# Correlation

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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 | ... | ... |

... | ... | ... |