Understanding data requires you to find relationships among the different parts of the data. Evaluating these relationships and how strongly they appear is where correlations come in.
Correlations are a statistic used by researchers to indicate the strength of the relationship between two variables as well as the direction of that relationship.
Direction of Correlations
To understand direction, consider someone trying to lose weight. The amount someone eats is positively related to their weight. As the amount someone eats increases, the amount they weigh will increase (both variables increase together). On the other hand, the amount of exercise someone gets is negatively related to their weight. As the amount someone exercise increases, the amount they weigh will decrease (one variable increases, while the other decreases).
Correlations range from -1.00 to 1.00.
- Negative numbers indicate negative relationships.
- Positive numbers indicate positive relationships.
- A correlation of 0.00 indicates no relationship.
Thus, the sign of the correlation (negative or positive) indicates the direction.
Strength of Correlations
The number itself (what we call the magnitude) indicates the strength. Generally, the closer the magnitude is to 1.00 the stronger the relationship. Researchers have found it useful to develop ranges to help categorize the strength of a relationship.
Many methods of categorizing correlations have been suggested, and each has merits. Researchers suggest that relying on a single method for all research is too simplistic and that different guidelines may be appropriate to different types of studies (Hemphill, 2003).
After careful consideration, Stay Metrics has decided that the commonly used method in the table below (Evans, 1996; StatsTutor, 2014) is best suited to the research it conducts and how it works with its clients.
|Magnitude of Correlation||Description of Strength|
|0.01 to 0.19||Very Weak|
|0.20 to 0.39||Weak|
|0.40 to 0.59||Moderate|
|0.60 to 0.79||Strong|
|0.80 to 1.00||Very Strong|
A Note of Caution
As has often been quoted:
Correlation does not equal causation.
Establishing causation is another process entirely. However, correlations give us a hint at what to look at to determine causation. They also give carriers signposts to determine how well they are doing and if changes they make are having an effect.
Perhaps we will tackle causation in another blog.
About the Author
Dr. Bradley Fulton is Director of Research and Analytics at Stay Metrics. He leads a team of analysts that help clients understand data and find patterns that lead to effective change.
He lives with his wife, two daughters, as well as a dog, hamster, guinea pig, and bearded dragon. In addition to pets, he likes gaming, camping, nature walks/hikes, and cooking. He also enjoys coffee; lots of coffee!
- Cohen J. 1988. Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Hillsdale, NJ: Erlbaum.
- Evans JD. 1996. Straightforward Statistics for the Behavioral Sciences. Brooks/Cole Publishing; Pacific Grove, Calif.: 1996.
- Hemphill JF. 2003. Interpreting the Magnitude of Correlation Coefficients. American Psychologist, 58(1), 78-80.
- Leard Statistics. 2018. Pearson Product Moment Correlation. https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php.
- Rumsey DJ. 2019. How to Interpret a Correlation Coefficient r. https://www.dummies.com/education/math /statistics/how-to-interpret-a-correlation-coefficient-r/.
- StatsTutor. 2014. Pearson’s Correlation. http://www.statstutor.ac.uk/resources/uploaded/pearsons.pdf.