Barely Significant
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Edge detection in landing budgerigars (Melopsittacus undulatus).

PLoS One · 2009 · PMC2752810 · PMID 19809500

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hedged sentences
0.0001
closest p · 0.0× alpha
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boldest claim

The sentences

highly significantP<0.00005actually significant
The trained birds' preference for the Dreadnought Grey disc was statistically highly significant (P<0.00005, using the binomial statistics described in “ Methods ”).

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marginally significantno p-value reported
With the Dreadnought Grey disc the value of α was closest to 1.0, and was different from this value at only a marginally significant level, implying that in this condition the birds landed nearly randomly all over the test surface even though this grey disc is (at least for humans) clearly distinguishable from the Kingfisher Blue background ( Figure 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.