Chapter 12--Multisample Inference

There are three genotypes at the locus for mpi mpi

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Unformatted text preview: cifically as one-way ANOVA because there was one factor with k levels (treatments). Suppose there are two factors, say A and B ; factor A has a levels and factor B has b levels. Each combination of levels of factor and levels of factor B is called a treatment. So there are a · b treatments. Suppose n (equal number of) experimental units (replications) are to be used for each of the a · b treatments. This does not always have to be the case, but we will assume it is for this section. See the example later for unequal replications. The treatments are randomly assigned to the experimental units in such a way that n experimental units receive each of the treatments. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: Genetics A biologist assayed the activity of the enzyme mannose-6-phosphate isomerase (MPI) in the Platorchestia platensis, a species of sand flea, an amphipod crustacean that lives on beaches. There are three genotypes at the locus for MPI, Mpiff , Mpifs , and Mpiss , and the researcher wanted to know whether the genotypes had different activity. Because the researcher didn’t know whether sex would affect activity, she also recorded the sex. Each amphipod was lyophilized, weighed, and homogenized; then MPI activity of the soluble portion was assayed. MPI activity in ∆ O.D. units/sec/mg dry weight were computed for each amphipod. Is there sex-genotype interaction on the activity of the enzyme? Is there a sex effect on activity? Is there a genotype effect on activity? Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Data from Two-Way layout in CRD 1 1 Factor A 2 a Mean y111 y112 y11. ¯ ... y11n y211 y212 y21. ¯ ... y21n ... ya11 . . . ya1. ¯ ya1n y.1. ¯ Chapter 12: Multisample Inference Factor B 2 ... y121 y122 y12. ¯ ... y12n y221 y222 y22. ¯ ... y22n ... ya21 . . . ya2. ¯ ya2n y.2. ¯ ... ... ... ... ... Stat 491: Biostatistics b y1b1 y1b2 y1b. ¯ ... y1bn y2b1 y2b2 y2b. ¯ ... y2bn ... yab1 . . . yab. ¯ yabn y.b. ¯ Mean y1.. ¯ y2.. ¯ ... ya.. ¯ y... ¯ Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Model The model for the observation yijk is: yijk = µ + τi + βj + γij + εijk where µ: τi : βj : γij : is the overall mean (unknown constant). is an effect due to the i th level of factor A (unknown constant). is an effect due to the j th level of factor B (unknown constant). is an effect due to the interaction between i th level of factor A and the j th level of factor B (unknown constants). εijk : is the error associated with the k th experimental unit receiving the i th level of factor A and j th level of factor B . εijk are 2 indep. normally distributed with mean 0 and variance σε . τ s and β s are known as main effects and γ s are known as interaction effects. Chapter...
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This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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