ANOVA–simultaneous component analysis  Analysis of variance – simultaneous component analysis (ASCA or ANOVA–SCA) is a method that partitions variation and enables interpretation of these partitions by SCA, a method that is similar to principal components analysis (PCA). This method is a multivariate or even megavariate extension of analysis of variance (ANOVA). The variation partitioning is similar to ANOVA. Each partition matches all variation induced by an effect or factor, usually a treatment regime or experimental condition. The calculated effect partitions are called effect estimates. Because even the effect estimates are multivariate, interpretation of these effects estimates is not intuitive. By applying SCA on the effect estimates one gets a simple interpretable result. In case of more than one effect this method estimates the effects in such a way that the different effects are not correlated. Many research areas see increasingly large numbers of variables in only few samples. The low sample to variable ratio creates problems known as multicollinearity and singularity. Because of this, most traditional multivariate statistical methods cannot be applied. This section details how to calculate the ASCA model on a case of two main effects with one interaction effect. It is easy to extend the declared rationale to more main effects and more interaction effects. If the first effect is time and the second effect is dosage, only the interaction between time and dosage exists. We assume there are four time points and three dosage levels. Let X be a matrix that holds the data. X is mean centered, thus having zero mean columns. Let A and B denote the main effects and AB the interaction of these effects. Two main effects in a biological experiment can be time (A) and pH (B), and these two effects may interact. In designing such experiments one controls the main effects to several (at least two) levels. The different levels of an effect can be referred to as A1, A2, A3 and A4, representing 2, 3, 4, 5 hours from the start of the experiment. The same thing holds for effect B, for example, pH 6, pH 7 and pH 8 can be considered effect levels. A and B are required to be balanced if the effect estimates need to be orthogonal and the partitioning unique. Matrix E holds the information that is not assigned to any effect. The partitioning gives the following notation:  Find all rows that correspond to effect A level 1 and averages these rows. The result is a vector. Repeat this for the other effect levels.