Example (ANOVA command)

The following analysis list specifies three factor variables named A, B, and C:

ANOVA VARIABLES=Y BY A,B,C(0,3).

The following table summarizes the three methods for decomposing sums of squares for this example.

With the default regression approach, each factor or interaction is assessed with all other factors and interactions held constant.
With the classic experimental approach, each main effect is assessed with the two other main effects held constant, and two-way interactions are assessed with all main effects and other two-way interactions held constant. The three-way interaction is assessed with all main effects and two-way interactions held constant.
With the hierarchical approach, the factor main effects A, B, and C are assessed with all prior main effects held constant. The order in which the factors and covariates are listed on the ANOVA command determines the order in which they are assessed in the hierarchical analysis. The interaction effects are assessed the same way as in the experimental approach.

Table 1. Terms adjusted for under each option
Effect	Regression (UNIQUE)	Experimental	Hierarchical
A	All others	B,C	None
B	All others	A,C	A
C	All others	A,B	A,B
AB	All others	A,B,C,AC,BC	A,B,C,AC,BC
AC	All others	A,B,C,AB,BC	A,B,C,AB,BC
BC	All others	A,B,C,AB,AC	A,B,C,AB,AC
ABC	All others	A,B,C,AB,AC,BC	A,B,C,AB,AC,BC