Barely Significant
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The effects of training managers on management competencies to improve their management practices and work engagement of their subordinates: A single group pre- and post-test study.

J Occup Health · 2020 · PMC6970398 · PMID 31493339

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Subgroup analyses showed that regardless of whether a manager and a subordinate have the same gender, the relationship between managers’ integrity and subordinate work engagement was positive while in the same gender group, it did not reach statistical significance.

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marginally significantno p-value reported
They measured two factors of work engagement (vigor and dedication) and found a marginally significant intervention effect on vigor, which remained in the intervention group while it decreased in the control group.

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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.