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Survey bias happens when a survey method systematically pushes results away from the truth. This cheat sheet helps students identify the most common types of bias before interpreting survey conclusions. It is useful for statistics problems involving polls, questionnaires, sampling plans, and real-world claims. Recognizing bias helps students decide whether survey results are trustworthy. The core idea is that a good survey should represent the population and collect honest, clear responses. Important concepts include selection bias, undercoverage, nonresponse bias, voluntary response bias, response bias, and wording bias. Students should also know that random sampling reduces bias but does not automatically fix poor question wording or low response rates. A useful measure is response rate, given by response rate=number of responsesnumber selected×100%\text{response rate} = \frac{\text{number of responses}}{\text{number selected}} \times 100\%.

Key Facts

  • Selection bias occurs when the sampling method favors some members of the population over others.
  • Undercoverage is a type of selection bias where part of the population has little or no chance of being included.
  • Voluntary response bias occurs when people choose whether to participate, often causing strong opinions to be overrepresented.
  • Nonresponse bias occurs when selected people do not respond and the nonresponders differ from responders in an important way.
  • Response bias occurs when answers are inaccurate because people lie, forget, feel pressured, or misunderstand the question.
  • Wording bias occurs when a question is leading, confusing, emotionally loaded, or suggests a preferred answer.
  • The response rate is response rate=number of responsesnumber selected×100%\text{response rate} = \frac{\text{number of responses}}{\text{number selected}} \times 100\%.
  • A simple random sample gives every group of size nn from a population of size NN an equal chance of being selected.

Vocabulary

Population
The population is the entire group of individuals or objects that a survey wants to describe.
Sample
A sample is the smaller group selected from the population to provide data.
Selection Bias
Selection bias is a systematic error caused by choosing a sample that does not fairly represent the population.
Nonresponse Bias
Nonresponse bias happens when people chosen for the survey do not respond and their missing answers would change the results.
Response Bias
Response bias happens when the answers given are inaccurate because of pressure, memory errors, dishonesty, or misunderstanding.
Wording Bias
Wording bias happens when the wording of a question influences people toward a particular answer.

Common Mistakes to Avoid

  • Calling every bad survey random error is wrong because bias is systematic and tends to push results in a consistent direction.
  • Assuming a large sample removes bias is wrong because a large biased sample can still give a very inaccurate estimate.
  • Ignoring who was left out is wrong because undercoverage can make the sample different from the target population.
  • Treating voluntary online polls as representative is wrong because people with strong opinions are more likely to respond.
  • Blaming only the sample when the question is leading is wrong because wording bias can affect responses even with a well-chosen sample.

Practice Questions

  1. 1 A school emails a survey to 800800 students, and 240240 respond. Find the response rate using response rate=number of responsesnumber selected×100%\text{response rate} = \frac{\text{number of responses}}{\text{number selected}} \times 100\%.
  2. 2 A city survey calls 500500 landline phone numbers to estimate how many residents support a new bus route. Identify the most likely type of bias and explain why.
  3. 3 In a poll of 1,2001{,}200 website visitors, 900900 vote in favor of a new rule. What percent of the voluntary respondents support the rule?
  4. 4 A survey asks, "Do you agree that our excellent school lunch program should continue?" Explain why this question may produce biased results.