This discussion of interactions is based on Anderson (1961b), which discussed the twin issues of interaction model and response measure illustrated in Table 7.1 and Figure 7.3. These issues were pursued further in Anderson (1962b, 1963). Useful discussion has been added by Bogartz and Wackwitz (1971) and reemphasized by Bogartz (1976), Harris (1976), and Loftus (1978).
All this work, however, rested on the gratuituous assumption that the Anova model was a valid process model. And on the arbitrary assumption that the measured response was a true linear scale (see e.g., Anderson, 1969, 1972b, 1977, 1979b, 1982, Section 7.11); see also Section 7.4.
The critical issue is to find a process model for forgetting. The proportional change model is restrictive since it requires the forgetting rate to be constant over time. A more general shape function model (Anderson, 1963) has shown promise, especially in cogent extensions by Bogartz (1990a, b), who discusses related models, and by Paul (1994), who discusses statistical analysis (see also Wixted, 1990).
change in response = Y1 − Y0 = w (Ψ1 − Ψ∞) or Y1 = Y0 + w (Ψ1 − Ψ∞),
where Y0 denotes the response before the given stimulus, Y1 denotes the response after the stimulus, w denotes the change parameter, Ψ1 denotes the value of the given stimulus, and Ψ∞ denotes asymptotic response. In Figure 7.3, w was ½ for both groups.