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Louis Lyons states here (bottom of the first page) that historically there have been cases of physical effects/phenomena existing at $3\sigma$ which would later be proven false when more data was collected. This is presented as an historical reason for the need of higher $\sigma$-significance levels such as $5\sigma$.

Is anyone aware of any of these experiments or 'discoveries' true at $3\sigma$ but disproved by more data?

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How about the purported 750GeV particle at the LHC?

Depending on exactly how you calculate the significance (whether you include the look elsewhere effect) the signficance was $3.9$ and $3.4$ standard deviations at ATLAS and CMS respectively.

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