Positive estimation of the between-group variance component in one-way anova and meta-analysis

Abstract

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 maximum 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.