Standard Article

Union–Intersection Principle

  1. V. M. Chinchilli

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15170

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Chinchilli, V. M. 2005. Union–Intersection Principle. Encyclopedia of Biostatistics. 8.

Author Information

  1. Penn State College of Medicine, Hershey, PA, USA

Publication History

  1. Published Online: 15 JUL 2005


Multivariate analysis is the branch of statistics that involves inferential methods with two or more response (dependent) variables simultaneously. Therefore, multivariate analysis tends to be more complex than univariate analysis (one dependent variable) with respect to its mathematical development and its interpretation. The union–intersection principle is an approach that provides a basic approach for hypothesis testing in certain multivariate situations. We illustrate an application of the union–intersection principle to the situation in which there are pretreatment and posttreatment measurements on p dependent variables for a sample of n experimental units.


  • multivariate analysis;
  • Hotelling's T-squared distribution;
  • simultaneous confidence intervals