Table 1.

Point estimators for the heterogeneity parameter

Point estimator for${\mathit{\tau }}^2$		Author (year)	Computation	Range	Assume normality	Estimation method
Cochran (Hedges-Olkin)	CA	Cochran (1954) [10]	Direct	Non-negative	No	Method of the moments
Mandel-Paule	MP	Mandel & Paule (1970/82) [11, 12]	Iterative	Non-negative	No	Method of the moments
DerSimonian-Laird	DL	DerSimonian & Laird (1986) [13]	Direct	Non-negative	No	Method of the moments
Hartung-Makambi	HM	Hartung & Makambi (2002) [14]	Direct	Positive	No	Method of the moments
Two-step Cochran	CA2	DerSimonian & Kacker (2007) [15]	Direct	Non-negative	No	Method of the moments
Two-step DerSimonian-Laird	DL2	DerSimonian & Kacker (2007) [15]	Direct	Non-negative	No	Method of the moments
Positive DerSimonian-Laird	DLp	Kontopantelis et al. (2013) [16]	Direct	Positive	No	Method of the moments
Lin-Chu-Hodges r	LCHr	Lin et al. (2017) [17]	Iterative	Non-negative	No	Method of the moments
Lin-Chu-Hodges m	LCHm	Lin et al. (2017) [17]	Iterative	Non-negative	No	Method of the moments
Multistep DerSimonian-Laird	DLm	vanAert & Jackson (2018) [18]	Direct	Non-negative	No	Method of the moments
Median-unbiased Mandel-Paule	MPM	Viechtbauer (2021) [19]	Iterative	Non-negative	No	Method of the moments
Median-unbiased Gen. Q	GENQM	Viechtbauer (2021) [19]	Iterative	Non-negative	No	Method of the moments
Maximum likelihood	ML	Hardy & Thompson (1996) [20]	Iterative	Non-negative	Yes	Maximum likelihood
Restricted maximum likelihood	REML	Viechtbauer (2005) [21]	Iterative	Non-negative	Yes	Maximum likelihood
Sidik-Jonkman	SJ	Sidik & Jonkman (2005) [22]	Direct	Non-negative	Yes	Least squares
Sidik-Jonkman (prior CA estimation)	SJ(CA)	Sidik & Jonkman (2007) [23]	Direct	Positive	Yes	Least squares
Non-parametric bootstrap DerSimonian-Laird	DLb	Kontopantelis et al. (2013) [16]	Direct	Non-negative	No	Non-parametric
Malzahn-Böhning-Holling	MBH	Malzahn et al. (2000) [24]	Direct	Non-negative	No	Non-parametric
Hunter-Schmidt (weighted by inversed variance)	HSiv	Hunter & Schmidt (1990) [25]	Direct	Non-negative	No	Artifact correction
Hunter-Schmidt (weighted by sample size)	HSss	Hunter & Schmidt (1990) [25]	Direct	Non-negative	No	Artifact correction
Hunter-Schmidt (corrected by small sample size)	HSk	Morris et al. (2015) [33]	Direct	Non-negative	No	Artifact correction
Fully Bayesian	FB	Smith et al. (1995) [26]	Iterative	Non-negative	Yes	Bayesian
Rukhin Bayes	RB	Rukhin (2013) [27]	Direct	Non-negative	No	Bayesian
Rukhin Bayes positive	RBp	Rukhin (2013) [27]	Direct	Positive	No	Bayesian
Bayes Modal	BM	Chung et al. (2013a, 2013b) [28, 29]	Iterative	Positive	Yes	Bayesian

Heterogeneity point estimators included in the present study, their abbreviation, authors and year of publication, type of calculation required to obtain the corresponding estimate, the range of real values for the${\tau }^2$estimates obtained, whether they assume or not normality assumptions regarding the random-effects distribution, and the underlying estimation method they are based on