  Meta-analysis combines pertinent information from existing studies to provide
an overall estimate of population parameters/effect sizes, as well as to
quantify and explain the differences between studies. However, testing the
between-study heterogeneity is one of the most troublesome topics in
meta-analysis research. Additionally, no methods have been proposed to test
whether the size of the heterogeneity is larger than a specific level. The
existing methods, such as the Q test and likelihood ratio (LR) tests, are
criticized for their failure to control the Type I error rate and/or failure to
attain enough statistical power. Although better reference distribution
approximations have been proposed in the literature, the expression is
complicated and the application is limited. In this article, we propose
bootstrap based heterogeneity tests combining the restricted maximum likelihood
(REML) ratio test or Q test with bootstrap procedures, denoted as B-REML-LRT
and B-Q respectively. Simulation studies were conducted to examine and compare
the performance of the proposed methods with the regular LR tests, the regular
Q test, and the improved Q test in both the random-effects meta-analysis and
mixed-effects meta-analysis. Based on the results of Type I error rates and
statistical power, B-Q is recommended. An R package \mathtt{boot.heterogeneity}
is provided to facilitate the implementation of the proposed method.
