"Nearly half the case participants had more gray matter after getting COVID" - as did the controls. It's almost like there's variability in the readings. If only someone would invent a subspeciality of mathematics about how to interpret noisy data and attempt to draw conclusions about the results.

I'm not totally sold on this study either, mind you. I'm just amazed at how many people are rushing to judgement in the other direction - the whole "just a flu" conclusion is wildly premature.

Yes, I mention the high variance. And indeed there are standard ways to interpret the effect size magnitude, given noisy data. The authors chose not to report Cohen's d. They do provide an r value (.16), which we can use to compute the the coefficient of determination. Since you are an advocate for reliance on traditional statistical interpretations, you should appreciate the meaning of r^2=.025

Furthermore the authors report a P=.01. They bootstrap this P, presumably because alpha significance level after multiple comparison adjustment renders cutoff well below .01. They also claim no a priori hypothesis wrt. gray matter increase or decrease. A 2-tailed alpha is typically shifted from p<.05 to p<.01 which their measured P value does not surpass. Nevertheless they claim statistical significance. Finally, after normalization, there is roughly an equal chance any given person will have more or less gray matter after getting covid - this doesn't require one to glean the importance of each ounce of gray matter to understand the effect size is small. I contend there is good reason this study has not yet passed peer review, if it ever will.

Figure 2 is the one you want https://els-jbs-prod-cdn.jbs.elsevierhealth.com/cms/attachme...

Which does show effect increasing with severity of the case. I've seen plots like that before in similar articles.

See also table 2.