"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MH59-HBX : accessed 23 July 2015), Joseph Hall, Jackson county, Jackson, Alabama, United States; citing family 730, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"United States Census, 1860," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:M8W3-P11 : accessed 23 July 2015), Joseph Hall, Riley Township, Yell, Arkansas, United States; from "1860 U.S. Federal Census - Population," database, Fold3.com (http://www.fold3.com : n.d.); citing p. 61, household ID , NARA microfilm publication M653 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 803,052.
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It may be possible to confirm family relationships with Joseph by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage (beta) of DNA with Joseph: