Testing for order among K populations: Theory and examples

Ori Davidov, Amir Herman

Research output: Contribution to journalArticlepeer-review


Testing for stochastic order among K populations is a common and important problem in statistical practice. It arises in the analysis of both planned experiments and observational studies. The authors develop a new nonparametric test for order among K populations that can accommodate any stochastic ordering. The test is based on a maximally selected chi-bar-square statistic. The authors find its limiting distribution and use simulations to derive critical values. Three important examples are used to illustrate the applicability of the general method. The authors find that the new tests outperform the existing methods in many practical cases.

Original languageEnglish
Pages (from-to)97-115
Number of pages19
JournalCanadian Journal of Statistics
Issue number1
StatePublished - Mar 2010


  • Dose-response
  • Maximally selected chi-bar-square statistic
  • Minimal effective dose
  • Msc 2000: primary 62G10
  • Order restricted inference
  • Partitioning principle
  • Secondary 62G30
  • Statistical selection
  • Stochastic order

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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