Confidence intervals on the ratio of expected mean squares (theta 1 + d theta 2)/theta 3.

The variance component ratio delta = (theta 1 + d theta 2)/theta 3 is of interest in many fields of application. This paper proposes and compares two methods for constructing confidence intervals on delta. The better method is compared with a method proposed by Graybill and Wang (1979, Journal of the American Statistical Association 74, 368-374) for the special problem of constructing an interval on sigma 2E/(sigma 2A + sigma 2B + sigma 2E) in a two-fold nested design. An example concerning a heritability study is provided.