The graph in the summary showing "SWA in the right PFC" is almost comically unconvincing.
Remove the two or three most extreme data points and the effect disappears completely. Even removing a single one of those extreme data points is probably enough to toss the significance of the fit and be fully consistent with zero correlation.
The full article has 5 of these graphs. I'm staring at them and I still can't believe the tiny p values. Is the data of the graph available? Can someone repeat those graphs and explain the small p values?
[My guess is that the slope is caused by the cluster at (SWA=150%, Risk=2m) in the graph.]
You can correlate those brain waves with anything really: predisposed to eat oranges to climb hills, likes color blue. Even infinitely small p won't save those studies.
I'm not knowledgeable about statistics and studies like this in general; do you mean this is a "green jelly beans cause acne" [1] situation, where you test for many hypotheses and one of them turns out to be significant?
Exactly, if you test many many things against each other you will always find correlations between them by chance. That's why you always need to start with a "serious" hypothesis.
Remove the two or three most extreme data points and the effect disappears completely. Even removing a single one of those extreme data points is probably enough to toss the significance of the fit and be fully consistent with zero correlation.