The other approach to revealing structure is to start with a general model, identify interesting one-dimensional parameters, and perform statistical inferences on these parameters. This parametric approach requires that the general model involve parameters that are easily interpretable. We use the parametric approach for one-way analysis of variance, balanced multifactor analysis of variance, and simple linear regression. In particular, the parametric approach to analysis of variance presented here involves a strong emphasis on examining contrasts, including interaction contrasts. In analyzing two-way tables of counts, we use a partitioning method that is analogous to looking at contrasts.
All statistical models involve assumptions.
Checking the validity of these assumptions is crucial because the models we use are never correct. We hope that our models are good approximations to the true condition of the data and experience indicates that our models often work very well . Nonetheless, to have faith in our analyses, we need to check the modeling assumptions as best we can. Some assumptions are very difficult to evaluate, e.g., the assumption that observations are statistically independent. For checking other assumptions, a variety of standard tools has been developed.