DOI link for Balanced Experiments
Balanced Experiments book
This chapter begins the examination of more complicated treatment and design structures, while keeping things balanced for ease of presentation and analysis. Experimental designs are sometimes referred to as factorial designs since they are built from several factors, or treatments. To examine the two-factor interactions directly, draw interaction plots using estimated means for factor pairs, averaged over the other factor. Experiments involving three or more factors can become quite large. There are potentially many distinct components for main effects and interactions to be considered. Only a fraction of the factor combinations are employed in a balanced fractional factorial design. The two-factor case allows segregation of the effects of factor combination into a component for each factor and a component measuring the synergy or antagonism among factors. One may fit a model with two two-factor interactions and then examine interaction plots for further evidence of three-factor interactions.