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L. (1975). On splitting the tails unequally: A new perspective on one- versus two-tailed tests. Educ. Psychol. Meas. 35, 283–301. [12] Casella, G. and Berger, R. L. (1987). Reconciling Bayesian and frequentist evidence in the one-sided testing problem. J. Amer. Statist. Assoc. 82, 106–111. 30 J. P. , Boyett, J. , Kuo, M-L. and Roussel, M. F. (2004). Statistical significance threshold criteria for analysis of microarray gene expression data. Stat. Appl. Genet. Mol. Biol. com/sagmb/vol3/iss1/art36.

2002). Multiplicity, directional (Type III) errors, and the null hypothesis. Psychol. Meth. 7, 356–369. [58] Shaffer, J. P. (2004). Optimality results in multiple hypothesis testing. The First Erich L. Lehmann Symposium – Optimality, Lecture Notes–Monograph Series, Vol. 44. Institute of Mathematical Statistics, 11–35. ´, B. (1989). Statistical ”discoveries” and effect size estimation. J. Amer. [59] Soric Statist. Assoc. 84, 608–610. [60] Spjøtvoll, E. (1972). On the optimality of some multiple comparison procedures.

They also consider an empirical Bayes variation of their method, and point out that their results provide theoretical support for an empirical finding of Shaffer [56], which demonstrated similar error properties for her modification of the Duncan [17] approach to provide control of the FWER and the Benjamini and Hochberg [3] FDR-controlling procedure. Lewis and Thayer [43] point out that the empirical Bayes version of their assumptions can be alternatively regarded as a random-effects frequentist formulation.

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