All included studies reported the Pearson product-moment correlation
coefficient (r). As the Pearson correlation is not normally
distributed, each effect size was converted to Fisher’s z using
the following formulas (Borenstein & Hedges, 2019, pp. 220–221):z = 0.5 × 1n !!”#” (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1)
!$#
The variance and the standard error of Fisher’s z were calculated
as follows:
; SEz = √𝑣’ (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 2 𝑎𝑛𝑑 3)
Fisher’s z is then converted back to the Pearson correlation
using the following equation:
(!”$!
(!””!
where 𝑒) is the anti-log function.
(𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 4)
As a majority of the studies reported more than one effect size (e.g.,
effect size per EI subscale or for each EI test), a three-level
meta-analysis approach was adopted, where (a) Level 1 referred to
sampling error, (b) Level 2 referred to between-studies variance, and
(c) Level 3 referred to the across-studies variance. All multilevel
analyses were conducted using SAS® Studio. The full
codes for running analyses can be found in Van den Noortgate et al.
(2015,
p. 20). The full model can be presented as follows:
𝑌*’ = 𝛾++ + 𝑢+’ +
𝑟*’ + 𝑒*’ (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 5)
Where 𝑌*’ represents observed effect size,
𝛾++ represents the overall mean effect size,
𝑢+’ represents Level 3 random effect,
𝑟*’ represents Level 2 random effect, and
𝑒*’ represents Level 1 random effect. The full model,
when all moderators are included, can be presented as follows:
𝜋*’ = 𝛽+’ +
𝛽!’𝑋!*’ + ⋯ +
𝛽,’𝑋,*’ + 𝑟*’, (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛
6)
Where 𝛽+’ and 𝛽!’ represent regression
coefficients, and 𝑋!*’ and 𝑋,*’represent moderators (Konstantopoulos, 2011).