Running a Statistical Investigation
Plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences.
Bivariate means two variables measured on the same thing. The whole investigation exists to answer one question: do they move together? And if so, can you say why?
Builds onYr 10 · Bias in Statistical Claims
Method
Write the question before collecting anything
A vague question produces data you cannot use. Name both variables and the group being studied.
Bivariate means paired
Each data point is two measurements from the same individual. Two separate lists are not bivariate data.
Describe an association three ways
Strength, direction and linearity. All three, every time.
Report the limitations
Sample size, how it was chosen, what was not measured. Findings without limitations are incomplete answers.
Worked example
e.g.
- State the question with both variables and the population named.
- Decide how each variable will be measured. Decide how the sample will be chosen.
- Collect paired values. Every point must come from the same student.
- Plot them on a scatterplot. The explanatory variable goes on the horizontal axis.
- Describe the association: strength, direction, linearity.
- Draw a conclusion that answers the question asked, in context.
- Report the limitations, then say what you would do differently.
Practice
There is no calculation here. Judge the investigation.
ReasoningExplain why. Say it in your own words.
1
A student collects hours of homework from one class and test scores from a different class. What is wrong?
AnswerThe data is not paired. Bivariate data needs both measurements from the same individual, otherwise no point on the scatterplot means anything.
2
A scatterplot shows points scattered widely but trending upward. How do you describe it?
AnswerWeak, positive, and roughly linear. Give all three descriptors — naming only the direction is a partial answer.
3
The investigation finds a strong positive association and concludes homework causes higher marks. What is the flaw?
AnswerAssociation is not causation. Stronger students may simply choose to do more homework, so the causation could run the other way, or a third factor could drive both.
AppliedThe same maths, inside a real question.
1
Your sample is the 28 students in your own class. State two limitations.
AnswerThe sample is small, so one unusual student shifts the pattern noticeably. It is also not random — one class shares a teacher, a timetable and a year level, so the finding cannot be extended to the school or beyond.
2
Your scatterplot shows one point far from the rest. What should you do?
AnswerInvestigate rather than delete. Check whether it is a recording error, and if it is genuine, report the analysis both with and without it, saying what difference it makes.