In microarray experiments, several steps may cause sub-optimal quality and the need for quality control is strong. Often the experiments are complex, with several conditions studied simultaneously. A linear model for paired microarray experiments is proposed as a generalisation of the paired two-sample method by Kristiansson et al. (2005). Quality variation is modelled by different variance scales for different (pairs of) arrays, and shared sources of variation are modelled by covariances between arrays. The gene-wise variance estimates are moderated in an empirical Bayes approach. Due to correlations all data is typically used in the inference of any linear combination of parameters. Both real and simulated data are analysed. Unequal variances and strong correlations are found in real data, leading to further examination of the fit of the model and of the nature of the datasets in general. The empirical distributions of the test-statistics are found to have a considerably improved match to the null distribution compared to previous methods, which implies more correct p-values provided that most genes are non-differentially expressed. In fact, assuming independent observations with identical variances typically leads to optimistic p-values. The method is shown to perform better than the alternatives in the simulation study.