A Proof That Kramer's Multiple Comparison Procedure for Differences Between Treatment Means Is Level-α for 3, 4, or 5 Treatments
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multiple comparisons
simultaneouos test procedure
simultaneous confidence intervals
one way ANOVA
Kramer's procedure
Statistics and Probability
simultaneouos test procedure
simultaneous confidence intervals
one way ANOVA
Kramer's procedure
Statistics and Probability
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Let Xij, i = 1, ..., p; j = 1, ... . N1 be independent normal variables with E(Xij) = μi, Var Xij = σ2. Let Xi = Ni-1 ∑j=1Ni Xij and S2 = (∑(Ni-1))-1 ∑(Xij-Xi)2. Then if p ≤ 5 we show Pr(|(μi-μj) - (Xi-Xj) | ≧ S(Ni-1 + Nj-1) qp(α), √21/2 for some i≠ j) ≤α
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1979
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This paper was published by the Statistics Center, Cornell University (1979).