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Tests for a simple tree order restriction with application to dose–response studies
Author(s) -
Peddada Shyamal D.,
Haseman Joseph K.,
Tan Xiaofeng,
Travlos Greg
Publication year - 2006
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2006.00549.x
Subject(s) - simple (philosophy) , tree (set theory) , computer science , nonparametric statistics , test (biology) , algorithm , data mining , statistics , mathematics , mathematical analysis , paleontology , philosophy , epistemology , biology
Summary. We propose ‘Dunnett‐type’ test procedures to test for simple tree order restrictions on the means of p independent normal populations. The new tests are based on the estimation procedures that were introduced by Hwang and Peddada and later by Dunbar, Conaway and Peddada. The procedures proposed are also extended to test for ‘two‐sided’ simple tree order restrictions. For non‐normal data, nonparametric versions based on ranked data are also suggested. Using computer simulations, we compare the proposed test procedures with some existing test procedures in terms of size and power. Our simulation study suggests that the procedures compete well with the existing procedures for both one‐sided and two‐sided simple tree alternatives. In some instances, especially in the case of two‐sided alternatives or for non‐normally distributed data, the gains in power due to the procedures proposed can be substantial.