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Positive estimators of the between-study variance are proposed. Explicit variance formulae for the estimators are given and approximate confidence intervals for the between-group variance are constructed, thus helping to partly solve a long outstanding and open problem. By Monte Carlo simulation, the bias and standard deviation of the proposed estimators are compared with a standard estimator in meta-analysis. Attained confidence coefficients of the constructed confidence intervals are also presented. To illustrate the application of the proposed procedures, three examples are given, the first is from agriculture, the other two are from clinical trials with normal and binary outcomes, respectively.
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