Standard Article

Correlation

  1. Peter Armitage

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a09009

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Armitage, P. 2005. Correlation. Encyclopedia of Biostatistics. 2.

Author Information

  1. University of Oxford, Oxford, UK

Publication History

  1. Published Online: 15 JUL 2005

Abstract

In a loose sense, two variables are correlated if changes in one tend to be accompanied by changes in the other. More specifically, correlation implies a linear relationship with superimposed random variation. The product–moment correlation coefficient was introduced by Galton and greatly exploited by Karl Pearson. Its square is the proportion of the variance of one variable “explained” by linear regression on a second variable. Standard tests are described in the article. An important extension is to intraclass correlation for measurements on individuals falling into groups, which measures the association between individuals in the same group.

Keywords:

  • association;
  • bivariate;
  • product–moment;
  • regression;
  • intraclass;
  • variance components;
  • rank;
  • causation;
  • Fisher's z