"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MVW4-Y15 : accessed 11 June 2016), William Laurence in household of N D Laurence, Leesville, Vernon, Louisiana, United States; citing sheet 21A, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,820,633.
"United States Census, 1930", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XMT8-N2K : accessed 11 June 2016), William Laurence in entry for Mrs. Elizabeth Laurence, 1930.
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DNA Connections
It may be possible to confirm family relationships with William by comparing test results with other carriers of his ancestors' Y-chromosome or 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 of DNA with William: