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REMINDER 1) GLM Review on Friday 2) Exam II on Monday

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Chapter 13.6 Nested Random Effects (Hierarchical ANOVA)

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Introduction Nested ANOVA Similar to: One-way Two-way

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Example Mosquito wing lengths Two measurements made on the left wings of 4 mosquitos in each of 3 cages Verbal model: Does mosquito wing length vary among cages as well as among mosquitoes?

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Graphical model

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Formal model Execute analysis lm1 <- lm(wlen~cage/fly, data=m) anova(lm1)

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3.Evaluate the model – ok 4.State population and whether sample is representative. – mosq.’s in cages...bla bla 5.Decide on mode of inference. Is hypothesis testing appropriate? – yup 6.State H A /H o pairs, test statistic, distribution, tolerance for Type I error. – Interaction: – Cage: – Fly ⊂ Cage:

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7.ANOVA. Calculate df and SS, partition according to model. – n = 24

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7.ANOVA. Calculate df and SS, partition according to model.

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8.Decide whether to recompute p-value. – no 9.Declare decision about terms. – Significant variance among flies F = 147.07; df = 9, 12; p < 0.0001 – No significant cage effect F = 1.741; df = 2, 9; p = 0.23 10.Report and interpret parameters of biological interest.

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