Two terms that are sometimes used interchangeably are correlation and association. However, in the field of statistics these two terms have slightly different meanings.
In particular, when we use the word correlation we’re typically talking about the Pearson Correlation Coefficient. This is a measure of the linear association between two random variables X and Y. It has a value between -1 and 1 where:
- -1 indicates a perfectly negative linear correlation between two variables
- 0 indicates no linear correlation between two variables
- 1 indicates a perfectly positive linear correlation between two variables
Conversely, when statisticians use the word association they can be talking about any relationship between two variables, whether it’s linear or non-linear.
To illustrate this idea, consider the following examples.
Visualizing Correlation vs. Association with Scatterplots
We use two words to describe the correlation between two random variables:
1. Direction
- Positive: Two random variables have a positive correlation if Y tends to increase as X increases.
- Negative: Two random variables have a negative correlation if Y tends to decrease as X increases.
2. Strength
- Weak: Two random variables have a weak correlation if the points in a scatterplot are loosely scattered.
- Strong: Two random variables have a strong correlation if the points in a scatterplot are tightly packed together.
The following scatterplots illustrate examples of each type of correlation:
Compared to correlation, the word association can tell us whether or not there is any relationship between two random variables: linear or non-linear.
The following scatterplots illustrate some examples:
The scatterplot in the top left corner illustrates a quadratic relationship between two random variables, which means there is an association between the two variables but it’s not a linear one.
If we calculated the correlation between the two variables, it would likely be close to zero because there is no linear relationship between them.
However, just knowing that the correlation between the two variables is zero can be misleading because it hides the fact there there exists a non-linear relationship instead.
Correlation vs. Association: A Summary
The terms correlation and association have the following similarities and differences:
Similarities:
- Both terms are used to describe whether or not there is a relationship between two random variables.
- Both terms can use scatterplots to analyze the relationship bewteen two random variables.
Differences:
- Correlation can only tell us if two random variables have a linear relationship while association can tell us if two random variables have a linear or non-linear relationship.
- Correlation quantifies the relationship between two random variables by using a number between -1 and 1, but association does not use a specific number to quantify a relationship.
Additional Resources
An Introduction to the Pearson Correlation Coefficient
An Introduction to Scatterplots
Correlation vs. Regression: What’s the Difference?