  Blocking is often used to reduce known variability in designed experiments by
collecting together homogeneous experimental units. A common modelling
assumption for such experiments is that responses from units within a block are
dependent. Accounting for such dependencies in both the design of the
experiment and the modelling of the resulting data when the response is not
normally distributed can be challenging, particularly in terms of the
computation required to find an optimal design. The application of copulas and
marginal modelling provides a computationally efficient approach for estimating
population-average treatment effects. Motivated by an experiment from materials
testing, we develop and demonstrate designs with blocks of size two using
copula models. Such designs are also important in applications ranging from
microarray experiments to experiments on human eyes or limbs with naturally
occurring blocks of size two. We present methodology for design selection, make
comparisons to existing approaches in the literature and assess the robustness
of the designs to modelling assumptions.
