A classic study by Kathy Gilliland provides a clear example of a cross-over interaction by examining how caffeine affects the verbal test scores of introverts and extraverts. The research revealed that introverts achieved better scores than extraverts when no caffeine was consumed. In stark contrast, extraverts outperformed introverts after ingesting $$4$$ mg of caffeine per kilogram of body weight. Because the performance effect of caffeine completely reversed depending on personality type, it serves as a perfect illustration of a cross-over interaction.

Example of a Cross-over Interaction

Interaction effects in factorial experiments can be visually interpreted and analyzed using either bar graphs or line graphs. In these visualizations, spreading interactions are identifiable when there is a large difference in the dependent variable at one level but little to no difference at the other. Cross-over interactions are characterized by a distinct reversal in the pattern of bar heights or by line graphs where the plotted lines literally intersect and cross over one another.

Graphing Interactions

How is a cross-over interaction defined in the context of factorial designs?

A cross-over interaction occurs when an independent variable has an effect at both levels of a second independent variable, but these effects operate in completely opposite directions. In graphical representations, this type of interaction is visually distinctive because the lines plotting the different conditions will physically intersect and cross over each other.

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In factorial research designs, the effect of one independent variable can depend on the specific level of another variable in several distinct ways. The two primary ways these complex relationships manifest are through spreading interactions, where an effect is present at one level but weak or absent at another, and cross-over interactions, where the independent variable produces opposite effects depending on the second variable's level.

Types of Interactions

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KPU Research Methods in Psychology - 4th American Edition

A spreading interaction is a specific form of interaction effect in which one independent variable has a prominent impact at one level of a second independent variable, but exhibits either a noticeably weaker effect or no effect at all at the other level. When visualized, this pattern typically appears as a significant difference in bar heights or as diverging lines in one condition, contrasting with minimal differences in the other.

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