Cyclic presentation order designs for consumer research

Williams Latin square designs are used widely in consumer research to plan complete block experiments. It is demonstrated how these designs are a subset of a wider class of cyclic designs and how alternative designs, for odd numbers of samples p, are preferable both to obtain positional and carry-over balance at twice as many values of n the number of consumers. A consequence is that the new designs give better robustness to the variable number of consumers who turn up at a central location test. An algorithm is described that is used to sample from the wider class of designs and is sufficiently fast to be used for the interactive construction of designs within a computer package. Other specialist designs for situations where there may be factorial structure among the consumers are also described. Tables are given that list the first rows of cyclic designs generated by the algorithm, these give pairs, as well as triples of balanced Latin squares for between five and 19 products. Practical advice is given on how they may be used to construct suitable presentation order designs.