Stat 1102 lecture notes 8

One experimental unit from each block is randomly

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One experimental unit from each block is randomly assigned to each treatment, resulting in a total of n = bk responses. Conditions required for a Valid ANOVA F-test: Randomized Block Designs The b blocks are randomly selected, and all k treatments are applied (in random order) to each block. The distributions of observations corresponding to all bk block- treatment combinations are approximately normal. The bk block-treatment distributions have equal variances Factorial Experiments A complete factorial experiment is one in which every factor-level combination is employed – that is, the number of treatments in the experiment equals the total number of factor-level combinations. The factor interaction component is used to test whether the factors combine to affect the response. The factor main effect components are used to determine whether the factors separately affect the response. Balanced design the same number of observations are made for each treatment o That is, we assume that r experimental units are randomly and independently selected for each treatment. Conditions required for valid F-tests in factorial experiments
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o The response distribution for each factor-level combination (treatments) is normal. o The response variance is constant for all treatments. o Random and independent samples of experimental units are associated with each treatment.
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