Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- A statistic from a sample estimates a parameter of the population.
- Bias is a systematic error in the sampling method: the statistic tends to be consistently above, or consistently below, the parameter.
- Chance variation is different: random samples miss the parameter by small amounts on both sides.
- Nonrandom samples (convenience, voluntary response) do not use chance to choose individuals, so they are open to bias.
- A larger sample does not remove bias.
Key relationships
| Kind of bias | Stage | What happens | Quick example |
|---|---|---|---|
| Undercoverage | Who can be chosen | Part of the population is left out or less likely to be picked | Online-only survey misses people without internet |
| Voluntary response | How they are chosen | The sample is made up entirely of volunteers; strong opinions are over-represented | Phone-in poll on a radio show |
| Convenience (nonrandom) | How they are chosen | Easiest-to-reach individuals are used | Asking only your own class |
| Nonresponse | Who answers | Chosen individuals do not reply, and they differ from those who do | 28% of posted questionnaires returned, mostly by keen families |
| Response | What they say | Answers or measurements drift one way from the truth | Leading question; self-reported exercise; a scale that reads heavy |
Assumptions and conventions
- Bias belongs to the method, judged over many samples taken the same way. One sample can land near the parameter by luck.
- Random selection prevents bias in who is chosen only. Nonresponse, response bias and an incomplete list can still bias a random sample.
- Nonresponse: the researcher chose the people. Voluntary response: the people chose themselves.
Mistakes to avoid
- No direction. Say whether the estimate is likely too high or too low, and why.
- No context. Name the people who are missed or over-represented in this study.
- Mixing up nonresponse and voluntary response.
- Saying a bigger sample fixes bias. It only makes a biased estimate more precise.
- Calling every difference from the parameter “bias”. Chance variation is not bias.
- Stopping at “it could be biased” without naming the kind of bias.
Quick self-check
- A gym emails a questionnaire to 400 randomly chosen members and 90 reply. What is the response rate, and what kind of bias should you worry about? (90 ÷ 400 = 22.5%; nonresponse bias)
- A website asks visitors to rate a new film; 3,000 do. Which bias is most likely? (Voluntary response bias)
- “Wouldn’t you agree that homework is a waste of time?” Which bias, and which direction for the proportion who think homework is a waste of time? (Response bias from question wording; the proportion is likely too high)
Next: practice questions.