Scaling of grammaticalness of self-embedded English sentences

Native speakers of English estimated the relative grammaticalness of simple declarative sentences, self-embedded sentences, right-branching sentences, and anagram strings. Simple declarative and right-branching sentences were, for the most part, judged to be completely grammatical; anagram strings were judged to be most ungrammatical. The estimated “ungrammaticalness” of self-embedded sentences seems to grow as a power function of the number of embeddings above a “threshold” of 1.5 embeddings. The exponent of the power function appears to lie between 0.25 and 0.30.