A Rankit Analysis of Paired Comparisons for Measuring the Effect of Sprays on Flavor

Experiments on consumer preference have taken many forms. In that known as paired comparisons, the several treatments or stimuli are compared in pairs, each treatment appearing with every other treatment in the same pair. It is an especially appropriate design for testing the effect upon a food of chemically different pesticides. These may produce qualitative differences in flavor which the subject finds easier to compare in pairs. Usually he is asked to report a simple preference for one of the two samples in each pair. Scheffe [1952] has extended this procedure by asking each subject to note the degree of his preference within each pair as well as its direction. A recent experiment of this type concerned the relative palatability of apples sprayed with two different insecticides and with two different fungicides in a 2 X 2 factorial design. In its analysis, several statistical methods were to be compared in respect to their sensitivity, consistency and computational requirements. Among them were the Mosteller [1951a,b] modification of the original proposal by Thurstone, the Bradley-Terry [1952a,b; 1953] analysis, and the Scheffe [1952] technique. In the course of the study, a new approach was developed which shows particular promise. It is based upon the mean normal deviate, tabled by Fisher and Yates [1953] and called the by Ipsen and Jerne [1944]. It answered several questions which we could not otherwise resolve so readily, if at all. We will describe this rankit analysis in its present application and compare it with alternative procedures. The experiment had several objectives. One was to arrange the treatments on a linear scale, spaced so as to reflect the average degree of preference expressed by the tasters. Criteria were needed for judging the significance on this scale of effects associated with factorial combinations of the individual treatments. The scale had to be validated by a test of its additivity or subtractivity. If, for example, B was preferred to