Question 4
Which statement about association and causation is correct?
That is it. Step through the hints below to see why.
Not quite. You treated a strong association as proof of causation. Strength cannot rule out coincidence or another variable.
Not quite. You treated $R^2$ as a measure of cause. $R^2$ only measures how much of the variation in the response the linear model explains.
Not quite. You chose a statement that is too absolute: a causal link can still give a weak association when other factors also affect the response.
Solid arrows: another variable affects each variable. The two variables then move together without one causing the other.
A strong straight-line pattern, yet another variable drives both variables. Neither causes the other.
The points sit close to a line, so $R^2$ is close to 1, yet another variable drives both variables. Neither causes the other.
Solid arrow: the cause changes the effect. Dotted arrow: other factors also affect the response, so the points spread into a weak scatter.
Choose an option to see its statement beside a small diagram.
Statement (A): An association between two variables can be explained by the influence of another variable.
Statement (B): A strong association between two variables shows that a change in one variable causes a change in the other.
Statement (C): A coefficient of determination close to 1 shows that the explanatory variable causes the response variable.
Statement (D): Two variables with a weak association cannot have a causal relationship.
(A) is correct: an observed association can come from coincidence or from another variable that affects both variables.
(B) fails: this association is strong, but another variable drives both variables. Strength cannot rule out coincidence or another variable.
(C) fails: $R^2$ only measures how much of the variation in the response the linear model explains. It says nothing about cause.
(D) fails: here the cause really does change the effect, but other factors spread the points into a weak association.
Try the question first. Choose a hint above when you want one.
An observed association can be explained by coincidence or by the influence of another variable that affects both.
So (A) is correct.
An association on its own never establishes causation.
An association can be explained by coincidence or by another variable that affects both, so an association on its own never establishes causation. Only (A) is consistent with that.
Only mark this done when you could do it without help. Reading the solution does not count.
A Tangent Tuition mock exam question. It is not a past QCAA question, and Tangent Tuition is not affiliated with the QCAA.
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