Plotting Paired Observations as Points
A scatter diagram plots paired values from two numerical variables as points. For example, we can place study time on the -axis and exam scores on the -axis.
Each point represents one paired observation, such as one student's study time and score. The point cloud shows whether the pairs form a recognizable pattern.
Choosing a Scatter Diagram
A scatter diagram is especially useful when we want to:
- check whether one numerical variable tends to rise, fall, or show no consistent change as the other variable changes, such as height and weight or study time and scores.
- examine the direction and form of that pattern, including a positive, negative, or unclear tendency.
A scatter diagram differs from other diagrams:
- Bar chart: compares values between categories, such as the number of students in different classes.
- Line chart: shows development over time or another fixed sequence, such as daily temperatures.
- Pie chart: shows parts of a whole, such as the distribution of preferred fruit types.
When the main question concerns a possible relationship between two numerical variables, a scatter diagram is an appropriate starting point.
Scatter Diagram Examples and Correlation Patterns
The following examples show three typical point patterns. Each pattern is named by the direction of its points and by how closely they follow a line, and that name carries into the description of .
Positive Correlation
If the points tend to rise from the bottom left to the top right, it means there is a positive correlation. As the value of increases, the value of also tends to increase.
Negative Correlation
If the points tend to fall from the top left to the bottom right, it means there is a negative correlation. As the value of increases, the value of tends to decrease.
No Clear Linear Correlation with Two Groups
If the points are scattered without a clear straight-line pattern, the linear correlation is weak or absent. We can also display different groups in one diagram.
The direction, shape, and spread of the points provide an initial description of how two variables vary together. Separate colors or markers distinguish the patterns of different groups. A scatter diagram describes association, but it does not by itself prove that one variable causes the other.