Meta-analytic Approach

All analyses were performed using the publicly available R environment, version 4.1.3. Effect sizes are expressed as r. Correlations reported as φ were converted to r. To synthesize effect sizes across studies, all r were converted to Fisher’s z (using the function “transf.rtoz,” package metafor 3.4.0). After estimating the meta-analytic models, we reconverted the meta-analytic mean Fisher’s z¯ metrics to pooled correlation coefficients r¯ (function “transf.ztor,” metafor 3.4.0 package).

We searched for outliers, defined as a Fisher’s z whose residuals had z scores > 3 [28]. No more than two outliers were identified within any subsample. Outlying values were excluded from subsequent analyses.

Independence of effect sizes is a crucial assumption of conventional meta-analytic procedures. We assumed that athletes involved in different studies, male and female athletes, and athletes from different sports were from independent samples. However, in several studies, athletes’ performance data were collected from various junior age categories within sexes and sports, where the extent of sample independence or dependence was not always clear from the primary reports. Becker [40] described four central approaches for dealing with partially dependent samples. The four approaches are: (1) treating data as independent, (2) combining across different outcomes, (3) creating independent data sets, and (4) modeling dependence.

Given the nature of the data in our synthesis, we decided to apply the following approaches to estimate the overall pooled correlation and compare the respective models: (1) assuming independence of all samples; (2) combining across different effect sizes; for this approach, Cheung and Chan [41] described a sample-wise adjustment by individual effect size (see Cheung and Chan’s R script “MADependentESFunctions.r” in [41]); (3) modeling dependence by application of three-level modeling using cluster-robust variance estimation (RVE, metaphor 3.4.0 package, functions “rma.mv” and “robust” [42]), and with using a structural equation modeling approach (metaSem 1.2.5.1 package, function “meta3”).

Pooled effects were similar across the different models, 0.145 ≤ r¯ ≤ 0.151 (model differences 0.597 ≤ p ≤ 0.955). Following Becker’s recommendations, the most complete and accurate portrayal of the effects of dependence requires the modeling of this dependency. Therefore, we used three-level RVE modeling for subsequent moderator analyses. We estimated the overall effect of junior performance on senior performance by conducting a random effects meta-analysis (k = 129) and then employed mixed-effect models to analyze whether defined subsample characteristics moderated effects. All subsamples are provided separately in the ESM 1.