1. Analysis of Covariance
KNNL – Chapter 22

2. 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

3. Single Factor Model with 1 Covariate

4. Additive Model – Homogeneity of Slopes

5. Interaction Model – Heterogeneity of Slopes

6. Model Generalizations
Random Xij - 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

7. Regression Model for 1-Way ANCOVA

8. Comparing (Adjusted) Treatment Means

9. Testing for Common Slopes