A Generalized Modification of Scheffé’s Paired Comparisons: A theoretical approach to decrease the number of experiments

Summary

In the sensory evaluation, Scheffé’s paired comparisons are theoretically interesting and also practically used many times. However, the number of its experiments is so large that there are a few cases in which its experiments can not be carried out. On those occasions, Scheffé’s method can not be used. The current study proposes a generalized modification of Scheffé’s method and demonstrates the parameter estimation and testing, with a manageable number of experiments by keeping the minimum structure of Scheffé’s model. To do this, we suppose the following assumption for all experiments. (1) The scores do not have order effects. (2) Combination effect may exists in a few combination, and the value is constant γ. (3) The observation is considered a random sample drawn from the same population. It is of interest to see if the number of experiments can be reduced without sacrificing the estimation process.