How does a factorial experiment study more than one factor?

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statistics Figure 1: A bar graph showing the marital status of 100 individuals.

A factorial design studies multiple factors by considering all possible combinations of those factors and their respective levels. By testing these combinations, researchers can draw conclusions about the influence of each factor on the response variable.1

In this design, if you have two factors—where factor 1 has a levels and factor 2 has b levels—the experiment collects data on all a × b treatment combinations. This approach is not limited to two variables; it can be extended to include more than two factors or utilized in partial factorial designs to investigate complex relationships between multiple variables simultaneously.1