This article proposes several new indices that measure the heterogeneity for individual studies in a meta-analysis. These indices directly assess how inconsistent an individual study is compared to the rest of studies used in the meta-analysis, that is, how much impact the specific study has on the scientific conclusion of the meta-analysis and further on the generalization of the conclusion. The proposed indices can be intuitively interpreted as the proportion of total variance from all studies in a meta-analysis that can be accounted for by the heterogeneity from specific studies. Further, each proposed index over all the studies sums to the collective measure of heterogeneity for the meta-analysis. Therefore our proposed study-specific indices of heterogeneity can be regarded as a generalization of the collective index of heterogeneity in meta-analyses proposed by various authors. We examine the difference among the proposed study-specific measures of heterogeneity and assess the variation associated with each proposed index of heterogeneity through a large simulation study. Finally, we demonstrate the proposed methodology by assessing the effect of individual studies on the overall estimate to the difference of an antecedent biomarker of Alzheimer's disease (AD) between different Apolipoprotein E (ApoE) genotypes.