Part V

Correlation

In this part we deal with tests on coefficients measuring types of association between two variables. The correlation coefficient of two random variables is a measure of the linear relationship between them and takes values between −1 and +1. If the correlation coefficient is −1 there is a perfect negative linear relation, if it is +1 there is a perfect positive linear relation, both with probability one. The sample correlation coefficient, also called Pearson's product moment correlation coefficient, aims at measuring the strength of the linear dependence based on a sample from the two random variables. It can be applied to data coming from a joint continuous bivariate distribution. The Spearman rank correlation coefficient more generally measures a monotonic relationship. We also discuss the partial correlation coefficient and a test on the difference between two correlation coefficients.