The purpose of this chapter is to demonstrate an analysis method for 4-stage within-subject designs having two values for each of two factors, A and B. Much current analysis of data from this design follows recommendations by authors such as Girden (1992) and Kirk (1995) who considered the possibility of main effects of A and B plus their interactions, as well as interactions of subjects and those factors. (Winer, Brown, & Michels, 1991, made comparable suggestions for a more complicated design with one between-subjects factor in addition to the two within-subject factors just mentioned.) They do not assess time-related effects such as stage effects and carryover effects. However, when more than one of the 24 possible sequences of the 4 basic treatment combinations (pairs), AIBl AlB2 A2B] A2B2, are employed in an experiment, performance differences on a given treatment pair for subjects from different sequences might very well suggest that time-related effects are present. If three or more appropriate sequences are employed, it will be possible to disentangle treatment effects from the specific stage and carryover effects assumed in the model equation to be presented shortly.