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Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model
Author(s) -
Mosier Michael C.,
Graybill Franklin A.
Publication year - 1995
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.4710370304
Subject(s) - confidence interval , mathematics , statistics , degrees of freedom (physics and chemistry) , random variable , variable (mathematics) , variance (accounting) , cdf based nonparametric confidence interval , combinatorics , mathematical analysis , physics , accounting , quantum mechanics , business
When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in confidence intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used. As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑ Q g =1a q θ q , where a 1 …, a Q are known constants, U q = n q S 2 q/θ q is a chi‐squared random variable with n q degrees of freedom, for each q = 1,…, Q , and X,U 1 ,…, U Q are mutually independent. In this paper, we consider the case where Q = 3 and a 3 ≤0.