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2vij actual significance level amount of conservativeness analysis of variance Appendix calculate simultaneous confidence Chapter confidence intervals provided conservative procedure construct covariance matrix density diagonal(1/n Duncan equal equation 1.1 equation 5.4 exact confidence intervals exact set exact simultaneous confidence F-statistic F-test GT2 procedure Hayter independent inequality in equation intervals are longer intervals in equation joint confidence level Kramer Lemma mean square error model of section multiple comparisons procedures multivariate normal distribution one-way fixed effects pairs pairwise contrasts pairwise differences positive numbers probability inequality proof random variable Scheffe procedure section 1.4 set of confidence set of contrasts set of simultaneous simultaneous confidence intervals Spurrier and Isham statistician Stoline subset theorem theoretical justification three populations treatment means Tukey procedure applied Tukey's confidence intervals Tukey's conjecture Tukey's first conjecture Tukey's intervals unbalanced Anova model unbalanced model upper a point Uusipaikka Va2+ values variance heterogeneity vii+ vjj zero