Two-way ANOVA is an ANOVA model with two categorical factors. A fixed effects model with an interaction has the form
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It separates variation associated with the first main effect, the second main effect, their interaction, and the residual error.
An interaction means that the effect of one factor depends on the factor level of the other. When an interaction is present, isolated interpretations of the main effects can be misleading. Replication within combinations of factor levels is needed to estimate a general interaction separately from random error.
