Abstract In comparing several unknowns, e.g. the means μ 1 , μ 2 , …, μ k of k > 2 populations, the classical approach would recommend starting with a test of equality, i.e. test the hypothesis H 0 : μ 1 = μ 2 = … = μ k . 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 μ i exist, then which pairs μ i , μ i ' 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.
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