
@ARTICLE{Phipson2010-xi,
  title    = "Permutation P-values should never be zero: calculating exact
              P-values when permutations are randomly drawn",
  author   = "Phipson, Belinda and Smyth, Gordon K",
  abstract = "Permutation tests are amongst the most commonly used statistical
              tools in modern genomic research, a process by which p-values are
              attached to a test statistic by randomly permuting the sample or
              gene labels. Yet permutation p-values published in the genomic
              literature are often computed incorrectly, understated by about
              1/m, where m is the number of permutations. The same is often
              true in the more general situation when Monte Carlo simulation is
              used to assign p-values. Although the p-value understatement is
              usually small in absolute terms, the implications can be serious
              in a multiple testing context. The understatement arises from the
              intuitive but mistaken idea of using permutation to estimate the
              tail probability of the test statistic. We argue instead that
              permutation should be viewed as generating an exact discrete null
              distribution. The relevant literature, some of which is likely to
              have been relatively inaccessible to the genomic community, is
              reviewed and summarized. A computation strategy is developed for
              exact p-values when permutations are randomly drawn. The strategy
              is valid for any number of permutations and samples. Some simple
              recommendations are made for the implementation of permutation
              tests in practice.",
  journal  = "Stat. Appl. Genet. Mol. Biol.",
  volume   =  9,
  pages    = "Article39",
  month    =  oct,
  year     =  2010,
  language = "en"
}
