It is easy to do non-crank statistical art history (I’ve provided some examples on this blog recently). The most important step is to phrase the theory you are testing in the language and using the concepts of art history rather than in vague and irrelevant terms from breathless tabloid business reporting like “innovation” or “value”. Asking how turquoise the derivatives market is won’t get you published in the Wall Street Journal. Not because it’s too daring an idea, or the establishment is closing its ranks, or because of a lack of imagination on the part of anyone else but because as a combination of aesthetics and economics it is incoherent.
I reviewed David Galenson’s self-refuting marketarian art history on this blog last year. Galenson had an earlier book applying statistical methods to art history, comparing early and late blossoming artistic innovators. You can find an exert of a review here. The claims of amazing new discoveries phrased in incoherent terms along with accusations of rejection by the mainstream fit the definition of crank science. Crank aesthetics possibly? There’s a discussion of the book on the Two Blowhardsblog, along with links to more reviews, here. Two Blowhards reviews another book that applies statistics to the artistic canon here, just as critically.