Wuchap_02b_09fall - Pulp Experiment Revisited • In the...

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Unformatted text preview: Pulp Experiment Revisited • In the pulp experiment the effects τ i are called fixed effects because the interest was in comparing the four specific operators in the study. If these four operators were chosen randomly from the population of operators in the plant, the interest would usually be in the variation among all operators in the population. Because the observed data are from operators randomly selected from the population, the variation among operators in the population is referred to as random effects. • One-way random effects model : y ij = η + τ i + ε ij , ε ij ’s are independent error terms with N ( , σ 2 ) , τ i are independent N ( , σ 2 τ ) , and τ i and ε ij are independent (Why? Give an example.); σ 2 and σ 2 τ are the two variance components of the model. The variance among operators in the population is measured by σ 2 τ . 27 One-way Random Effects Model: ANOVA and Variance Components • The null hypothesis for the fixed effects model: τ 1 = ··· = τ k should be replaced by H : σ 2 τ = . Under H , the F test and the ANOVA table in Section 2.1 still holds. Reason: under...
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This note was uploaded on 12/12/2010 for the course STAT 425 taught by Professor Ma,p during the Fall '08 term at University of Illinois, Urbana Champaign.

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Wuchap_02b_09fall - Pulp Experiment Revisited • In the...

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