Lecture 4: Factorial ANOVA & MANOVA (ARMS, Utrecht University)

Factorial ANOVA

A 2x3 ANOVA means there were two factors, one with two and one with three levels.

In this case you test three hypotheses:

1. H₀ : no main effect of factor 1 on dependent variable
2. H₀ : no main effect of factor 2 on dependent variable
3. H₀ : no interaction effect of factor 1 & 2 on dependent variable

Definition interaction effect: the effect of one factor is different for different levels of another factor. For example: the effect of the treatment is different for men and women.

If you found a significant interaction effect, it does not tell you the story of interest (which subgroups score higher/lower than others). Follow-up tests are needed, these are called Simple (Main) Effects. Here you look at the effect of one factor within one level of the other factor (for example only for women).

In the interaction plot you can quickly see whether there is an interaction or not: if the lines are parallel, there is no interaction. But disadvantage: you don’t know the confidence intervals from the plot only.

In a 2x3 ANOVA there are 2+3=5 simple main effects you could test. 

In SPSS, you can only run a simple main effect test through the syntax.

Effect sizes for all effects (main and interaction) for factorial ANOVA are: partial eta-squared.

In factorial ANOVA, you can use contrast testing as alternative to post-hoc pairwise comparisons. This only tests pre-specified hypotheses. No alpha corrections are needed --> more power. Disadvantage: it’s unlikelier you expose unexpected results that may be interesting for future research.

• Simple contrast: compare each group to the first (or last; which your control group is) group.

• Repeated contrast: compares each group except the first is compared to the previous group

MANOVA

With MANOVA, you can compare two or more groups on multiple dependent variables simultaneously with one test.

The advantes of a MANOVA are important to understand and know. These advantages are:

• Revealing (multivariate) differences not seen with several ANOVA’s
• Protection for inflated type 1 error rate

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