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Confidence Intervals and Tests of Hypotheses on Variance Components in an Unbalanced Two‐fold Nested Design
Author(s) -
Hernandez Ramon P.,
Burdick Richard K.,
Birch Nancy J.
Publication year - 1992
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.4710340402
Subject(s) - confidence interval , statistics , mathematics , variance (accounting) , robust confidence intervals , cdf based nonparametric confidence interval , variance components , confidence distribution , coverage probability , analysis of variance , statistical hypothesis testing , tolerance interval , accounting , business
Confidence intervals and tests of hypotheses on variance components are required in studies that employ a random effects design. The unbalanced random two‐fold nested design is considered in this paper and confidence intervals are proposed for the variance components σ2/A and σ2/B. Computer simulation is used to show that even in very unbalanced designs, these intervals generally maintain the stated confidence coefficient. The hypothesis test for σ2/A based on the lower bound of the recommended confidence interval is shown to be better than previously proposed approximate tests.