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In statistics, two quantities are said to be correlated if greater values of one tend to be associated with greater values of the other (positively correlated), or if greater values of one tend to be associated with lesser values of the other (negatively correlated). The correlation (or, more formally, correlation coefficient) between two variables is a number measuring the strength and usually the direction of this relationship.

In the case of interval or ratio variables, non-zero correlation is often apparent in a scatterplot of the data points: positive correlation is reflected in an overall increasing trend in the points (when viewed from left to right on the graph), whereas negative correlation appears as an overall decreasing trend.

## Measures of correlation

Most measures of correlation take on values from −1 to 1, or from 0 to 1. Zero correlation means that greater values of one variable are associated with neither higher nor lower values of the other, or possibly with both. A correlation of 1 implies a perfect positive correlation, meaning that an increase in one variable is always associated with an increase in the other (and possibly with an increase of the same size always, depending on the correlation measure being used). Finally, a correlation of −1 means that an increase in one variable is always associated with a decrease in the other (possibly always the same size).

Some measures of correlation include the following:

Name Used to measure Range of values
Pearson product-moment correlation coefficient degree of linear association between interval or ratio variables −1 to 1
Spearman's rho ... ...
Kendall's tau ... ...
Yule's Q ... ...
... ... ...