title: Testing trend for count data with extra-Poisson variability.
abstract: Trend tests for monotone trend or umbrella trend (monotone upward changing to monotone downward or vise versa) in count data are proposed when the data exhibit extra-Poisson variability. The proposed tests, which are called the GS1 test and the GS2 test, are constructed by applying an orthonormal score vector to a generalized score test under an rth-order log-linear model. These tests are compared by simulation with the Cochran-Armitage test and the quasi-likelihood test of Piegorsch and Bailer (1997, Statistics for Environmental Biology and Toxicology). It is shown that the Cochran-Armitage test should not be used under the existence of extra-Poisson variability; that, for detecting monotone trend, the GS1 test is superior to the others; and that the GS2 test has high power to detect an umbrella response.
authors.affiliation: Institute of Statistics, Jakarta Timur, Indonesia.
authors.forename: Erni Tri
authors.initials: ET
authors.lastname: Astuti
authors.forename: Takashi
authors.initials: T
authors.lastname: Yanagawa
mesh_terms: D000818:Animals; D001391:Azo Compounds / Q000633:toxicity; D001699:Biometry / Q000379:methods*; D003621:Daphnia / Q000187:drug effects / Q000502:physiology; D003627:Data Interpretation, Statistical; D005260:Female; D006540:Herbicides / Q000633:toxicity; D009153:Mutagens / Q000633:toxicity; D009282:Naphthalenesulfonates / Q000633:toxicity; D010647:Phenyl Ethers / Q000633:toxicity; D012098:Reproduction / Q000187:drug effects; D012475:Salmonella / Q000187:drug effects / Q000235:genetics; D014116:Toxicology / Q000706:statistics & numerical data*; D014874:Water Pollutants, Chemical / Q000633:toxicity
chemical_list: D001391:Azo Compounds; D006540:Herbicides; D009153:Mutagens; D009282:Naphthalenesulfonates; D010647:Phenyl Ethers; D014874:Water Pollutants, Chemical; C087595:C.I. Acid Red 114; C007350:nitrofen