The triangle test has been used frequently in sensory difference testing. Attempts have been made to augment the basic information from triangle tests with scores on degree of difference between the sample selected as the variant and the remaining 2. In this paper a mathematical model has been developed to permit formal utilization of the degree-of-difference scores. It is assumed that a stimulus-response scale exists and that 2 standard samples and 1 variant sample evoke responses x1, X2 and y on this scale. These responses are taken to have independent normal distributions with variances [sigma]2 and means zero for the x-variates and mean [mu] for the y-variate. Conditional distributions for degree-of-difference scores are obtained, the likelihood function for N independent trials of the triangle test is developed, and a procedure for testing that [mu] = 0 is given.