Describing Association
Learn to describe how two variables are associated for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-06). From a scatter plot you describe its form, strength and direction, or say there is no correlation when no trend shows.
You will decide whether the pattern is linear or non-linear, judge whether a linear trend is weak, moderate or strong, call it positive or negative, then combine all three in one clear sentence — such as “a moderate negative linear association between hours of gaming and running distance”.
Theory
The association on a scatter plot is described by its direction (positive or negative), its strength (strong, moderate or weak) and its form (linear or non-linear) — or as no correlation when there is no trend. This Year 12 Standard 1 (NSW) guide shows how to put the three together in one clear sentence.
Read the points from left to right. The direction is positive if the points rise, negative if they fall, and there is no correlation if they neither rise nor fall.
The strength is how closely the points follow the trend: very close to a line is strong, a clear trend with some scatter is moderate, and a trend only just visible is weak.
The form is linear if the points follow a straight line and non-linear if they follow a curve. Put it together, strength first: e.g. “a strong positive linear association”.
There is no formula — describe the scatter in this order:
| Feature | Choices | What to look for |
|---|---|---|
| Direction | positive / negative / none | do the points rise or fall from left to right? |
| Strength | strong / moderate / weak | how close are the points to the trend? |
| Form | linear / non-linear | a straight line or a curve? |
How to describe the association on a scatter plot
- Read left to right: rising is positive, falling is negative, no trend is no correlation.
- Judge the strength by how closely the points follow the trend.
- Decide the form: straight line (linear) or curve (non-linear).
- Write one sentence, strength first, naming both variables.
Work through direction, then strength, then form.
| \(d\uparrow,\ F\uparrow\) | \(\Rightarrow\) | \(\text{positive}\) |
| \(\text{very close to a line}\) | \(\Rightarrow\) | \(\text{strong}\) |
| \(\text{straight-line pattern}\) | \(\Rightarrow\) | \(\text{linear}\) |
A strong positive linear association.
Decide the direction, then how much the points scatter about the trend.
| \(g\uparrow,\ D \text{ tends to fall}\) | \(\Rightarrow\) | \(\text{negative}\) |
| \(\text{clear trend, some scatter}\) | \(\Rightarrow\) | \(\text{moderate}\) |
A moderate negative association.
Ask whether one straight line could follow the points.
| \(\text{yield rises, then falls}\) | \(\Rightarrow\) | \(\text{a curve}\) |
| \(\text{a curve}\) | \(\Rightarrow\) | \(\text{non-linear}\) |
The association is non-linear; a straight line would not describe it well.
Check whether \(E\) rises or falls as \(n\) increases.
| \(n\uparrow\) | \(\Rightarrow\) | \(E \text{ neither rises nor falls}\) |
| \(\text{spread evenly, no trend}\) | \(\Rightarrow\) | \(\text{no correlation}\) |
There is no correlation between house number and electricity use.
Common pitfalls
Frequently asked questions
How do you describe the association in a scatter plot?
Give the strength, direction and form, for example a strong positive linear association. If the points show no trend at all, say there is no correlation.
What is the difference between a positive and a negative association?
Reading left to right, a positive association rises: as one variable increases, the other tends to increase. A negative association falls: as one increases, the other tends to decrease.
How do you tell if an association is strong, moderate or weak?
Look at how closely the points follow the trend. Very close to a line is strong, a clear trend with some scatter is moderate, and a trend that is only just visible is weak.
Does a steeper scatter plot mean a stronger association?
No. Strength is about how close the points are to the trend, not how steep it is. A gentle slope can be strong and a steep one can be weak.
What does non-linear mean on a scatter plot?
It means the points follow a curve instead of a straight line, such as a pattern that rises and then levels off or falls. A curve is not the same as no correlation.