Design sequences for sensory studies: Achieving balance for carry-over and position effects

In sequences of human sensory assessments, the response toa stimulus may be influenced by previous stimuli. When investigating this phenomenon experimentally with several types or levels of stimulus, it is useful to have treatment sequences which are balanced for first-order carry-over effects. The requirement of balance for each experimental participant leads us to consider sequences of n symbols comprising an initial symbol followed by n 'blocks' each containing a permutation of the symbols. These sequences are designed to include all n² ordered pairs of symbols once each, and to have treatment and sequence position effects which are approximately or thogonal. Such sequences were suggested by Finney and Outhwaite (1956), who were able to find examples for particular values of n. We describe and illustrate acomputer algorithm for systematically enumerating the sequences for those values of n for which they exist. Criteria are proposed for choosing between the sequences according to the nearness to orthogonality of their treatment and position effects.