Factorial analysis of variance is an extension of one-way ANOVA, and is probably more frequently used. Factorial ANOVA allows the researcher to examine the effects of more than one independent variable at a time.
For example, suppose a researcher wanted to examine how participants react to the characteristics of fictional actors placed in particular scenarios. The researcher might create 4 scenarios, one with a man acting in an assertive manner, a second with a man acting in a passive manner, a third with a woman acting in an assertive manner, and a fourth with a woman acting in a passive manner. He might then ask participants to rate the extent to which they find each of the actors likeable in each of the scenarios. Here, the researcher might be interested in examining the effects of two variables. First, he might want to see if participants tended to rate females or males more positively. Second, he might want to see if participants rated assertive or passive behaviors more positively. So, here we have two independent variables: gender and assertiveness/passiveness, and one dependent variable: likeability.
Factorial ANOVA allows the researcher to take the analysis one step further, however. He or she can now examine interaction effects. An interaction effect takes into account the effects of both variables. For example, if the researcher found that the passive woman was rated as more likeable than the assertive woman, while the assertive man was rated more likeable than the passive man, this would represent an interaction effect. If you were to graph an interaction effect, it would look like this: PLEASE SEE ATTACHED FILES
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