Trend Analyses in Multifactor Designs

Frequently, a multifactor design has one or more numerically valued factors. When this occurs, trend analyses can be performed on main effects and interactions involving these factors. Just as in the one-way design, the theory of trend analysis differs for fixed and random numerical factors. For multifactor designs with random factors, however, the problem can be complicated; random factors with numerical values exert important influences on tests involving only fixed effects. In this chapter we will discuss designs in which all of the numerical factors are fixed; in Chapter 15 we will discuss designs that can be regarded as having numerically valued random factors.