Barely Significant
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Progesterone promotes immunomodulation and tumor development in the murine mammary gland.

J Immunother Cancer · 2021 · PMC8103939 · PMID 33958486

2
hedged sentences
0.0600
closest p · 1.2× alpha
0.0600
boldest claim

The sentences

failed to reach statistical significancep=0.06so close (0.05 < p ≤ 0.1)
While CD4+ and CD8+ T cell populations did not differ between genotypes, NKT (natural killer T) cells were decreased in PR/Gal4 mice but failed to reach statistical significance (p=0.06, online supplemental figure 32 ).

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Though the tumors from PR/Gal4 mice tended to be larger in size than those of the control mice, these data did not reach statistical significance ( figure 5A ).

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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.