost, getting only \(46 \%\) of the vote. Do you think the newspaper's faulty prediction is more likely to be a result of bias or sampling error? Explain.

Short answer

The incorrect prediction is more likely due to bias than sampling error.

Step-by-step solution

Understanding Bias

Bias in a poll refers to systematic errors that skew results in a particular direction. This could occur if the survey method, questions, or sampling procedure favored one outcome over others. For instance, asking leading questions or excluding certain demographics can introduce bias.

Understanding Sampling Error

Sampling error is the natural variability that arises from having to estimate the population's characteristics from a sample rather than a complete count. Even in a perfectly executed survey, results will not be exact due to the random nature inherent in sampling.

Analyzing the Polling Method

The poll used stratified sampling by political party, age, sex, and area of residence, which generally helps to reduce bias by ensuring that all groups are adequately represented. However, if the final composition was not reflective of actual voter turnout, it could introduce bias.

Comparing Results with Actual Outcome

The expected result was Amabo receiving 52% whereas the actual was 46%. This is a difference of 6%, which is relatively large and could suggest an issue beyond the natural sampling variability, indicating potential bias.

Concluding Likely Cause

Given the size of the error, bias seems a more plausible explanation than sampling error, particularly if unmeasured factors or incorrect assumptions about voter turnout influenced the stratification process.

Key concepts

Bias in Statistics

When we talk about bias in statistics, we are referring to a systematic error that skews the results of a study. This occurs when certain groups are overrepresented or underrepresented. Imagine you're asking people their favorite fruit, but you only survey kids at a banana-themed birthday party. Your results will likely be biased toward bananas. In polls, bias can creep in at various stages, whether through the phrasing of questions, the method of data collection, or the sample selection process.

• Leading questions can mislead respondents and incline results.
• Excluding specific demographics can make findings less credible.

Recognizing and minimizing bias is critical as it ensures the integrity and accuracy of predictive data. Reducing bias helps us make fair and informed decisions based on statistics.

Sampling Error

Sampling error reflects the natural variability when estimating a population's traits from a sample. Think about exams where you select a few questions to answer; your score might not perfectly represent your knowledge if all questions were considered. In statistics, sampling error is the difference between the actual population values and the sample results. This error is unavoidable but should be minimized with proper sampling methods.

• Even in ideal surveys, results will never match the entire population exactly.
• Understanding sampling error helps in setting realistic expectations from the poll outcomes.

By acknowledging the role of sampling error, statisticians can adjust their interpretations and recommendations, ensuring a more nuanced approach to data analysis.

Stratified Sampling

Stratified sampling is a statistical method that can help reduce bias by ensuring that all population subgroups are represented. Think of it like preparing a salad where you want equal parts of each vegetable type for a balanced flavor. In stratified sampling, the population is divided into subgroups, or "strata," based on shared characteristics like age, political affiliation, or residence. From each subgroup, a sample is taken proportionate to its size in the total population.

• This method helps capture diversity and ensures comprehensive representation.
• It improves the accuracy of the predictions compared to random sampling.

Using stratified sampling in polls is advantageous, but the process must be calibrated to match real-world conditions like voter turnout to avoid skewed predictions.

Polling Methods

Polling methods encompass the strategies used to collect and analyze public opinion data. The effectiveness of polling relies heavily on the choice and execution of these methods. A reliable poll should reflect the true opinions of the entire population, not just a segment of it.

• Methods can include telephone surveys, online questionnaires, or face-to-face interviews.
• Each method has its own strengths and weaknesses, like reaching different demographics or handling non-responses.

Stratified sampling is one such method, aimed at getting a more accurate sample by accounting for variables like party, age, and sex. It's crucial that polling methods adapt to reflect true population behavior and compositions to minimize room for error.