[brucephillips]

> the paper shows a very weak statistical significance

How so? The p values are quite low.

[tempay]

They're not low enough to account for the look elsewhere effect[1] (known by a different name in this field, but the idea is the same). In this case they look at 500,000 measurements so finding p-values of 10⁻⁵/10⁻⁶ is expected.

[1] https://en.wikipedia.org/wiki/Look-elsewhere_effect