  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.
