Models with factors and covariates ANCOVA Models with factors and covariates

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?

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

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

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