Lecture 16 - Course Project Abstracts due on Friday April 4...

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Course Project Abstracts due on Friday, April 4, 2008 (same day as exam 3) Abstracts should be brief and to the point: Tentative Project Title and Four Sentences 1. Objective of the study 2. Summary/Source of the data 3. Anticipated method(s) to be applied 4. How the study relates to your major
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Exam 3 is on Friday, April 4. That exam will cover Chapters 8, 9, and 10 (even though we will get into Chapter 11 before April 4). Homework assignment 3 will subsequently include problems from chapters 8-10 only.
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ANOVA Assumptions 2 1... , 1... ~( , ) Normal input population All populations have the same variance ij i ij ij xi I j J NO μ σ =+ τ + ∈= = −∈ The form of the linear model generating observations is assumed to be: Illustration of the One Way ANOVA Data Layout
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() 2 11 . 2 _ . 2 . # Replicates # Factor .. I- J- Per Factor Levels Level .. ( 1) Treatment mean .. ; /( ;/ ( ( 1 ) ) IJ ij ij i i ij i x SST x x with IJ df x SSTr x x MSTr SSTr I SSE x x MSE SSE I J SST == =− = ⎛⎞ = −= ⎜⎟ ⎝⎠ = ∑∑ SSTr SSE =+
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22 .. 11 .. . 1 : (1 / ) ) ) IJ ij ij I i i ComputingFormulas SST x IJ x SSTr J x IJ x SSE SST SSTr == = =− ∑∑
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The total variation in the data is comprised of the variation between groups (due to treatments) and the variation within groups (due to error): SST = SSTr + SSE
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In effect, the ANOVA procedure is testing the following hypothesis: H 0 : μ 1 = μ 2 =… μ I vs. H a : at least one of the treatment means is different It does this by examining whether: E(MSTr) = E(MSE)
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If H 0 is false, then E(MSTr)>E(MSE)= σ 2 , i.e., more of the total variation is explained by the treatment levels than by noise. The result is a one sided F-test where F = MSTr/MSE
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The procedure is based on the following ANOVA table : Source df SS MS F Treatments I-1 SSTr SSTr/(I-1) MSTr/MSE Error I(J-1) SSE SSE/(I(J-1)) Total IJ-1 SST Reject H 0 of F > F α , I-1, I(J-1)
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Problem 10-3 (page 378) Using the ANOVA Table Problem 10-6 (page 378) Performing the ANOVA Calculations
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10-3 I=3 , J=8 SSE=4773.3 SSTr=591.2 123 At least one : vs. :
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This note was uploaded on 04/08/2008 for the course ENGR 2600 taught by Professor Malmborg during the Spring '08 term at Rensselaer Polytechnic Institute.

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Lecture 16 - Course Project Abstracts due on Friday April 4...

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