chapter13 - Analysis of Covariance Combines linear...

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Analysis of Covariance Combines linear regression and ANOVA Can be used to compare g treatments, after controlling for quantitative factor believed to be related to response (e.g. pre-treatment score) Can be used to compare regression equations among g groups (e.g. common slopes and/or intercepts) • Model: ( X quantitative, Z 1 ,..., Z g -1 dummy variables) 1 1 1 1 ) ( - - + + + + = g g Z Z X Y E β α
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Tests for Additive Model • Relation for group i ( i =1,. .., g -1): E ( Y )= α + β X+ i Relation for group g : E ( Y )= + X H 0 : 1 =...= g -1 =0 (Controlling for covariate, no differences among treatments)
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Interaction Model Regression slopes between Y and X are allowed to vary among groups 1 1 1 1 1 1 1 1 ) ( - - - - + + + + + + + = g g g g XZ XZ Z Z X Y E γ β α • Group i ( i =1,. .., g -1): E ( Y )= + X+ i + i X= ( + i )+( + γ i )X Group g : E ( Y )= + X • No interaction means common slopes: 1 =...= g -1 =0
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chapter13 - Analysis of Covariance Combines linear...

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