"Ontario Births, 1869-1912," database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/QV94-21NH : 15 January 2016), William Arthur Coates, 28 Mar 1905; citing Birth, Brantford, Brant, Ontario, Canada, citing Archives of Ontario, Toronto; FHL microfilm 2,257,200.
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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: