StringArray comparisions return BooleanArray
xref https://github.com/pandas-dev/pandas/issues/29556

cc @jorisvandenbossche 
Thanks! Fixed all those I think.

Tangentially related: we'll need a docs section discussing the behavior of `pd.NA` and arrays using `pd.NA` in comparison operations (propagate rather than unequal). I think it makes sense to combine `user_guide/integer_na.rst` and `user_guide/boolean.rst` into a single "nullable types" document which discusses all of this? What do you think? > I think it makes sense to combine user_guide/integer_na.rst and user_guide/boolean.rst into a single "nullable types" document which discusses all of this? What do you think?

I was floating the idea in my head (but didn't make an issue or so yet) to create a "user_guide/data_types" directory and move the integer and boolean files there (so an extra nesting in the left sidebar). And then the main "data types" page could have a short intro to extension dtypes, pointing to those pages. 
But, if the content is relatively limited, it might also make sense to just combine both on a single page for now.

 > I don't think you are really testing this. I think you actually need to take some of our existing indexing tests,

This does not yet add indexing, this only changes the comparison operations. Indexing is one of the next steps on the list in https://github.com/pandas-dev/pandas/issues/29556 > > I don't think you are really testing this. I think you actually need to take some of our existing indexing tests,
> 
> This does not yet add indexing, this only changes the comparison operations. Indexing is one of the next steps on the list in #29556

ok that's fair. 

would at like to at least in this PR put into place an xfail test that assures that if we try to do indexing with a BooleanArray it fails Indexing seems independent right? BooleanArray comparisons already return BooleanArray, and AFAIK those aren't tested in indexing yet.

I'm happy to write those tests / work on the implementation, but it feels like a separate piece of work. Yes, let's keep it separate > Indexing seems independent right? BooleanArray comparisons already return BooleanArray, and AFAIK those aren't tested in indexing yet.
> 
> I'm happy to write those tests / work on the implementation, but it feels like a separate piece of work.

they are separate until sometries to assign a BooleanArray to a column and use it. We have *nothing* for this, certainly do in a separate PR. What I am suggesting is a single test to validate that this raises (for now) Do we know what the defined behavior is yet? In https://github.com/pandas-dev/pandas/issues/28778 it sounds like we're contemplating either raising or propagating. This should be good to go. Thanks!