Abstract

We consider experiments on a number of subjects, and examine how the links between subjects in an experiment, affect the optimal design. For example, in a marketing experiment, it is reasonable to believe that a product may be preferred more by a subject whose ‘friend’ also prefers that product, and we may wish to use this ‘friendship’ information to improve our design.

We present optimal designs to measure both the direct effect and the network effect. We discuss how the structure of the network has a large influence on the optimal design, but show that even if we know many properties of the network, as represented by the eigenvalues of a graph, we cannot determine an absolute design.

We present examples based on marketing experiments, and show how the results can be applied to experiments in social sciences and elsewhere.