Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Dependent F Ratios Sharing a Common Cenominator in ANOVA Table

  • Kang, Phillee (Department of Mathematics, University of Hannam, Taejon)
  • Published : 1995.06.01
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Abstract

Let $F_1$ and $F_2$ be two F ratios with independent numerators and a common denominator. They are known to be positively dependent. The probabilities of simultaneous rejection and conditional rejection are numerically computed for both null and nonnull cases. The probabilities are presented in tables and graphics to show the influence of the seven parameters, the degrees of freedom of the numerators and the denominator, the non-centralities of the numerators, and the two levels of significance of the tests. The values of the correlation coefficient between $F_1$ and $F_2$ are also presented. Finally, a conjecture on the dependence order of the family of distributions of $(F_1, F_2)$ is given.

Keywords

References

  1. American Statistician v.40 The Correlation and Dependence Between Two F Statistics with the Same Denominator Feingold, Marica;Korsog,P.E.
  2. American Statistician v.30 Dependence of F Ratios Sharing a Common Denominator Mean Square Hurlburt,Russell T.;Spiegel,Douglas K.
  3. Distributions in Statistic Continuous Univariate Distributions-1, -2 Johnson,Norman L.;Kotz, Samuel
  4. J. American Statistical Association v.79 The Efect of Nonorthogonality on the Dependence of F Ratios Sharing a Common Denominator Johnson,Robert E.;Herr,David G.
  5. The Annals of Mathematical Statistics v.22 On Dependent Tests of Significance in the Analysis of Variance Kimball, A.W.
  6. Biometrika v.25 On a Method of Determining Whether a Sample of Size n Supposed to Have Been Drawn From a Parent Population Having a Known Probability Integral Has Probably Been Drawn at Random Peason,K.