Barely Significant
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Rock sparrow song reflects male age and reproductive success.

PLoS One · 2012 · PMC3426517 · PMID 22927955

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hedged sentences
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closest p · 1.2× alpha
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boldest claim

The sentences

failed to reach significanceP = 0.06so close (0.05 < p ≤ 0.1)
Despite their greater overall reproductive success, older males had more extra-pair young in their own nests, though this difference failed to reach significance (median and IQR, older males: 1.00, 0.00–2.50, yearlings: 0.00, 0.00–0.00, U = 27.0, N yearling = 8, N older = 12, P = 0.06).

also in 4,113 other papers

However, song rate as predictor variable was significant only in the final model and song amplitude marginally failed to reach statistical significance ( Table 3 ).

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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.