At this point, Oxfordians usually object that this method presupposes the order in which the plays were written in order to work, and thus assumes something that (according to Oxfordians) is far from settled. This would be a valid objection if it were true, but it isn't. Foster's study does NOT depend on our knowing the order of the plays ahead of time; it automatically accounts for the relative order of the plays and would work just as well if we had no idea of their order (though it might take longer to interpret the results); in fact, it can be used as evidence in some cases for disputed orderings. Allow me to explain it a little more fully, abstracting away from complications and rough edges. You take a play, say Hamlet. One by one, you compare it to each of the other plays in the canon according to Foster's shared rare word tests. Roughly speaking, the other plays will divide into two groups. In the first group, the shared rare words will be divided proportionally among all the characters in Hamlet. Lo and behold, this group consists of the plays which, according to the traditional chronology, were written before Hamlet. In the second group, the shared rare words are disproportionately concentrated in the roles of the Ghost and the Player King. Lo and behold, these are the plays which according to the standard chronology were written after Hamlet. Hmmm. Now, take another play, say 1 Henry 4. You also compare it one by one to each other play in the canon according to the rare word test. These, too, will divide into two groups. The first group will have the shared rare words distributed proportionally among the parts; this group will consist of a subset of the parallel group for Hamlet, and will include those plays which according to standard chronology were written before 1 Henry 4. The second group will, in each case, have the shared rare words disproportionately concentrated in the role of King Henry. This group will consist of the analogous group for Hamlet, plus the plays which, according to the standard chronology, were written between 1 Henry 4 and Hamlet --- 2 Henry 4, Twelfth Night, etc. It doesn't matter whether we know ahead of time whether 1 Henry 4 or Hamlet was written first --- the pattern of rare words tells us by itself. The above is oversimplified, of course, but I hope it makes it clear what the study really does, and that it does not rely on knowing the order of the plays ahead of time.
Now, all this is pretty strong circumstantial evidence that William Shakespeare of Stratford wrote these plays, since we know that he was an actor and sharer in the theater company which produced them. (And of course everybody said at the time that he was the author, but I'm applying Oxfordian standards and ignoring that.) But in addition, SHAXICON provides evidence about the dating of the plays, and it correlates remarkably well with the external evidence to confirm, for the most part, the orthodox dating of the plays. For example, we know from the cast lists in the Ben Jonson First Folio that William Shakespeare acted in Jonson's Every Man in His Humour (1598) and Sejanus (1603). Don Foster has entered these two plays in the SHAXICON database, and the rare-word patterns indicate that the author of Shakespeare's plays acted in both of them, in the roles of Old Kno'well (Every Man In) and Macro and Sabinius (Sejanus). (Coincidentally, tradition --- first recorded by Thomas Davies in 1785 --- says that Shakespeare played Old Kno'well in Johnson's Every Man In.) Furthermore, we have documentary evidence that Every Man In was performed in 1598 and 1604, and words from this play come pouring into the Shakespeare plays which, according to the standard chronology, were written in 1598 and 1604; similarly, we know that Sejanus was acted in 1603, and words from this play appear disproportionately in Shakespeare's plays which, according to the standard chronology, were written around then. In fact, wherever we have documentation of a performance of a Shakespeare play during his lifetime, SHAXICON indicates that the play in question was being performed in the appropriate year. For a detailed explanation of the use of SHAXICON for dating plays and identifying sources, see the essay on Romeo and Juliet on Don Foster's web page.