Wuchap_02b_09fall

# Wuchap_02b_09fall - Pulp Experiment Revisited In the pulp...

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PulpExperimentRevisited Inthepulpexperimenttheeffects τ i arecalled fixed effectsbecausethe interestwasincomparingthefour specific operatorsinthestudy.Ifthese fouroperatorswerechosenrandomlyfromthepopulationofoperatorsin theplant,theinterestwouldusuallybeinthevariationamongalloperators inthepopulation.Becausetheobserveddataarefromoperatorsrandomly selectedfromthepopulation,thevariationamongoperatorsinthe population isreferredtoas random effects. One-wayrandomeffectsmodel: y ij = η + τ i + ε ij , ε ij ’sareindependenterrortermswith N ( 0 , σ 2 ) , τ i areindependent N ( 0 , σ 2 τ ) , and τ i and ε ij areindependent(Why?Giveanexample.); σ 2 and σ 2 τ arethe two variancecomponents ofthemodel.Thevarianceamongoperatorsin thepopulationismeasuredby σ 2 τ . 27 One-wayRandomEffectsModel:ANOVAand VarianceComponents Thenullhypothesisforthefixedeffectsmodel: τ 1 = ··· = τ k shouldbe replacedby H 0 : σ 2 τ = 0 . Under H 0 ,the F testandtheANOVAtableinSection2.1stillholds.

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