You have described distributions of one variable. To see how two variables relate, plot each pair as a point on the coordinate plane: that is a scatter plot.
Why it works
Each point stands for one person or thing, measured two ways: hours studied and test score, say. Putting all the points on one grid turns a long list of pairs into a picture, and patterns that are invisible in the list become shapes in the cloud of points.
Key idea
Describe a scatter plot by its direction (positive: up to the right; negative: down to the right; or no association), its form (linear or curved), its strength (tight or spread out), and any clusters or outliers (points far from the pattern).
Worked examples
Worked example: Describe a plot
Describe the scatter plot above.
- As hours increase, scores tend to increase: a positive association.
- The points lie close to a straight line: linear and fairly strong.
- One student studied 3.5 hours and scored 40, far below the pattern: an outlier.
Answer: positive, linear, fairly strong, with one outlier
Worked example: Predict the direction
What association would you expect between the age of a car and its value? Between a person’s shoe size and their favorite number?
- Older cars are usually worth less: a negative association.
- Shoe size has nothing to do with a favorite number: no association.
Answer: negative; none
An association does not prove that one thing causes the other. Ice cream sales and sunburns rise together, but both are caused by hot, sunny weather.
Common mistake
Calling a downward pattern “no association.” A cloud that falls from left to right shows a negative association, which is a real relationship. No association means no upward or downward trend at all.