Multiway ANOVA

By means of a one-way ANOVA, the effect of one factor can be investigated at different levels. In our example, the effect of a laboratory on the results of determinations was tested. In many applications, several factors have to be evaluated simultaneously. For example, apart from the laboratory effects, influences by the operator and the quality ofthe instrumentation are to be expected. These effects can be studied by using the two- or multiway analysis of variance. 

In principle, the ANOVA is not restricted to two factors. Common software usually offers multiway analysis where the tests can be performed for as many factors as the problem to be solved requires. 

The effects of the different factors can be investigated independently of each other, or the interactions of factors can be considered in the ANOVA. The data for multiway ANOVA are ordered in a matrix, such that the rows represent the individual runs and the columns contain the factor levels as well as the responses (Table 2.18). This treatment of data corresponds to those used in experimental designs (see Section 4.2). 

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