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, the bias and standard deviation of the proposed estimators are compared with the truncated versions of the maxi- mum likelihood (ML) estimator, restricted maximum likelihood (REML) estimator and a (lately) standard estimator in meta-analysis. Attained confidence coefficients of the constructed confidence intervals are also presented.
random effects model positive estimates of the between-group variance confidence intervals on the between-group variance Patnaik's approximation