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On the Effects of Departure from Normality on the F ‐Ratios in a Nested Random Effect Model by Mixture of Normals
Author(s) -
Tan W. Y.,
Wong S. P.
Publication year - 1979
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710210302
Subject(s) - normality , mathematics , statistics , random effects model , nested set model , econometrics , type i and type ii errors , variance (accounting) , computer science , economics , meta analysis , relational database , medicine , accounting , database
Abstract In this paper we consider the following nested random effect modelwhere the α i 's, the β ij 's and the e ijk are independent random variables. By assuming that these variables follow a mixture of two normal densities, we study the effects of departure from normality on the classical JT‐tests for variance components. It is shown that the departure from normality has little effects on the type 1 error and the power function; this indicates that the classical F ‐tests are quite robust with respect to departure from normality.