{"title":"Upper Bound of the Generalize p-Value for the Behrens-Fisher Problem with a Known Ratio of Variances","authors":"Rada Somkhuean, Suparat Niwitpong, Sa-aat Niwitpong","volume":81,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1436,"pagesEnd":1440,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/16727","abstract":"<p>This paper presents the generalized p-values for testing the Behrens-Fisher problem when a ratio of variance is known. We also derive a closed form expression of the upper bound of the proposed generalized p-value.<\/p>\r\n","references":"<p>[1] E. Schechtman, and M. Sherman, “The two-sample t-test with a known\r\nratio of Variances”, Statistical Methodology, Vol.4, pp. 508-514, 2007.\r\n[2] F.E. Satterthwaite, “An approximate distribution of estimates of variance\r\ncomponents”, Biometric Bulletin, Vol.6, pp. 110-114, 1946.\r\n[3] S. Niwitpong, and Sa. Niwitpong, “Confidence interval for the difference\r\nof two normal population means with a known ratio of variances”, Applied\r\nMathematical Sciences, Vol.4, pp. 347359, 2010.\r\n[4] B.L. Welch, “The significance of the difference between two means when\r\nthe population variances are unequal”, Biometrika, Vol.29, pp. 350-362,\r\n1983.\r\n[5] S. Weerahandi, “Exact Statistical Methods for Data Analysis”, Springer,\r\nNewYork, 1995.\r\n[6] K-W. Tsui, and S. Weerahandi, “Generalized p-values in significance\r\ntesting of hypotheses in the presence of nuisance parameters”, J. Amer\r\nStatist Assoc, Vol.84, pp. 60207, 1989.\r\n[7] S. Tang,and K-W. Tsui, “Distributional properties for the generalized\r\np-value for the BehrensFisher problem”, Statistics Probability Letters,\r\nVol.77, pp. 18, 2007.<\/p>\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 81, 2013"}

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