Revisit the Two Sample t-Test with a Known Ratio of Variances

References

[1] A. Maity and M. Sherman, “The Two Sample t-Test with One Variance Unknown,” The American Statistician, Vol. 60, No. 2, 2006, pp. 163-166.
doi:10.1198/000313006X108567

[2] A. Wong and Y. Wu, “Likelihood Analysis for the Difference in Means of Two Independent Normal Distributions with One Variance Unknown,” Journal of Statistical Research, Vol. 42, 2008, pp. 17-35.

[3] E. Schechtman and M. Sherman, “The Two-sample t-Test with a Known Ratio of Variances,” Statistical Methodology, Vol. 4, No. 4, 2007, pp. 508-514.
doi:10.1016/j.stamet.2007.03.001

[4] D. A. Sprott and V.T. Farewell, “The Difference between Two Normal Means,” The American Statistician, Vol. 47, No. 2, 1993, pp. 126-128. doi:10.2307/2685194

[5] O. E. Barndorff-Nielsen, “Inference on Full and Partial Parameters, Based on the Standardized Signed Log-like- lihood Ratio,” Biometrika, Vol. 73, 1986, pp. 307-322.

[6] O. E. Barndorff-Nielsen, “Modified Signed Log-likeli- hood Ratio,” Biometrika, Vol. 78, No. 3, 1991, pp. 557- 563. doi:10.1093/biomet/78.3.557

[7] T. DiCiccio, C. Field and D. A. S. Fraser, “Approximation of Marginal Tail Probabilities and Inference for Scalar Parameters,” Biometrika, Vol. 77, 1990, pp. 77-95.
doi:10.1093/biomet/77.1.77