A good statistical investigation follows a clear, ethical process. Start with a specific, answerable question. Choose a fair sampling method — random selection, not just asking whoever is convenient (which can bias results toward people similar to you). Collect data consistently, using the same method and questions for everyone. When reporting findings, be honest about uncertainty — a sample gives an estimate, not a certain fact, and ethical reporting acknowledges the sample size, method, and any limitations rather than overstating confidence in the result.
Example
Investigating "what proportion of Year 8 students at this school walk to school?" by only asking your own friends would bias the result toward students who live near you. A fairer method randomly selects students across the whole year level, then reports the result honestly: "based on a random sample of 40 students, an estimated 35% walk to school" — not an overstated "35% of students walk to school" stated as pure fact.
Key terms
Bias:
A systematic skew in results caused by an unfair sampling or collection method.
Ethical reporting:
Honestly acknowledging a result's sample size, method and limitations, rather than overstating certainty.
Questions
1. A good statistical investigation starts with:
A specific, answerable question
Guessing an answer first
Skipping straight to conclusions
No plan at all
2. A fair sampling method involves:
Random selection
Only asking whoever is convenient
Only asking your friends
Choosing people who agree with you
3. Bias in a survey means:
A systematic skew caused by an unfair method
A perfectly fair, random result
A type of data collection error that never happens
Nothing important
4. Only asking your own friends about a school-wide question would likely:
Bias the results
Guarantee a perfectly fair result
Have no effect on the results
Be the most accurate method possible
5. Ethical reporting of survey results means:
Being honest about sample size, method and limitations
Overstating confidence in the result
Hiding how the data was collected
Ignoring the sample size entirely
6. A sample gives you:
An estimate, not a certain fact
A guaranteed, exact fact
No useful information at all
The same as a full census always
7. Collecting data consistently means:
Using the same method and questions for everyone
Changing the question for each person
Only collecting data once from one person
Ignoring consistency entirely
8. Why might a survey question worded as "Don't you agree this policy is great?" be considered biased?
It leads respondents toward a particular answer rather than asking neutrally
This wording has no effect on how people respond
Leading questions always produce more accurate results
Bias can only occur in sampling, never in question wording
9. Why is randomly selecting participants generally fairer than choosing whoever is easiest to reach?
Convenient sampling can systematically over-represent certain types of people, skewing results
Convenience sampling always produces identical results to random sampling
Randomness has no effect on fairness
Ease of access has no connection to bias
10. Reporting "based on a sample of 40 students, an estimated 35% walk to school" rather than stating it as pure fact demonstrates:
Ethical, honest acknowledgement of uncertainty
Dishonest, misleading reporting
A meaningless distinction with no real difference
An error in the investigation
11. Why might using inconsistent questions for different survey participants make the results unreliable?
Comparing answers to different questions doesn't give a fair, consistent picture of the same thing
Inconsistent questions always produce more accurate results
Consistency in surveying has no bearing on reliability
Every participant should always be asked something different
12. A researcher only surveys people online, missing those without internet access. This is an example of:
A potential source of sampling bias
A perfectly representative sampling method
An ethical method with no drawbacks
A random sampling method
13. Why should a statistical investigation start with a specific question rather than a vague one?
A specific question can actually be answered clearly with collected data
Vague questions are always easier to answer with data
Specificity has no effect on the quality of an investigation
A vague question always produces more useful results
14. Why is acknowledging a small sample size an important part of ethical reporting?
It helps readers judge how much confidence to place in the finding, rather than assuming it as certain fact
Acknowledging sample size makes a result seem less trustworthy for no reason
Ethical reporting should hide the sample size to seem more confident
Sample size is irrelevant to how a result should be interpreted
15. Why might a company selectively reporting only the survey results that support their product be considered unethical?
It misleads the audience by hiding relevant, contradicting information
Selective reporting is always the most honest approach
Companies have no ethical obligations when reporting survey data
Hiding unfavourable results has no effect on how trustworthy the report seems
16. A student investigating "what percentage of students prefer online or in-person learning" surveys only students already enrolled in an online course. Why is this a flawed sampling method?
These students are likely to already prefer online learning, biasing the sample toward one answer
This sampling method perfectly represents the whole student population
Surveying a pre-selected group never introduces bias
This is actually the most representative approach possible
17. Why might a well-designed statistical investigation include a plan for how data will be analysed before collecting it, rather than deciding afterward?
Planning analysis in advance helps prevent selectively interpreting data in a way that fits a desired conclusion
Analysis plans have no effect on the fairness or ethics of an investigation
Deciding how to analyse data after seeing it is always the more rigorous approach
Pre-planning analysis makes an investigation less reliable
18. Why is transparency about a study's limitations (small sample, potential bias, method) considered a mark of good statistical practice, not weakness?
It allows others to fairly judge how much weight to give the findings, supporting trust in the research
Acknowledging limitations always makes a study worthless
Good research should hide any weaknesses to appear stronger
Transparency has no bearing on the credibility of research
19. A student's investigation into sleep habits only surveys classmates who are already awake and alert during a morning class. Why might this undercount how many students struggle with sleep?
Students who struggle most with sleep might be absent, late or less alert, making them less likely to be surveyed as usual
This sampling approach has no effect on the accuracy of the sleep data
Every possible sleep pattern would be equally represented in this classroom
This is the fairest, most representative way to investigate sleep habits
20. A council wants to know if residents support a new bike lane, and surveys people leaving a cycling club meeting. Why is this a flawed approach to planning the investigation?
Cyclists are far more likely to already support the bike lane, systematically skewing the result toward "yes"
Surveying any group of residents always gives an equally fair result
This is the most representative sample the council could choose
Sampling location has no effect on the fairness of a survey
21. Understanding how to plan a fair, ethical statistical investigation mainly helps you to:
Design and report research that genuinely and honestly reflects a population, not just a convenient or biased slice of it
Choose the sampling method that produces the most convenient result
Avoid ever acknowledging a study's limitations
Treat every survey result as an absolute, certain fact
Answer key (parent copy)
1. A specific, answerable question
2. Random selection
3. A systematic skew caused by an unfair method
4. Bias the results
5. Being honest about sample size, method and limitations
6. An estimate, not a certain fact
7. Using the same method and questions for everyone
8. It leads respondents toward a particular answer rather than asking neutrally
9. Convenient sampling can systematically over-represent certain types of people, skewing results
10. Ethical, honest acknowledgement of uncertainty
11. Comparing answers to different questions doesn't give a fair, consistent picture of the same thing
12. A potential source of sampling bias
13. A specific question can actually be answered clearly with collected data
14. It helps readers judge how much confidence to place in the finding, rather than assuming it as certain fact
15. It misleads the audience by hiding relevant, contradicting information
16. These students are likely to already prefer online learning, biasing the sample toward one answer
17. Planning analysis in advance helps prevent selectively interpreting data in a way that fits a desired conclusion
18. It allows others to fairly judge how much weight to give the findings, supporting trust in the research
19. Students who struggle most with sleep might be absent, late or less alert, making them less likely to be surveyed as usual
20. Cyclists are far more likely to already support the bike lane, systematically skewing the result toward "yes"
21. Design and report research that genuinely and honestly reflects a population, not just a convenient or biased slice of it