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. Author manuscript; available in PMC: 2016 Mar 30.
Published in final edited form as: Biom J. 2013 Jan 16;55(2):266. doi: 10.1002/bimj.201200256

Author’s reply

Frank Bretz, Martin Posch, Ekkehard Glimm, Florian Klinglmueller, Willi Maurer, Kornelius Rohmeyer
PMCID: PMC4813751  EMSID: EMS67347  PMID: 23322384

We thank Drs. Xie and Chen for their interest in the gMCP package (Rohmeyer and Klinglmueller, 2012). Their observation of a seeming size inflation is explained by the fact that they apply the gMCP package to p-values of two-sided instead of one-sided tests. It is well-known that in many multivariate test situations two-sided tests cannot be constructed from one-sided tests by simply halving the significance levels or doubling p-values. For this reason, already Dunnett (1955) as well as standard text books (e.g. Hochberg and Tamhane, 1987) provided separate tables with critical values for both one- and two-sided cases. The methodology described in Bretz et al. (2011) applies generally to both one- and two-sided hypotheses tests. The gMCP package implements only the one-sided case when correlations between test statistics are exploited. This avoids the intrinsic problems occurring with directional decisions for stepwise multiple test procedures applied to two-sided hypotheses (Shaffer, 1980; Bauer et al., 1986), in particular because two-sided hypothesis tests can lead to counterintuitive decisions in the context of stepwise procedures.

References

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