Tests of hypotheses for variance components are often of interest in r
andom effects analysis of variance models. However, in many applicatio
ns, exact tests are not available and approximate methods must be used
. Many investigators form approximate tests based on ''quasi'' F ratio
s. A different approach based on a confidence interval for the varianc
e component is proposed in this paper. The approach is illustrated wit
h a random effects three-factor crossed design, and guidelines are pro
vided for application to other designs.