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Testing for order among K populations: theory and examples
Author(s) -
Davidov Ori,
Herman Amir
Publication year - 2010
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10041
Subject(s) - nonparametric statistics , statistical hypothesis testing , statistic , stochastic ordering , test statistic , statistics , econometrics , test (biology) , mathematics , limiting , observational study , order (exchange) , order statistic , computer science , engineering , economics , mechanical engineering , paleontology , finance , biology
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. The Canadian Journal of Statistics 38: 97–115; 2010 © 2009 Statistical Society of Canada