The variance function of the optimal estimator of the overall mean in a heteroscedastic one-way ANOVA model is dominated by positive semi-definite quadratic functions. This makes it possible to develop closely related tests on the nullity of the overall mean parameter in one-way fixed and random...

Positive estimators of the between-group (between-study) variance are proposed. Explicit variance formulae for the estimators are given and approximate confidence intervals for the between-group variance are constructed, as our proposal to a long outstanding problem. By Monte Carlo simulation,...