Barely Significant
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Olfactory attraction of the hornet Vespa velutina to honeybee colony odors and pheromones.

PLoS One · 2014 · PMC4280141 · PMID 25549358

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near-significantno p-value reported
A p value below α corrected was considered as statistically significant, while a value between α corrected and the standard 0.05 threshold was only regarded as near-significant (but potentially biologically relevant).

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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.