To obtain scale values for a set of stimuli (e.g., political issues, physical objects) pairs of stimuli may be presented to judges who are required to select the stimulus which possesses the greater quantity of a specified attribute. This technique, known as pair comparisons (Guilford, 1954) is often tedious and impractical since the number of pairs, k(k 1)/2 where k is the number of stimuli, increases rapidly as the number of stimuli increases. To make the method more manageable, alternatives to presenting all pairs to all judges have been developed. Most of the alternate methods have involved other scaling techniques or ways of reducing the number of pairs to be judged. Such scaling techniques as the methods of equal-appearing intervals, successive categories, and rank orderings (Guilford, 1954) have been modified to approximate pair comparison judgments. The number of pairs has been reduced by comparing stimuli to designated standards (Guilford, 1931), by comparing stimuli only within a number of subsets of stimuli (Uhrbrock & Richardson, 1933), by presenting only a systematically selected portion of the possible pairs of stimuli (McCormick & Bachus, 1952), and by pairing adjacent stimuli subsequent to a preliminary rank ordering (Guilford, 1954). Because comparisons of all pairs of stimuli are not made, these alternatives have required modifications of the methodology used to compute scale values for the stimuli. Recently, Shoemaker (1971) applied matrix sampling methodologies to the method of pair comparisons. Using the data from a complete set of judgments of six stimuli, he reported results of ex post facto sampling plans based upon different combinations of numbers of subsets of items, items per subset, and examinees who responded to each subset. From the simulated sampling results Shoemaker concluded that scale values can be approximated through matrix sampling and that the approximation becomes more accurate as the number of observations resulting from the sampling plan increases.