The idea, step by step
Bias has a direction
Selection bias favours some groups through the sampling method. Leading wording or pressure can cause response bias. Non-response matters if those who reply differ systematically from those who do not. These are different from ordinary variation between fair random samples; an unexpected result is not automatically a biased result.
Do not overstate the evidence
Report “in this sample” when describing respondents. Check unusual observations for genuine recording errors, but do not delete valid values merely to improve a result. Selective scales or time periods can promote a viewpoint. Explain uncertainty and analytical choices so a reader can judge the claim.
A common trap
Delete a surprising observation so the result looks sensible.
Instead: Check for error, but retain valid unusual observations and discuss their effect.
See the thinking
Worked example 1
A gym survey finds 90% exercise daily. Can it be confidently generalised to all students?
- Gym visitors are likely to exercise more often.
- The frame favours a relevant group.
- A larger gym-only sample would retain the problem.
Worked example 2
Two fair samples of 50 find 27 and 31 supporters. Compare their percentages.
- 27/50=54%; 31/50=62%.
- Difference=8 percentage points.
- Variation alone might explain this difference.
Check your understanding
What is wrong with “Don’t you agree our excellent canteen deserves more funding?”
Show answer
Leading wording.
Praise and suggested agreement may influence responses.
Your turn
6 questions · 15 marks · Work at your own pace.
Read the questions online
- Rewrite “Don’t you agree homework is a waste of time?” neutrally.2 marks
- Of 100 invitees, 40 reply and 24 say yes. Find the yes percentage among respondents and state a limitation.3 marks
- A fair sample of 40 includes 12 walkers. Estimate the number among 800 students and state a limitation.3 marks
- Must one calculation be wrong if two random samples have different means?2 marks
- A report calls the single week with the longest queue typical. Explain the concern.2 marks
- Give a transparent way to discuss a valid outlier.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Rewrite “Don’t you agree homework is a waste of time?” neutrally.2 marks
Remove the suggested judgement.
For example: “How useful do you find homework?” with balanced response options. - Of 100 invitees, 40 reply and 24 say yes. Find the yes percentage among respondents and state a limitation.3 marks
24/40×100=60%.
The remaining 60 invitees have not supplied answers.
60%; non-respondents’ views are unknown. - A fair sample of 40 includes 12 walkers. Estimate the number among 800 students and state a limitation.3 marks
12/40=0.3.
0.3×800=240.
About 240; another fair sample may differ. - Must one calculation be wrong if two random samples have different means?2 marks
Ordinary sampling variation is possible.
No. Different sampled values can correctly produce different means. - A report calls the single week with the longest queue typical. Explain the concern.2 marks
Selective timing can promote a misleading conclusion.
An exceptional selected period may not represent ordinary conditions. - Give a transparent way to discuss a valid outlier.3 marks
Do not silently remove inconvenient valid data.
Report it, examine its effect, and explain any comparison with and without it.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Population, census and sample; observational versus experimental data; random and non-random sampling; primary/secondary data; reviewing numerical displays and summary statistics; comparing samples and sample sizes; bias, variation and uncertainty; planning, conducting and reporting a fair investigation.
Official curriculum source ↗