Barely Significant
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A national megastudy shows that email nudges to elementary school teachers boost student math achievement, particularly when personalized.

Proc Natl Acad Sci U S A · 2025 · PMC12002261 · PMID 40127270

2
hedged sentences
0.0040
closest p · 0.1× alpha
0.0800
boldest claim

The sentences

marginally significantP = 0.004actually significant
As shown in Models 2 and 5 in SI Appendix , Table S12 , Nudging Weekly Logins showed a directional BH-adjusted impact on student progress during weeks 5 to 8 (additional lessons completed = 0.08, 4.49% increase; d = 0.02; unadjusted P = 0.01, BH-adjusted P = 0.11) and a marginally significant BH-adjusted impact during weeks 9 to 12 (additional lessons completed = 0.07, 5.31% increase; d = 0.02; unadjusted P = 0.004, BH-adjusted P = 0.06).

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marginal significanceP = 0.08so close (0.05 < p ≤ 0.1)
Preregistered F-tests allow us to reject the null hypothesis that the effects of all 15 interventions are equal to zero [χ 2 (15) = 27.09, P = 0.03], and to reject the null hypothesis that 15 effects have the same true value at marginal significance [χ 2 (14) = 21.89, P = 0.08].

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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.