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A factorial experiment can be expanded to include multiple independent variables, each with its own set of levels. For example, a researcher might investigate a psychological treatment by incorporating three distinct independent variables: the type of psychotherapy (such as cognitive versus behavioral), the duration of the psychotherapy (such as two weeks versus two months), and the sex of the psychotherapist (such as female versus male). This specific structure serves as an example of a $$2 	imes 2 	imes 2$$ factorial design. Because each of the three independent variables has exactly two levels, multiplying them together ($$2 	imes 2 	imes 2$$) yields a total of eight unique experimental conditions.

Example of a $$2 	imes 2 	imes 2$$ Factorial Design

In an experiment investigating a psychological treatment, a researcher includes three independent variables: type of psychotherapy (cognitive vs. behavioral), duration of psychotherapy (two weeks vs. two months), and sex of the psychotherapist (female vs. male). How many unique experimental conditions are generated in this 2 x 2 x 2 factorial design?

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