DOI QR코드

DOI QR Code

Derivation of error sum of squares of two stage nested designs and its application

이단계 지분계획법의 오차제곱합 유도와 그 활용

  • Kim, Daehak (Department of Mathematics, Catholic University of Daegu)
  • Received : 2013.10.23
  • Accepted : 2013.11.20
  • Published : 2013.11.30

Abstract

The analysis of variance for randomized block design or two way classification data is well known. In this paper, particularly, we considered two stage nested design in which the levels of one factor is not identical for different levels of another factor. We investigate the structural properties of two stage nested design and the properties of error sum of squares for random effect model. For the application of two way nested design, we consider two-period crossover design which is used commonly for the equivalence test to bio-similar product. The confidence interval estimation of the difference of two population means in the crossover design is discussed based on statistical package SPSS.

확률화 블록계획법이나 교차된 이원분류표에 대한 분산분석과 오차제곱합의 성질은 널리 알려져있다. 본 논문에서는 인자에 따른 수준에 또 다른 인자들이 내포되어 있는 지분계획 특히 이단계 지분계획에 대하여 구조적 특징을 설명하고 오차제곱합의 성질에 대하여 살펴보았다. 또한 이단계 지분계획의 활용으로 크로스오버 계획을 소개하고 생물학이나 약학 등의 분야에서 많이 사용되는 동등성 검정의 신뢰구간 구축에 대하여 설명하였고 실제자료와 SPSS 통계 페키지를 이용하여 분석함으로서 응용성을 부각시켰다.

Keywords

References

  1. Biswas, N. and Raghavarao, D. (1996). Nested residual effects design. The Indian Journal of Statistics, 58, 240-244.
  2. Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978). Statistics for experimenters : An introduction to design, data analysis and model building, John Wiley & Sons, New York.
  3. Box, G. E. P., Hunter, W. G. and Hunter, J. S. (2005). Statistics for experimenters : Design, innovation, and discovery, John Wiley & Sons, New York.
  4. Choi, J. (2010). A mixed model for repeated split-plot data. Journal of the Korean Data & Information Science Soceity, 21, 1-9.
  5. Choi, J. (2011). Variance components in one factor random model by projection. Journal of the Korean Data & Information Science Soceity, 22, 381-387.
  6. Choi, Y. H. (2012). Power study for 4 ${\times}$ 4 graeco-latin square design. Journal of the Korean Data & Information Science Soceity, 23, 683-691. https://doi.org/10.7465/jkdi.2012.23.4.683
  7. Kempthorne, O. (1952). The design and experiments, John Wiley & Sons, New York.
  8. Kim. D. H., Kang, S. G. and Lee, W. D. (2005). Noninformative priors for the nested design. Journal of Statistical Planning and Inference, 133, 453-462. https://doi.org/10.1016/j.jspi.2004.01.015
  9. Kim, D. H. and Park, S. Y. (2004). Analysis of variance using SPSS, Kyowoosa, Seoul.
  10. Lee, H. (2012). Equivalence margin of the biosimilar product. Journal of Korean Society for Clinical Pharmacology and Therapeutics, 20, 17-33. https://doi.org/10.12793/jkscpt.2012.20.1.17
  11. Meyers-Levy, J. and Barnes, J. (2001). How to analyze data from a nested design. Journal of Consumer Psychology, 10, 21-24.
  12. Montgomery, D. C. (2001). Design and analysis of experiments, John Wiley & Sons, New York.
  13. Paik, W. B. (1989). Experimental design and analysis, Freedom Academy, Seoul.
  14. Park, S. H. (2009). Modern experimental design, Minyoungsa, Seoul.
  15. Pereira, M. G. and Teixeira, A. (2001). Estimation of genetic components in popcorn based on the nested design. Crop Breeding and Applied Biotechnology, 1, 3-10. https://doi.org/10.13082/1984-7033.v01n01a01
  16. Searle, S. R. (1971). Linear models, John Wiley & Sons, New York.