On the Behrens-Fisher distribution and its generalization to the pairwise comparisons

Viktor Witkovský

Discussiones Mathematicae Probability and Statistics (2002)

  • Volume: 22, Issue: 1-2, page 73-104
  • ISSN: 1509-9423

Abstract

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Weerahandi (1995b) suggested a generalization of the Fisher's solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. In this paper, we present a brief outline of the Fisher's solution and its generalization as well as the methods to calculate the p-values required for deriving the conservative joint confidence interval estimates for the pairwise mean differences, refered to as the generalized Scheffé intervals. Further, we present the corresponding tables with critical values for simultaneous comparisons of the mean differences of up to k = 6 normal populations with unequal variances based on independent random samples with very small sample sizes.

How to cite

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Viktor Witkovský. "On the Behrens-Fisher distribution and its generalization to the pairwise comparisons." Discussiones Mathematicae Probability and Statistics 22.1-2 (2002): 73-104. <http://eudml.org/doc/287668>.

@article{ViktorWitkovský2002,
abstract = {Weerahandi (1995b) suggested a generalization of the Fisher's solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. In this paper, we present a brief outline of the Fisher's solution and its generalization as well as the methods to calculate the p-values required for deriving the conservative joint confidence interval estimates for the pairwise mean differences, refered to as the generalized Scheffé intervals. Further, we present the corresponding tables with critical values for simultaneous comparisons of the mean differences of up to k = 6 normal populations with unequal variances based on independent random samples with very small sample sizes.},
author = {Viktor Witkovský},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Behrens-Fisher distribution; pairwise comparisons; unequal variances; generalized p-values; generalized -values},
language = {eng},
number = {1-2},
pages = {73-104},
title = {On the Behrens-Fisher distribution and its generalization to the pairwise comparisons},
url = {http://eudml.org/doc/287668},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Viktor Witkovský
TI - On the Behrens-Fisher distribution and its generalization to the pairwise comparisons
JO - Discussiones Mathematicae Probability and Statistics
PY - 2002
VL - 22
IS - 1-2
SP - 73
EP - 104
AB - Weerahandi (1995b) suggested a generalization of the Fisher's solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. In this paper, we present a brief outline of the Fisher's solution and its generalization as well as the methods to calculate the p-values required for deriving the conservative joint confidence interval estimates for the pairwise mean differences, refered to as the generalized Scheffé intervals. Further, we present the corresponding tables with critical values for simultaneous comparisons of the mean differences of up to k = 6 normal populations with unequal variances based on independent random samples with very small sample sizes.
LA - eng
KW - Behrens-Fisher distribution; pairwise comparisons; unequal variances; generalized p-values; generalized -values
UR - http://eudml.org/doc/287668
ER -

References

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