# Chapter 4 Measures of Association between Variables

We will now consider two measures that can be used to measure the relationship between two variables.

The first is the * covariance*, and the second is the

*, often denoted \(r\). (Note that \(r\) is the sample correlation coefficient, whereas the population correlation coefficient is usually denoted \(\rho\)).*

**correlation coefficient**If the

and**covariance**values are positive, this indicates that the two variables are positively related. In other words, when one increases, the other one generally also increases.**correlation**On the other hand, if the

and**covariance**values are negative, this indicates that the two variables are negatively related. That is, when one increases, the other will typically decrease.**correlation**and**Covariance**values of 0 indicate that the two variables are unrelated (at least in a linear sense).**correlation**

Apart from its sign (positive or negative), the * covariance* value can be hard to interpret, especially if the two variables are on different scales. However,

*is a standardised measure, meaning it is much easier to interpret. The correlation coefficient is always between -1 and 1. The closer \(|r|\) (the absolute value of \(r\)) is to 1, the stronger the linear relationship between the two variables.*

**correlation**The below table can be used as a guide when interpreting the correlation coefficient \(r\).

Range of |r| | Strength of correlation |
---|---|

0 to 0.3 | None or very weak |

0.3 to 0.5 | Weak |

0.5 to 0.8 | Moderate |

0.8 to 1 | Strong |

We will see some examples in the next section.