Geodesic
On A.~Wald Test Comparing Two Normal Samples
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 16-30

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The well known Wald test comparing the means of two normal samples with unequal variances is of the form: $|\bar x-\bar y/s_2|\geqq\varphi(s_1/s_2)$ (critical zone). A. Wald constructed the function $\varphi$ for which the test is approximately similar with respect to $\sigma_1$ and $\sigma_2$. The present article shows that even under mild conditions on the function $\phi$, Wald's exact similar test is impossible. 
@article{TVP_1964_9_1_a1,
     author = {Yu. V. Linnik},
     title = {On {A.~Wald} {Test} {Comparing} {Two} {Normal} {Samples}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {16--30},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a1/}
}
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Yu. V. Linnik. On A.~Wald Test Comparing Two Normal Samples. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 16-30. http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a1/