In the research by Sechrist and Sangor (2001) on prejudice, why did their use of a factorial design (with interactions) provide them with more information than a single variable would have?

What will be an ideal response?

In their study, they identified two IVs: whether a person was high or low in prejudice and whether they thought people held the same attitudes that they did. The interaction effects were important here because they showed that people altered the distance they sat from a black confederate of the experimenter depending on whether they thought other people on their campus had similar views.
People high in prejudice sat closer to the confederate when they thought others on campus thought differently about race than they did compared to the case when they thought others were in agreement with them. People low in prejudice reversed this pattern, sitting farther from the black confederate when they thought people were generally in agreement with them. On whole, though, those low in prejudice sat closer than people higher in prejudice.