Statistics - Factorial Anova

Thomas Bayes


A factorial ANOVA is done when the independent variables are categorical.

By adding a second independent variable, we are entering in factorial ANOVA.

Factorial ANOVA is a special case of multiple regression (of GLM) where the predictors are not correlated (with perfectly independent predictors (IVs)), independent by design

Difference between a one-way and a factorial ANOVA

Difference between a one-way and a factorial ANOVA:

Independent by design

Main effects and interaction effect are:

  • independent from one another
  • orthogonal.
  • unrelated.
  • independent by design (An equal number of the subjects are randomly assigned to all conditions)

That's why we can test multiple hypotheses in one experiment.

I could have main effects and have an interaction, or have main effects and no interaction.


After a significant interaction in factorial ANOVA, you should test simple effects (not post-hoc comparisons , not main effects) in order to:

  • explore that interaction,
  • to figure out where that interaction is coming from.

The way to do that is through simple effects analysis.

When you had a significant main effect in a one-way ANOVA, you had to follow that up with post-hoc tests to see where the main effect was coming from, if you had three or more levels (categorie).

degree of freedom

If we sum the degree of freedom all up, it should come out to the total number of subjects in the experiment minus 1.

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