Abstract
The classical F-test for testing the hypothesis of no fixed main effects in a mixed effects design is valid under the assumption of normality, symmetry and variance homogeneity of the error terms assumption. We consider the two-way mixed effects design which does not require these three assumptions. A test procedure for the hypothesis of no main fixed effects is developed under this flexible model. The asymptotic distribution of the test statistic is studied for a large number of levels of the random effects.
Highlights
The assumption of independence of the random main and interaction e¤ects is called the symmetry assumption
The classical F -test for testing the hypothesis of no ...xed main e¤ects in a mixed e¤ects design is valid under the assumption of normality, symmetry and variance homogeneity of the error terms assumption
The asymptotic distribution of the test statistic is studied for a large number of levels of the random e¤ects
Summary
The assumption of independence of the random main and interaction e¤ects is called the symmetry assumption. C 2021 Ankara University C om munications Faculty of Sciences U niversity of A nkara-Series A 1 M athem atics and Statistics For this case, Hotelling’s T 2 test for testing of the hypothesis of no main ...xed e¤ects is suggested when two-way mixed e¤ects design is balanced. The contribution of this paper is to present a new test for testing the hypothesis of no main ...xed e¤ects for the unbalanced two-way mixed model under departure of three main assumptions: normality, variance homogeneity of the error terms and symmetry.
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