Barely Significant
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Directional preference in dogs: Laterality and "pull of the north".

PLoS One · 2017 · PMC5612717 · PMID 28945773

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highly significantno p-value reported
This effect was highly significant in small and medium-sized breeds but not in larger breeds, highly significant in females, in older dogs, in lateralized dogs but less significant or not significant in males, younger dogs, or ambilateral dogs.

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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.