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Inference

A Revisit to the Behrens–Fisher Problem: Comparison of Five Test Methods

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Pages 1064-1085 | Received 21 Dec 2006, Accepted 04 Jan 2008, Published online: 22 May 2008

References

  • Aspin , A. A. ( 1948 ). An examination and further development of a formula arising in the problem of comparing two mean values . Biometrika 35 : 88 – 96 .
  • Casella , G. , George , E. I. ( 1992 ). Explaining the Gibbs Sampler . Amer. Statistician 46 : 167 – 174 .
  • Chang , C. H. , Pal , N. ( 2008 ). A Computational approach to one-way ANOVA and its model robustness . (Submitted)
  • Cochran , W. G. , Cox , G. M. ( 1950 ). Experimental Designs . New York : John Wiley and Sons .
  • Davison , A. C. , Hinkley , D. V. ( 1997 ). Bootstrap Methods and Their Application . Cambridge : Cambridge University Press .
  • Efron , B. ( 1982 ). The Jackknife, Bootstrap, and Other Resampling Plans. CBMS . Vol. 38 . Philadelphia , PA : SIAM–NSF .
  • Fisher , R. A. ( 1935 ). The fiducial argument in statistical inference . Ann. Eugenics 6 : 391 – 398 .
  • Fisher , R. A. ( 1941 ). The asymptotic approach to Behren' integral with further tables for the test of significance . Ann. Eugenics 11 : 141 – 172 .
  • Giles , J. A. , Giles , D. E. A. (1993). Pre-testing estimation and testing in econometrics: recent developments. J. Econ. Surv. 7:145–197.
  • Gupta , A. K. , Wang , Y. ( 1999 ). Some tests with specified size for the Behrens–Fisher problem . Commun Statist. Theor. Meth. 28 ( 3,4 ): 511 – 517 .
  • Hjorth , J. S. U. ( 1994 ). Computer Intensive Statistical Methods: Validation, Model Selection and Bootstrap . London : Chapman and Hall .
  • Karian , Z. A. , Dudewicz , E. J. ( 2000 ). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods . Boca Raton : FL : CRC Press .
  • Kim , S. H. , Cohen , A. S. ( 1998 ). On the Behrens–Fisher problem: a review . J. Education. Behavior. Statist. 23 ( 4 ): 356 – 377 .
  • Lee , A. F. S. , Gurland , J. ( 1975 ). Size and power of tests for equality of means of two normal populations . J. Amer. Statist. Assoc. 70 : 933 – 944 .
  • Pal , N. , Lim , W. K. , Ling , C. H. ( 2007 ). A computational approach to statistical inferences . J. Appl. Probab. Statist. 2 ( 1 ): 13 – 35 .
  • Ruben , H. ( 2002 ). A simple conservative and robust solution of the Behrens–Fisher problem . Sankhya Ind. J. Statist. Ser. A 64 : 139 – 155 .
  • Satterthwaite , F. E. ( 1946 ). An approximate distribution of estimates of variance components . Biometrics Bull. (now called Biometrics) 2 : 110 – 114 .
  • Singh , P. , Saxena , K. K. , Srivastava , O. P. ( 2002 ). Power comparisons of solutions to the Behrens–Fisher problem . Amer. J. Mathemat. Manage. Sci. 22 : 233 – 250 .
  • Tsui , K. W. , Weerahandi , S. ( 1989 ). Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters . J. Amer. Statist. Assoc. 84 : 602 – 607 .
  • Wang , Y. ( 1971 ). Probabilities of the Type-I errors of the Welch tests . J. Amer. Statist. Assoc. 66 : 605 – 608 .
  • Weerahandi , S. ( 1994 ). Exact Statistical Methods for Data Analysis . Springer Series in Statistics . New York : Springer-Verlag .
  • Welch , B. L. ( 1936 ). Specification of rules for rejecting too variable a product, with particular reference to an electric lamp problem . J. Roy. Statist. Soc. Supp. 3 : 29 – 48 .
  • Welch , B. L. ( 1947 ). The generalization of ‘Student's’ problem when several different population variances are involved . Biometrika 34 : 28 – 35 .
  • Welch , B. L. ( 1949 ). Further notes on Mrs. Aspin's tables . Biometrika 36 : 293 – 296 .
  • Zaman , A. ( 1996 ). Statistical Foundations for Econometric Techniques . New York : Academic Press .

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