ABSTRACT
This chapter notes with a two-way matrix that the cell totals were a result of the relevant between-treatments effects and the two-way interaction. In the same way, the cell totals in a three-way matrix are the result of the relevant between-treatments effects, the relevant two-way interactions, and a three-way interaction. Just as a two-way matrix can be used to calculate a two-way interaction, the three-way matrix can be used to calculate a three-way interaction. There must be more than one score in each combination of treatments from the three factors, for calculation of a three-way interaction. In a four-factor ANOVA there must be more than one score in each combination of treatments from the four factors or else one cannot calculate a four-way interaction; one will still get two- and three-way interactions. The three-way interactions are obtained from the three-way matrices, the four-way interaction from the four-way matrix.
