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 Sunlight | Filtered Sunlight | |
| Watering – once per day | Plant growth = 10 cm | Plant growth = 6 cm |
| Watering – twice per day | Plant growth = 5 cm | Plant 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.
References
- https://www.scribbr.com/frequently-asked-questions/what-is-a-factorial-anova/
- https://www.statology.org/factorial-anova/
- https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/factorial-anova/
- http://www.crumplab.com/statistics/factorial-anova.html
- http://pytolearn.csd.auth.gr/d1-hyptest/12/ptl_anova2.html
