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Generalized Maximum Range Tests for Pairwise Comparisons of Several Populations
Author(s) -
Royen Th.
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310804
Subject(s) - mathematics , bonferroni correction , section (typography) , pairwise comparison , range (aeronautics) , intersection (aeronautics) , statistics , combinatorics , multivariate statistics , random variable , discrete mathematics , computer science , materials science , engineering , composite material , aerospace engineering , operating system
A multiple comparison procedure (MCP) is proposed for the comparison of all pairs of several independent samples. This MCP is essentially the closed procedure with union‐intersection tests based on given single tests Q ij for the minimal hypotheses H ij . In such cases where the α‐levels of the nominal tests associated with the MCP can be exhausted, this MCP has a uniformly higher all pair power than any refined Bonferroni test using the same Q ij . Two different general algorithms are described in section 3. A probability inequality for ranges of i.i.d. random variables which is useful for some algorithms is proved in section 4. Section 5 contains the application to independent normally distributed estimates and section 6 the comparisons of polynomial distributions by multivariate ranges. Further applications are possible. Tables of the 0.05‐bounds for the tests of section 5 and 6 are enclosed.