  Quantifying the heterogeneity is an important issue in meta-analysis, and
among the existing measures, the $I^2$ statistic is the most commonly used
measure in the literature. In this paper, we show that the $I^2$ statistic was,
in fact, defined as problematic or even completely wrong from the very
beginning. To confirm this statement, we first present a motivating example to
show that the $I^2$ statistic is heavily dependent on the study sample sizes,
and consequently it may yield contradictory results for the amount of
heterogeneity. Moreover, by drawing a connection between ANOVA and
meta-analysis, the $I^2$ statistic is shown to have, mistakenly, applied the
sampling errors of the estimators rather than the variances of the study
populations. Inspired by this, we introduce an Intrinsic measure for
Quantifying the heterogeneity in meta-analysis, and meanwhile study its
statistical properties to clarify why it is superior to the existing measures.
We further propose an optimal estimator, referred to as the IQ statistic, for
the new measure of heterogeneity that can be readily applied in meta-analysis.
Simulations and real data analysis demonstrate that the IQ statistic provides a
nearly unbiased estimate of the true heterogeneity and it is also independent
of the study sample sizes.
