Statistics - Factorial Anova
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Table of Contents
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.
- N Independent Variables (IVs). Variables that are manipulated.
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
2 - Articles Related
3 - Difference between a one-way and a factorial ANOVA
Difference between a one-way and a factorial ANOVA:
- the number of independent variables (treatments)
- the number of F-ratios
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.