"United States Census, 1860," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:MHDR-5QZ : accessed 18 July 2015), Madison Hall in household of Catharine Hall, Division No 4, Jackson, Alabama, United States; from "1860 U.S. Federal Census - Population," database, Fold3.com (http://www.fold3.com : n.d.); citing p. 69, household ID 475, NARA microfilm publication M653 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 803,011.
"United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MHK8-N8K : accessed 18 July 2015), Matison J Hall in household of Noah Shelton, Alabama, United States; citing p. 16, family 121, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 545,519.
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It may be possible to confirm family relationships with Madison 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 Madison: