Standard Article

Runs Tests

Statistical Theory and Methods

  1. Christophe Ley1,
  2. Davy Paindaveine2

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn094

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Ley, C. and Paindaveine, D. 2013. Runs Tests. Encyclopedia of Environmetrics. 5.

Author Information

  1. 1

    Université Libre de Bruxelles, Bruxelles, Belgium

  2. 2

    Université Libre de Bruxelles, Bruxelles, Belgium

Publication History

  1. Published Online: 15 JAN 2013


Given a sequence of two or more types of symbols, a run is defined as a succession of – one or more – identical symbols that are followed and preceded by a different symbol (or by no symbol at all). Runs tests are based on the length of the longest run or on the total number of runs. They figure among the oldest nonparametric procedures, and can be used in various setups. We review the different definitions of runs, their development over the last 100 years, describe the domains of application of runs tests, and discuss their extension to the multivariate case.


  • distribution-freeness;
  • multi-sample problems;
  • quality control;
  • robustness;
  • runs;
  • tests of randomness;
  • tests of symmetry;
  • time series