1. Models with factors and covariates
ANCOVA
Models with factors and covariates

2. Can we answer these questions?
Is there an advantage of ANCOVA over ANOVA?
Hint: Write down the F test in terms of the parts of the variance.
There are a few important assumptions about the covariate’s effect on the dependent variable. Can we articulate those assumptions?
Can we create an example of a research question for an ANCOVA analysis?
Can we draw a conceptual model for this example?
Can we restate the assumptions in this context?
Can we think of some interesting situations that would violate the assumptions?

3. ANCOVA Overall Mean Effects of Factors Dependent Variable
Effects of Covariates
Unexplained Effects

4. Relate everything to standard ANOVA
Between groups
variance
Within groups
Variability due to
membership of
groups
measurement
error
Variability due to differences
between subjects + =
Variability due to differences
between subjects

5. Order of the computation
Traditional:
Covariates first
Experimental effects last
Current:
Matter of choice based on model circumstances