Association between two quantitative variables is described by the direction of a scatter-plot pattern—positive when larger values of one variable tend to accompany larger values of the other, and negative when they tend to accompany smaller values—and by its strength, based on how closely the points follow a consistent pattern. The description may note weak, strong, or no apparent association and the influence of outliers, without treating association as proof of causation; calculating correlation coefficients or modeling more advanced nonlinear relationships is beyond this scope.
To describe an association, look at a scatter plot and answer two questions:
What is the direction?
How strong is it?
A teacher records how many hours students studied and their test scores.
| Study time (hours) | Test score |
|---|---|
| 1 | 55 |
| 2 | 61 |
| 3 | 67 |
| 4 | 73 |
| 5 | 79 |
| 6 | 85 |
Imagine plotting study time on the horizontal axis and test score on the vertical axis.
Step 1: Look from left to right.
As study time increases, the test scores also tend to increase.
Step 2: Name the direction.
Because both variables tend to increase together, the association is positive.
Step 3: Look at how closely the points follow the pattern.
The points are close to an upward-sloping pattern, with little spread.
Step 4: Describe the strength.
The association is strong and positive.
A complete description is:
There is a strong positive association between study time and test score. Students who study more hours tend to have higher test scores.
This description shows a pattern, but it does not prove that studying more caused the higher scores.
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?