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The American Statistician Volume 35, 1981 - Issue 1
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Original Articles

Some Computational and Model Equivalences in Analyses of Variance of Unequal-Subclass-Numbers Data

S. R. Searle Biometrics Unit, Cornell University, Ithaca, NY, 14853, USA
,
F. M. Speed Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA, 70803, USA
&
H. V. Henderson Biometrics Section, Ruakura Agricultural Research Centre, Hamilton, New Zealand
Pages 16-33 | Received 01 Mar 1979, Published online: 12 Mar 2012

References

  • Gosslee , D. G. and Lucas , H. L. 1965 . “Analysis of Variance of Disproportionate Data When Interaction Is Present” . Biometrics , 21 : 115 – 133 .
  • Harvey , Walter R. 1970 . “Estimation of Variance and Covariance Components in the Mixed Model” . Biometrics , 26 : 485 – 504 .
  • Henderson , C. R. 1959, 1969 . “Design and Analysis of Animal Husbandry Experiments” . In Techniques and Procedures in Animal Science Research , Corvallis , Oreg. : American Society of Animal Science . (pp. 2–55, 1st ed. 1959; pp. 1–35, 2nd ed. 1969)
  • Hocking , R. R. , Hackney , O. P. and Speed , F. M. 1978 . “The Analysis of Linear Models With Unbalanced Data” . In Contributions to Survey Sampling and Applied Statistics, Festschrift for H.O. Hartley , Edited by: David , H. A. New York : Academic Press .
  • Hocking , R. R. and Speed , F. M. 1975 . “A Full Rank Analysis of Some Linear Model Problems” . Journal of the American Statistical Association , 70 : 706 – 712 .
  • Marsaglia , George and Styan , George P. H. 1974 . “Equalities and Inequalities for Ranks of Matrices” . Linear and Multilinear Algebra , 2 : 269 – 292 .
  • Searle , S. R. 1966 . Matrix Algebra for the Biological Sciences , New York : John Wiley .
  • Searle , S. R. 1971 . Linear Models , New York : John Wiley .
  • Searle , S. R. “Using the R( )-Notation for Reductions in Sums of Squares when Fitting Linear Models” . paper presented at the Spring Regional Meetings . Ames , Iowa : Eastern North American Region of the Biometric Society .
  • Searle , S. R. “Relationships Between the Estimable Functions of SAS GLM Output for Unbalanced Data and Hypotheses Tested by Traditional F-statistics” . Proceedings of the 4th Annual SAS Users’ Group International Conference . pp. 196 – 208 . Raleigh , N.C. : SAS Institute .
  • Searle , S. R. 1979b . “Annotated Computer Output for Analysis of Variance of Unequal-Subclass-Numbers Data” . The American Statistician , 33 : 222 – 223 .
  • Speed , F. M. 1969 . A New Approach to the Analysis of Linear Models , Houston , Tex. : National Aeronautics and Space Administration . a NASA technical memo, NASA TM X–58030
  • Speed , F. M. and Hocking , R. R. 1976 . “The Use of the R( )-Notation With Unbalanced Data” . The American Statistician , 30 : 30 – 33 .
  • Speed , F. M. , Hocking , R. R. and Hackney , O. P. 1978 . “Methods of Analysis of Linear Models With Unbalanced Data” . Journal of the American Statistical Association , 73 : 105 – 112 .
  • Urquhart , N. S. and Weeks , D. L. 1978 . “Linear Models in Messy Data: Some Problems and Alternatives” . Biometrics , 34 : 696 – 705 .
  • Urquhart , N. S. , Weeks , D. L. and Henderson , C. R. 1973 . “Estimation Associated With Linear Models: A Revisitation” . Communications in Statistics , 1 : 303 – 330 .
  • Yates , F. 1934 . “The Analysis of Multiple Classifications With Unequal Numbers in the Different Classes” . Journal of the American Statistical Association , 29 : 51 – 66 .

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