Interpreting Scatterplots

Overview

A scatterplot is used to examine the relationship between two quantitative variables. Each point represents one observation, with one variable plotted on the x-axis and the other variable plotted on the y-axis.

Key Idea:
When interpreting a scatterplot, look for form, direction, strength, and outliers.

Step 1: Look at the Form

First, look at the overall shape of the points. The relationship may follow a relatively straight pattern or may follow a curved pattern.

Form	What to Look For	What It Means
Linear	The points generally follow a straight-line pattern.	The relationship can be reasonably described by a straight line.
Curvilinear	The points follow a noticeable curve rather than a straight line.	The relationship changes direction or rate as one variable increases.

Important:
A relationship can be strong even when it is curvilinear. However, Pearson's correlation is designed to measure linear relationships, and cannot properly measure curvilinear patterns. Instead, alternative tests like a Spearman Correlation are used.

Step 2: Look at the Direction

If the relationship is linear, determine whether the variables move in the same direction or in opposite directions.

Direction	What to Look For	Interpretation
Positive	As one variable increases, the other variable increases.	The variables move in the same direction.
Negative	As one variable increases, the other variable decreases.	The variables move in opposite directions.
No Relationship	The points do not show a consistent pattern.	Knowing one variable does not provide much information about the other variable.

Direction Examples

Remember:
The direction of a relationship is described as positive or negative. The strength of a relationship is described separately.

Step 3: Look at the Strength

Strength describes how closely the points follow the overall pattern. The closer the points are to the pattern, the stronger the relationship.

Strength	What to Look For
Strong	The points are tightly clustered around the overall pattern.
Moderate	The points show a clear pattern, but there is noticeable variation around it.
Weak	The points show a slight or inconsistent pattern.
No Relationship	The points are scattered without a clear pattern or direction.

Strength Examples

Step 4: Look for Outliers

An outlier is an observation that is noticeably separated from the overall pattern of the other points. Outliers can occur in either variable and may have a substantial effect on the results of a correlation analysis.

Important:
Always look for outliers before interpreting a correlation. A single unusual observation can make a relationship appear stronger, weaker, or different from the pattern shown by the rest of the data.

With an Outlier

Outlier Removed

How to Identify an Outlier

Look for a point that is far away from the other observations.
Determine whether the point follows the overall pattern.
Consider whether the point may have a meaningful explanation or may represent an error.

An outlier does not automatically mean that something is wrong with the data. It may represent a legitimate observation that is simply unusual compared with the rest of the sample.

What You See	What It May Mean
Point follows the overall pattern	The observation may be unusual in value but still consistent with the relationship.
Point is far from the overall pattern	The observation may be an outlier that could influence the correlation.
Several unusual points	The apparent relationship may be more complex than a simple linear pattern.

Do not automatically delete an outlier.
First determine whether it is a data-entry or measurement error. If the observation is legitimate, it should generally remain in the analysis, and its potential influence should be considered when interpreting the results.

Putting It All Together

A complete interpretation of a scatterplot considers form, direction, strength, and outliers.

Feature	Question to Ask
Form	Is the pattern linear or curvilinear?
Direction	Is the relationship positive, negative, or does it have no clear direction?
Strength	Is the pattern strong, moderate, weak, or absent?
Outliers	Are there any observations that fall far from the overall pattern?

Example:
A scatterplot may show a strong, positive, linear relationship. This means the points closely follow a straight-line pattern and, as one variable increases, the other variable generally increases as well.