Published Online: 15 SEP 2006
Copyright © 2002 John Wiley & Sons, Ltd
Encyclopedia of Environmetrics
How to Cite
Edwards, D. 2006. Multiple Comparisons. Encyclopedia of Environmetrics. 4.
- 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 H0: μ1 = 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.