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Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing
Open accessAbstract
Consider the problem of testing k hypotheses simultaneously. In this article we discuss finite- and large-sample theory of stepdown methods that provide control of the familywise error rate (FWE). To improve on the Bonferroni method or on Holm's stepdown method, Westfall and Young made effective use of resampling to construct stepdown methods that implicitly estimate the dependence structure of the test statistics. However, their methods depend on an assumption known as “subset pivotality.” Our goal here is to construct general stepdown methods that do not require such an assumption. To accomplish this, we take a close look at what makes stepdown procedures work; a key component is a monotonicity requirement of critical values. By imposing monotonicity on estimated critical values (which is not an assumption on the model but rather is an assumption on the method), we show how to construct stepdown tests that can be applied in a stagewise fashion so that at most k tests need to be computed. Moreover, at each stage, an intersection test that controls the usual probability of a type 1 error is calculated, which allows us to draw on an enormous resampling literature as a general means of test construction. In addition, it is possible to carry out this method using the same set of resamples (or subsamples) for each of the intersection tests.
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“Similar to traditional multiple-hypothesis testing procedures, such as the Bonferroni or Holm procedures (see, e.g., Lehmann and Romano (2005), for a discussion of these procedures), the stepdown algorithm of Romano and Wolf (2005) exhibits strong FWER control, in contrast with the classical tests like the F or χ2.”
From Analyzing social experiments as implemented: A reexamination of the evidence from the HighScope Perry Preschool Program (2010) · cites this paper as Romano and Wolf (2005)
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“The validity of this procedure follows from the analysis of Romano and Wolf (2005), who provide general results on the use of stepdown multiple-hypothesis testing procedures.”
From Analyzing social experiments as implemented: A reexamination of the evidence from the HighScope Perry Preschool Program (2010) · cites this paper as Romano and Wolf (2005)
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“Romano and Wolf (2005) show that their monotonicity assumption is weaker than the subset pivotality assumption.”
From Analyzing social experiments as implemented: A reexamination of the evidence from the HighScope Perry Preschool Program (2010) · cites this paper as Romano and Wolf (2005)
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Metadata
- Authors
- Romano, J. P., & Wolf, M.
- Affiliations
- Stanford University (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2005-03
- Volume
- 100
- Issue
- 469
- Pages
- 94-108
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W3124231044
- Cited by
- 609
- References
- 23
- Citations by year
- 2026: 44 · 2025: 63 · 2024: 51 · 2023: 52 · 2022: 60 · 2021: 47 · 2020: 38 · 2019: 33 · 2018: 38 · 2017: 29 · 2016: 25 · 2015: 15 · 2014: 22 · 2013: 11 · 2012: 14
- FWCI
- 10.03
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Journal of the American Statistical Association (publishedVersion)
- SSRN Electronic Journal (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Repositori digital de la UPF (Universitat Pompeu Fabra) (submittedVersion, cc-by-nc-nd)
- RECERCAT (Consorci de Serveis Universitaris de Catalunya) (submittedVersion, other-oa)
- Funders
- National Science Foundation
- Ministerio de Ciencia y Tecnología
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- multiple comparisons, family-wise error rate, resampling, Bonferroni correction, intersection tests, asymptotic theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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