Nonparametric Hypotheses and Rank Statistics for Unbalanced Factorial Designs

Michael G. Akritas, Steven F. Arnold, Edgar Brunner

Research output: Contribution to journalArticlepeer-review

178 Scopus citations


Factorial designs are studied with independent observations, fixed number of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics are derived for testing the nonparametric hypotheses of no main effects, no interaction, and no factor effects in unbalanced crossed classifications. The formulation of all results includes tied observations. Extensions of these procedures to higher-way layouts are given, and the efficacies of the test statistics against nonparametric alternatives are derived. A modification of the test statistics and approximations to their finite-sample distributions are also given. The small-sample performance of the procedures for two factors is examined in a simulation study. As an illustration, a real dataset with ordinal data is analyzed.

Original languageEnglish (US)
Pages (from-to)258-265
Number of pages8
JournalJournal of the American Statistical Association
Issue number437
StatePublished - Mar 1 1997

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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