18
Views
3
CrossRef citations to date
0
Altmetric
Theory and Method

On Approximating the Null and Nonnull Distributions of the F Ratio in Unbalanced Random-Effect Models from Nonnormal Universes

&
Pages 655-662 | Received 01 May 1978, Published online: 12 Mar 2012

References

  • Atiqullah , M. 1962a . “On the Effect of Nonnormality on the Estimation of Components of variance,” . Journal of the Royal Statistical Society , 24 : 140 – 147 . Ser. B
  • Atiqullah , M. 1962b . “The Estimation of Residual Variance in Quadratically Balanced Least-Squares Problems and the Robustness of the F-Test,” . Biometrika , 49 : 83 – 91 .
  • Box , G. E. P. and Tiao , C. H. 1968 . “A Bayesian Approach to Some Outlier Problems,” . Biometrika , 55 : 119 – 129 .
  • David , F. N. and Johnson , N. I. 1951 . “The Effect of Nonnormality on the Power Function of the F-Test in the Analysis of Variance,” . Biometrika , 38 : 43 – 57 .
  • David , F. N. and Kendall , M. G. 1949 . “Tables of Symmetric Functions—Part I,” . Biometrika , 36 : 431 – 449 .
  • Davis , A. W. 1976 . “Statistical Distributions in Univariate and Multivariate Edgeworth Populations,” . Biometrika , 63 : 661 – 670 .
  • Gideon , R. A. and Gurland , J. 1977 . “Some Alternative Expansions of the Distribution Function of a Noncentral Chi-Square Random Variable,” . SIAM Journal of Mathematical Analysis , 8 : 100 – 110 .
  • Hyrenius , H. 1950 . “Distribution of ‘Student’-Fisher's t in Samples From Compound Normal Distribution,” . Biometrika , 37 : 429 – 442 .
  • Hyrenius , H. 1952 . “Sampling From Bivariate Nonnormal Universes by Means of Compound Normal Distributions,” . Biometrika , 39 : 238 – 246 .
  • Kendall , M. G. and Stuart , A. 1958 . The Advanced Theory of Statistics , Vol. I. , London : Griffin .
  • Lee , A. F. S. and Gurland , J. 1977 . “One-Sample t-Test When Sampling From a Mixture of Normal Distributions,” . Annals of Statistics , 5 : 803 – 807 .
  • Olson , C. L. 1974 . “Comparative Robustness of Six Tests in Multivariate Analysis of Variance,” . Journal of the American Statistical Association , 69 : 894 – 908 .
  • Pearson , E. S. and Tiku , M. L. 1970 . “Some Notes of the Relationship Between the Distributions of Central and Noncentral F,” . Biometrika , 51 : 175 – 177 .
  • Subrahmaniam , K. 1972 . “On Quadratic Forms From Mixtures of Two Normal Populations,” . South African Statistics Journal , 6 : 103 – 120 .
  • Subrahmaniam , K. , Subrahmaniam , K. and Messeri , J. Y. 1975 . “On the Robustness of Some Tests of Significance in Sampling From a Compound Normal Population,” . Journal of the American Statistical Association , 70 : 435 – 438 .
  • Tan , W. Y. 1977 . “On the Distributions of Sums of Squares in Unbalanced Random Effect Models,” . Statistica , 37 : 439 – 462 .
  • Tan , W. Y. and Chang , W. C. 1972 . “Convolution Approach to the Analysis of Quantitative Characters in Self-Fertilized Populations,” . Biometrics , 28 : 1073 – 1090 .
  • Tan , W. Y. and Wong , S. P. 1977 . “On the Roy-Tiku Approximation to the Distribution of Sample Variance From Non-normal Universe,” . Journal of the American Statistical Association , 72 : 875 – 881 .
  • Tan , W. Y. and Wong , S. P. 1978a . “On Approximating the Central and Noncentral Multivariate Gamma Distributions,” . Communications in Statistics , B7 : 227 – 243 .
  • Tan , W. Y. and Wong , S. P. 1978b . “On the Effects of Departure From Normality of the F-Test in a Nested Random Effect Model by Mixtures of Normals,” . Biometrische Zeitschrift , 20 : 441 – 451 .
  • Tiao , C. H. and Ali , M. M. 1971 . “Effect of Nonnormality on Inference About Variance Components,” . Technometrics , 13 : 625 – 650 .
  • Tiao , C. H. and Lund , D. 1970 . “The Use of OLUMV Estimators in Inference Robustness Studies of the Location Parameter of a Class of Symmetric Distributions,” . Journal of the American Statistical Association , 65 : 370 – 386 .
  • Tiku , M. L. 1964 . “Approximating the General Nonnormal Variance-Ratio Sampling Distributions,” . Biometrika , 51 : 83 – 95 .
  • Tiku , M. L. 1965 . “Laguerre Series Forms of Noncentral χ2 and F-Distributions,” . Biometrika , 52 : 415 – 427 .
  • Tiku , M. L. 1971 . “Power Function of the F-Test Under Nonnormal Situations,” . Journal of the American Statistical Association , 66 : 913 – 916 .
  • Tiku , M. L. 1975 . “Laguerre Series Forms of the Distributions of Classical Test-Statistics and Their Robustness in Nonnormal Situations,” . In Applied Statistics , Edited by: Gupta , R. P. New York : American Elsevier .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.