Automated assembly of optimally spaced and balanced paired comparisons: controlling order effects

To control order effects in questionnaires containing paired comparisons, Ross (1934) described an optimal ordering of the pairings. The pairs can also be balanced so that every stimulus appears equal numbers of times as the first and the second member of a pair. First, we describe and illustrate the optimally spaced, balanced ordering of pairings. Then we show how the optimally spaced, balanced order can be used to implement a matrix-sampling design or a fully incomplete design when the number of stimuli n is so large that respondents cannot reasonably be expected to judge all n(n - 1)/2 pairs. The algorithm for balancing and optimally spacing the list of pairs is described.