Publication detail

Comparison of the power of the tests in one-way ANOVA type model with Poisson distributed variables

HRDLIČKOVÁ, Z.

Czech title

Porovnání sil testů v modelu typu jednoduché ANOVY s Poissonovskými proměnnými

English title

Comparison of the power of the tests in one-way ANOVA type model with Poisson distributed variables

Type

journal article - other

Language

en

Original abstract

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.

Czech abstract

Článek se zabývá zobecněným lineárním modelem typu jednoduché ANOVY, který je nejčastější metodou volenou v případech, kdy nejsou splněny předpoklady klasické jednoduché ANOVY. Pozornost je věnována zvláště modelu s Poissonovskými proměnnými, předevšímpak silám testů založených na nejčastěji užívaných statistikách – devianci, Pearsonově a skórové statistice. Asympototické síly studovaných testů jsou získány buď analyticky nebo pomocí simulací. Poté jsou tyto síly srovnány se silami testů založených na jiné metodě – klasickém lineárním modelu transformovaných veličin. Na závěr je provedena analýza síly na biometrických datech, jejíž výsledkem je návrh vhodného plánu experimentu, který by umožňoval rozlišit předem zadané rozdíly ve středních hodnotách.

English abstract

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.

Keywords in English

generalized linear model power function, one-way ANOVA, Poisson distribution, variance-stabilizing transformation

Released

20.03.2006

Publisher

John Wiley & Sons, Ltd.

Location

Johannesburg, JAR

ISSN

1180-4009

Book

Environmetrics, TIES Conference, 2003

Journal

Environmetrics

Volume

17

Number

3

Edition number

17

Pages from–to

227–237

Pages count

11

BIBTEX


@article{BUT46658,
  author="Zuzana {Hübnerová},
  title="Comparison of the power of the tests in one-way ANOVA type model with Poisson distributed variables",
  journal="Environmetrics",
  booktitle="Environmetrics, TIES Conference, 2003",
  year="2006",
  volume="17",
  number="3",
  month="March",
  pages="227--237",
  publisher="John Wiley & Sons, Ltd.",
  address="Johannesburg, JAR",
  issn="1180-4009"
}