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Comparison of the power of the tests in one‐way ANOVA type model with Poisson distributed variables
Author(s) -
Hrdličková Zuzana
Publication year - 2006
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.745
Subject(s) - deviance (statistics) , statistic , analysis of variance , poisson distribution , mathematics , statistics , type i and type ii errors , generalized linear model , variance (accounting) , linear model , mixed design analysis of variance , multivariate analysis of variance , accounting , business
This article deals with the one‐way ANOVA type generalized linear model, the method most often used if the assumptions of the classical one‐way ANOVA are not satisfied. In particular, the model with Poisson distributed response variables is considered. The article aims at the powers of tests based on the most frequent statistics—deviance, Pearson and score statistic. The asymptotic powers of the considered tests are obtained either analytically or by means of simulation. Afterwards, these powers are compared with powers of the tests obtained by an alternative method—a variance‐stabilizing transformation followed by the classical linear model with known or unknown variance. Finally, a power analysis is carried out on biometrical data to find an experimental design suitable for detecting a priory given differences in expected values. Copyright © 2006 John Wiley & Sons, Ltd.