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Topic 14

# Topic 14 - Topic 14 Experimental Design Crossover Nested...

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1 Topic 14 – Experimental Design Crossover Nested Factors Repeated Measures

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2 Overview We will conclude the course by considering some different topics that can arise in a multi-way ANOVA, as well as some other miscellaneous topics. Some of these are discussed a little bit in Chapters 21, 23, and 24. As there will be no HW covering this topic, the coverage on the final exam will be limited to identification and/or discussion of concepts.
3 Types of Designs Crossed Factors Nested Factors Repeated Measures

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4 Crossover Design Factors A and B are considered crossed if every level of B occurs with every level of A. Note: The two-way and three-way ANOVA that we have discussed to this point has generally had crossed factors (obs. in every cell). Can investigate interactions assuming that we have replication (multiple obs. per cell). Basically, we have only been doing crossover designs so far!
5 Diagrams of Crossover Design

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6 Example We want to examine three different drugs to determine their effects on blood pressure. We will have 12 men and 12 women on each drug, and also have a control group as well. Drug and Gender are crossed factors (and are both fixed effects as well).
7 ANOVA Table Source DF DRUG ___ (fixed, 4 levels) GENDER ___ (fixed, 2 levels) DRG*GNDR ___ (fixed) Error ___ Total 95

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8 Nested Design Factor B is considered to be nested within Factor A if each level of B occurs with only one level of Factor A. Can arbitrarily number the levels of B Cannot investigate interactions. Denoted B(A) instead of B in ANOVA table.
9 Example (Nested) We want to compare two fertilizers. We have a field that is divided into 4 sections and each section is randomly assigned one of the two fertilizers (each is assigned twice). After two weeks, three plants from each section are dug up and the number of root tips for each plant is obtained.

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10 Example (Nested) Factors include Fertilizer Section (nested within Fertilizer) – also this is the Experimental Unit! Plant (nested within Section, Fertilizer) – note that this effect will actually be the error term since there is nothing “below” it. Fertilizer 1 2 Section 1 3 2 4 Plant 1 2 3 4 5 6 7 8 9 10 11 12 Response 18 22 17 22 28 25 17 15 14 12 15 16
11 Example (Nested) Are the observations (plants) within a section independent? This is an example of subsampling (a form of “repeated measures” that results in a nested design). By subsampling, we reduce the variance associated with our experimental units (the sections). But as we will see, it does not gain DF for testing the fertilizer effect.

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12 Degrees of Freedom 12 observations 11 total DF. Have variability between sections and
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Topic 14 - Topic 14 Experimental Design Crossover Nested...

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