Barely Significant
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Brain structural abnormalities in obesity: relation to age, genetic risk, and common psychiatric disorders : Evidence through univariate and multivariate mega-analysis including 6420 participants from the ENIGMA MDD working group.

Mol Psychiatry · 2021 · PMC8589644 · PMID 32467648

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highly significantno p-value reported
Multivariate pattern recognition analyses Multivariate pattern classification analyses further confirmed the relationship between obesity and brain structure by yielding highly significant single-subject differentiation between obese (BMI > 30, n = 1223) and normal weight subjects (BMI 18.5–25, n = 2917) with a balanced accuracy rate of 68.7% (BAC = 0.687, StD = 0.019, p < 0.001; sensitivity = 0.695; specificity = 0.678; F1score = 0.565; ROC-AUC = 0.687).

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failed to reach significanceno p-value reported
Yet, it is important to acknowledge that BMI was associated with lower cortical thickness in adolescent participants but might have failed to reach significance due to limited sample size in this analysis (see Supplementary Results for power analysis).

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Quoted from the open-access full text in Europe PMC under the licence the publisher applied. The sentence is reproduced exactly as published; the emphasis is ours.