Testing Interaction and Estimating Variance Components in Block Designs - Based on a Linear Model

Randomized complete block designs (RCBD) introduced by [3] are probably the most widely used experimental designs. Despite many advantages, they suffer from one serious drawback. It is not possible to test interaction effects in analysis of variance (ANOVA) as there is only one observation for each combination of a block and factor level. Although there are some attempts to overcome this problem none of these methods are used in practice, especially as most of the underlying models are non-linear. A review on such tests is given by [6] and [1]. Here a new method is introduced which permits a test of interactions in block designs. The model for RCBDs is linear and identical to that of a two factorial design. The method as such is not restricted to simple block designs, but can also be applied to other designs like Split-Plot-design, Strip-Plot-design, ...and probably to incomplete block designs. ANOVA based on this method is very simple. Any common statistical program packages like SAS, SPSS, R, ...can be used. Although a test on interaction in two- or multi- factorial designs makes sense only for fixed and a certain class of mixed models, the proposed method can also be used for estimating variance components in any kind of block models (fixed, random, mixed) if the sample size is not too small.