Journal Article10.1080/01621459.1986.10478341
Modified Sequentially Rejective Multiple Test Procedures
TL;DR: In this article, a modified Bonferroni procedure with greater power than the B procedure was introduced, and the criterion continues to be modified in a stagewise manner, with the denominator of α′ reduced by 1 each time a hypothesis is rejected, so that tests can be conducted at successively higher significance levels.
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Abstract: Suppose that n hypotheses H 1, H 2, …, H n with associated test statistics T 1, T 2, …, T n are to be tested by a procedure with experimentwise significance level (the probability of rejecting one or more true hypotheses) smaller than or equal to some specified value α. A commonly used procedure satisfying this condition is the Bonferroni (B) procedure, which consists of rejecting H i , for any i, iff the associated test statistic T i is significant at the level α′ = α/n. Holm (1979) introduced a modified Bonferroni procedure with greater power than the B procedure. Under Holm's sequentially rejective Bonferroni (SRB) procedure, if any hypothesis is rejected at the level α′ = α/n, the denominator of α′ for the next test is n − 1, and the criterion continues to be modified in a stagewise manner, with the denominator of α′ reduced by 1 each time a hypothesis is rejected, so that tests can be conducted at successively higher significance levels. Holm proved that the experimentwise significance level...
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References
A Simple Sequentially Rejective Multiple Test Procedure
TL;DR: In this paper, a simple and widely accepted multiple test procedure of the sequentially rejective type is presented, i.e. hypotheses are rejected one at a time until no further rejections can be done.
Simultaneous test procedures-some theory of multiple comparisons'
TL;DR: The Simultaneous Test Procedure (STP) as discussed by the authors is a generalization of the notion of multiple comparisons for means, which was originally proposed by Aitchison and Roy.
A Study of the Powers of Several Methods of Multiple Comparisons
Israel Einot,K. R. Gabriel +1 more
TL;DR: In this paper, the power of multiple comparisons procedures for fixed maximal experimentwise levels was studied for fixed-maximal experimentwise level, and the authors generally recommend the Tukey technique for its elegant simplicity and existent confidence bounds, which is little below that of any other method.
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Comparison of Means: An F Test Followed by a Modified Multiple Range Procedure:
TL;DR: In this paper, the authors compared the performance of modified and unmodified procedures in error control and showed that the modified procedure has advantages over the unmodified procedure under some circumstances, and also compared the alternative of using the non-modified range test without a preliminary F test.
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