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

  • Masaya Iizuka
  • Katsumi Ujiie
Conference paper

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.

Keywords

Paired Comparison Sensory Evaluation Generalize Modification Projection Matrix Combination Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Ujiie. K and Iizuka. M (2000). A Generalized Modification of Scheffé’s Paired Comparisons -Theoretical Approach to Decrease the Number of Experiments-. Proceedings of the International Conference on Measurement and Multivariate Analysis, 2, 234–237. Banff, Alberta, CanadaGoogle Scholar
  2. Ujiie. K, Iizuka. M and Nonaka. T (1996). Modified Scheffé’s paired comparisons. Proceeding s of the 10th Symposium of the Japanese Society of Computational Statistics. 1–8–111Google Scholar
  3. Ujiie.K and Nonaka. T (1996). Modified Scheffé’s paired comparisons -Theoretical Approach to Decrease the Number of Experiments-. Proceedings of the 26th symposium on the sensory analysis. Union of Japanese Scientists and Engineers (JUSE), 189–196 (in Japanese)Google Scholar
  4. Scheffé,H. (1952). An analysis of variance for paired comparisons. Journal of American Statistical Assosiation, 47. 381–400MATHGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Masaya Iizuka
    • 1
  • Katsumi Ujiie
    • 2
  1. 1.Faculty of LawOkayama UniversityOkayamaJapan
  2. 2.Department of Mathematics, School of ScienceTokai UniversityHiratsukaJapan

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