ABSTRACT
When a researcher designs an experiment involving factors that are random effects, she often wishes to make inferences about speci c variance components speci ed in the model. In particular, if su2 is the variance component corresponding the distribution of the levels of factor A, the experimenter may wish to determine if there is enough evidence to conclude that su2 > 0. An appropriate decision can be made by 1) testing the hypothesis H0: su2 = 0 vs Ha: su2 > 0; 2) by constructing a con dence interval about su2; or 3) by constructing a lower con dence limit for su2. This chapter addresses these kinds of inference procedures for random effects models where methods for hypotheses testing are described in Section 20.1 and the construction of con dence intervals (lower bounds) is described in Section 20.2. The construction of con dence intervals for variance components has been a fertile area of research and many authors have developed specialized con dence intervals for speci c functions of the variance component parameters. The methods described in this chapter are available in current software and some are available for speci c problems. The discussion is not exhaustive, but rather points to the types of con dence intervals that have been addressed. A more complete discussion is available in Burdick and Graybill (1992) as well as papers in the current statistical journals.
