Statistical analysis

For the main analysis, we estimated the standardized mean difference (Hedge’s g) in 2D:4D among substance or computer-using subjects and controls. Thus, correlative data were transformed into Hedge’s g using common transformation formulas (Borenstein et al. 2009, pp 45–49). Hedge’s g is an effect size that quantifies mean differences in a similar way to Cohen’s d, but it corrects the pooled standard deviation (Hedges 1981). The interpretation of Hedge’s g and Cohen’s d is comparable. The analysis was performed for both sexes combined and for men and women separately to detect sex-specific effects. We tested with fixed-effect models whether male and female meta-analysis estimates differed significantly.

Then, we tested for standardized mean differences in Dr-l in substance and computer-using subjects and non-dependent controls. Low Dr-l values have been associated with high prenatal testosterone load beyond 2D:4D (Manning 2002, pp 21–22). This analysis was feasible for all studies which reported means and standard deviations of an affected and a non-affected group. Dr-l was computed as the difference between the mean right-hand 2D:4D and mean left-hand 2D:4D, and related standard deviations were approximated by the pooled standard deviation of the right-hand 2D:4D and left-hand 2D:4D variances.

Furthermore, we tested whether males had a smaller 2D:4D than females and whether the right-hand 2D:4D is smaller than the left-hand 2D:4D among subjects in our analysis. Both are prominent findings and often replicated in 2D:4D research (Hönekopp and Watson 2010; Xu and Zheng 2015). All analyses were conducted using the metafor package (Viechtbauer 2010) within the open-source software environment R, version 3.4.2. (R Core Team 2018).

We performed univariate meta-analyses using restricted maximum likelihood estimation. The point estimate for each study was weighted by the inverse of its variance. Nonindependence among effect sizes was accounted for by aggregating. Heterogeneity among effect sizes within datasets was assessed using the I² statistic. This statistic can be interpreted as the percentage of the total variability in a set of effect sizes due to between-study variability (Cochrane Training 2018). The Cochrane handbook proposes a tentative classification where an I² of 0–40% might not be important, I² of 30–60% indicates moderate heterogeneity, I² of 50–90% indicates substantial heterogeneity, and I² greater than 75% indicates considerable heterogeneity.

To explain the residual heterogeneity and to understand the potential effect of contextual factors on the outcomes, we ran pre-specified meta-regression analyses for the following moderators: study quality, mean age, and procedure of measuring 2D:4D. The latter refers to whether 2D:4D was measured by multiple independent raters, multiple times by one rater, once by one rater, or by the participants themselves. Thus, the slope of the meta-regression line (β coefficient) indicates the strength of the association between the moderator and outcome.

The meta-regressions were Bonferroni-corrected for multiple testing. We performed pre-specified subgroup analyses to investigate the difference in the outcome measures between (1) the definition of caseness (studies comparing dependent with non-dependent subjects according to diagnostic criteria versus studies examining other parameters of substance and computer use); (2) the left hand and right hand; (3) the different addiction forms: alcohol, illegal drugs, tobacco, or addictive computer use (it was not possible to test for gambling separately since only one independent study reported relevant data); and (4) the different methods of measuring 2D:4D. The latter was dichotomized into “measurement without soft-tissue deformation” (comprising X-rays and direct measurement from the participants’ palm) and “measurement with soft-tissue deformation” (comprising photocopies and hand scans).

Concerning the definition of caseness, two subgroups were formed as follows. A study was assigned to the group of studies comparing dependent with non-dependent subjects when cases were identified according to ICD-10, DSM-IV, or DSM-5 criteria, as well as comparable questionnaires that allow for clear, diagnostic decisions, such as the Internet Addiction Test (Young 1998) and the Video Game Addiction Scale (CSAS-II) (Rehbein et al. 2010). The remaining studies were clustered into the group of “other studies” since they did not compare dependent with non-dependent subjects according to dependency criteria but studied other parameters of addictive behavior.¹

Publication bias and small study effects were assessed with the funnel function of R, which produced contour-enhanced funnel plots for the visual detection of asymmetries. In addition, the Egger regression test was used to detect asymmetry in the funnel plots (Egger et al. 1997). We considered analyses to be biased if the intercept differed from zero at p = 0.10, as the authors originally proposed (Egger et al. 1997). We evaluated the sensitivity of our analysis by comparing models with and without effect sizes, which we assume to be influential outliers (Viechtbauer and Cheung 2010). A study may be considered to be influential if at least one of the following is true: (1) the absolute DFFITS value is larger than 3√(p/(k – p)), where p is the number of model coefficients, and k the number of studies. (2) The lower tail area of a Chi-squared distribution with p degrees of freedom cut off by the Cook’s distance is larger than 50%. (3) The hat value is larger than 3(p/k). (4) Any DFBETAS value is larger than 1 (Viechtbauer and Cheung 2010).

P < 0.05 (two-sided) was considered statistically significant, except for the regression test for small study effects as stated above.