Bonferroni procedures for logically related hypotheses
Bonferroni procedures for logically related hypotheses
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DOI：
10.1016/s0378-3758(99)00035-x
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发表时间：
1999-12-01
影响因子：
0.9
通讯作者：
Bernhard, G
中科院分区：
文献类型：
--
作者：
Hommel, G;Bernhard, G
Shaffer (1986. J. Amer. Statist. Assoc. 81, 826-831) proposed an improvement of the general Bonferroni-Holm procedure (Holm, 1979. Scand. J. Statist. 6, 65-70) for logically related hypotheses, by replacing the bounds of Helm's procedure by larger bounds using information on logical interrelationships between the hypotheses. A second more powerful improvement was also mentioned by Shaffer, in which the bounds are determined in a dynamic way, depending on the hypotheses rejected in previous steps. Further improvements ('Procedure 3', 'Procedure 4') were proposed by Bergmann and Hommel (Springer, Berlin, 1988, pp. 100-115) who showed that the decisions of Procedure 4 are identical to those of the closure test using Bonferroni global tests.We discuss some properties of the procedures including computational work, power, monotonicity and generality.An algorithm and a computer program (Bernhard, Doctoral Thesis, Mainz, 1992) were presented which enables Procedure 4 to be performed for systems of linear hypotheses, as for multiple comparison problems and systems of (partially) nested hypotheses. The gain in power is illustrated by a well-known numerical example. With slight modifications, it is also possible to apply Procedure 4 using information on the dependence structure of the test statistics and/or to compute adjusted p-values. (C) 1999 Elsevier Science B.V. All rights reserved. MSC: 62J15.
