Simultaneous Statistical Inference

Dickhaus, Thorsten

doi:10.1007/978-3-642-45182-9

Cited by 105 publications

(40 citation statements)

References 120 publications

(170 reference statements)

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“…Thus, the first hypothesis is tested at level α, the second at α / 2, the third at α / 3, and so on until the last hypothesis is tested at level α / m. If any p-value in the sequence is significant, then all smaller p-values are also declared significant and testing stops. Hochberg's procedure controls the FWER (except in certain situations; see Dmitrienko et al, 2010) and is more powerful than Holm's, but generally does not allow computation of confidence intervals (Dmitrienko et al, 2010;Guilbaud, 2012).…”

Section: Controlling the Pfer Using The Bonferroni Proceduresmentioning

confidence: 99%

“…Some other stepwise procedures for controlling the FWER are more powerful than Hochberg's (e.g., Hommel, 1988;Rom, 1990), but they are more computationally complex and, like Hochberg's method, generally do not allow computation of confidence intervals (Dmitrienko et al, 2010;Guilbaud, 2012). There are also methods that control the FWER in specific contexts.…”

Section: Controlling the Pfer Using The Bonferroni Proceduresmentioning

confidence: 99%

“…There are also methods that control the FWER in specific contexts. For example, Dunnett's (1955) procedure and its variations (see Dmitrienko et al, 2010) can be used when comparing multiple treatment groups to a placebo group. There are also Šidák based methods (see Bird & Hadzi-Pavlovic, 2013), which are not necessarily applicable to one sided tests.…”

Section: Controlling the Pfer Using The Bonferroni Proceduresmentioning

confidence: 99%

“…The Bonferroni procedure is often described as "overly conservative" (as noted by Gordon, Glazko, & Yakovlev, 2007), or as being "improved" through modifications such as Holm's and Hochberg's (see Dickhaus, 2014;Posch & Futschik, 2008;Simes, 1986). This framing is legitimate if the goal is to control the FWER.…”

Section: Confusion About the Utility Of The Bonferroni Proceduresmentioning

confidence: 99%

“…For example, in statistics textbooks for the social and behavioral sciences, there is generally no mention of the PFER even when the FWER is addressed (e.g., Goodwin, 2010;Hinton, 2004;Howell, 2014;Mertler & Vannatta, 2010;Meyers, Gamst, & Guarino, 2006;Sirkin, 2006;Stevens, 2009;Tabachnick & Fidell, 2012;WetcherHendricks, 2011). And although some classic texts on simultaneous inference discuss the PFER (e.g., Hochberg & Tamhane, 1987;Miller, 1966;Tukey, 1953), many newer books on the subject do not (e.g., Dickhaus, 2014;Dmitrienko et al, 2010;Hsu, 1996). This study briefly describes some popular Type I error rate controlling procedures, distinguishing PFER control from FWER control.…”

Section: Introductionmentioning

confidence: 96%

See 4 more Smart Citations

Are Per-Family Type I Error Rates Relevant in Social and Behavioral Science?

Frane

2015

J. Mod. App. Stat. Meth.

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Section: Controlling the Pfer Using The Bonferroni Proceduresmentioning

confidence: 99%

Section: Controlling the Pfer Using The Bonferroni Proceduresmentioning

confidence: 99%

Section: Controlling the Pfer Using The Bonferroni Proceduresmentioning

confidence: 99%

Section: Confusion About the Utility Of The Bonferroni Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 3 more Smart Citations

Are Per-Family Type I Error Rates Relevant in Social and Behavioral Science?

Frane

2015

J. Mod. App. Stat. Meth.

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Multivariate multiple test procedures based on nonparametric copula estimation

et al. 2018

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Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are high-dimensional, but possess pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable power. In the present paper, we express dependency structures in the most general manner, namely, by means of copula functions. One class of nonparametric copula estimators is constituted by Bernstein copulae. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family-wise error rate (FWER) of multiple test procedures that are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. This extends a similar approach by Stange et al. (2015) in the parametric case. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power that can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or Šidák corrections. Finally, we demonstrate an application of the proposed methodology to real-life data from insurance.

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False discovery rate control for multiple testing based on discretep‐values

Chen

2020

Biometrical J

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For multiple testing based on discrete p‐values, we propose a false discovery rate (FDR) procedure “BH+” with proven conservativeness. BH+ is at least as powerful as the BH (i.e., Benjamini‐Hochberg) procedure when they are applied to superuniform p‐values. Further, when applied to mid‐p‐values, BH+ can be more powerful than it is applied to conventional p‐values. An easily verifiable necessary and sufficient condition for this is provided. BH+ is perhaps the first conservative FDR procedure applicable to mid‐p‐values and to p‐values with general distributions. It is applied to multiple testing based on discrete p‐values in a methylation study, an HIV study and a clinical safety study, where it makes considerably more discoveries than the BH procedure. In addition, we propose an adaptive version of the BH+ procedure, prove its conservativeness under certain conditions, and provide evidence on its excellent performance via simulation studies.

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Simultaneous Statistical Inference

Cited by 105 publications

References 120 publications

Are Per-Family Type I Error Rates Relevant in Social and Behavioral Science?

Are Per-Family Type I Error Rates Relevant in Social and Behavioral Science?

Multivariate multiple test procedures based on nonparametric copula estimation

False discovery rate control for multiple testing based on discretep‐values

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