The evidence for Watson seems quite weak to me, but the real question is whether we have strong evidence for Shakespeare -- and co-authorship -- in the first place. Are there really two or more playwrights at work here? Was Shakespeare one of them?
Examining the rare vocabulary in the play
Running the Shakespeare Affinity Test on the play, we get a scatter plot that looks like this (click on the image to see the full plot):
Each dot is a word that occurs in a First Folio play but is relatively rare in the corpus of 500+ plays. I've marked in red an obvious cluster of "hits" which correspond to Act 3 in modern editions of the play. (see Gutenberg.org) As far as I can tell, this is roughly the section identified as being "by Shakespeare" by Taylor and others.
Any test that tries to identify the hand of Shakespeare has to rely on Shakespeare's later works. This is going to weaken the result on a very early play like Arden of Faversham. We are dealing with a span of 20 years of writing, so much of the vocabulary and unique characteristics of Shakespeare's works wouldn't be evident in 1591. We should expect fewer Shakespeare-like characteristics, even if it was indeed written by the same author.
As a whole, the play doesn't score very high on the Shakespeare Affinity Test. It scores quite a bit lower than Titus Andronicus, for instance, another early play with a low score.
Is the identification of Shakespeare plausible?
That cluster above marked in red does have a high density of "hits"; it's what one might expect from a play written by Shakespeare.
Some passages that very much read like Shakespeare. For instance:
Such deep pathaires, like to a cannon’s burstReaders of this blog know about Cannons in the Canon, my look at cannon imagery in the works of Shakespeare. This fits right into that pattern, even with a reference to "forging".
Discharged against a ruinated wall,
Breaks my relenting heart in thousand pieces.
Ungentle Alice, thy sorrow is my sore;
Thou know’st it well, and ’tis thy policy
To forge distressful looks to wound a breast
Where lies a heart that dies when thou art sad.
It is not love that loves to anger love.
Is co-authorship the best explanation?
So we have a cluster of hits that really seem to indicate a decent likelihood of Shakespeare's hand in the play, but how are we to interpret that empty bits of the scatter plot? Another author is certainly one possibility, and that seems to be the consensus of scholars who attribute part of the play to Shakespeare.
However, there isn't any independent external evidence for co-authorship of the play and very limited internal evidence. Just because certain parts of the play show up as more Shakespeare-like in a test, that doesn't mean someone else wrote the other bits. The variability could be due to stylistic choices of a single author. It could also be due to sections of the play being written or revised at different times by one author.
Digital tools are limited
The digital tools we have for analyzing plays are not very robust to begin with. Plus, there are very few extant plays from the 1590-1595 period. So they are even more limited since there is so little data available for comparison. So we shouldn't rely too heavily on any digital analysis to give us firm conclusions about authorship.
Conclusion
Lexical tests on Arden of Faversham do indicate sections that seem to strongly suggest an affinity with the vocabulary used in the works of Shakespeare. However, we shouldn't over-interpret this result. Since we have so few plays from the period and such under-developed digital tools, we really should be cautious in jumping to assumptions about co-authorship without strong independent evidence.
