Review.

Today gave a quick overview of the final examination and distributed a study sheet (downloadable from Blackboard).

ANCOVA and assumptions.

Today we focused on classic ANCOVA and its assumptions. In particular we looked at cases where the covariate and the treatment interact. We also considered the use of adjusted means (sometimes called least squares means) to make inferences such as multiple comparisons involving group means while controlling for the covariate.

Introduction to the analysis of covariance.

The analysis of covariance (ANCOVA) is a design and model that is a nice bridge between analysis of variance and regression. As we saw in our discussion of regression, we can incorporate both categorical and quantitative explanatory variables. A classic ANCOVA is essentially a linear model for a completely randomized design but with a quantitative explanatory variable.

Residual analysis.

Today we focused on residual analysis — i.e., the use of residuals to investigate possible violations of assumptions of regression. I reviewed the four underlying assumptions of regression and illustrated how residuals and plots of residuals can be used to detect violations of the assumptions.