4 Treatment contrasts and multiple comparisons
A significant \(F\) test says that the treatment means are not all equal. It does not say which differ, or how. Those questions are answered by contrasts, and when many of them are asked of the same data, by methods that control the error rate over the whole family. Throughout, the one-way model of Section 3 holds with \(MSE\) on \(N - t\) degrees of freedom.
4.1 Contrasts
4.2 Orthogonal contrasts
4.3 Multiple comparisons
4.4 Orthogonal polynomials
4.5 Practice problems
4.2 Orthogonal contrasts
4.3 Multiple comparisons
4.4 Orthogonal polynomials
4.5 Practice problems
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