We discuss factorial treatment designs with more than one treatment factor and extend the analysis of variance framework to handle these designs. The variation is then decomposed into several contributions for the different treatment factors. A new type of effect is interactions between factors, and we discuss their interpretation in detail. We consider linear contrasts and power analysis for factorial designs, and provide more general discussion on the advantages of these designs and strategies for analyzing them. Analysis of variance for unbalanced data and its problems is briefly considered.