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314791

On the Two - Way Analysis of Variance Under Heteroscedasticity

Article

Last updated: 05 Jan 2025

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Abstract

In the analysis of variance linear models, a problem of interest is to test linear hypotheses under the assumption of heterogeneity of experimental errors. In this work, the two-way analysis of variance model under the assumption of unequal variances between rows for independent gaussian errors is considered. By a clear-cut geometric approach, the interdependence structure of the involved sums of squares as well as the type of problems arising in testing statistical hypotheses concerning the different effects are investigated and Box results are achieved. Furthermore, in a special case of the model it is shown that the classical F-test is appropriate in testing the rows effects. An approximate test is developed for the columns effects. The exact null distribution of the test statistic is derived and the level of the test is examined as a function of the variances. The approach used in this work can be easily extended to the three-way model which will be the subject of a next paper.

DOI

10.21608/esju.1996.314791

Keywords

Experimental Errors, Geometric Approach, heteroscedasticity, Linear Models, Testing Hypotheses, Two - Way Analysis of Variance

Authors

First Name

Sanaa

Last Name

EL Gayar

MiddleName

M.

Affiliation

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Volume

40

Article Issue

2

Related Issue

43152

Issue Date

1996-12-01

Publish Date

1996-12-01

Page Start

191

Page End

210

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_314791.html

Detail API

https://esju.journals.ekb.eg/service?article_code=314791

Order

6

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

On the Two - Way Analysis of Variance Under Heteroscedasticity

Details

Type

Article

Created At

28 Dec 2024