As for the connection, it is repeatedly and well-documented in biographies of this particular Welsh family here in Wisconsin that Jane Roberts was a cousin of Foulk Roberts, a son of the second marriage of Robert Roberts (b. 1752). Foulk was the pioneer immigrant who first came before the rest two days after he was married in Wales on 18 September 1844. He paved the way for the rest who settled in this area of my state.
These biographies also go on to state that "several other of her family" settled there, including Hugh Roberts and his descendants, who seem to have been involved in some way with the Calvinistic ministry.
I've been unable to get through to any parentage of Jane by direct research, so I am using a flanking maneuver in a search of her family hoping to find the connection. If she were a cousin to Foulk Roberts (b. 1820 Llandeiniolen) that would indicate she was the child of one of Foulk's uncles or aunts, hence the search within his immediate family. The relationship seems to be rather close, which is why I am thinking we're talking about first cousins here, not fourth or fifth...
Jane appears on various official documents as both Jane Roberts and Jane Jones. For example, her name appeared as Jane Roberts on her 1825 wedding registration, and in multiple biographies in local histories here in Wisconsin. However, her name was registered on her children's baptism entries as Jane Jones. My Welsh researcher friend suggested that this was likely due to patronymics and the church member recording her surname interpreting her name as he saw fit based on his use or non-use of that naming convention, based on differing patronymic practices.
My friend (a veteran genealogist of 30 years) further suggested that there was a good possibillity that based on patronymics that her father's name likely would have been John Roberts or Robert Jones (i.e. - child could be given last name Jones from John, Jones or simply take Roberts from Robert or surname Roberts). It just so happens that Foulk Roberts had an uncle named John Roberts...Of course, this is just a lead I am following up on, like a detective, but my other avenues have dried up.
One thing is clear to me, the more I learn about the family of Foulk Roberts (b. 1820), his father Robert Roberts (b. 1752) and Foulk's grandparents (Robert L. E. Roberts and Jane Jones), the more likely the possibility that I will find one of those ancestors will be Jane's parent(s).
Oh yes, I should also note that the Jane Roberts mentioned by two of you in replies as having been born in 1785 - close, but no cigar - she died in the early 1800's. My Jane lived until 13 October 1872 and died here in Wisconsin. I saw that Jane on sveeral trees over the weekend and was sure I'd found the link, until I see she died a young woman.
The search continues...
Steve Jones