Factorial orthogonality in the presence of covariates

  • Rahul Mukerjee
  • Haruo Yanai


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.

Key words

Factorial orthogonality covariate reduced normal equation orthogonal projector orthonormal contrast proportional frequency criterion 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1986

Authors and Affiliations

  • Rahul Mukerjee
    • 1
  • Haruo Yanai
    • 1
  1. 1.Indian Statistical InstituteNational Center of Entrance Examination for UniversityIndia

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