Barely Significant
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Organic production enhances milk nutritional quality by shifting fatty acid composition: a United States-wide, 18-month study.

PLoS One · 2013 · PMC3857247 · PMID 24349282

1
hedged sentence
0.0001
closest p · 0.0× alpha
0.0001
boldest claim

The sentences

highly significantP <0.0001actually significant
conventional FA concentrations in 2 tables, about 2 findings of P = 0.05 and 0.5 finding of P = 0.01 can be expected there by chance alone, but our key findings are highly significant ( P <0.0001) and not vulnerable to Type-I errors (incorrectly rejecting the null hypothesis).

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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.