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Journal of Probability and Statistics
Volume 2013, Article ID 708540, 11 pages
Research Article

Testing for Main Random Effects in Two-Way Random and Mixed Effects Models: Modifying the Statistic

1Department of Statistics, Carnegie Mellon University, 5000 Forbes Avenue, 132B Baker Hall, Pittsburgh, PA 15213, USA
2Department of Statistics, Penn State University, 325 Thomas Building, University Park, PA 16802, USA

Received 3 August 2012; Accepted 4 February 2013

Academic Editor: Jose Sarabia

Copyright © 2013 Trent Gaugler and Michael G. Akritas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A procedure for testing the significance of the main random effect is proposed under a model which does not require the traditional assumptions of symmetry, homoscedasticity, and normality for the error term and random effects. To accommodate this level of model generality, and also unbalanced designs, suitable adjustments to the F-test are made. The extensive simulations performed under the random effects model, and the unrestricted and restricted versions of the mixed effects model, indicate that the classical F procedure is extremely liberal under heteroscedasticity and unbalancedness. The proposed test procedure performs well in all settings and is comparable to the classical F-test when the classical assumptions are met. An analysis of a dataset from the Mussel Watch Project is presented.