Hypothesis tests have been largely used in analysis of variance in order to study sources of variation. The F test for treatments when there are more than one degree of freedom provides only a general information, related to the comparison of means. More specific information is obtained by orthogonal decomposition of the degrees of freedom, often using contrasts. However, this technique becomes complex and difficult to implement as the number of treatments increases. In order to overcome this problem it was studied auxiliary variables to test differences among groups and facilitate orthogonal decomposition of treatment degrees of freedom. It was used as example , experimental data from a maize trial consisting of nine hybrids, classified as simple, double or triple assayed in randomized complete block design. After the decomposition, each factor in the model, receives a specific codification, the value referring the level of the factor when the treatment is of that type or, alternatively, zero if not. The use of auxiliary variables showed to be a usefull and simple way to test differences between groups. This can be also done with the CONTRAST function of the PROC GLM of SAS software, but with a more complex procedure.
orthogonal decomposition; contrasts; auxiliary variables
