Quantifying the heterogeneity is an important issue in meta-analysis, and among the existing measures, the $I^2$ statistic is most commonly used. In this paper, we first illustrate with a simple example that the $I^2$ statistic is heavily dependent on the study sample sizes, mainly because it is used to quantify the heterogeneity between the observed effect sizes. To reduce the influence of sample sizes, we introduce an alternative measure that aims to directly measure the heterogeneity between the study populations involved in the meta-analysis. We further propose a new estimator, namely the $I_A^2$ statistic, to estimate the newly defined measure of heterogeneity. For practical implementation, the exact formulas of the $I_A^2$ statistic are also derived under two common scenarios with the effect size as the mean difference (MD) or the standardized mean difference (SMD). Simulations and real data analysis demonstrate that the $I_A^2$ statistic provides an asymptotically unbiased estimator for the absolute heterogeneity between the study populations, and it is also independent of the study sample sizes as expected. To conclude, our newly defined $I_A^2$ statistic can be used as a supplemental measure of heterogeneity to monitor the situations where the study effect sizes are indeed similar with little biological difference. In such scenario, the fixed-effect model can be appropriate; nevertheless, when the sample sizes are sufficiently large, the $I^2$ statistic may still increase to 1 and subsequently suggest the random-effects model for meta-analysis.

翻译：量化异质性是元分析中的一个重要问题，在现有度量指标中，$I^2$ 统计量最为常用。本文首先通过一个简单实例阐明，$I^2$ 统计量严重依赖于研究样本量，这主要是因为它用于量化观测效应量之间的异质性。为降低样本量的影响，我们引入一种替代度量方法，旨在直接衡量元分析中所涉及研究总体之间的异质性。进一步地，我们提出一个新估计量，即 $I_A^2$ 统计量，用于估计新定义的异质性度量。在实际应用中，我们还推导了在效应量为均值差（MD）或标准化均值差（SMD）这两种常见情形下 $I_A^2$ 统计量的精确公式。模拟研究和真实数据分析表明，$I_A^2$ 统计量能够为研究总体间的绝对异质性提供渐近无偏的估计量，并且与预期一致，它也不受研究样本量的影响。综上所述，我们新定义的 $I_A^2$ 统计量可作为异质性的补充度量指标，用于监测研究效应量实际相似且生物学差异极小的情况。在此类情形下，固定效应模型可能是合适的；然而，当样本量足够大时，$I^2$ 统计量仍可能增至1，从而建议采用随机效应模型进行元分析。