Geodesic
On a two-sample test of the variance analysis
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 831-836

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A two-sample test for a linear hypthesis about mean values of $r$ normal populations $\mu_i,\sigma$ is constructed. The power of the test depends on $\Sigma(\mu_i-\overline{\mu})^2$ and is independent of $\sigma$. Two asymptotic methods are proposed for determining the sample size with given probabilities of the errors of the first and the second kind. 
@article{TVP_1973_18_4_a15,
     author = {I. N. Volodin},
     title = {On a two-sample test of the variance analysis},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {831--836},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a15/}
}
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I. N. Volodin. On a two-sample test of the variance analysis. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 831-836. http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a15/