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Practical recipes to solve the Behrens‐Fisher problem
Author(s) -
Thomasse A. H.
Publication year - 1974
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1974.tb00744.x
Subject(s) - mathematics , normality , population , confidence interval , sample (material) , sample size determination , statistics , power (physics) , moment (physics) , calculus (dental) , combinatorics , demography , physics , thermodynamics , sociology , medicine , dentistry , classical mechanics
The comparison of the unknown means of two populations with unknown variances is called the B ehrens ‐F isher problem, if the populations are assumed to be normal and the ratio of the variances is not known. In this paper a summary of recipes is given to solve this problem in practice, as published in the past 35 years by B anerjee , F isher and B ehrens , P agurova , W ald and H ajek , W elch , W elch and A spin , together with two large sample solutions and one solution often used as an approximate one without justification. The solutions are presented mainly in terms of confidence intervals for the difference of the population means. Some remarks are made concerning the lengths of these intervals and the power of the corresponding tests. The solutions in this paper are dependent on the means and the variances of samples drawn from the two populations only. All solutions discussed, except the disqualified approximate one, are robust against violations of the normality assumptions with respect to the populations and they provide, at least asymptotically, good measures for the difference of the population means if the samples are drawn from populations whatsoever with finite second moment.