Analysis of Covariance KNNL – Chapter 22. Analysis of Covariance Goal: To Compare treatments (1-Factor or Multiple Factors) after Controlling for Numeric.

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Presentation transcript:

Analysis of Covariance KNNL – Chapter 22

Analysis of Covariance Goal: To Compare treatments (1-Factor or Multiple Factors) after Controlling for Numeric Predictor(s) that is (are) related to response Makes use of Multiple Linear Regression Model with numeric and categorical predictors Covariates (aka Concomitant Variables) can not be effected by the treatments assigned to units (often covariate is pre-treatment or baseline score) Purpose is to reduce experimental error when it is large Alternative to blocking: uses fewer degrees of freedom, and can be measured after trt assignment

Single Factor Model with 1 Covariate

Additive Model – Homogeneity of Slopes

Interaction Model – Heterogeneity of Slopes

Model Generalizations Random X ij - Model is treated as conditional of observed values of X Nonlinear relation between Response and Covariate – Include linear and quadratic centered X values More than one covariate – No problem extending to multiple covariates More than one treatment factor – No problem having multiple factors

Regression Model for 1-Way ANCOVA

Comparing (Adjusted) Treatment Means

Testing for Common Slopes