"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MLRH-DCX : accessed 27 April 2018), Laurance Peteres in household of Giddeon Peteres, Ludington Ward 5, Mason, Michigan, United States; citing enumeration district (ED) ED 63, sheet 8B, family 188, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 663; FHL microfilm 1,374,676.
"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MZQZ-7SK : accessed 27 April 2018), Laurence Peters in household of Gedion Peters, Ludington Ward 3, Mason, Michigan, United States; citing ED 92, sheet 12A, line 41, family 277, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, 1992), roll 783; FHL microfilm 1,820,783.
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It may be possible to confirm family relationships with Laurence 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 Laurence: