An alternative model for the analysis of variance with random effects

The standard model for the analysis of variance with random effects implies, for the case of two independent variables, that single effects must be tested not against the error, but against the interaction mean squares. This causes, in comparison with the fixed effects AV, a considerable loss of test power, particularly for the 2 × 2 table. An alternative modelling of the interaction effect is proposed which completely avoids the loss of power.