Abstract
We consider different ways of constructing weighted Hochberg-type step-up multiple test procedures including closed procedures based on weighted Simes tests and their conservative step-up short-cuts, and step-up counterparts of two weighted Holm procedures. It is shown that the step-up counterparts have some serious pitfalls such as lack of familywise error rate control and lack of monotonicity in rejection decisions in terms of p-values. Therefore an exact closed procedure appears to be the best alternative, its only drawback being lack of simple stepwise structure. A conservative step-up short-cut to the closed procedure may be used instead, but with accompanying loss of power. Simulations are used to study the familywise error rate and power properties of the competing procedures for independent and correlated p-values. Although many of the results of this paper are negative, they are useful in highlighting the need for caution when procedures with similar pitfalls may be used.
Original language | English (US) |
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Pages (from-to) | 279-294 |
Number of pages | 16 |
Journal | Biometrika |
Volume | 95 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2008 |
Funding
This research was partially supported by the National Heart, Lung and Blood Institute and the National Security Agency. We are grateful to two referees and Professor D. M. Titterington for extensive comments and suggestions that led to a thorough revision of the paper.
Keywords
- Bonferroni test
- Closed procedure
- Familywise error rate
- Holm procedure
- Multiple comparisons
- P-Value
- Simes test
- Step-down procedure
- Step-up procedure
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Agricultural and Biological Sciences (miscellaneous)
- General Agricultural and Biological Sciences
- Statistics, Probability and Uncertainty
- Applied Mathematics