Anova tables, tests and estimates of variance components

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The data

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The model and hypothesis

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The model and hypothesis

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Matrix formulation

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Matrix formulation

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Estimating equations for $\alpha$ and $\beta$

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Restricted maximum likelihood estimates of variances

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Likelihood ratio test of hypothesis

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Estimate with all effects fixed

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The ssformulas in the ANOVA tables

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SS computed by 'hand'

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Maximum likelihood estimates

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Compare estimates of fixed effects

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Compare variance and SS estimates

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Compare results from assuming fixed vs random effects

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Discussion

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