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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.

Cross-over Interaction

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.

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