A full model includes all of the possible terms. A reduced model does not include all the possible terms. You might reduce a model if terms are not significant or if you need additional error degrees of freedom and you can assume that certain terms are zero.

For example, suppose you have a two factor design, with factors, A, and B. The full model would include:

- all one factor terms: A and B
- all two-factor interactions: A * B

It becomes a reduced model by omitting the interaction term. You might reduce a model if the interaction term is not significant or if you need additional error degrees of freedom and you can assume that the interaction term is zero.