What Does a Correlation Coefficient of Zero Mean?

by Andrew Gellert
Correlation analysis can show the strength of association between two different variables.

Correlation analysis can show the strength of association between two different variables.

In statistics, the correlation coefficient is a measure of how much two variables move together. The correlation coefficient can show how well associated two variables are, although it does not necessarily show that one causes the other to change. A correlation coefficient of zero means that two variables do not have a correlational association of any kind.

Covariance

The covariance of a pair of variables is a useful metric for comparison. Covariance is a measure of how two variables move together. Negative covariance implies that two variables are inversely related, and positive covariance means that the two variables are positively correlated, meaning they go up or down at the same time. The correlation coefficient is based on covariance.

Correlation Coefficient

The covariance of two variables is helpful for interpretation, but it is useful to transform it into the correlation coefficient, which has no units and is scaled to between -1 and 1. To get the correlation coefficient, take the covariance of the two variables and divide by the product of the variables' respective standard deviation. This yields the correlation coefficient.

Interpreting Correlation Coefficient

The correlation coefficient will always be between -1 and 1. A correlation coefficient close to -1 implies that the two variables move in opposite directions. When one goes up, the other goes down. They are negatively correlated. A value close to 1 implies the opposite. If the value is zero, or close to zero, that means that the two variables do not share any particular correlation. There is no strong correlation relationship in one direction or the other.

About the Author

Andrew Gellert is a graduate student who has written science, business, finance and economics articles for four years. He was also the editor of his own section of his college's newspaper, "The Cowl," and has published in his undergraduate economics department's newsletter.

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