From the looks of your posts in the past, you have spent a good deal of time in your efforts to unravel the ancestry of William b 1832.
Some people I have corresponded with suspect your William b 1832 is the William age 18 in the household of Valentine Alexander in the 1850 census in Allegany Co., MD.
Also some people further suspect this Valentine is a descendant of the Francis b abt 1654 Ireland who is listed as one of the 7 brothers and 2 sisters in the book "Alexander Kin".
I am the volunteer coordinator of the Alexander DNA Project, and can assure you if you can find a male Alexander relative to test his DNA, you will know more than you know now regarding the ancestry of your William b 1832.
The test kit you receive from the testing company consists of a tiny, plastic toothbrush-shaped device and a tiny vial. The instructions ask you to rub the inside of the cheek for 30 seconds, then place the brush tip in the vial. Then return the kit to the testing company.
In the Alexander DNA Project, over 250 Alexander men have done this and learned to which of those men they are related (or not).
Of the 250+ members, there are about 70+ different Alexander DNA's, or "families". That is a good size data base for you to compare to.
No one yet tested can trace himself back to the brother Francis b 1655. That is partly a result of a relative lack of documentation on Francis plus he had few children apparently.
The project DOES have members who trace themselves back to the brothers Andrew, James the weaver, Joseph and Samuel. And those members have many matches who CANNOT document back to the "7+2"
Furthermore, the alleged brother William b abt 1646 has descendants in the Project and THEY do NOT match the above Andrew, James the weaver, Joseph and Samuel.
Alexander DNA is fun and interesting and is making more discoveries as time goes on.
If you want some information on the Project's details, I will send you my write-up; drop a note to firstname.lastname@example.org
. The lineages, grouped in "DNA families", of all members is also available
The best of luck to you.