Randomization tests for small samples: An application for genetic expression data

Gary L. Gadbury, Grier P. Page, Moonseong Heo, John D. Mountz, David B. Allison

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


An advantage of randomization tests for small samples is that an exact P-value can be computed under an additive model. A disadvantage with very small sample sizes is that the resulting discrete distribution for P-values can make it mathematically impossible for a P-value to attain a particular degree of significance. We investigate a distribution of P-values that arises when several thousand randomization tests are conducted simultaneously using small samples, a situation that arises with microarray gene expression data. We show that the distribution yields valuable information regarding groups of genes that are differentially expressed between two groups: a treatment group and a control group. This distribution helps to categorize genes with varying degrees of overlap of genetic expression values between the two groups, and it helps to quantify the degree of overlap by using the P-value from a randomization test. Moreover, a statistical test is available that compares the actual distribution of P-values with an expected distribution if there are no genes that are differentially expressed. We demonstrate the method and illustrate the results by using a microarray data set involving a cell line for rheumatoid arthritis. A small simulation study evaluates the effect that correlated gene expression levels could have on results from the analysis.

Original languageEnglish (US)
Pages (from-to)365-376
Number of pages12
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Issue number3
StatePublished - 2003
Externally publishedYes


  • Additivity
  • Microarray
  • Nonparametric test
  • Permutation
  • Randomization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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