{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T06:57:03Z","timestamp":1790578623050,"version":"4.1.0"},"reference-count":58,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Psychol."],"abstract":"\n Introduction<\/jats:title>\n 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\u2014such as directionally contrary evidence and shape consistency\u2014that conventional mean-focused meta-analytic models obscure.<\/jats:p>\n <\/jats:sec>\n \n Methods<\/jats:title>\n \n 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 (\n W<\/jats:italic>\n 1<\/jats:sub>\n ) distances, a distributional heterogeneity measure\n H<\/jats:italic>\n \n w<\/jats:italic>\n <\/jats:sub>\n , and distributionally robust optimization (DRO). Against a zero-effect benchmark,\n W<\/jats:italic>\n 1<\/jats:sub>\n 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.\n H<\/jats:italic>\n \n w<\/jats:italic>\n <\/jats:sub>\n was compared against the location-only prediction 1\u2212\n I<\/jats:italic>\n 2<\/jats:sup>\n \/100, and DRO stability margins (expressed as signal-to-noise ratios) were benchmarked against conventional trim-and-fill publication-bias corrections.\n <\/jats:p>\n <\/jats:sec>\n \n Results<\/jats:title>\n \n 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 (\n I<\/jats:italic>\n 2<\/jats:sup>\n = 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.\n <\/jats:p>\n <\/jats:sec>\n \n Discussion<\/jats:title>\n 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.<\/jats:p>\n <\/jats:sec>","DOI":"10.3389\/fpsyg.2026.1916455","type":"journal-article","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T06:31:46Z","timestamp":1790577106000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Beyond the pooled mean: distributional structure in the attentional-focus meta-analysis"],"prefix":"10.3389","volume":"17","author":[{"given":"Boyi","family":"Zeng","sequence":"first","affiliation":[{"name":"School of Physical Education, Xihua University","place":["Chengdu, Sichuan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xupeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Sichuan Jiaotong Polytechnic University","place":["Chengdu, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Physical Education, Xihua University","place":["Chengdu, Sichuan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"1807","DOI":"10.1080\/02640414.2015.1012102","article-title":"Performance of gymnastics skill benefits from an external focus of attention","volume":"33","author":"Abdollahipour","year":"2015","journal-title":"J. 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