Testing effects of experimental design factors using multi-way analysis

Analysing experimental design data is usually performed by analysis of variance (ANOVA). In situations where the higher orders of interactions hold the most relevant information, generalised multiplicative analysis of variance (GEMANOVA), which is based on parallel factor analysis (PARAFAC), may be a useful supplement to ANOVA. By GEMANOVA the information in the data is compressed down to a few multiplicative components describing the main variation in the data including relevant interaction phenomena. GEMANOVA is best used as an explorative tool. Still there is a need for validation criteria to assist the model building. In the present publication we present such a validation criterion for GEMANOVA models based on bootstrap methodology. The method is demonstrated on a data set consisting of a pot experiment, measuring the nitrogen-to-sulfur ratio in wheat grown under different fertilising schemes. It was found that GEMANOVA revealed complex patterns in the data which were unobservable by ANOVA.