This paper presents the generalized p-values for testing the Behrens-Fisher problem when one variance is unknown. We also derive a closed form expression of the upper bound of the proposed generalized p-value.
<p>[1] A. Maity, and M. Sherman, “The Two Sample T-test with One Variance
Unknown”, The American Statistician, Vol. 60, No.2, pp. 163-166, 2006.
[2] F.E. Satterthwaite, “Synthesis of variance”, Psychometrik, Vol. 6, pp. 309-
316, 1941.
[3] F.E. Satterthwaite, “An approximate distribution of estimates of variance
components”, Biometric Bulletin, Vol. 6, pp. 110-114, 1946.
[4] S. Niwitpong, “Confidence intervals for the difference of two normal
population means with one variance unknown”, Thailand Statistician, Vol.
7, pp. 161-177, 2009.
[5] B.L. Welch, “The significance of the difference between two means when
the population variances are unequal”, Biometrika, Vol. 29, pp. 350-362,
1983.
[6] S. Weerahandi, “Exact Statistical Methods for Data Analysis”, Springer,
NewYork, 1995.
[7] K-W. Tsui, and S. Weerahandi, “Generalized p-values in significance
testing of hypotheses in the presence of nuisance parameters”, J. Amer
Statist Assoc, Vol. 84, pp. 60207, 1989.
[8] S. Tang, and K-W. Tsui, “Distributional properties for the generalized
p-value for the BehrensFisher problem”, Statistics Probability Letters,
Vol. 77, pp. 18, 2007.</p>
<p>[1] A. Maity, and M. Sherman, “The Two Sample T-test with One Variance
Unknown”, The American Statistician, Vol. 60, No.2, pp. 163-166, 2006.
[2] F.E. Satterthwaite, “Synthesis of variance”, Psychometrik, Vol. 6, pp. 309-
316, 1941.
[3] F.E. Satterthwaite, “An approximate distribution of estimates of variance
components”, Biometric Bulletin, Vol. 6, pp. 110-114, 1946.
[4] S. Niwitpong, “Confidence intervals for the difference of two normal
population means with one variance unknown”, Thailand Statistician, Vol.
7, pp. 161-177, 2009.
[5] B.L. Welch, “The significance of the difference between two means when
the population variances are unequal”, Biometrika, Vol. 29, pp. 350-362,
1983.
[6] S. Weerahandi, “Exact Statistical Methods for Data Analysis”, Springer,
NewYork, 1995.
[7] K-W. Tsui, and S. Weerahandi, “Generalized p-values in significance
testing of hypotheses in the presence of nuisance parameters”, J. Amer
Statist Assoc, Vol. 84, pp. 60207, 1989.
[8] S. Tang, and K-W. Tsui, “Distributional properties for the generalized
p-value for the BehrensFisher problem”, Statistics Probability Letters,
Vol. 77, pp. 18, 2007.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65115", author = "Sa-aat Niwitpong and Rada Somkhuean and Suparat Niwitpong", title = "Behrens-Fisher Problem with One Variance Unknown", abstract = "This paper presents the generalized p-values for testing the Behrens-Fisher problem when one variance is unknown. We also derive a closed form expression of the upper bound of the proposed generalized p-value.
", keywords = "Generalized p-value, hypothesis testing, upper bound.", volume = "7", number = "9", pages = "1440-4", }