Correlation coefficient

A correlation coefficient measures the association between two variables. A correlation matrix measures the correlation between many pairs of variables.

The type of relationship between the variables determines the best measure of association:

• When the association between the variables is linear, the product-moment correlation coefficient describes the strength of the linear relationship.

  The correlation coefficient ranges from -1 to +1. +1 indicates a perfect positive linear relationship, and -1 indicates a perfect negative linear relationship. Zero indicates the variables are uncorrelated and there is no linear relationship. Normally the correlation coefficient lies somewhere between these values.

• When the association between the variables is not linear, a rank correlation coefficient describes the strength of association.

  Rank correlation coefficients range from -1 to +1. A positive rank correlation coefficient describes the extent to which as one variable increases the other variable also tends to increase, without requiring that increase to be linear. If one variable increases, as the other tends to decrease, the rank correlation coefficient is negative.

It is best to use a scatter plot to identify the type of association between the variables and then use an appropriate measure of association for the relationship. Do not be tempted just to look for the highest correlation coefficient.

A correlation matrix measures the correlation between many variables. It is equivalent to a covariance matrix of the standardized variables.