Weighting of studies in meta-analysis is usually implemented by using the estimated inverse variances of treatment effect estimates. However, there is a possibility of one study dominating other studies in the estimation process by taking on a weight that is above some upper limit. We implement an estimator of the heterogeneity variance that takes advantage of dominance adjusted weights. The performance of this estimator is compared with that of the commonly used estimator in meta-analysis, the DerSimonian--Laird estimator. Two test procedures for the overall treatment effect are proposed that are based on the quadratic form associated with the proposed heterogeneity variance estimator. An example is given to illustrate the application of these procedures.