Standard Article

Multiple Comparisons


  1. D.G. Edwards

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vam042

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Edwards, D. 2006. Multiple Comparisons. Encyclopedia of Environmetrics. 4.

Author Information

  1. University of South Carolina, SC, USA

Publication History

  1. Published Online: 15 SEP 2006


In comparing several unknowns, e.g. the means μ1, μ2, …, μk of k > 2 populations, the classical approach would recommend starting with a test of equality, i.e. test the hypothesis H0μ1 = μ2 = … = μk. The process known as multiple comparisons has historically been considered as the logical next step following a rejection of this ‘omnibus’ test: if we can be confident that some differences among the μi exist, then which pairs μi, μi are different (1 ≤ i ≠ i′ ≤ k) and (perhaps) how large are these differences? Modern multiple comparisons analysis retains the goal of answering these sorts of questions, though the preliminary test of equality is no longer sacrosanct.