I have a Q? for anyone willing to answer.

How did previous Arney surname family researchers "tie" these people together?
(because, at this point, truly, I don't know)

How did they know, that . . .

Jacob Arney and Anna Ursula Kron, were the parents of:
Christian "Christy" Arney, Sr. (1755-1834)
Adam "Lawerence" Arney (1751-1802)
Johann Heinrich "Henry" Arney, Sr. (1755-1830)
Anna Elisabeth Arney-Setser/Setzer (1761-1849)

What documentation (or as I refer to it, "DTP" Definitive Tangible Proof) did they find that led them to these conclusions?

Jacob Arney and Elizabeth (surname/maiden name, unconfirmed), were the parents of:
Peter Arney (1772-1845)
Catherine Arney-Edleman (1774-????)

Until the 1850 US Federal Census, as a research tool, the names of individuals in a "household" were not individually mentioned (yes, we all know this)

So, how did they know:

Peter Arney and Margaret (surname/maiden name, unknown), were the parents of:
Margaret Arney (1793-????)
Adam Arney (1797-1870)
Henry Arney (1799-????)
John Arney (1802-1880)
Hiram Arney (1804-????)
Lucretia Arney (1805-????)
William Arney (1815-1880)
Matthew Arney (1818-1902)
James Arney (1822-1865)
Hardy Arney (1827-1880)

After all, Peter Arney died in 1845, 5 years before the 1850 US Federal Census.

Henry Arney (1799-????), can "supposedly" be found in the 1830 & 1840 Census, but disappears after that (meaning he can't be found, anywhere).

Hiram Arney (1804-????), cannot be found in any Tennessee Census, so where did he go after his fathers, Peter's, death?

Q? How did these early Arney family researchers (and I'm talking about a few that did research in the 1950's, like Ms. Edna Williams) fit or tie these people together, to believe they were part of the same family?

I mean, I'm just as guilty as many researchers out there, in this regard, in what I term, "Stand on the shoulders of Others" researching. Meaning, simply "accepting" that these people knew what they researched and were talking about, therefore I can build upon their research to continue mine.

Can someone explain to me, how they were able to tie these people together?

Thank you, for your time, consideration, and cooperation, I truly appreciate it.