On the Two - Way Analysis of Variance Under Heteroscedasticity | ||||
| The Egyptian Statistical Journal | ||||
| Article 6, Volume 40, Issue 2, December 1996, Page 191-210 PDF (14.81 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.1996.314791 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Sanaa M. EL Gayar* | ||||
| Dep. of Statistics, Faculty of Economics & Political Science, Cairo University, Egypt. | ||||
| 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. | ||||
| Keywords | ||||
| Experimental Errors; Geometric Approach; Heteroscedasticity; Linear Models; Testing Hypotheses; Two - Way Analysis of Variance | ||||
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