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 subs et 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-ov er balance at twice as many Values of n the number of consumers. A conseque nce is that the new designs give better robustness to the variable number o f consumers who turn up at a central location test. An algorithm is describ ed that is used to sample from the wider class of designs and is sufficient ly fast to be used for the interactive construction of designs within a com puter package. Other specialist designs for situations where there may be f actorial structure among the consumers are also described. Tables are given that list the first rows of cyclic designs generated by the algorithm, the se give pairs, as well as triples of balanced Latin squares for between fiv e and 19 products. Practical advice is given on how they may be used to con struct suitable presentation order designs. (C) 2001 Elsevier Science Ltd. All rights reserved.