Statistics - Factorial Anova

> (Statistics|Probability|Machine Learning|Data Mining|Data and Knowledge Discovery|Pattern Recognition|Data Science|Data Analysis)

1 - About

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


3 - Difference between a one-way and a factorial ANOVA

Difference between a one-way and a factorial ANOVA:

4 - 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.


5 - After

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).

6 - 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.