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Factorial orthogonality in the presence of covariates

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Summary

The present paper obtains necessary and sufficient conditions for factorial orthogonality in the presence of covariates. In particular, when interactions are absent, combinatorial characterizations of the conditions, as natural generalizations of the well-known equal and proportional frequency criteria, have been derived.

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References

  1. Addelman, S. (1963). Techniques for constructing factorial replicate plans.,J. Amer. Statist. Ass.,58, 45–71.

    Article  MathSciNet  Google Scholar 

  2. Chakravarti, I. M. (1956). Fractional replications in asymmetrical factorial designs and partially balanced arrays,Sankhya,17, 143–164.

    MathSciNet  MATH  Google Scholar 

  3. Cochran, W. G. and Cox, G. M. (1957).Experimental Designs, 2nd ed., John Wiley, New York.

    MATH  Google Scholar 

  4. Cotter, S. C., John, J. A. and Smith, T. M. F. (1973). Multifactor experiments in nonorthogonal designs,J. Roy. Statist. Soc., B,35, 361–367.

    MathSciNet  MATH  Google Scholar 

  5. Cox, D. R. (1958).Planning of Experiments, John Wiley, New York.

    MATH  Google Scholar 

  6. Kshirsagar, A. M. (1966). Balanced factorial design,J. Roy. Statist. Soc., B,28, 559–569.

    MathSciNet  MATH  Google Scholar 

  7. Kurkjian, B. and Zelen, M. (1963). Applications of the calculus for factorial arrangements. I. Block and direct product designs,Biometrika,50, 63–73.

    MathSciNet  MATH  Google Scholar 

  8. Kuwada, M. and Nishii, R. (1979). On a connection between balanced arrays and balanced fractionalsm factorial designs,J. Japan Statist. Soc.,9, 93–101.

    MathSciNet  Google Scholar 

  9. Lewis, S. M. and John, J. A. (1976). Testing main effects in fractions of asymmetrical factorial experiments,Biometrika,63, 678–680.

    Article  MathSciNet  Google Scholar 

  10. Mukerjee, R. (1979). Inter-effect-orthogonality in factorial experiments,Calcutta Statist. Soc. Bull.,28, 83–108.

    MathSciNet  MATH  Google Scholar 

  11. Mukerjee, R. (1980). Orthogonal fractional factorial plans,Calcutta Statist. Soc. Bull.,29, 143–160.

    MathSciNet  MATH  Google Scholar 

  12. Rao, C. R. and Yanai, H. (1979). General definition and decomposition of projectors and some application to statistical problems,J. Statist. Plann. Inf.,3, 1–17.

    Article  MathSciNet  Google Scholar 

  13. Seber, G. A. F. (1964). Orthogonality in analysis of variance,Ann. Math. Statist.,35, 705–710.

    Article  MathSciNet  Google Scholar 

  14. Takeuchi, K., Yanai, H. and Mukherjee, B. N. (1982).The Foundation of Multivariate Analysis, Wiley Eastern, New Delhi.

    MATH  Google Scholar 

  15. Wishart, J. (1950). Field trials II. The analysis of covariance,Commonwealth Bureau of Plant Breeding and Genetics, Tech. Communication No. 15.

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Authors and Affiliations

  1. Indian Statistical Institute, National Center of Entrance Examination for University, India

    Rahul Mukerjee & Haruo Yanai

Authors
  1. Rahul Mukerjee
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  2. Haruo Yanai
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Mukerjee, R., Yanai, H. Factorial orthogonality in the presence of covariates. Ann Inst Stat Math 38, 331–341 (1986). https://doi.org/10.1007/BF02482521

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  • DOI: https://doi.org/10.1007/BF02482521

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