AP Statistics 1.12 Potential Problems with Sampling Study Notes - New Syllabus
AP Statistics 1.12 Sources of Bias in Sampling Methods Study Notes – New Syllabus
AP Statistics 1.12 Sources of Bias in Sampling Methods Study Notes – As per latest AP Statistics Syllabus.
LEARNING OBJECTIVES
- 1.12.A Identify potential sources of bias in sampling methods.
ESSENTIAL KNOWLEDGE:
- 1.12.A.1 Bias in a sampling method is a systematic error in the sampling procedure that results in a statistic being consistently larger or consistently smaller than the parameter the statistic is used to estimate.
- 1.12.A.2 Voluntary response bias is a bias that may occur when a sample consists entirely of volunteers.
- 1.12.A.3 Undercoverage bias may occur when the sampling method fails to include part of the population or a part of the population is less likely to be selected based on the sampling method.
- 1.12.A.4 Nonresponse bias may occur because of a failure to obtain responses from some individuals chosen to be sampled. The respondents and nonrespondents could differ significantly in ways that are important for the study.
- 1.12.A.5 Response bias may occur when responses to a survey or measurements of observational units tend to differ from the “true” value in one direction. Examples include questions that are confusing or leading (question wording bias) or self-reported responses.
- 1.12.A.6 Nonrandom sampling methods (e.g., samples chosen by convenience or voluntary response) introduce potential bias because they do not use random chance to select the individuals.
1.12.A.1 Bias in Sampling Methods
A bias is a systematic error in the sampling procedure that causes sample statistics to consistently overestimate or underestimate the true population parameter.
Because the error is systematic, the sample is not representative of the population.
As a result, conclusions drawn from the sample may be inaccurate.
Bias is different from random variability.
- Random variability occurs naturally because different random samples produce slightly different results.
- Bias consistently pushes the results in one direction.
| Random Variability | Bias |
|---|---|
| Results vary naturally from sample to sample. | Results are consistently too high or too low. |
| Occurs even with good sampling methods. | Occurs because of flaws in the sampling procedure. |
| Can be reduced with larger samples. | Cannot usually be fixed by increasing sample size. |
Important AP Statistics Idea
Bias always affects the sample in a consistent direction.
The sample statistic may be:
- Consistently larger than the population parameter.
- Consistently smaller than the population parameter.
Example
A survey estimates the average number of hours students study each week by asking only students attending after-school tutoring sessions.
Explain why this sampling method is biased.
▶️ Answer / Explanation
The sample is biased because it includes only students who attend tutoring.
These students are likely to study more than the average student.
As a result, the estimated average study time will likely be consistently higher than the true population average.
1.12.A.2 Voluntary Response Bias
Voluntary response bias occurs when a sample consists entirely of individuals who choose to participate.
- People with strong opinions or strong personal interest in the topic are often more likely to respond.
- As a result, the sample may not represent the entire population.
- Because participation is voluntary, certain viewpoints may be overrepresented while others may be underrepresented.
Common Examples
- Online opinion polls.
- Call-in television surveys.
- Social media polls.
- Website questionnaires completed by volunteers.
| Feature | Voluntary Response Bias |
|---|---|
| Who participates? | Individuals choose to participate. |
| Main Problem | People with strong opinions are more likely to respond. |
| Result | The sample may not represent the population. |
Example
A news website asks visitors,
“Should school uniforms be required?”
Anyone visiting the website may vote.
Identify the source of bias.
▶️ Answer / Explanation
This survey suffers from voluntary response bias.
Only people who choose to participate are included.
Individuals with strong opinions are more likely to vote, making the sample unrepresentative of the entire population.
1.12.A.3 Undercoverage Bias
Undercoverage bias occurs when part of the population is excluded from the sampling process or has little chance of being selected.
- As a result, some groups are underrepresented or completely missing from the sample.
- If the excluded individuals differ from those included, the sample statistic may be biased.
- Undercoverage often occurs when the sampling frame does not include every member of the population.
Common Examples
- Surveying only landline telephone users.
- Surveying only students present on one particular day.
- Using an outdated membership list.
- Surveying only people with internet access.
| Feature | Undercoverage Bias |
|---|---|
| Cause | Part of the population is excluded. |
| Main Problem | Some individuals have little or no chance of selection. |
| Result | The sample is not representative of the population. |
Example
A city wants to estimate residents’ opinions about public transportation.
Researchers survey only households with listed landline telephone numbers.
Identify the source of bias.
▶️ Answer / Explanation
This sampling method suffers from undercoverage bias.
Residents without landline telephones cannot be selected.
Because part of the population is excluded, the sample may not accurately represent all city residents.
1.12.A.4 Nonresponse Bias
Nonresponse bias occurs when individuals selected for the sample do not respond or cannot be contacted.
- If the people who do not respond differ significantly from those who do respond, the sample may no longer represent the population accurately.
- Even if the original sample was selected randomly, nonresponse can introduce bias because the final respondents may not reflect the characteristics of the entire population.
Nonresponse bias is common in surveys that have:
- Low response rates.
- People refusing to participate.
- Unanswered survey questions.
- Individuals who cannot be contacted.
| Feature | Nonresponse Bias |
|---|---|
| Cause | Some selected individuals do not respond. |
| Main Problem | Respondents may differ from nonrespondents. |
| Result | The final sample may not represent the population. |
Example
A random sample of 500 employees is selected to complete a job satisfaction survey.
Only 180 employees respond.
Many employees who are dissatisfied choose not to participate.
Identify the source of bias.
▶️ Answer / Explanation
This study suffers from nonresponse bias.
Although the original sample was random, many selected employees did not respond.
If dissatisfied employees are less likely to respond, the survey results will overestimate overall job satisfaction.
1.12.A.5 Response Bias
Response bias occurs when respondents provide answers that differ systematically from their true values or opinions.
This bias is caused by the way responses are collected rather than by the sampling method itself.
Response bias may occur because:
- The survey question is confusing.
- The wording of the question is leading.
- Respondents give socially desirable answers instead of truthful answers.
- Individuals inaccurately report personal information.
Examples include:
- Leading questions.
- Loaded questions.
- Self-reported height or weight.
- Questions about sensitive topics.
| Feature | Response Bias |
|---|---|
| Cause | Responses differ from the true value. |
| Common Causes | Leading questions, confusing wording, self-reporting, social desirability. |
| Result | Survey responses become systematically inaccurate. |
Example
A survey asks:
“Don’t you agree that our school cafeteria provides excellent lunches?”
Identify the source of bias.
▶️ Answer / Explanation
This question creates response bias.
The wording is leading because it encourages respondents to answer positively.
As a result, responses may not accurately reflect students’ true opinions.
1.12.A.6 Bias from Nonrandom Sampling Methods
Nonrandom sampling methods do not use random chance to select individuals.
Because not every individual has an equal opportunity to be selected, these methods often produce biased samples.
Two common examples are:
- Convenience Sampling — selecting individuals who are easiest to reach.
- Voluntary Response Sampling — allowing individuals to choose whether to participate.
Since these methods do not rely on random selection, they may systematically overrepresent certain groups while underrepresenting others.
| Sampling Method | Why It Can Be Biased |
|---|---|
| Convenience Sampling | Only easily available individuals are selected. |
| Voluntary Response Sampling | Only individuals who choose to participate are included. |
Important AP Statistics Idea
- Random sampling methods help reduce bias because every individual has a known chance of being selected.
- Nonrandom sampling methods increase the risk of obtaining an unrepresentative sample.
Example
A researcher wants to estimate the average amount of time college students spend studying each week.
The researcher surveys only students sitting in the campus library on a Saturday afternoon.
Identify the source of bias.
▶️ Answer / Explanation
This study uses convenience sampling, a nonrandom sampling method.
Students studying in the library are easier to reach, but they may study more than the average student.
Therefore, the sample is likely biased and may overestimate the average study time for all college students.