A correlation in your sample (especially at that size) does not imply a correlation in the population, even if you validate it with additional sham tests.
The study performed statistical hypothesis testing to determine that the means of the two groups are probably different.
Edit: and more to your point, correlation of the sample implies correlation of the population if the sample is representative. Is this the case for this particular paper? I don't know and neither does anyone else; that's why replication is the gold standard of scientific validity.
> A correlation in your sample (especially at that size) does not imply a correlation in the population
At least quote the article correctly.
> That is, correlation in the data you happen to have (even if it happens to be “statistically significant”) does not necessarily imply correlation in the population of interest.
(Emphasis mine)
Otherwise you might as well throw out centuries of mathematical, statistical and scientific progress. That laptop of yours? Throw it in the trash as it is the culmination of thousands of sham tests and correlations and is therefore clearly impossible.
The study performed statistical hypothesis testing to determine that the means of the two groups are probably different.
Edit: and more to your point, correlation of the sample implies correlation of the population if the sample is representative. Is this the case for this particular paper? I don't know and neither does anyone else; that's why replication is the gold standard of scientific validity.