2026-10-14T15:14:50Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34010376 2026-09-28T06:31:47Z category_173 portal_316 item_type_3 month_year_09_2026

Supplementary file 1_Beyond the pooled mean: distributional structure in the attentional-focus meta-analysis.docx Boyi Zeng (25120503) Xupeng Zhang (1493305) Pan Wang (198097) Applied Psychology attentional focus distributionally robust optimization effect size distributions external focus meta-analysis publication bias Wasserstein distance Introduction<p>Meta-analyses of attentional focus in motor learning and performance have focused almost exclusively on pooled mean effect sizes, leaving potential distributional features under-examined. This study evaluates whether distributional tools applied to study-level effect-size posterior mixtures can capture evidence structures—such as directionally contrary evidence and shape consistency—that conventional mean-focused meta-analytic models obscure.</p>Methods<p>We reanalyzed 200 effect sizes from the published attentional-focus literature using three distributional frameworks applied to study-level effect-size posterior mixtures rather than participant-level raw distributions: Wasserstein-1 (W₁) distances, a distributional heterogeneity measure H_w, and distributionally robust optimization (DRO). Against a zero-effect benchmark, W₁ was decomposed into the pooled mean and a non-negative residual equal to twice the expected negative part of the mixture, quantifying the proportion of evidence opposing the recommended instructional focus. H_w was compared against the location-only prediction 1−I²/100, and DRO stability margins (expressed as signal-to-noise ratios) were benchmarked against conventional trim-and-fill publication-bias corrections.</p>Results<p>The directional residual derived from accounted for 36.4% of the transport distance for transfer outcomes, 20.5% for retention, and 13.5% for immediate performance; its bootstrap confidence intervals excluded zero across all evaluated outcomes, demonstrating that no sub-literature in this sample is fully summarized by its mean alone. The distributional heterogeneity measure exceeded location-only predictions across all five outcomes, most prominently for the distance effect (0.66 vs. 0.22), indicating greater agreement in distributional form than traditional variance-based indices suggest. Conversely, the outcome with the highest variance heterogeneity (I² = 87.8% for EMG efficiency) exhibited the smallest directional residual (8.5%), as its contrary evidence lay close to the null point. DRO stability margins consistently exceeded trim-and-fill corrections across all primary outcomes.</p>Discussion<p>Distributional metrics complement conventional pooled-mean comparisons by decoupling directional complexity from variance-based heterogeneity and providing robust stability bounds against data perturbation. However, because these analyses operate on study-level posterior mixtures, claims regarding individual participant-level tail behavior or extreme outcomes remain constrained and require access to raw participant-level data.</p> 2026-09-28T06:31:47Z Dataset Dataset 10.3389/fpsyg.2026.1916455.s001 https://figshare.com/articles/dataset/Supplementary_file_1_Beyond_the_pooled_mean_distributional_structure_in_the_attentional-focus_meta-analysis_docx/34010376 CC BY 4.0