Class Meeting 21

Class Meeting 21 - CHEN 3010 Applied Data Analysis Class...

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CHEN 3010 Applied Data Analysis Class Meeting #21 Tuesday, Nov. 11 th Today's Topics Reading for Tuesday: pages 274 - 285 Homework #9 posted on the web, due November 18 th Feedback on Test 2 Analysis of Variance Simple Linear Regression

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Analysis of Variance (ANOVA) Example Scenario: results on strength of a fiber Entries are tensile strength Test results show variability Analysis of variance addresses the question: How much of the variability in tensile strength results is due to the different levels of % cotton?
Underlying Concept of Analysis of Variance divide up (“partition”) the variability of the response into components that are attributable to different factors then judge whether the variability due to a given factor is significant or not variability due to replication at each % cotton level variability due to % cotton How is the total variability defined/computed? ( ) an 2 T ij .. i1j1 SS y y = = = ∑∑ Total sum of squares: the “dot” subscript indicates all levels of that subscript

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Different Averages and Elements ij y i th level of % cotton, j th observation Grand Average n i. ij j1 1 yy n = = Average at i th level of % cotton an .. ij i1j1 1 na = = = ∑∑
average of all results n=5 replicate observations at each % cotton level a=5 levels of % cotton SST from shortcut: =VAR(results)*(n*a-1) Computing Total Variability

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( ) ( ) ( ) ( ) an 2 2 T ij .. ij i.
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This note was uploaded on 10/11/2011 for the course CHEN 3010 taught by Professor Kompala,dh during the Spring '08 term at Colorado.

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Class Meeting 21 - CHEN 3010 Applied Data Analysis Class...

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