"England and Wales Census, 1881," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q275-726K : 20 August 2016), Arthur Calverley in household of Judith Calverley, Wardleworth, Lancashire, England; from "1881 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing p. 25, Piece/Folio 4115/78, The National Archives, Kew, Surrey; FHL microfilm 101,775,166.
"England and Wales Census, 1891," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QBBQ-42M : 1 April 2016), Arthur Calverley in household of Judith Calverley, Wardleworth, Lancashire, England; from "1891 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO RG 12, Lancashire county, subdistrict, The National Archives of the UK, Kew, Surrey.
"England and Wales Census, 1901," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:X9L8-CY8 : 8 April 2016), Arthur Calverley in household of Judith Calverley, Rochdale, Lancashire, England; from "1901 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing Wardleworth subdistrict, PRO RG 13, The National Archives, Kew, Surrey.
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DNA Connections
It may be possible to confirm family relationships with Arthur by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: