factorial ANOVA :

An ANOVA where the groups are classified using more than one factor.

In a one-way ANOVA, two or more groups are compared to each other. For instance, a researcher might be comparing the average levels of a stress hormone for people in four situations: male shoppers, female shoppers, male drivers, and female drivers. The result of the ANOVA would simply indicate whether there are differences between the groups.

However, the groups can be divided using two factors: gender and task. Two of the groups have entirely males, and two have entirely females. Similarly, two of the groups were involved in shopping, and two involved in driving.

The advantage of this is that the result of the ANOVA gives much more information: instead of one significance value, three are obtained: one for the first factor, one for the second factor, and one for the interaction.

The interaction is of great interest and importance in factorial ANOVAs, because it indicates whether the two factors have influence each others effect on the dependent variable.

For instance, perhaps males exhibit higher stress levels than females, and driving is more stressful than shopping. In that case, both factors will probably show a significant effect. However, it is possible that males find shopping more stressful- relatively- than females. In this case, the effect of situation on stress depends on whether males or females are involved. Such a situation is called an interaction.