In which scenario would a factorial design be more efficient?

A factorial design is particularly efficient in scenarios that involve examining multiple variables simultaneously and understanding how these variables interact with one another. This design allows researchers to assess not just the main effects of individual factors but also interaction effects, which can be critical for a comprehensive understanding of the phenomenon being studied.

For instance, if a researcher is interested in how both stress levels and diet impact academic performance, a factorial design enables them to explore not just the independent effects of stress and diet but also how different combinations of these factors may contribute to academic outcomes. This simultaneous examination is far more efficient than running separate studies for each variable, as it reduces the number of participants needed and yields more nuanced insights into complex relationships.

In contrast, scenarios involving a single variable with a limited number of participants, qualitative data examination, or a focus on longitudinal studies do not leverage the strengths of factorial designs, which are optimized for exploring interactions across multiple variables.