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Three-Way Variance Analysis

Bogdan Anastasiei shows how to perform a three-way variance analysis when the third-order and second-order effects are both statistically significant:

In the formula above the interaction effect is, of course, dosegendertype. The ANOVA results can be seen below (we have only kept the line presenting the third-order interaction effect).

Df Sum Sq Mean Sq F value   Pr(>F)
dose:gender:type   2    187    93.4  22.367 3.81e-10

The interaction effect is statistically significant: F(2)=22.367, p<0.01. In other words, we do have a third-order interaction effect. In this situation, it is not advisable to report and interpret the second-order interaction effects (they could be misleading). Therefore, we are going to compute the simple second-order interaction effects.

This is definitely not a trivial article, but there are useful techniques in it.