Factorial ANOVA

Photo by Kate Kalvach on Unsplash

What is a Factorial ANOVA?

Factorial ANOVAs have two or more categorical independent variables. Categorical data consists of discrete groups.

Let’s talk about a simple factorial ANOVA design: the 2 x 2. A 2 x 2 (said “two by two”) factorial ANOVA is the simplest design. A 2 x 2 factorial ANOVA has two independent variables, each with two levels. In this example, direct sunlight and filtered sunlight are the two categories of the variable “sunlight”. For the “watering frequency” variable, the groups are once per day and twice per day. Both variables form four groups:

Direct SunlightFiltered Sunlight
Watering – once per dayPlant growth = 10 cmPlant growth = 6 cm
Watering – twice per dayPlant growth = 5 cmPlant growth = 6.5 cm

Main and Interaction Effects

Factorial ANOVA can be used to look at interaction effects. Interactions could suggest that the relationship between X on the outcome differs depending on the condition of X.


Cheyenne Chooi, PhD Student (Neuropsychology)

Cheyenne is a graduate of the University of Western Australia where she received a Bachelor's degree in Science, and a Bachelor's degree in Science with Honours in psychology. She is currently a third year PhD Student researching factors related to Alzheimer's disease. Her current research focuses on the concept of cognitive reserve.

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