A hierarchical statistical model that contains an interaction term retains its associated lower-order effects. For two categorical predictors this means keeping both main effects when keeping their interaction. A nonsignificant averaged main effect may coexist with large opposite effects in different groups. Dropping its lower-order term while retaining the interaction can make the model depend on arbitrary factor coding.
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The Principle of Marginality, often associated with economics and decision-making theories, suggests that in assessing the impact or utility of a decision, one should focus on the effects of incremental changes rather than the total or average effects. This principle emphasizes that when making decisions, individuals or organizations should consider the marginal benefits and marginal costs—the additional benefits gained from an action compared to the additional costs incurred.