I'm trying to get a bunch of work done on a couple gaming-related projects by Christmas so I'm not spending much time keeping up with things in the blogosphere, but a person drew my attention to a tweet and I had to highlight it:
Actually correlations are by definition symmetrical so the relation holds both ways (the abstract highlights one direction only). The crucial point is that across 2 studies endorsement of 2 *contradictory* theories was always correlated. Ergo contradiction.
— Stephan Lewandowsky #FBPE (@STWorg) December 12, 2017
It's really quite obscene. If you don't know why it's so outrageous, read my response to it:
What he says is technically true, in that simple correlation tests require univariate normality in the data set thus will necessarily represent a symmetrical relationship.
The problem is his data set violates that requirement, making the test invalid, thus not showing symmetry.
— Brandon S? (@Corpus_no_Logos) December 13, 2017
Lewandowsky and many of his compatriots of his field of study have completely misused simple correlation tests by applying them to highly skewed data sets, violating basic requirements for the tests. The tests require data have a symmetrical distribution (which you can't have in a heavily skewed data set), and because of that requirement, the relationships their results represent will be symmetrical.
Lewandowsky has amazing chutzpah to violate the requirement his data have a symmetrical distribution then turn around and say his results prove there is a symmetrical relationship.