Abstract
A two-stage procedure based on the statistic introduced by Scheffé (1943) to solve the Behrens-Fisher problem is considered in estimating the difference between the mean values of two normal distributions having unequal and unknown variances. Samples of unequal size are considered at each stage. A numerical example is given where the two-stage procedure is compared with the Satterthwaite (1946) approximate method.
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References
Chapman DG (1950) Some two-sample tests. Ann Math Statist 21:601–606
Desu MM, Raghavarao D (1990) Sample size methodology. Academic Press
Ghosh BK (1975) A two-stage procedure for the Behrens-Fisher problem. J Amer Statist Assoc 70:457–462
Koopmans L, Qualls C (1971) Fixed length confidence intervals for parameters of the normal distribution based on two-stage sampling procedures. Rocky Mountain J Math 1:587–602
Moshman J (1958) A method for selecting the size of the initial sample size in the Stein’s two-sample procedure. Ann Math Statist 29:1271–1275
Satterthwaite FE (1946) An approximate distribution of estimates of variance components. Biom Bull 2:110–114
Scheffé H (1943) On solutions of the Behrens-Fisher problem based on thet-distribution. Ann Math Statist 14:35–44
Seelbinder BM (1953) On Stein’s two-stage procedure. Ann Math Statist 24:640–649
Snedecor GW, Cochran WG (1989) Statistical methods. Iowa State University Press
Stein C (1945) A two-sample test for a linear hypothesis whose power is independent of variance. Ann Math Statist 16:243–258
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Targhetta, M.L. A two-stage sampling by unequal size samples from two normal populations with unknown variances. Metrika 45, 31–37 (1997). https://doi.org/10.1007/BF02717091
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DOI: https://doi.org/10.1007/BF02717091