 Solution

TODO: directions, magnitudes and inferential conclusions require the unavailable coefficient table, coding and model specification. For illustration of interpretation only, let $D$ and $S$ be binary indicators whose reference levels are explicitly defined. If an ordinary linear model includes both factors and their interaction, its conditional mean has the formThen the distance difference is ${\beta }_D$ at the reference size and ${\beta }_D+{\beta }_{DS}$ at the other size; the interaction is the difference between those differences. If the interaction is omitted, the model assumes a common distance difference across sizes. These are conditional model meanings, not a claim that the missing analysis used this model or that either predictor had an observed effect. The uncertainty of a coefficient sum also involves their covariance, not merely their separate p-values.