Effect Size Calculation and Statistical Analyses

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) !$# The variance and the standard error of Fisher’s z were calculated as follows:
vz = !
%$&
; 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).