On confidence intervals for the among-group variance in the one-way random effects model with unequal error variances

Based on a quadratic form of the group means, we consider two different approaches to construct a confidence interval for the among-group variance in the one-way random effects model with unequal error variances. In one approach the limits of the interval are determined by solving non-linear equations whereas in the second approach the bounds are given explicitly. By using correction terms for convexity in both approaches, we improve the primary intervals and obtain intervals whose actual confidence coefficients are closer to the nominal confidence coefficient. By means of a simulation study, we show that an improved confidence interval from each approach can be recommended for the practical use.