Journal of Probability and Statistics
Volume 2012 (2012), Article ID 935621, 10 pages
Research Article

Sample Size Growth with an Increasing Number of Comparisons

1Department of Medicine, UCLA School of Medicine, Los Angeles, CA 90095, USA
2Division of Biostatistics, NYU School of Medicine, New York, NY 10016, USA

Received 30 March 2012; Accepted 8 June 2012

Academic Editor: Wei T. Pan

Copyright © 2012 Chi-Hong Tseng and Yongzhao Shao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An appropriate sample size is crucial for the success of many studies that involve a large number of comparisons. Sample size formulas for testing multiple hypotheses are provided in this paper. They can be used to determine the sample sizes required to provide adequate power while controlling familywise error rate or false discovery rate, to derive the growth rate of sample size with respect to an increasing number of comparisons or decrease in effect size, and to assess reliability of study designs. It is demonstrated that practical sample sizes can often be achieved even when adjustments for a large number of comparisons are made as in many genomewide studies.