Confidence intervals on linear combinations of variance components that are unrestricted in sign

A new method is proposed for constructing confidence intervals on where the sign of γ is unrestricted and unknown, and are independently distributed chi-squared random variables with ni degrees of freedom for Computer simulation is used to illustrate that the method provides a confidence coefficient that is generally close to the stated level. The method is illustrated by using it to test a main effect in a random three-factor crossed design.