SB replied: Yes, this isn't absolutely settled. 

Michael Penn wrote:  A different one is does the admittedly problematic dating of the plays create a secondary problem in terms of who could've been the author?

SB replied: No. Stylistic analysis of the plays credited to Shakespeare prove - or, if that's too strong a word, strongly indicate - that they are the work of the same person, often working in collaboration with another writer. So the first three parts of Henry VI are written by Shakespeare and Christopher Marlowe (the latter now officially credited by The New Oxford Shakespeare), Macbeth contains work by Thomas Middleton,  John Fletcher co-wrote Henry VIII (or "All Is True) and The Two Noble Kinsmen.

As posted before, the role of collaboration compounds the difficulties in arguing that someone other than Will of Stratford was the author, or co-author, of the plays attributed to him in the First Folio.