Have you ever fallen asleep during an afternoon lecture, or at least found it really hard to pay attention and then later remember what you were taught? Imagine we are interested in studying the effect of time on day on memory for lecture material. We might also expect that caffeine intake influences the extent to which people can stay alert and attend during the lectures. So, we design an experiment with two independent variables, each with two levels: time of day (morning or afternoon); caffeine intake (placebo or one dose of caffeine). This would be a factorial design. A factorial design simply means that we have two or more independent variables (each with at least two levels) in our experiment. Factorial designs can be useful for adding an extra independent variable with relatively little effort, but also for studying interactions. In other words, we can see how the effect of one independent variable changes according to the levels of the other independent variable. This can often be more interesting than just studying main effects (i.e., the effect of a single independent variable).

Specifying a Factorial Design

You may have seen journal articles use a particular style to describe a factorial design. For example, you might see something like:

The experiment was a 3 x 2 between-subjects design (time of day: morning, afternoon, or evening; caffeine intake: placebo or one dose of caffeine).

The “3 x 2” indicates that there were three levels of the first factor/independent variable – morning, afternoon, and evening – and two levels of the second factor/independent variable – placebo and one dose of caffeine. A 3 x 2 design like this will result in six “cells” (six means). Note that we should always specify if the design is between-subjects (each cell represents different participants), within-subjects (each cell represents the same participants), or mixed (both between- and within-subjects – more on that in a later chapter!).